cross-sectional predictability of stock returns: pre-world war i evidence

FACULTY OF APPLIED ECONOMICS

DEPARTMENT OF ACCOUNTING AND FINANCE

DISSERTATION

Cross-Sectional Predictability of Stock Returns:

Pre-World War I evidence

THESIS SUBMITTED IN ORDER TO OBTAIN THE DEGREE

OF

DOCTOR IN APPLIED ECONOMICS

Author: Supervisor:

Lord Mensah Prof. Dr. Jan Annaert

September, 2011

This research was funded by the Faculty of Applied Economics, from the 2007 to 2011

research grant for the Accounting and Finance Research group.

Cross-Sectional Predictability of Stock return: Pre-World War I Evidence

Lord Mensah, Antwerpen, Belgium, 2011

ISBN: 978-90-8994-044-5

Printed by: Universitas Antwerpen

© Copyright 2011, Lord Mensah

All rights reserved. No part of this book may be reproduced or transmitted in any form

by any electronic or mechanical means (including photocopying, recording or

information storage and retrieval) without permission in writing from the author.

Doctoral Jury

Internal members

Prof. Dr. Jan Annaert (Supervisor)

Universiteit Antwerpen, Belgium

Department of Accounting and Finance

[email protected]

Prof. Dr. Marc De Ceuster (chair/PhD committee chair)



[email protected]

Dr. Frans Buelens (PhD committee member)



[email protected]

Prof. Dr. Joseph Plasmans


Department of Economics

[email protected]

External Members

Prof. Dr. Wim Janssens (PhD committee member)

Universiteit Hasselt, Belgium

Department of Marketing

[email protected]

Prof. Dr. Laurens Swinkels

Erasmus School of Economics, Rotterdam, Netherlands

Vice President, Robeco Investment Solutions, Rotterdam

[email protected]

Prof. Dr. Patrice Fontaine

EUROFIDAI and University of Grenoble 2, France

[email protected]

mailto:[email protected]

ACKNOWLEDGEMENTS

In as much as writing a PhD thesis requires independent study and scientific research, the

success marked in this project depend on the environment I worked in and the people

around me. As a result, I may like to express my profound gratitude to everyone who

contributed to the success of this project both professionally and personally.

Primarily, I would like to thank my supervisor Prof. Dr. Jan Annaert for the confidence

pose in me, and giving me the opportunity to be part of the research project. You guided

me through the research and thought me how to select the literature to support my

arguments. In a mother-child scenario, I will say you know the right food combination

you will give to your child in order to mature quickly. I also appreciate how quick you

read my chapters and direct me for changes here and there. In short, this dissertation

would not be what it is now without your suggestions, encouragement and guidance.

Secondly, I would like to express my sincere gratitude to my PhD committee members

Prof. Dr. Mark De‟Ceuster, Prof. Dr. Wim Janssens and Dr. Frans Buelens. Your

comments and suggestions have been of immense value in completing this dissertation.

Dr. Frans Buelens, thank you very much for the updates you gave me on the data. In

addition, I am also thankful to the external doctoral jury members Prof. Dr. Joseph

Plasmans, Prof. Dr. Laurens Swinkels and Prof. Dr. Patrice Fontaine for taking your time to read

and discuss my work. Your comments and suggestions have been of great value to improve and

polish the chapters in this thesis.

Genuinely, I have enjoyed every moment at work for the past four years. On this note, I

want to thank all my colleagues from the Accounting and Finance department of the

University of Antwerp. Specifically, my sincere gratitude goes to the secretariat office

for their beaming smiles and friendly services. I want to thank the department head for

the annual outing, lunches and visit to museums in Antwerp. This allows me to release

stress at work for the past four years. I hope that we will stay in touch for the future.

Finally, the period of writing PhD thesis comes with moments of joy and doubt.

However, how to handle the stress depends on the people around you after office work. I

have been blessed with supportive family. Firstly, I owe an immense debt to my wife

Sefam Ekua Lord-Mensah. What you have done for the past four years goes beyond your

call to duty. I have come to understand that only few people are fortunate to have caring

and supporting wife like you. Completion of my PhD, gives me the opportunity to thank

you for the unconditional love and support you have given me, since we got married.

Second words go to my lovely kids Lakeisha Lord-Mensah, Zita Lord-Mensah and

Nhyira Lord-Mensah. Thank you for making my home a place of endless happiness.

Thank you for your patience and not been on your sight ten to eleven hours every day.

My final words go to all those who made my education a success by contributing

financially. Special thanks to my one and only Uncle Maxford Kwadwo Kwakye who

contributed to my senior high school education. I do appreciate your support, and I will

always remember you.

Lord Mensah

Table of Contents

CHAPTER 1 .................................................................................................................................. 1

1 INTRODUCTION, DATA DESCRIPTION AND SUMMARY ................................... 1

Introduction .................................................................................................................... 1 1.1

1.1.1 The aim of this Dissertation .................................................................................... 6

Data Description and Methodology ................................................................................ 7 1.2

1.2.1 The Risk-free rate and the Market Index .............................................................. 11

1.2.2 Methodology ......................................................................................................... 14

Summary of the chapters .............................................................................................. 20 1.3

1.3.1 Chapter 2 ............................................................................................................... 20

1.3.2 Chapter 3 ............................................................................................................... 21

1.3.3 Chapter 4 ............................................................................................................... 22

1.3.4 Chapter 5 ............................................................................................................... 23

CHAPTER 2 ................................................................................................................................ 25

2 ASSESSMENT OF BETA IN THE 19th

CENTURY BSE ........................................... 25

Introduction and Literature Review .............................................................................. 25 2.1

Beta Coefficient Descriptive Statistics .......................................................................... 33 2.2

Beta Stability ................................................................................................................. 37 2.3

2.3.1 Blume and Vasicek stability adjustment techniques............................................. 39

Beta Bias ........................................................................................................................ 44 2.4

Impact of outlying observations on Beta ...................................................................... 47 2.5

Conclusion..................................................................................................................... 51 2.6

CHAPTER 3 ................................................................................................................................ 52

3 THE TEST OF CAPITAL ASSET PRICING MODEL (CAPM) AND THE SIZE

EFFECT IN 19th

CENTURY BSE ............................................................................................. 52


Expected returns of portfolios sorted on betas ............................................................ 54 3.2

3.2.1 The Cross-Sectional Regressions ........................................................................... 59

Expected Returns, Beta, and the Size Effect ................................................................. 66 3.3

3.3.1 Fama-MacBeth Cross-Sectional Regressions to Test the Size Effect..................... 71

Conclusion..................................................................................................................... 79 3.4

CHAPTER 4 ................................................................................................................................ 80

4 DOES THE MOMENTUM EFFECT EXIST IN THE 19TH

CENTRURY? ............. 80


Momentum Trading Strategies and their Returns ......................................................... 85 4.2

4.2.1 Expected Returns and Average Size of Quintile Portfolios ................................... 90

4.2.2 Momentum Profit within Size and Beta-based Subsamples ................................. 91

Seasonality and Sub-period Analysis of the Momentum Profit .................................... 94 4.3

Post holding Period Momentum Profits ........................................................................ 98 4.4

The Momentum profit and the Market State ............................................................. 103 4.5

Conclusion................................................................................................................... 106 4.6

CHAPTER 5 .............................................................................................................................. 109

5 THE COMBINED EFFECT OF DIVIDEND YIELD, SIZE, TOTAL RISK

AND MOMENTUM (1868-1913 EVIDENCE)....................................................................... 109

Introduction and Literature Review ............................................................................ 109 5.1

Measures of Characteristics ........................................................................................ 115 5.2

Descriptive Summary Statistics of the Characteristics ................................................ 118 5.3

5.3.1 Size-Dividend yield double sorts ......................................................................... 118

5.3.2 Momentum-Dividend yield double sorts ............................................................ 121

5.3.3 Total risk-Dividend yield double sorts ................................................................. 125

Average Excess Returns on Portfolio Sorts ................................................................. 130 5.4

The Cross-Sectional regressions .................................................................................. 136 5.5

5.5.1 Pervasiveness of the Cross-Sectional Relationships ........................................... 140

Conclusion ................................................................................................................... 143 5.6

6 CONCLUSION .............................................................................................................. 144

References .................................................................................................................................. 150

NEDERLANDSTALIGE SAMENVATTING ........................................................................ 157

TABLES

Table 1.1: Summary Statistics for Risk-free rate and the Value-Weighted Index ......................... 13

Table 2.1: Beta coefficient descriptive statistics for the 15 estimated periods ............................ 34

Table 2.2: Average beta and average coefficient of determination of the size based sub-samples

....................................................................................................................................................... 36

Table 2.3: Weighted average of correlation and Spearman rank order correlation across

successive periods ......................................................................................................................... 38

Table 2.4: Measurement of regression tendency of estimated beta coefficient for individual

stocks ............................................................................................................................................. 40

Table 2.5: Predictive performance of Blume and Vasicek (Bayesian) procedures of estimating

beta ............................................................................................................................................... 42

Table 2.6: Modified Diebold-Mariano test statistics (p-value in parentheses) ............................. 44

Table 2.7: Dimson Aggregate Coefficient (AC) beta Adjustment .................................................. 45

Table 2.8: Comparison of the market model betas and the iterative reweighted least square

betas .............................................................................................................................................. 48

Table 2.9: Test of equal predictive accuracy between MM and IRLS models ............................... 50

Table 3.1: Time Series Mean (%), Standard Deviation (%), and Post-ranking Betas of Decile

portfolios formed from pre-ranking betas in Jan. 1868-Dec. 1913 .............................................. 58

Table 3.2: Average time series slopes from the Fama-MacBeth Cross-Sectional Regressions in

Jan. 1868-Dec. 1913 ...................................................................................................................... 61

Table 3.3: Average Time Series Slopes from Fama-French Cross-Sectional Regression in Jan.

1868-Dec. 1913 ............................................................................................................................. 64

Table 3.4: Sub-period look into estimated slopes and excess market returns ............................. 65

Table 3.5: Beta Estimate and Mean Excess Return for the BSE equally weighted size portfolios,

Jan. 1868- Dec. 1913 ..................................................................................................................... 68

Table 3.6: Equally weighted portfolios excess returns without the first-size decile group .......... 69

Table 3.7: Average time series slopes and intercept from the Fama-MacBeth cross-sectional

regression: Jan 1868-Dec. 1913 .................................................................................................... 73

Table 3.8: Average Time Series Slopes and Intercepts from the Fama-French Cross-Sectional

Regressions: Jan. 1868-Dec. 1913 ................................................................................................. 76

Table 3.9: Average Time Series Slopes and Intercepts from the Fama-French Cross-Sectional

Regressions without the First-Size Decile: Jan. 1868-Dec.1913 .................................................... 78

Table 4.1: Profitability of momentum Strategies on BSE (Jan.1868-Dec. 1913) ........................... 89

Table 4.2: Average Returns and Average Size of Quintile Momentum Portfolios ........................ 91

Table 4.3: Portfolio Returns of the Momentum Strategies with Size and Beta Subsamples ......... 92

Table 4.4: Seasonality in momentum profits ................................................................................ 95

Table 4.5: Sub-period Analysis of Momentum Profit .................................................................... 97

Table 4.6: Long Horizon Momentum Profits ............................................................................... 100

Table 4.7: The Momentum profit and the Market State ............................................................ 104

Table 5.1: Summary statistics for Size-Dividend double-sorts .................................................... 119

Table 5.2: Summary statistics for Momentum-Dividend yield double sorts .............................. 123

Table 5.3: Summary statistics of total risk- dividend yield double sorts .................................... 126

Table 5.4: Annual Time Series Average of the correlation between the entire characteristic and

Average return ............................................................................................................................ 129

Table 5.5: Equal and Value-weighted portfolios excess returns (%) of double-sorted

characteristics ............................................................................................................................. 131

Table 5.6: Cross-Sectional Regression of Excess Returns on Dividend Yield, Size, Total Risk and

Momentum ................................................................................................................................. 138

Table 5.7: Cross-Sectional regression of Excess Returns on Dividend Yield, Size, Total Risk and

Momentum of Size subsamples .................................................................................................. 141

FIGURES

Figure 1.1: Number of listings on the 19th Century Brussels Stock Exchange ................................. 9

Figure 1.2: Total market capitalization of the BSE ........................................................................ 10

Figure 1.3: Evolution of the value weighted market index in the two sub-periods of our study . 12

Figure 2.1: The graph of the average beta of each period for large stocks and small stocks ....... 36

Figure 2.2: Plot of average market model betas and IRLS betas for stocks with outlier

observation less than 4 ................................................................................................................. 49

Figure 3.1: Number of stocks in our selection criteria for the entire period of the pre-world war I

SCOB data ...................................................................................................................................... 55

Figure 3.2: Sixty months moving average of the cross-sectional slopes and excess market returns

using Dimson beta estimates ........................................................................................................ 65

Figure 3.3: Size Portfolio betas ...................................................................................................... 70

Figure 4.1: Number of common stocks in our sample for the momentum studies...................... 86

Figure 4.2: Time line of sample periods ........................................................................................ 86

Figure 4.3: Average returns of the momentum profit in all calendar months ............................. 95

Figure 4.4: Cumulative Returns for Five years after portfolio formation ................................... 101

Figure 5.5.1: Percentage of Zero-dividend paying stocks and their Relative Market Capital: 1868-

1913 ............................................................................................................................................. 116

1

CHAPTER 1

1 INTRODUCTION, DATA DESCRIPTION AND SUMMARY

More than fifty variables have been used to predict returns. The overall picture remains murky, because

more needs to be done to consider the correlation structure among the variables, use a comprehensive set

of controls and discern whether the results survive simple variations in methodology1.

Introduction 1.1

The issue about why stock returns differ in the cross-section from one another at a

particular time has been a hot topic of financial research for the past decades. The capital

asset pricing model (CAPM) proposed by Sharpe (1964), Lintner (1965) and Mossin

(1966) seems to provide an adequate description of the cross-section of stock returns

until the 1980s. The model postulates a linear relationship between expected returns and

the covariance between the market portfolio returns and the returns of an asset (beta).

This implies that the asset beta with respect to the market portfolio is sufficient to

determine its expected returns. However, since the 1980s, documentation on deviations

from the model (anomalies) has been an extremely active area of research. Either the

anomalies represent inadequacies in the CAPM, inefficiencies in the market (profit

opportunities) or a data snooping bias. If the presence of an anomaly truly indicates the

inadequacy of the CAPM, then factors other than beta can predict stock returns. This

implies that anomalies would continue to exist before and after their discovery. While

many have accepted the factors other than beta to predict returns, others believe that they

were discovered out of luck and are due to data snooping bias (Lo and MacKinlay

1 Subrahmanyam, Avanidhar, 2010, The cross-section of expected stock returns: What have we learnt from

the past twenty-five years of research?, European Financial Management 16, 27-42.

2

(1990)). The possible ways that data snooping bias can occur are (i) when researchers

continuously test the properties of a data set or the outcomes of other studies on data set

(ii) form predictive models based on the characteristics of the previous results and (iii)

test the power of their models on the same data set. As a result, any anomaly found

might appear to be valid within the data set, but they would have no statistical

significance outside the sample from which it was discovered. Indeed, Schwert (2003)

documents that anomalies often seem to disappear, reverse, or attenuate after they have

been documented and analyzed in the academic literature. The problem can be addressed

by using data from markets that have not been searched exhaustively, or by making

predictions using periods that are new to asset pricing research. The situation remains

murky, as more needs to be done to distinguish between the data snooping hypothesis

and the persistence of the characteristics other than beta. Many studies have tried to

differentiate between the two possibilities, but most of them concentrate on the post-

World War I data, usually limited to the USA. On the international front, Haugen and

Baker (1996) find some degree of commonality in the characteristics that are most

important in determining comparative expected returns among different stocks. Because

of this, testing the asset pricing models on a new data set provides an obvious way to

distinguish between the data snooping hypothesis and the persistence of the

characteristics identified to predict returns. This is to test whether the anomaly exists in a

new and independent sample. This dissertation fills these gaps in the literature by

introducing an independent data set and a different set of characteristics to test the cross-

sectional predictability of stock returns.

3

Several characteristics have been studied in the literature to predict stock returns. Among

them are size (market capitalization: measured as price times shares outstanding), book

to market value ratio, momentum, return reversal, price earnings ratio, dividend yield,

accruals, illiquidity, net issues, asset growth, profitability, total risk (idiosyncratic risk),

etc. Subrahmanyam (2010) categorizes the origins of the predictive characteristics based

on four principles. These are:

Theoretical motivation based on risk-return model variants.

Informal Wall Street wisdom (such as value and size investing)

Predictors originated from the behavioral biases of investors.

Models that include market frictions (illiquidity).

The theoretically motivated risk/return models conduct a test to see whether a higher

return has been associated with higher risk (measured as beta). Black, Jensen and Scholes

(1972), Sharpe and Cooper (1972) and Fama and MacBeth (1973) find support for the

CAPM in the 70s. On the contrary, Fama and French (1992) find that their data do not

appear to support the CAPM. The traditional CAPM argues that only market risk should

be incorporated into asset prices and command compensation. However, Malkiel and Xu

(2006) document that the CAPM may not hold when some investors are not able to hold

the market portfolio, due to various reasons such as transaction costs. Investor‟s inability

to hold market portfolios will force them to care about the total risk, not simply the

market risk, as implied by the CAPM. Hence, idiosyncratic risk would be priced in the

market. In effect, there is a positive relationship between idiosyncratic risk and average

returns. On the contrary, Ang, Hodrick, Xing and Zhang (2006) find a negative

relationship between idiosyncratic risk and expected returns. The negative relationship

4

between idiosyncratic risk and expected returns remains debatable, since no theoretical

framework has been established to determine the source. Idiosyncratic risk may also

limit arbitrageurs from exploiting mispricing opportunities on the market. That is, for

high idiosyncratic risk stocks, it is a challenge to execute arbitrage activity that is free

from idiosyncratic risk; hence, such stocks are more likely to trade at a price far from

their fundamental values. Doukas, Kim and Christos (2010) find a positive relationship

between mispricing and idiosyncratic risk, which is consistent with the limited arbitrage

argument. The arbitrage theory posits that mispricing can persist whenever the cost of

arbitrage exceeds the benefit. In addition, as a specific example, McLean (2010) finds a

strong reversal mispricing in high idiosyncratic risk firms.

The Wall Street wisdom characteristics are just found by chance or motivated by

informally appealing to the knowledge of finance professionals. The premise of these

characteristics is not based on any prior theoretical reasoning. For example, Basu (1977)

documents the negative relationship between price/earnings ratio and abnormal returns.

He partially based his assertion on the notion that recommending stocks based on

price/earnings ratio is common on the Wall Street. Similarly, Banz (1981) documents

that stocks with low market capitalization outperforms those with high market

capitalization. The literature on the informal Wall Street characteristics is given a

magnificent boost by Fama and French (1992). They document the importance of size

and book/market value in the cross-section of expected stock returns. In addition, they

show the CAPM is not supported in their data. Fama and French (1993) build on the role

of size and value to postulate that a three factor model based on factors formed on size,

book/market value characteristics and the market returns can explain expected returns.

5

On the return predictions based on past performance, Jegadeesh and Titman (1993)

document the prediction of three to twelve months of past returns. They find that stocks

or portfolios that have performed well in the past 3 to 12 months will continue to do so in

the next 3 to 12 months (momentum). However, the source of the momentum effect is

subject to debate. Conrad and Kaul (1998) and Bulkley and Nawosah (2009) argue that

the effect is mainly due to the cross-sectional variation in expected returns. On the

contrary, Jegadeesh and Titman (2001) do not only address the data-mining critique in

explaining momentum effect but also document that models of investor behavioral bias

offer a good explanation of the momentum effect. Their argument is because momentum

profit is due to delay in overreactions that are eventually reversed. However, they

indicate the support for the behavioral model should be tempered with caution. Others

believe momentum effect can be explained by the state of the market (Cooper, Gutierrez

and Hameed (2004) and Chabot, Ghysels and Jagannathan (2009)).

The characteristics derived from behavioral biases or cognitive challenges are based on

informal arguments about investor overreaction and underreaction to information. The

premise of the behavioral notion is that the conventional financial theory ignores how

investors take decisions. Daniel, Hirshleifer and Subrahmanyam (1998) argues that if an

investor places more weight on his private information signal, it causes stock price

overreaction. As information that is more public arrives, the prices move closer to their

fundamental values. The overreaction correction pattern is consistent with a long run

negative autocorrelation in stock returns (long-term reversal in returns). On the other

hand, if the investor begins with unbiased beliefs about his private information signal, he

tends to see a new public information signal as a confirmation of his private signal. This

6

suggests that the public can also trigger further overreaction to the preceding private

signal, thereby causing momentum in security prices. In effect, the biased self-attribution

implies the short-run momentum and long-term reversal. With the notion of investor

reactions to value, Cooper, Gulen and Schill (2008) show that growth in book assets are

cross-sectionally related to future returns, and the implication is that investors underreact

to information in the time series of balance sheets.

Investors require compensation for market friction (illiquidity). Hence, market friction is

a predictor of stock returns. The most difficult issue in relating market illiquidity to

expected returns is the measure of illiquidity. There is a pack of measures in the literature

related to illiquidity. Some of these include the bid-ask spread, absolute return to the

dollar trading ratio, relationship between price changes and order flows, share turnover,

the proportion of zero returns, market capitalization, etc. Amihud and Mendelson (1986)

find a significant premium for the bid-ask spread measure. In a reaction to the possible

problem associated with providing a consistent liquidity measure for all markets, Amihud

(2002) proposes price impact measures, defined as the absolute value of stock returns

divided by the dollar volume. He finds a positive relationship between his illiquidity

measure and average return. From emerging markets, Bekaert, Harvey and Lundblad

(2007) use the proportion of zero returns as a measure of illiquidity to establish a positive

relationship with expected returns.

1.1.1 The aim of this Dissertation

In this dissertation, we study the robustness of the cross-sectional patterns in stock

returns, using the completely independent database of the Brussels Stock Exchange (BSE

from here onwards) in the 19th

century and the first few years of the 20th

century. Apart

7

from the quality of the data set, it allows us to study the influence of strong varying

conditions in the economic and institutional environment on stock returns. The period of

the data set avoids the data mining critique. With this data,

We will test the validity of the CAPM.

In addition, we test whether other characteristics can explain the cross-sectional

variation in stock returns.

As of the time of writing this dissertation, accounting and transaction data has not been

digitalized for the 19th

century BSE, so we will not be able to investigate the

predictability of accounting-related characteristics on stock returns. However, we

investigate whether size, momentum (short run past returns), total risk (firm specific risk)

and dividend yield (an asset value' indicator like the book-to-market value ratio) can

cross-sectionally predict returns.

With the importance of illiquidity, in the absence of volume and transaction data, we

follow Bekaert et al. (2007) to measure illiquidity as a proportion of zero returns in the

last 30 months. However, our unreported results indicate that zero-return illiquidity

measure is strongly correlated with market capitalization (also a proxy for liquidity) and

stock price level.

Data Description and Methodology 1.2

It is worthy to reiterate that empirical research on the stock market return predictability

has a long tradition. The large body of the financial literature in this area uses data from

the Center for Research in Security Prices (CRSP). The CRSP data consist of

comprehensive and accurate historical returns for all stocks listed on the NYSE, the

8

Amex and the NASDAQ stock markets in the USA. Researchers make use of the long

time series (NYSE from 1926 to date, Amex and NASDAQ from 1962 and 1973,

respectively to date) and high quality financial data to carry out research about general

equilibrium asset pricing models and predictable patterns in returns, among others.

However, the obsessed and continuous search for predictable patterns in a single data set

will likely reveal an interesting (spurious) pattern (Lo and MacKinlay (1990)). Since one

of the most studied quantities on the market to date is the stock return, the tests on

financial asset pricing models seem especially at risk. Recent anomalies detected in

empirical studies call for researchers to suggest a modification to standard economic

theories about asset prices. However, the CRSP data are mostly used in asset pricing

research due to the non-availability of reliable and independent data sources. There is a

considerable danger of inducing data mining/snooping bias when a single data set is used

repeatedly. This may attenuate the reliability of statistical analysis on the data. Data

from financial markets of other countries are normally used to investigate asset return

predictability. However, common characteristics have been identified that can predict

returns on contemporary markets.

To reduce the doubts regarding inferences of the test of asset pricing predictability, we

analyze a completely new and unique historical data set of stock returns from the BSE

during the 19th

century and the beginning of the 20th

century. The data set was

constructed at the University of Antwerp in Belgium (Studiecentrum voor Onderneming

en Beurs (SCOB)). The data for our study start from 1832 and ends at 1914, just before

the outbreak of World War I. During the World War I period, the BSE was closed and

this can be regarded as a natural breaking point of the long time series of the stock

9

returns. The BSE was considered one of the biggest markets in the world at that time,

because Belgium was one of the first nations on the European continent to become

industrialized (see Van der Wee (1996) and Neymarck (1911)). On the industrial output

per head ladder, Belgium stood second after Britain in 1860, and third in 1913, after the

UK and the USA (see Bairoch (1982)). During this period, highly developed banking

system coupled with liberal stock market regulations attracted a great deal of domestic

and foreign capital in Belgium. In confirmation, Van Nieuwerburgh, Buelens and

Cuyvers (2006) document that the development of the financial sector, accompanied with

the stock market-based financing of firms, played an important role in the economic

growth of 19th

century Belgium.

Figure 1.1: Number of listings on the 19th

Century Brussels Stock Exchange

Source: Annaert, Buelens and De Ceuster (2004)

Figure 1 indicates the number of listings on the 19th

century BSE. The figure depicts the

rising popularity of the BSE. The bold line shows the number of common stocks, bonds

10

and preferred stocks. The evolution of common stock listings is represented with the

dashed line. It is clear from the figure that the BSE almost exclusively lists common

stocks until the mid-1850s. The importance of the common stocks declines to about 65%

just before the World War I. To illustrate the international attraction of the BSE, the

faint line shows the common stock listings of foreign companies. About one fifth of the

common stock listings from the late 1870s are for foreign companies. The number of

common stock listings on the BSE is quite important, even if we limit our attention to

Belgian common stocks. From 1868 onwards, at least 100 Belgian common stocks are

listed, gradually increasing to about 600 just before the World War I.

Figure 1.2: Total market capitalization of the BSE

Source: Annaert, Buelens and De Ceuster (2004)

It is obvious from Figure 2 that increasing number of common stock listings increases the

market capitalization of the BSE. Notably, the financial liberalization from the early

1970s onwards reflects in the growth of the total market capitalization. Annaert, Buelens

and De Ceuster (2004) shows that in the 19th

century stock market capitalization was

11

27% of gross national product in 1846, 57% in 1880 and steadily growing to 80% by the

end of the period of our study.

Annaert et al. (2004) classified all companies listed on the BSE into five categories,

based on the geographical location of the major production facilities and the company‟s

country of residence. However, in this research, we restrict ourselves to the analysis of

data from the securities of Belgium owned companies. The stocks on the BSE are well

diversified across industries such as transportation, mining and extraction, financials,

utilities and industrials. The BSE provides monthly data on stock prices, dividends and

the number of shares outstanding for more than 1000 different companies officially

quoted on the exchange. This enables the computation of the market capitalization and

total returns for individual common stocks on the exchange. The total returns of the

common stocks on the BSE were computed by considering dividends, stocks splits,

mergers, delisting and other capital operations. The data permit us to test the robustness

of the predictive power of characteristics on common stock returns, and the analysis of

the anomalies identified in the existing literature on asset pricing. All available

information begins in January and ends in December of each year.

1.2.1 The Risk-free rate and the Market Index

We use the annualized short rate converted to a monthly rate as a proxy for the risk-free

rate. The short rate is based on the commercial rate from the official quotation list of the

Antwerp Stock Exchange. The rate is extracted from the newspapers in the period of our

study.2 For the market index, we employ the all share monthly value weighted index

constructed by Annaert et al. (2004). We concentrate on the value-weighted index as it

2 Journal du Commerce, d‟Anvers, L‟Avenir, Moniteur des Intérêts Matériels and Het Handelsblad.

12

mirrors the return evolutions of the investable assets' universe. The value-weighted index

is constructed by considering the market capital of the individual stocks in the index

portfolios. The index represents the total returns of the stock market investable assets.

Figure 1.3: Evolution of the value weighted market index in the two sub-periods of our study

It is clear from Figure 1.3 that, 100 Belgian Franc invested in the index would have

grown to about 500 Belgian Franc at the end of the period of strict regulation and

industrial revolution (Jan.1832-Dec.1867). Evidence from the Figure depicts a market

0

50

100

150

200

250

300

350

400

450

500

1830 1835 1840 1845 1850 1855 1860 1865 1870

Value-weighted index evolution in the period of industrial revolution: Jan. 1832-Dec.1867

0

200

400

600

800

1000

1860 1870 1880 1890 1900 1910 1920

Value-weighted index evolution in the period of deregulation and expansion: Jan. 1868-Dec.1913

13

drop in 1948, the year of industrial revolution across Europe. In the period of the

deregulation and expansion period, 100 Belgian Franc invested in the beginning of the

period would have grown to about 1000 Belgian Franc at the end of the period (Jan.1868-

Dec.1913).

Table 1.1: Summary Statistics for Risk-free rate and the Value-Weighted Index

Table 1.1 shows the time series summary statistics of the risk-free rate and the value-

weighted index. As indicated in Annaert et al. (2004), the period from 1832 to 1913 is

divided into two sub-periods based on the environment in which the BSE was operating.

These were the periods of the industrial revolution and high regulation (1832-1867) and

the period of deregulation and expansion (1868-1913). We show the summary statistics

in the entire period and both sub-periods. The average risk-free rate, as well as the

average value weighted return for the entire period, is almost the same in the two sub-

periods. On the other hand, the standard deviation of the value-weighted index is high in

the first period as compared to the second period. The high standard deviation and

Standard 1st Order

Mean Deviation Skewness Kurtosis Min Median Max Autocorr.

Risk-free 0.26% 0.08% 0.59 3.13 0.12% 0.25% 0.60%

Value-Weighted Index 0.40% 2.42% 0.02 20.92 -20.68% 0.27% 15.78% 0.28*

Risk-free 0.28% 0.07% 0.19 2.54 0.17% 0.29% 0.53%

Value-Weighted Index 0.41% 3.01% -0.15 18.61 -20.68% 0.21% 15.78% 0.30*

Risk-free 0.24% 0.08% 0.99 4.26 0.12% 0.23% 0.60%

Value-Weighted Index 0.40% 1.86% 0.55 9.28 -8.16% 0.34% 11.99% 0.25*

autocorrelation of the value-weighted index series of the risk-free rate and the value-weighted market index.The Ta-

ble also displays the descriptive statistics for two subperiods.That is the period of the industrial revolution (1832-1867)

and the period of deregulation and expansion (1868-1913). * = significantly different from zero at 5% (two sided).

Jan. 1832-Dec. 1913

Jan. 1868-Dec. 1913

Jan. 1832-Dec. 1867

Note : In this Table, we compute the descriptive statistics of the risk-free rate and the value-weighted market index.

We calculate the time series mean, standard deviation, skewness, minimum, median, maximum and the first order

14

kurtosis in the first period are not surprising, as the period is characterized with (i) a large

market drop in 1848, a year of revolution across Europe (although not in Belgium) and

(ii) strong restrictions on joint stock holdings that may affect the volatility of prices

(Annaert et al. (2004)). The standard deviation recorded on the 19th

century BSE is low

compared to the high values recorded on the USA market. However, it is close to the

values recorded on the UK market in the period 1870-1913 (see Grossman and Shore

(2006) page 281, Table 2).

The average difference between the value weighted index and the risk-free rate is

between 0.13% and 0.16% for the overall period and the two sub-periods. This implies a

risk premium of 1.92% per annum. This might be too low compared to the annual risk

premium of 4.61% recorded on the USA markets. However, the low risk premium

recorded on the 19th

century BSE is not surprising as Grossman and Shore (2006) record

far too low annual risk premium on the UK market between 1870 and 1913 ( risk

premium of 0.53% and 1.93% for value weighted and equally weighted respectively).

1.2.2 Methodology

As shown in the diagram below, basically, there are two methods for testing the cross-

sectional predictability of stock returns. These are the sorting and the regression method.

The sorting method is sub-divided into the univariate, independent and conditional

double sorts. The univariate sort method ranks stocks on beta, or their characteristic, and

groups them to form portfolios. The average returns of the portfolios should be a

monotonic function of the characteristic. The method tests the significance of the

difference in average returns between the high and low ranked portfolios. A univariate

sort has the disadvantage of not being able to disentangle the effect of two (or more)

15

characteristics. To distinguish between the effects of two characteristics on the cross-

section of stock returns, the conditional double sort is applied. In the conditional double

sort method, stocks are first ranked on a single characteristic and split into groups. The

stocks in each group are then sorted on the second characteristic. The conditional double

sorting method keeps one characteristic constant and tests the effect of the other

characteristic on the cross-section of expected returns.

Fama and French (1992) adopted the conditional double sort to disentangle the effects of

beta and size on average returns. The independent double sort method simultaneously

tests the effect of two characteristics on the cross-section of stock returns. In such a case,

one characteristic is expected to predict stock returns better, holding the other constant

and vice versa. Empirically, stocks are separately ranked on each characteristic and

grouped. Portfolios are formed from the stocks that exist at the intersections of the

groups. Asness (1997) used the independent double sort method to test the interactive

effect of value and momentum on the cross-section of stock returns. The advantage of the

Cross-Sectional

Predictability of

Stock Returns

Sorting

Regression

Independent Double Sort

Conditional

Double Sort

Time Series

Cross-Sectional

Univariate

sort

16

sorting methods is that they do not impose any functional relationship between

characteristics and expected returns. The method answers the question of whether the

high-ranked characteristic portfolio outperforms the low-ranked characteristic portfolio.

As stated before, the method test is based on whether the difference in the average

returns of the high and low- ranked portfolios are significantly different from zero. The

sign and the significance of the difference in average returns determine whether the

relationship is negative or positive. However, it is weak to use the information on the

high and low ranked portfolios to represent the cross-sectional effect of a characteristic

on expected returns. In addition, it is difficult to disentangle the marginal effect of

several characteristics because the sorting method cannot sort on more than three

characteristics. It also ignores the noisy nature of the stock or portfolio returns.

The regression method addresses some of the shortcomings of the sorting methods. The

two types of regressions used to test the cross-sectional predictability of stock returns are

the time series and the cross-sectional regression method. Black et al. (1972) initiated the

time series method, which was later developed by Gibbons, Ross and Shanken (1989).

The method is based on time series regression, for which the intercepts are tested to

determine whether they are significantly different from zero. The method runs the

regression of each asset base on the equation

,jt j j t jtr b F (1)

where rjt is the time series excess returns of asset j (usually portfolio of assets). Ft is the

factor portfolio, usually comprised of the market excess returns and portfolio returns,

formed from the difference in the high- and low-ranked characteristic portfolios. αj, bj

and ɛjt are the regression coefficients and the regression error. The estimated intercepts

17

are grouped together to form a vector. The intercepts represent pricing errors. If the

model can explain the cross-sectional variation in returns, the intercepts should not be

jointly significantly different from zero. Gibbons et al. (1989) suggest computing the

statistic

1

' 1 211 ~ ( , 1) ,

T NSR F N T N

N

where T is the length of the time series, N is the number of assets or portfolio of assets,

is vector of intercepts from the regression equation above, ∑ is the covariance matrix

of the residuals from the regression above and SR is the Sharpe ratio of the factor. Under

the null hypothesis that the intercept equals zero, the method compares the statistic to the

F- distribution with degrees of freedom N and T-N-1 (F (N, T-N-1)).

Unlike the time series method, which requires regressors that are also returns, the two-

pass cross-sectional regression method can take on factors that are not returns (see Fama

and MacBeth (1973)). The method often involves two regression stages (hence two-pass

regression) because of the test of CAPM. The first pass regression (time series) estimates

betas, which then serve as input for the second pass cross-sectional regression. In the

second pass regression, several characteristics can be combined as independent variables

or regressors. That is, for each time t, the cross-sectional regression method runs a

regression of the form

1 1 , 1

2

,C

jt ot t jt vt v jt jt

v

r

(2)

where rjt is the cross-sectional excess returns of all assets at the time t, and βjt-1 are the

time-varying beta estimates. Γv,jt-1 can be any characteristic determined prior to t. ɛjt is the

18

error term. 0 , ,t Ct is a vector of regression coefficients. Using the time series of the

regression coefficients, we estimate their expected values and test if they are significantly

different from zero. If the CAPM holds, the expected value of 0t should be zero and the

expected value of 1t , which is the risk premium on the market should be significantly

positive. Any characteristic that can explain the cross-sectional variation in stock returns

has an average coefficient significantly different from zero. We now form the t-test

vv

v

t

(3)

where 1

1 T

v vt

tT

and v is the standard error normally adjusted for the Newey

West heteroskedastic and autocorrelation consistency (HAC). The Newey-West standard

error is estimated as '

0

1

11

q

v w w

w

w

q

where

w vt vt vt w vtE and q is the number of lags.

Betas can be estimated with a rolling window or the full window regressions. The rolling

window regressions estimate betas with information in the period prior to t. The betas are

then used in the cross-sectional regression for the subsequent period. There is a tendency

to measure betas with error in the first regression. Using estimated betas in the second

pass regressions therefore induces an error-in-variable problem, biasing the slope

coefficient in small samples. Estimating betas over the full sample period mitigates the

measurement error, as the time series sample size T increases. In this case, the second

cross-sectional regression estimate is T-consistent. In the full window regression method,

portfolios are formed by sorting stocks on betas estimated in the period prior to t.

19

Portfolios are then rebalanced by repeating the process of beta estimation and portfolio

formation for each time t in the period studied. Finally, portfolio returns are computed.

Full sample betas are estimated using these time series of portfolio returns. Based on the

assumption that betas are constant throughout the sample period, the full sample betas

can be used in the cross-sectional regression (see Ibbotson, Kaplan and Peterson (1997)).

On the other hand, asset beta varies with time, so each time, the full sample betas can be

assigned to individual stocks in the portfolios. The main assumption underlying this

approach is that stocks in a portfolio have the same exposure to long-term systematic

risk. This approach will yield N and T consistent estimates, since it uses the full

information in the sample period and the cross-section. Fama and French (1992) utilized

the full-sample beta estimate in the test of the CAPM.

A second approach to minimize the error-in-variable problem induced by beta or any

other estimated variable is to multiply the denominator in equation 3 by a correction

factor. Shanken (1992) suggests an adjustment factor

2

0

21

m

m

r

r

. Where 2

mr is the

standard deviation of the market returns in excess of the risk-free rate, mr is the average

excess market returns and 0 is the average intercept series from the cross-sectional

regressions.

In this dissertation, we will use all the possible sorting methods depending on the task.

For instance, we will use the double sorting methods to disentangle the marginal effect of

each characteristic on average returns. The sorting method provides the advantage of not

placing any linear restrictions on the return/characteristic relationship. To test the effect

20

of several characteristics on returns, we will adopt the cross-sectional regression method.

This will serve as a confirmation of the result in the sorting method.

For all portfolio formations we adopt the Fama and MacBeth (1973) breakpoint method.

That is, if N is the number of stocks in year t and n is the number of portfolios required,

stocks are allocated to int( / )N n portfolios, where int /N n is the nearest integer less or

equal to /N n . The middle portfolios have int /N n stocks each. If N is even,

int / 1/ 2 int /N n N n N n stocks will be allocated to the first and the last

portfolio. If N is odd, one stock will be added to the last portfolio. The method

sometimes allocates more stocks to the extreme portfolios, which are of a great deal of

interest because of the formation of the hedge portfolio (top-ranked portfolio returns,

minus the bottom-ranked portfolio returns). It also ensures that no stock is lost in the

portfolio formation process.

Summary of the chapters 1.3

In this doctoral research, we conduct four empirical studies with the BSE data from the

19th

and the beginning of the 20th

century. We cover the assessment of beta in chapter 2.

In chapter 3, we test the validity of the CAPM and the size effect. The fourth chapter

tests the momentum effect. The combined effects of Size, Momentum, Total Risk and

Dividend yield on the cross-section of stock returns is studied in chapter 5. The last

chapter concludes the dissertation.

1.3.1 Chapter 2

In the second chapter, we focus on the assessment of beta. Beta serves as the main input

of the CAPM. It is an estimated variable that can be measured with error, thereby biasing

21

the test results of the CAPM. Beta instability, bias and non-robustness to outliers have

become the center stage of research since the development of the CAPM. The chapter

studies the relative performance of different methods of estimating beta, based on their

ability to predict the subsequent beta. Specifically, we compare the market model betas

to the betas estimated with the Blume (1971) and Vasicek (1973) auto-regressive

techniques.

We show that the individual stock market model betas are not stable. The predictability

of the market model betas can be improved by forming portfolios with at least ten or

more stocks. Most strikingly, there is no significant difference in the predictive accuracy

of Blume and Vasicek‟s adjusted betas. Using Dimson‟s method of estimating betas,

small numbers of stocks prove to have returns that lead or lag the market returns. To

account for outliers, we use iterative reweighted least square techniques (IRLS) to

estimate betas. The betas from the IRLS are small in magnitude compared to the market

model betas, but they have the same predictive accuracy as the market model. Based on

the study in chapter two, we determine how to estimate beta for the study of the CAPM.

1.3.2 Chapter 3

In the third chapter, we use the sorting and the Fama and MacBeth (1973) (from here on

FM) cross-sectional regression methods to investigate whether the CAPM is valid before

World War I. We will also test if the size effect (the propensity of small size to have

higher returns than large size stocks) exists in the 19th

century BSE.

With the sorting and the FM cross-sectional regression methods, we find no empirical

validity for the CAPM. We also show that the relationship between beta and returns

varies with time. If anything, the null hypothesis of the equality of the estimated slopes

22

from the cross-sectional regression and the market excess returns is not rejected in the

period 1868 through to 1893. On the contrary, using size-sorted portfolios (equally

weighted) in the cross-sectional regression establishes the beta-excess return relationship

for beta as the lonely regressor (the CAPM is valid). However, the conditional double

sorting method adopted by Fama and French (1992) separates the effect of beta and size

on expected returns. The method makes the average cross-sectional slope of the beta

insignificant, whether placed alone or together with size in the regression.

We find size to be negatively related to excess returns. Size is negatively significantly

related to excess returns (size effect), but beta does not relate to excess returns when

placed together in the cross sectional regressions. Detailed analysis of the data reveals

that the size effect is mainly due to small size stocks, which accounts for about 0.35% of

the total market size. Eliminating these small stocks destroys the relationship between

excess returns and beta or size. Both sorting and cross-sectional regression reveals that

the size effect disappears when stocks are value weighted to form portfolios. In

summary, the CAPM did not work in the 19th

century BSE. Estimating betas with the

market model, the Dimson and Vasicek method will not establish the model. The size

effect exists, but it is mainly due to a small group of stocks that represent a very small

portion of the total market capitalization.

1.3.3 Chapter 4

In chapter 4, we investigate whether the momentum strategy can generate abnormal

profit in the 19th

century BSE. The momentum strategy buys stocks that have performed

well in the past 3-12 months, and sells stocks that have performed poorly in the past 3-12

months. There is convincing evidence that the strategy is profitable on the 19th

century

23

BSE. Finding momentum in this era confirms the assertion that the momentum profit

found on the post-World War II markets is not mainly due to data-snooping biases.

Detailed analysis reveals that the momentum effect does not exist in the small size group

of stocks. Additional investigation into the momentum profit in each calendar month

shows that the profit was positive for all months. The January reversal effect, found in

the post-World War II USA markets, cannot be found in the 19th

century BSE. In fact,

January records the fourth highest momentum profit relative to the other months of the

year. We find that momentum profit is not strong in the first twenty years of our study

period.

In order to investigate the source of the momentum profit, we use the approach of

Jegadeesh and Titman (2001) to study the returns of the momentum portfolios in the

post-holding period. The momentum returns reverse in the second to fifth years after the

holding period. Further study reveals the reversal is mainly due to small size stocks. We

also test whether the momentum profit and the long run reversal in the cross-section of

stock returns depends on the state of the market. The 6-month formation and the 6- to 12-

month holding period strategies are profitable solely in periods of market gains.

1.3.4 Chapter 5

In this chapter, we investigate whether size, momentum, total risk and dividend yield can

explain the cross-section of stock returns between the years 1868 and 1913. We repeat

size and momentum characteristics in the analysis to test the pervasiveness and the

combined effect of these characteristics on the cross-section of excess returns. The size

sort also tests whether the effect of the other characteristics are not confined to the small,

illiquid group of stocks. Total risk for each stock is measured as the standard deviation of

24

the past 24 to 60 months excess returns. Each year, dividend yield for a stock is the sum

of all dividends paid within the last 12 months divided by the current month price. We

investigate whether the relationships are pervasive across all dividend yield, size, total

risk and momentum groups. Sorting and FM cross-sectional regression methods are

adopted in the analysis. We confirm that size has a negative significant relationship with

excess returns. However, repeating the analysis on different size groups reveals that the

negative relationship is completely driven by micro-size stocks accounting for less than

3.67% of the market capital. This confirms the finding in Chapter 3 that the size effect is

mainly due to the first decile size portfolio, which forms part of the micro size group. We

did not find a consistent relationship for total risk. Momentum shows a consistent

positive relationship with excess returns in stocks, which accounts for more than 96% of

the market capital. We find a negative relationship between dividend yield and

momentum among dividend-paying stocks, but each of them is positively related to

average excess returns. Dividend yield and momentum are positively related to the

average excess returns in our large stocks, which account for about 96% of the market

capital.

25

CHAPTER 2

2 ASSESSMENT OF BETA IN THE 19th

CENTURY BSE3

Beta risk estimation and the testing of asset pricing models have a long tradition in

financial literature. Beta serves as the main input of the CAPM, and it is assumed stable

in empirical applications. However, the instability, bias and non-robustness (to outliers)

of the beta have raised concerns in the literature. The notion of its estimation is of

fundamental importance to the testing of CAPM. The objective of this chapter is to

introduce the new data set from the 19th

century BSE to test the performance of the

alternative techniques of estimating beta. Studying the various techniques of estimating

beta, we may determine relatively unbiased and stable beta for the test of CAPM, which

posits a positive relationship between the beta and expected returns.

Introduction and Literature Review 2.1

Beta stability, bias and robustness evaluations have become the center stage of research

in finance since the development of the CAPM by Sharpe (1964), Lintner (1965) and

Mossin (1966). Beta, one of the parameters of a time series' regression, plays a key role

in CAPM applications. Beta is usually estimated with the standard market model (MM).

The MM is a statistical model that relates the return of any given stock to the return of

the market index. Therefore, for returns of a stock j in period t we write,

,jt j j mt jtR R (4)

3 This chapter was presented as a paper at the First World Finance Conference on the 27

th May 2010 at

Viana do Castelo, Portugal (blind reviewed)

26

where 2

jt jVar 4,

jtR and mtR are the period t returns on the stock j and the

market index return, respectively. The parameters jj , and 2

j are the parameters to

be estimated from the MM peculiar to stock j . The MM assumes that j (beta) is

constant over the estimation period. However, substantial evidence in the financial

literature has established that security betas are not stable over time. Blume (1971) and

(1975) pioneered the research on beta stability based on the cross-sectional correlation

between beta estimates for successive periods. He finds portfolio betas having stronger

correlation across successive periods than individual security betas. This indicates that

portfolio betas are more stable than individual stock betas. Blume (1971) and Vasicek

(1973) show that betas are not stable, but they revert towards their cross-sectional mean.

They propose autoregressive models to capture this variation in beta. The autoregressive

method adopted by Blume is the cross-sectional regression of betas in period t on the

betas in period t-1. That is,

1 ,jt jt jta b for j=1,…,N (5)

N is the number of stocks in the cross-section. a and b are the intercept and the slope of

the cross-sectional regression of betas in the period t on betas in the period t-1. The jt is

the error of the cross-sectional regression of betas in successive periods. The objective of

Blume‟s autoregressive model is based on the tendency of betas from successive periods

to revert to the mean. In effect, the method adjusts historical betas towards their cross-

sectional mean. The Vasicek autoregressive method not only adjusts betas toward their

cross-sectional mean, but the adjustment also depends on the uncertainty (standard error)

4 xE is the expected value of x , )(xVar is the variance of x.

27

about beta. Betas estimated with high standard errors have a greater tendency to deviate

from the cross-sectional mean of the betas. Therefore, high uncertainties call for greater

adjustment. Vasicek (1973) applied a Bayesian correction method to capture the

differences in standard errors. The Bayesian correction method places weights on the

cross-sectional average beta and the asset‟s beta estimate. The weights sum up to one,

and the more the uncertainty surrounding either estimate of beta, the lower the weight

placed on it. He used cross-sectional information from the previous period betas. That is,

beta is estimated with the model

21

1 12 2

1 1

varfor 1,2, , ,

var var

jt

jt jt jt

jt jt

j N

(6)

where jt is the mean of the posterior distribution of beta for stock ,j which serves as

the beta forecast. 2

is the standard error from the estimation of the market model

regression coefficient, 1jt . 1jt is the cross-sectional mean of betas in period 1t , and

1var jt is the variance of the cross-section of betas. Faff and John (1992) use

Australian data to confirm the evidence in beta nonstationarity. They show that there is a

strong connection between beta instability and the market index used to estimate beta. On

the contrary, Gregory-Allen, Impson and Karafiath (1994) use daily data to document

that portfolio betas are not more stable than individual security betas on the US market.

They show that, accounting for the variance around beta estimation will not make

portfolio betas more stable than individual stock betas.

Also, the literature has shown that nonsynchronous trading biases betas estimated with

the MM. When stocks are ranked based on their market capital (size), beta is biased

28

downward for small size stocks and upward for large size stocks. Scholes and Williams

(1977), Dimson (1979) and Fowler and Rorke (1983) developed methods to correct the

bias. Dimson (1979) adopted the aggregate coefficient method, which computes the lead

and the lag betas in a multiple regression of the stock return on a number of lead/lag

market returns. The sum of the estimated beta coefficients from the multiple regressions

is Dimson‟s estimate of beta. Dimson‟s technique involves estimating a multiple

regression of the form

,l

jt j j mt i jt

i l

R R

(7)

Dimson‟s beta estimate is then given bydim

l

i

i l

. The error term jt follows the

assumptions of the classical linear regression model. On the other hand, Scholes and

Williams (1977) compute the lead and lag beta coefficients by univariate regressions.

The literature has found that the bias in beta estimates is due to autocorrelation in returns

caused by infrequent trading. Ibbotson et al. (1997) found that beta estimates for small

stocks are severely biased downwards. This implies that the returns of small stocks are

more capable of exhibiting autocorrelation than large stocks. They recommend the

inclusion of the lagged market returns in the estimation of beta when securities are traded

infrequently. On the other hand, Bartholdy and Riding (1994) found that the MM betas

are less biased, more efficient and consistent on the New Zealand Market than the

Dimson, Scholes and Williams biased correction model betas.

The literature also highlights the impact of outliers (extreme observations) on the beta

estimates. Outlier observations in returns, depending on their location in the stock return/

29

market return plane, can have an extreme influence on beta when the MM is used to

estimate beta. Under idealized conditions, the MM beta produces the best estimate

because of the ordinary least squares method. The idealized conditions are that the paired

returns of the stock and the market conform to the linear model relationship with zero

mean error not correlated with the market returns. Unfortunately, these conditions often

fail in empirical settings. One explanation of the failure of the condition is the occurrence

of outlier observations in returns. Nevertheless, the MM does not consider the effect of

outlying observations on beta. Chatterjee and Jacques (1994) document the effect of

outlying “observations” on the beta parameter. Their detailed study compares the betas

estimated from the MM and the outlier resistance methods. They indicate that the MM

cannot detect a large number of outlying returns in their data. Identifying the outlying

observations and estimating betas with the outlying resistance method yield beta

estimates that are lower than the MM betas. Chan and Lakonishok (1992) said the robust

method (outlier detecting method) of estimating beta is good for stocks susceptible to

stock splits, dividend cuttings, and initial public offerings (IPO). Stocks that exhibit this

behavior are mostly small stocks. Martin and Simin (2003) confirmed that outlier

resistance beta is a better predictor of future beta than the market model beta. They also

reveal that small stocks betas are most vulnerable to outliers.

The literature proposes various techniques of minimizing the impact of outliers on beta

estimates. The weighted least square estimation technique is one of the methods used to

minimize the impact of outliers on beta estimates. Based on the assumption that outliers

have a lower probability of occurring in the future, less weight is placed on them (see

Martin and Simin (2003)). An alternative technique would be to remove the extreme

30

observations and perform the regression with fewer observations. The least squares

approach adopted by the MM minimizes the sum square residuals with respect to the

model parameters j and j :

2

,min ,

j j

jt j j mtR R

The squaring of the residuals magnifies the effect of the outliers on the estimated

parameters. For instance, expected return is likely to shift toward the outliers while the

covariance matrix will be inflated toward the outliers. To reduce the influence of outliers,

the statistics literature emphasizes the use of iterative reweighted least-squares (IRLS)

method. This method estimates beta by iteratively minimizing a weighted function that

depends on standardized return residuals:

,

min ,j j

j

jt j j mtR RW

(8)

with weight function W and j

the standard deviation of the return residual. We

estimate the regression parameters from the least squares regressions and use these

parameters as initial input for iteration. A weight function is applied to the standardized

residuals. We apply Huber or the bisquare weight function, defined as:

22

1,

0

jtjt

jt

jt

sfor s T

TW s

for s T

31

with the standardized residual

j

jt j j mt

jt

R Rs

and T , a tuning constant. Huber

(2004) sets the value of T to 4.685. Small values of T introduce more resistance to

outliers, but at the detriment of efficiency when returns are outlier free. He chose the

value of T so the method will have less influence on beta when there is no extreme

observation and it still provides protection against outliers. For the iterations, the initial

input is the coefficients from the MM. The residual from the MM is standardized and the

weight function defined above is used to transform them. Estimate the parameters by the

weighted least squares:

jRWWb 0'10'1

where ,mtR

with a vector of ones with the same size as mtR (market index returns). 0W is an initial

standardized weight diagonal matrix and 1b the estimated beta parameter. The new set

of parameters serves as input for the next iteration. The procedure above is repeated until

the parameter of interest (beta) converges. A standardized residual observation that

exceeds the tuning constant is assigned zero weight (outliers).

The literature also suggests that estimated betas vary with time and macroeconomic

conditions. Therefore, static beta CAPM should replace with time varying beta

conditional CAPM (see Jagannathan and Wang (1996)). In this dissertation, we did not

pursue the time-varying beta because, Ghysels (1998) used monthly NYSE data to

document that pricing errors with static beta models are smaller than those with time-

varying beta models. He indicated that time-varying beta model might be mispecified.

32

To the best of my knowledge, the literature has not traced the stability, bias and

robustness of beta using data before 1926 in any country. Luoma, Martikainen, Perttunen

and Pynnönen (1994) simulated returns data to generate artificial markets. They found

that various beta estimation techniques behave uniquely in different markets.

In this chapter, individual and portfolio betas from the various estimation techniques will

be compared based on their predictive accuracy. The root mean square error (RMSE)

criterion adopted by Blume (1971) and Klemkosky and Martin (1975) is used to

determine the predictive accuracy of the betas estimated from the various techniques.

The 19th

century data provide a very good platform to determine whether betas before

1914 exhibit a similar pattern as betas after 1914.

This chapter reveals that for individual stocks, the market model betas are weak in

predicting their future. Predictability can be improved when a portfolio of 10 or more

stocks components is formed. The study also shows no significant difference between the

Blume and Vasicek adjusted betas in terms of their predictive accuracy. Estimating betas

with the Dimson method reveals a very small number of stocks showing a lead and lag

relationship with the market returns. The iterative reweighted least squares method

produces betas that have the same predictive power as the MM betas, but are lower in

their magnitude on average.

The subsequent sections of the chapter are organized as follows: Section 2.2 provides

descriptive statistics of beta when estimated with the least squares regressions of the

MM. Section 2.3 examine the Blume correlation technique of detecting the stability of

beta. The autoregressive technique of Blume and Vasicek is used to adjust betas in

33

Subsection 2.3.1. The predictive accuracy of the adjustment techniques based on the

RMSE criterion is tested in the same section. The modified Diebold and Mariano test

proposed by Harvey, Leybourne and Newbold (1997) is used to test for equal predictive

accuracy of the models. In Section 2.4, we determine how the stocks in each period lead

or lag the market index using the Dimson‟s model. In Section 2.5, we compare outlier

resistant betas to the benchmark MM betas. The final section presents the conclusion.

Beta Coefficient Descriptive Statistics 2.2

The data sample is divided into 15 five-year non-overlapping periods it for 1,...,15.i

Stocks with complete returns data for five years are considered in each sub-period. For

the proxies of the market portfolio, we consider the value-weighted market index. Table

2.1 presents the number of stocks in each period under study, the statistical

characteristics of the betas estimated in each period and displays the 15 periods studied,

starting from January 1837 to December 1911. The number of stocks with full returns

data in each period ranges from 21 to 424 as shown in Column 2. It can be seen in Table

2.1 that the number of stocks that have five years of data does not exceed 100 before

1877. The beta coefficient of each stock in each period is estimated by simply regressing

the monthly returns of the stock in each period on the corresponding monthly value-

weighted index of the market by using the MM above. Cross-sectional statistics of the

betas in each period are computed and the result is displayed. The equally weighted

average beta and the value-weighted average beta are displayed in Columns 3 and 4,

respectively. We compute the value-weighted mean beta by considering individual stock

relative to market capitalization at the beginning of the period. From the high values of

equally weighted mean beta and low values of value-weighted mean beta in the periods

34

Table 2.1: Beta coefficient descriptive statistics for the 15 estimated periods

Note: This table displays cross-sectional descriptive statistics of betas estimated by market model (1) of returns on their market counterparts over the 15 five-year

sub-periods between January 1832 and December 1911. The number of stocks in the various periods ranges from 21 to 424 for stocks with full return data within

a period. The table also reports the percentage of beta sample in a period that is less than zero. The maximum and minimum beta of each period is also recorded.

The last column reports the average coefficient of determination 2R . Equally weighted (EW) and value-weighted (VW) mean betas are also displayed in the

table. The value-weighted mean is the average of the betas weighted by their market capital at the beginning of the period.

Percentage

Number of Average Average Standard of BETAS Mean

Period Stocks beta(EW) beta(VW) Deviation <Zero Minimun 0.10 0.25 0.50 0.75 0.90 Maximum R2(%)

1/1837-12/1841 21 1.37 1.24 0.67 0 0.38 0.50 0.77 1.35 1.83 2.29 2.90 29

1/1842-12/1846 33 1.10 1.01 1.84 12 -1.18 -0.04 0.27 0.79 1.39 2.21 10.19 18

1/1847-12/1851 32 0.69 1.05 0.72 0 0.04 0.15 0.33 0.48 0.83 1.24 3.92 25

1/1852-12/1856 33 0.76 0.98 0.55 3 -0.43 0.11 0.35 0.75 1.09 1.56 1.98 19

1/1857-12/1861 54 0.98 1.15 0.55 2 -0.19 0.28 0.71 0.99 1.25 1.55 2.74 27

1/1862-12/1866 72 0.83 1.01 0.73 4 -0.86 0.20 0.40 0.70 1.07 1.57 3.70 12

1/1867-12/1871 76 0.74 0.76 0.58 8 -0.91 0.09 0.42 0.67 1.02 1.35 2.36 11

1/1872-12/1877 82 1.05 0.96 1.01 10 -0.71 0.01 0.30 0.85 1.70 2.59 3.55 15

1/1877-12/1881 113 1.29 0.96 1.50 12 -3.54 -0.03 0.32 0.93 1.99 3.14 7.80 17

1/1882-12/1886 154 1.03 1.03 1.44 18 -1.33 -0.35 0.14 0.66 1.66 2.90 7.94 6

1/1887-12/1891 161 1.52 0.74 1.73 14 -0.76 -0.05 0.10 0.94 2.61 4.03 7.81 22

1/1892-12/1896 196 1.24 0.95 1.32 12 -1.74 -0.02 0.34 1.04 1.71 2.87 7.23 8

1/1897-12/1901 252 1.13 0.93 1.11 8 -3.03 0.02 0.27 1.09 1.71 2.38 5.47 14

1/1902-12/1906 374 1.24 1.03 1.36 11 -1.33 -0.08 0.33 1.15 1.74 2.63 8.92 10

1/1907-12/1911 424 1.16 1.05 1.18 9 -2.14 0.01 0.34 1.06 1.64 2.45 7.33 12

Fractiles

35

after 1873, we can conclude that small stocks have high betas in these periods. The

values in the last column show the average coefficient of determination 2R in

percentages, which is a measure of explanatory power of the MM. It is worthy to note the

percentage of negative betas in nearly all the sub-periods. Surprisingly, the literature

reports negative betas on different markets after World War I. For example, Altman,

Jacquillat and Levasseur (1974), Dimson and Marsh (1983) recorded a large number of

negative betas in their weekly returns interval estimation of beta on the French and the

American markets. It is also important to note the very high and low betas in the 19th

century BSE compared to the post-1926 market betas recorded in the literature. The

possible explanation for these extreme values of the beta and low coefficients of

determination might be linked to the infrequent trading effect and the influence of

extreme observations (outliers) in the returns series of the stocks. The removal of stocks

that did not trade fully within the five-year estimation periods does not introduce

survivorship bias since there is no significant difference in the beta coefficient

descriptive statistics when stocks with at least 24 observations are added to the sample

(not reported).

In order to capture the effect of size (market capitalization) on the average beta and 2R

values, we computed the same cross-sectional statistics for betas in each period.

However, the stocks in each period are sub-divided into three mutually exclusive size-

based sub-samples. The composition of the sub-samples is as follows: the sample of

stocks in each period is sorted in descending order based on their market capitalization

(size) at the beginning of the period.

36

Table 2.2: Average beta and average coefficient of determination of the size based sub-samples

Note: In this table, stocks in each period were sorted in descending order based on their market capital.

The first 30 percent of stocks in the periods are classified as large stocks, the next 40 percent as medium

stocks and last 30 percent as small stocks. Cross-sectional statistics of the betas of the sub-samples were

computed and their equally weighted averages of betas and coefficient of determination 2R are

displayed. The L, M and S subscripts on betas indicate large, medium and small stocks, respectively.

Figure 2.1: The graph of the average beta of each period for large stocks and small stocks

Note: The average beta estimates for large and small stocks are plotted against their corresponding periods

of estimation. The diamond points indicate the averages of large stocks and the square points for small

stocks. This depicts the extreme values of beta estimate recorded for the small stocks relative to the

benchmark beta of one.

Period mean(βiL) mean R2(%) mean(βiM) mean R2(%) mean(βiS) meanR2(%)

1/1837-12/1841 1.29 30.1 1.73 32.8 1.07 23.0

1/1842-12/1846 1.19 36.5 0.79 10.5 1.40 10.1

1/1847-12/1851 0.94 43.2 0.49 21.6 0.67 10.1

1/1852-12/1856 1.05 35.4 0.66 14.2 0.61 10.2

1/1857-12/1861 1.15 40.5 1.08 27.0 0.69 12.9

1/1862-12/1866 1.04 22.6 0.76 8.0 0.70 5.5

1/1867-12/1871 0.77 17.2 0.59 9.4 0.90 7.2

1/1872-12/1877 1.06 19.2 1.02 16.4 1.10 10.0

1/1877-12/1881 1.03 20.2 1.51 18.0 1.30 12.3

1/1882-12/1886 1.01 9.4 1.16 6.1 0.86 3.4

1/1887-12/1891 0.84 18.2 1.73 27.6 1.95 17.7

1/1892-12/1896 1.00 9.5 1.29 7.4 1.40 5.7

1/1897-12/1901 0.98 17.6 1.22 14.6 1.16 9.3

1/1902-12/1906 1.06 15.5 1.27 9.1 1.39 4.3

1/1907-12/1911 1.18 20.1 1.17 11.0 1.13 5.5

Large Medium Small

37

The first 30 percent of stocks are classified as the large stocks portfolio, next 40 percent

as medium stocks portfolio, and the last 30 percent as the small stocks portfolio. Table

2.2 reports the average beta and the 2R values for each sub-sample in each period.

Generally, the high values of 2R recorded for large stocks are striking because on the

UK market, Dimson (1979) recorded a similar pattern with 15 years of monthly data.

This might be attributed to the value-weighted index used in the computation, since the

index will have more explanatory power for large-sized stocks. Figure 2.1 depicts the

cross-sectional average beta of each period for large stocks and small stocks. It is clear

from Figure 2.1 that small stocks record comparatively low betas in the periods before

1867 and high betas thereafter. The result in the periods before 1867 corroborates the

assertion of Dimson (1979), Scholes and Williams (1977) and Beer (1997). They said

that if trading frequency is highly correlated with the market capitalization of the stock,

betas of small stocks (infrequently traded stocks) are lower when estimated with the

market model. On the contrary, Ibbotson et al. (1997), based on NYSE data between

1926 and 1994, found that small stock returns due to infrequent trading show a high

degree of autocorrelation and that they are capable of recording high betas. On the 19th

century BSE, we confirm their result in the periods after 1867. The only anomaly is the

period between 1882 and 1886, where the small stock average beta lies slightly below the

average beta of large stocks.

Beta Stability 2.3

Here, we adopt the Blume (1971) and Altman et al. (1974) correlation method of

investigating the stability of beta estimates. Blume (1975) shows that the beta coefficient

38

between two successive periods is stationary if5

1i it tE E

, 1i it tVar Var

,

1

, 1i it tcorr

where

it are the betas in period it . Betas in period it are used to rank

stocks existing in periods it and 1it in ascending order. In period it equally weighted

portfolios of ,...3,2,1s stocks are formed as follows: the first portfolio consists of stocks

with s smallest beta estimates. The next portfolio consists of stocks with the next

smallest beta estimates. This process of portfolio formation is repeated until the number

of stocks left is less than s. For each s, the betas of all portfolios in period 1it are also

computed. We compute the correlation and Spearman rank order correlation of the betas

between each two adjacent periods. Table 2.3 reports the weighted average correlation

across all the sub-periods studied. The weighted average correlation takes into account

the number of stocks or portfolios in each adjacent ten-year period.

Table 2.3: Weighted average of correlation and Spearman rank order correlation across successive periods

Note: This table shows the weighted average correlation and Spearman‟s rank correlation of betas of

individual stocks and portfolios in successive periods across the 15 periods studied. For a stock to be

included in this analysis, it has data for two complete consecutive periods. Betas in a period (estimation

period) are used to rank the betas in that period and the next adjacent period (prediction period) in

ascending order. Portfolios are formed with their constituency as follows: the first portfolio is the first s

stocks for s = (1,2,4,7,10,20). The second portfolio contains the following s stocks and so on until

available stocks is less than s . Assuming equal amounts are invested in each stock, then the portfolio beta

will be the mean of the betas of stocks included in the portfolio. We computed the weighted average

correlations by considering the number of portfolios in each ten-year period.

5 ),( yxcorr is the correlation between x and y .

per Portfolio Correlation

Spearman's

rank Correlation

No. of Stocks

0.92

0.95

0.56

0.64

0.72

0.77

0.91

0.96

0.54

0.62

0.72

0.76

1

2

4

7

10

20

39

The weighted average correlation across the successive periods ranges from 0.54 for

individual stocks to 0.95 for portfolios of 20 stocks. These values indicate that the beta of

individual stocks have, on average, less information about their future beta than the

portfolio beta. Blume (1971) found a similar result on the US market. Due to the limited

number of stocks, we were not able form up to 50-sized portfolios on the BSE. Blume

finds 0.62(0.67) and 0.91(0.93) mean correlation (rank correlation) for 1- and 10-sized

portfolios using 84-month estimation periods respectively. Furthermore, based on 52-

week estimation periods, Levy ( 1971) records 0.44 and 0.82 mean correlation for 1- and

10-sized portfolios on the same exchange. On the UK market between 1955 and 1979,

Dimson and Marsh (1983) used value-weighted market index, monthly returns interval

measurement and sixty-month estimation periods to obtain an average correlation of 0.56

and 0.91 for 1- or 10-sized portfolios respectively. The correlations in Table 2.3 show

that the betas from the 19th

century BSE are stable compared to the betas in post-1926

US and UK markets.

2.3.1 Blume and Vasicek stability adjustment techniques

Individual stock betas estimated from the MM are noted as unstable in the previous

section (also in Blume (1971), Collins, Ledolter and Rayburn (1987), Faff and John

(1992), Gregory-Allen et al. (1994), Eisenbeiss, Kauermann and Semmler (2007)). There

is a tendency for a high beta estimate to overstate its true value and vice versa. Therefore,

we use the Blume (1971) autoregressive adjustment model to improve the stability of

beta estimates for both individual stocks and portfolios. Table 2.4 presents regression

tendencies implied between adjacent periods, where a and b are the constant term and

slope coefficients, respectively. The values of the coefficients in the periods between

40

1837 and 1867 are striking. It is not consistent with the Blume assertion that all the

coefficients lie between zero and one. The last two Columns show the t-statistics of the

test of a hypothesis of the slope coefficient equal to zero or one. The t-statistics of the

slope coefficients show that the null hypothesis of the slope coefficient equal to zero is

rejected in the adjacent periods after 1872. In addition, the null hypothesis of the slope

coefficient equal to one is rejected in all the adjacent periods (except the first two

periods). The R2 values also show that the betas in the periods after 1872 have more

explanations for their prior betas than those before 1872. As can be seen in Table 2.4, the

coefficients change over time, but there are extreme coefficients outside the interval

between zero and one in the first two periods.

Table 2.4: Measurement of regression tendency of estimated beta coefficient for individual stocks

The extreme values may be attributed to the number of stocks in a period as we record

less than 50 stocks in our first two five-year periods. A result not reported shows that

increasing the length of the estimation period (such as seven years in Blume (1971))

Regression Tendency

Implied Between Periods a b R 2 (%) H0:b =0 H0:b =1

1/1842- 12/1846 and 1/1837- 12/1841 1.40 0.00 0 0.00 -1.31

1/1847- 12/1851 and 1/1842- 12/1846 0.74 -0.07 3 -0.96 -14.11

1/1852- 12/1856 and 1/1847- 12/1851 0.48 0.33 20 2.58 -7.60

1/1857- 12/1861 and 1/1852- 12/1856 0.53 0.54 26 3.22 -5.41

1/1862- 12/1866 and 1/1857- 12/1861 0.27 0.55 18 3.32 -5.43

1/1867- 12/1871 and 1/1862- 12/1866 0.63 0.13 3 1.38 -10.34

1/1872- 12/1876 and 1/1867- 12/1871 0.77 0.43 5 1.94 -4.04

1/1877- 12/1881 and 1/1872- 12/1876 0.65 0.70 20 3.99 -5.03

1/1882- 12/1886 and 1/1877- 12/1881 0.44 0.67 39 7.80 -10.91

1/1887- 12/1891 and 1/1882- 12/1886 0.86 0.69 31 7.66 -10.49

1/1892- 12/1896 and 1/1887- 12/1891 0.58 0.39 27 7.42 -18.75

1/1897- 12/1901 and 1/1892- 12/1896 0.60 0.38 27 7.81 -19.99

1/1902- 12/1906 and 1/1897- 12/1902 0.49 0.70 28 8.94 -11.98

1/1907- 12/1912 and 1/1902- 12/1906 0.78 0.39 15 7.67 -19.21

0.67 0.46 20 18.75 -41.46

null hypothesis of the slope coefficient (b ) equal to zero or one is also reported in the last two columns.

All periods

β jt =a+bβ jt- 1+η jt

Note: In this table beta of stock existing in a period are regressed on the betas of the same stocks in a prior adjacent peri-

od. R2(%) is the percentage of the variance of betas in the period t explained by betas in the period t -1. The t-statistic of the

41

improves the 2R values and the t-statistics but at the expense of losing more stocks, since

fewer stocks have complete returns' data for longer periods.

With the regression tendencies, suppose we want to forecast the beta for any stock or

portfolio in the period 1842-1846. We compute its beta in 1837-1841. The forecast of the

beta is obtained by substituting it for βt-1 in equation (5) with the coefficients in the first

row of Table 2.4. βt is then computed from the equation and used as the forecast. The

adjustment process is repeated for stocks in the subsequent 13 adjacent periods using

their respective coefficients. We also introduce the Vasicek adjustment model (6) to

adjust betas in successive adjacent periods. We test the predictive performance of the

various adjusted betas by using the root mean square error6 (RMSE) criterion. The

RMSE tests the performance of the autoregressive methods based on variation and

unbiasedness of their beta forecast. The adjustment method is repeated for all adjacent

periods on equally weighted portfolios of size 2, 4, 7, 10 and 20. In order to compare the

predictive performance of the MM betas and the autoregressive-adjusted betas, we

compute the RMSE of betas estimated with MM in adjacent periods. Table 2.5 displays

the average RMSE of the adjusted betas and MM betas across the 15 periods studied. It is

clear from the table that the average RMSE of the adjusted betas is lower than that of the

market model betas. Table 2.5 also shows that the predictive performance improves as

the number of stocks in a portfolio increases for both adjusted and the MM betas. For

individual stocks, the Bayesian adjustment technique proposed by Vasicek is superior to

Blume‟s adjustment as reflected in the small average RMSE. Blume (1971) and

6 The root mean square error was calculated by

1

2

i ijt jt

N

for Nj ,...,1

42

Klemkosky and Martin (1975) recorded similar patterns of the predictive performance on

the NYSE market. Their adjusted betas mean square errors were smaller than their MM

betas. For portfolios of size 7 or more, one cannot see much difference between the

Blume adjustment method and the Bayesian approach.

Table 2.5: Predictive performance of Blume and Vasicek (Bayesian) procedures of estimating beta

Note: Average RMSE across the 15 periods studied were used to compare the predictive performance of

the various adjusted betas and the market model (MM) betas in successive periods. The average RMSE

across the successive adjacent periods for the various equally weighted portfolio formations are displayed.

The conclusion is that on the 19th

century BSE, the predictive accuracy of betas estimated

by the MM can be improved by adjusting betas using either the Blume or Bayesian

adjustment methods and a portfolio with a sizeable number of stocks.

The reliability of the conclusion above can be confirmed by performing an additional test

on the root mean squared error values. The possible method is to test whether the

differences in the values of the RMSE‟s are statistically significant. Harvey et al. (1997)

presented a modified Diebold and Mariano test statistic that will be used for this purpose.

Therefore, suppose we want to compare the forecasts of Blume (BL) and Vasicek (VA)

models. BL and VA are the forecasting errors from the Blume and Vasicek models,

respectively. In our case, we consider the root mean square error function, BLf root

mean square error of the Blume adjusted betas. The test is based on the loss differential

Bayesian

0.48

0.38

0.31

0.27

0.27

0.23

No.of Stock

per Portfolio

1

2

0.40

1.08

4

7

10

0.57

MM Blume

Average RMSE

0.23

0.1920

0.45

0.57

0.44

0.35

0.29

0.76

0.25

43

function BL VA

j j jd f f for 1,...,j H . The null hypothesis of expected equal

predictive performance is H0: 0jE d and the alternative hypothesis of the Blume

model predicting worse than the Vasicek model is aH : 0.jE d The Modified

Diebold-Mariano (MDM) statistic is:

11 2

, 112

0

1

1 2 1. ~ 0,1 ,

2

H

i

i

H h H h h dMDM t

H

where 1

1

H

j

j

d H d

, cov ,i j j id d , h is the horizon of forecast and , 1(0,1)Ht

a

student‟s t distribution with 1H degrees of freedom and v is the significant level

usually set at 5%. The test compares the Diebold-Mariano test statistics to critical values

from the student‟s t distribution. We reject the null hypothesis of equal predictive

accuracy when the test statistic is greater than the critical value at level. In order to

apply this test, betas estimated with the Market, Blume and Vasicek models in all periods

are pooled together to form three series of length H. Then we perform the test on the

three series.

Table 2.6 reports the modified Diebold-Mariano test statistics between the various

models under study. Betas estimated from the various models are considered across the

entire period studied. The period studied is divided into two sub-periods based on the

environment in which the BSE operated, a period of strict regulation and a period of

deregulation and expansion. The values in the first row of the table reveal that we can

confidently reject the null hypothesis of one-step ahead equal predictive accuracy of the

44

Blume and MM betas. For instance, in the overall period of our sample the null

hypothesis can be rejected at the 5 percent level. During the strictly regulated period, we

find that Blume-adjusted beta significantly outperforms the market model beta. Between

the Vasicek adjusted betas and the MM betas, we can reject the null hypothesis of equal

predictive accuracy for the deregulated and expansion period.

Table 2.6: Modified Diebold-Mariano test statistics (p-value in parentheses)

The significance level of the rejection becomes weak in the strictly regulated period. The

equality in the predictive performance of the Vasicek and the MM betas is strongly

rejected in the entire period. The values from the bottom row of Table 2.6 show that there

is no significant difference between the Vasicek betas and the Blume betas in terms of

their one-step ahead forecast. Therefore, we cannot reject the null hypothesis of equal

predictive accuracy between the two models.

Beta Bias 2.4

Considering the period of the study and the trading frequency of the market, we might

expect that some stocks may not trade every month for economic reasons or because of

Models

βMM vs. βBL

βMM vs. βVA

βBL vs. βVA

Overall period

1/1837-12/1911

2.18

period

Strict Regulatory

1/1837-12/1871

Deregulation and

expansion period

1/1872-12/1911

(0.01)

1.99

(0.02)

2.87

(0.00)

3.75

(0.00)

4.11

(0.00)

1.44

(0.08)

Ha= E(d j ) >0

Note: This table reports the modified Diebold-Mariano test statistics for one step ahead equal forecast

accuracy between the market model, Blume and the Vasicek's adjusted betas. β MM =market model betas,

β BL = Blume's adjusted betas, β VA = Vasicek's adjusted betas. The hypothesis test H0 : E(d j ) = 0 and

0.56

(0.29)

0.78

(0.22)

0.19

(0.42)

45

regulatory conditions. These stocks may systematically lead or lag the market movement,

producing biased betas when beta is estimated with the MM. In order to expose the

presence of possible lead or lag effects, we test the significance of the coefficient of the

returns on the lagged or lead market index.

Table 2.7: Dimson Aggregate Coefficient (AC) beta Adjustment

Number of AC

Period stocks Beta β-3 β-2 β-1 β0 β1 β2 β3

1/1837-12/1841 21 1.37 0.03 0.05 -0.12 1.42 -0.07 -0.02 0.07

(10) (5) (5) (95) (0) (0) (5)

1/1842-12/1846 33 1.47 -0.11 0.37 0.10 1.06 0.12 -0.10 0.03

(3) (12) (18) (58) (15) (0) (6)

1/1847-12/1851 32 0.69 0.00 0.07 -0.16 0.76 -0.03 0.07 -0.02

(6) (13) (3) (72) (13) (13) (3)

1/1852-12/1856 33 0.80 0.06 0.03 0.00 0.76 0.01 -0.07 0.01

(3) (6) (0) (73) (6) (6) (0)

1/1857-12/1861 54 0.97 0.00 -0.02 0.07 0.99 -0.10 0.00 0.04

(2) (7) (6) (78) (4) (2) (11)

1/1862-12/1866 72 0.56 -0.21 0.19 -0.09 0.90 -0.16 0.05 -0.12

(4) (10) (8) (42) (0) (3) (0)

1/1867-12/1871 76 0.49 -0.09 -0.15 0.05 0.73 0.04 0.00 -0.08

(1) (3) (5) (67) (3) (3) (3)

1/1872-12/1877 82 1.17 0.07 -0.08 0.24 1.02 -0.17 0.12 -0.02

(10) (5) (11) (60) (7) (7) (7)

1/1877-12/1881 112 1.67 0.12 -0.05 0.10 1.19 0.07 0.09 0.15

(6) (7) (13) (55) (6) (11) (11)

1/1882-12/1886 154 0.74 -0.03 -0.03 -0.01 0.97 0.11 -0.10 -0.18

(6) (3) (6) (38) (9) (5) (1)

1/1887-12/1891 160 1.68 0.03 0.12 -0.09 1.58 -0.04 0.00 0.08

(4) (7) (5) (52) (7) (4) (6)

1/1892-12/1896 196 1.42 0.07 -0.07 0.12 1.19 0.08 0.08 -0.04

(6) (6) (6) (42) (8) (5) (4)

1/1897-12/1901 252 0.96 -0.07 -0.05 0.05 1.17 -0.18 0.06 -0.02

(9) (5) (6) (59) (4) (8) (7)

1/1902-12/1906 374 1.11 -0.04 0.09 0.22 1.18 -0.03 -0.16 -0.15

(4) (7) (10) (47) (3) (3) (4)

1/1907-12/1911 424 1.23 -0.03 0.04 0.12 1.13 0.04 -0.05 -0.01

(2) (3) (10) (56) (5) (6) (5)

Overall periods 2075 1.09 -0.01 0.03 0.04 1.07 -0.02 0.00 -0.02

(5) (6) (8) (53) (5) (5) (5)

Mean Lag,Match and the Lead beta estimates

Note: This table reports Dimson's aggregate coefficient adjusted beta in each five year period. The numbers in parenthesis are

the percentage of stocks in a period that reject the null hypothesis of the coefficient been zero at 5% significant level.

46

The Dimson bias adjustment equation with maximum lag or lead of three months is

considered, that is 3,...,3i . We use only three months lag and lead because beta bias

has been documented as not prevalent in monthly returns data (see Cohen, Hawawini,

Maier, Schwartz and Whitcomb (1983)). For each stock, the estimates of the parameters

i indicate the lagged, matched and lead beta coefficients. We test the hypothesis

0:0 iH against the alternative 0:1 iH for each stock.

Table 2.7 reports the cross-sectional average of the lag and lead betas in each period. The

numbers in parentheses are the percentage of stocks that reject the null hypothesis.

Evidence from this table indicates that beta coefficients i for 0i are not significantly

different from zero for the majority of the stocks. This shows that the explanatory power

of the model for 0i is approximately zero for most of the stocks. Unsurprisingly, there

are some stocks with lead and lag coefficients that are statistically significant, but their

numbers does not exceed the coefficients corresponding to the match. This indicates that

there is no severe timing problem in the 19th

century data.

As most of the lead and lagged coefficients are significantly equal to zero, we can

interpret this as evidence of the market model (MM) producing statistically reliable beta

estimates in relation to the other models, which incorporate the lagged and lead market

indexes. These results can be compared to the results from the post-World War I markets.

For example, Hawawini and Michel (1979) found a similar pattern of results on the

Belgium stock exchange by using weekly interval returns data between 1963 and 1976.

The result also follows Cohen et al. (1983) hypothesis that there is a strong relationship

between beta estimates and the length of the interval over which returns are measured.

47

They established that beta bias mostly shows up in the short length interval (daily) of

returns, and the bias disappears when the difference of the interval is lengthened

(monthly). Similarly, on the New Zealand market, Bartholdy and Riding (1994) used

monthly data to establish that betas estimated from MM are less biased. On the contrary,

Ibbotson et al. (1997) reports that lagged coefficients should be considered when

estimating beta.

Impact of outlying observations on Beta 2.5

The extreme (maximum/minimum) beta estimates recorded by some stocks in Table 2.1

for the five-year periods studied might be due to the influence of outliers or unexpected

movement by the stock or the market returns. The literature shows that outliers have a

tendency to reduce or increase the magnitude of the beta when it is estimated with the

MM (Chatterjee and Jacques (1994)). In such cases, reducing the impact of outliers in the

estimation of the beta can significantly change the value of beta. We apply the IRLS

(outlier resistant), which minimizes a weighted sum of squares of residuals. The weights

given to each return pair observation depends on the distance between the observation

and the fitted line (Martin and Simin (2003)).

Table 2.8 reports how the presence of outliers affects the beta value. The number of

stocks in each five-year period is grouped into two. As explained in Section 2.2, stocks

with identified outliers less than or equal to 4 are grouped into Category A and those with

identified outliers greater than 4 are grouped in category B. We compute the average beta

of each category. In each period, we compare the cross-sectional average betas of the

MM and IRLS for each category. For example, in the first period out of the 21 stocks,

three fall in Category A with an average market model (MM) beta estimate of 1.29 and

48

IRLS beta of 0.46. In Category A, the difference between the average MM beta and the

average IRLS beta is 0.83. Looking across periods, except for periods 1 to 3, the rest of

the periods have more stocks in Category A than Category B.

Table 2.8: Comparison of the market model betas and the iterative reweighted least square betas

Total Number of Number of detected Number of Average Average

Period stocks outlier observations Stocks MM IRLS βMM-βIRLS

1/1837-12/1841 21 A 3 1.29 0.46 0.83

B (18) 1.38 0.19 1.19

1/1842-12/1846 33 A 10 0.72 0.49 0.23

B (23) 1.26 0.03 1.24

1/1847-12/1851 32 A 9 0.60 0.52 0.08

B (23) 0.72 0.26 0.46

1/1852-12/1856 33 A 23 0.97 0.81 0.16

B (10) 0.28 0.07 0.21

1/1857-12/1861 54 A 41 1.10 1.00 0.10

B (13) 0.60 0.10 0.51

1/1862-12/1866 72 A 48 0.88 0.60 0.28

B 24 0.72 0.15 0.57

1/1867-12/1871 76 A 42 0.79 0.56 0.23

B (34) 0.67 0.06 0.61

1/1872-12/1877 82 A 54 1.21 0.80 0.42

B (28) 0.75 0.14 0.61

1/1877-12/1881 112 A 78 1.47 1.05 0.42

B (34) 0.91 0.20 0.71

1/1882-12/1886 154 A 110 1.19 1.13 0.06

B (44) 0.62 0.05 0.57

1/1887-12/1891 160 A 120 1.77 1.41 0.36

B (40) 0.80 0.16 0.63

1/1892-12/1896 196 A 146 1.45 1.06 0.39

B (50) 0.62 0.12 0.50

1/1897-12/1901 252 A 198 1.33 1.07 0.26

B (54) 0.40 0.07 0.34

1/1902-12/1906 374 A 290 1.36 1.07 0.29

B (84) 0.83 0.19 0.64

1/1907-12/1911 424 A 346 1.32 1.12 0.20

B (78) 0.47 0.07 0.40

Note: In this Table, stocks with outlier observations less or equal to 4 are grouped in Category A and those with outlying observ-

ations greater than 4 are grouped in category B. In each period, we estimate betas in each category by using the Market model and

iterative reweighted least square (IRLS) model. We also show the number of stocks that falls in each category. We compute the cross

-sectional average of the betas estimated with the market model and the IRLS model.

49

In each period, the difference between the MM betas and the IRLS betas for Category B

is greater than the difference in Category A (last column). This implies that the more the

outlier observations in the return series, the higher the market model overestimates beta.

Figure 2.2: Plot of average market model betas and IRLS betas for stocks with outlier observation less than 4

Notes: This figure depicts the average market model and iterative reweighted least square betas for stocks with at most

4 detected outliers across the 15 periods of study.

The MM beta is always greater than the IRLS beta in Category A (across periods in

Figure 2.2). It confirms the result by Chatterjee and Jacques (1994) that the weighted

least squares estimation reduces the MM betas by a certain percentage. As in Subsection

2.3.1, we apply the modified Diebold-Mariano test to compare one-step ahead predictive

accuracy of the MM and IRLS estimated betas. The modified Diebold Mariano test

statistics proposed by Harvey et al. (1997) are employed to test the null hypothesis of

equal predictive accuracy against the alternative of IRLS betas forecasting better than the

MM betas. A pooled sample of betas within the period studied is considered. The

modified Diebold- Mariano's test statistic between the two models is 1.37 with p-value of

0.09 for one-step forecasts in the period of our study.

50

Table 2.9: Test of equal predictive accuracy between MM and IRLS models

This shows that we cannot reject the null hypothesis of equal predictive accuracy at the 5

percent significance level in the overall period. The null hypothesis can be rejected only

at the 10 percent level. From the deregulation and expansion period, the null hypothesis

of equal predictive accuracy is not rejected. From Table 2.9, we conclude that on the 19th

century BSE, the IRLS method can help to curb the influence of outliers on estimated

betas, but it does not significantly outperform the standard MM in terms of their ability to

predict one-step ahead in the period of deregulation and expansion.

Models

βMM vs. βIRLS

betas, β IRLS = iterative resistive least squares method betas. The hypothesis test H 0 : E(d j ) = 0 and

Ha= E(d j ) >0. P-values are in parenthesis.

(0.01) (0.08) (0.09)

Note: This table reports the modified Diebold-Mariano test statistics for one step ahead equal forecast

accuracy between the market model and the iterative resistive least squares model. β MM =market model

1/1837-12/1871 1/1872-12/1911 1/1837-12/1911

2.29 1.43 1.37

Strict Regulatory Deregulation and

period expansion period Overall period

51

Conclusion 2.6

This chapter evaluates the relative performance of different methods of estimating beta

based on their ability to predict subsequent beta on the 19th

century BSE. The analysis of

the different beta techniques reveals that beta estimated with the market model is not

stable. Specifically, the study reveals that for individual stocks, the market model beta is

weak in its ability to predict the future beta. The predictability can be improved by

grouping 10 or more stocks to form a portfolio or adjusting betas with the Vasicek and

Blume autoregressive techniques. The study also shows no significant difference

between the Blume and Vasicek adjusted betas in terms of their predictive accuracy.

Applying the Dimson method, correcting nonsynchronous trading effect reveals that

returns of few stocks have a significant relationship with the lead and lag market returns.

There is no significant difference in the predictive accuracy of the betas estimated with

the IRLS method and the market model in the deregulation and expansion period.

In the next chapter, we study the ability of beta to explain returns in the cross-section of

stocks, which is the primary implication of the CAPM.

52

CHAPTER 3

3 THE TEST OF CAPITAL ASSET PRICING MODEL (CAPM)

AND THE SIZE EFFECT IN 19th

CENTURY BSE

The CAPM posits a positive relationship between the systematic risk (beta) and the

expected return of an asset. Despite the dominance of the CAPM in empirical finance, a

number of researchers have found evidence against the model. The purpose of this

chapter is to investigate if CAPM is valid before World War I, using the Brussels Stock

Exchange (BSE) data. In addition, we will investigate whether a company‟s market

capitalization (size) is related to its average excess returns (size effect). The use of the

pre-World War I (1868-1914) data will provide very good grounds for an out-of-sample

test of the CAPM and the size effect. This will minimize the data mining critique if the

CAPM is valid, and the size effect exists.


This section investigates the cross-sectional relationship between stock returns and beta.

We use pre-World War I Belgium data. Since the development of the CAPM in the

1960s by Sharpe (1964), Lintner (1965), and Mossin (1966), the literature has questioned

the validity of the model and suggest other characteristics than beta to explain expected

returns. The empirical study that supports the CAPM model in the 1970s is from Fama

and MacBeth (1973). It investigates whether there is a positive linear relationship

between expected returns and beta. In addition, it also examines whether other

parameters such as beta square and idiosyncratic risk can explain expected returns.

However, Banz (1981) finds a size effect in stock returns. The effect implies the

propensity for stocks with low market capitalization to outperform those with high

53

market capitalization. In addition, Lakonishok and Shapiro (1986) and Ritter and Chopra

(1989) do not detect any significant relationship between beta and expected returns. With

the debate on the validity of the CAPM still ongoing, Fama and French (1992) find no

association between betas and average returns, even when beta is the only explanatory

variable in their cross-sectional regressions. Instead, they conclude that size and the

book-to-market value ratio can explain the variation in expected returns when placed

together in a cross-sectional regression. In contrast, Kothari, Shanken and Sloan (1995)

use annual portfolio returns and equally weighted market index to document evidence in

support of the CAPM. The above literature on beta and size focuses on post-World War I

return data and sometimes mainly on data from the US. Another view is that the

characteristic may have been discovered out of luck through data snooping bias (see Lo

and MacKinlay (1990)). In this case, the effect should not be found in other periods.

Dimson and Marsh (1999) test the presence of the size effect by using FTSE all share

monthly returns data from the period 1955 to 1998 and document that the effect has

disappeared after 1979. In addition, Schwert (2003) documents that the size effect

disappears after 1981 in the US market using monthly data for the period 1962 to 2002.

Grossman and Shore (2006) use pre-World War I UK data to present evidence against

the size effect. They find a size effect among extremely small stocks, which account for

about 0.2% of market capitalization, but the size effect disappears when these stocks are

eliminated.

To distinguish between data snooping and the persistence of size effect, we investigate

the effect on another dataset. The anomaly is initially discovered outside the period of

our study. To add to the existing literature on asset pricing, this chapter introduces the

54

19th

century BSE data to test the validity of CAPM and the presence of the size effect. To

this end, we resort to the sorting and the FM cross-sectional regression methods

discussed in Chapter one.

We find no relationship between beta and expected returns. We also find a size effect on

the 19th

century BSE, but it disappears when stocks are value weighted to form

portfolios. Detailed investigation reveals that the size effect in our data is confined to

small stocks, which represent on average 0.35% of the total market capitalization.

The remainder of the chapter is organized as follows: In Section 3.2, we show the

expected returns of portfolios sorted on MM betas MM , Dimson betas dim , and

Vasicek betas V . The FM cross-sectional regressions are used to test the relationship

between beta and expected returns (CAPM) in Subsection 3.2.1. In Section 3.3, we

investigate the effect of size and beta on excess returns by using the sorting method. In

Section 3.4, we use FM cross-sectional regression analysis to confirm the above sorting

results. Section 3.4 concludes the chapter.

Expected returns of portfolios sorted on betas 3.2

In the sorting method, we rank stocks based on beta and group them to form portfolios.

As stated before, the question answered by this method is whether high-beta stocks

outperform low-beta stocks. As the aim of this chapter is to test the validity of the

CAPM, the method needed to estimate its input is worth considering. In testing the

CAPM, one needs to form portfolios in order to improve on the precisions of individual

betas. In the previous chapter, Table 2.3 shows that a beta-sorted portfolio should contain

at least seven stocks in order to have a reliably stable portfolio beta estimate. Figure 3.1

55

shows the number of stocks included in our portfolio formation every year. Evidence

from this figure shows that until 1868 decile portfolios will not have the minimum of

seven stocks. The changes in legislation in 1867 ease the establishment of a company,

which is reflected in the number of stocks listed on the BSE. Furthermore, Van

Nieuwerburgh et al. (2006) indicate the importance of the long-term relationship between

the development of the BSE and economic growth in Belgium after legal liberalization.

In addition, as shown in Chapter 2 (Table 2.4), individual betas before 1868 do not

predict well their subsequent five-year beta. Based on these reasons, this chapter and the

subsequent ones will focus on the data between 1868 and 1914.

Figure 3.1: Number of stocks in our selection criteria for the entire period of the pre-world war I SCOB data

For a stock to be included in the portfolio formation, it must have a minimum of 24

months of observations out of the 60 months required to estimate beta before the

56

portfolio formation year. In this chapter, we do not restrict our analysis to stocks with a

complete five-year returns data as in chapter two. This enables us to capture more stocks

in the cross-section. Including stocks with at least 24 months of returns does not change

the descriptive statistics of the prior betas (from here on pre-ranking betas).

For comparison purposes, we study three beta estimates in this chapter. The first is the

MM MM

beta, which is the traditional beta. It is the slope coefficient from the

regression equation

,jt ft MM mt ft jtR R R R (9)

where jtR is the return on a portfolio or stock for period t , ftR is the risk-free rate for

period t , and mtR is the market portfolio for period t . We use the value-weighted market

portfolio constructed by Annaert et al. (2004) as a proxy for the market portfolio. The

annualized money market rate, converted to a monthly rate, is used as a proxy for the

risk-free rate. We compute the second beta estimate using the Vasicek model introduced

in Chapter 2. The model is used to compute the posterior Vasicek betas V using the

cross-sectional information on betas estimated by equation (9).

We recall from Chapter 2 (Table 2.7) that some stocks systematically lead or lag behind

the market movement, which may produce biased betas, when we estimate beta by the

MM. Possible explanation for the significant lead (lagged) relationship is because large

(small) firm prices adjust quickly (slowly) to market wide information. Thus, since the

market index used in this analysis is heavily weighted towards large stocks, small stock

returns have the tendency to lead or lag behind in relation to the market wide returns. We

57

adjust for the lag effect by using the Dimson model in Chapter 2 to obtain a third beta

estimate. That is, we run the regression

,0 , 1 1 1 ,jt ft j j mt ft j mt ft jtR R R R R R (10)

where ,0j captures the contemporaneous co-variation between the returns of a stock

(portfolio) and the market returns. , 1j

captures the correlation between stock‟s current

period returns and the lagged market returns. Dimson one-month lagged beta is estimated

as ,0 , 1dim j j , which captures the correlation between the current period returns of

a stock and current and lagged market returns. For our monthly data, we use only one-

month lag because Chapter 2 (Section 2.6) reveals that infrequent trading effect is not a

severe problem. In addition, Dimson (1979) with UK data, documents that the infrequent

trading effect is not severe when monthly returns are used to estimate betas.

Stocks are assigned to decile portfolios using the FM breakpoint method. We estimate

post-ranking portfolio betas for the sample period (1868-1914) by using value-weighted

and equally weighted portfolio returns. Specifically, beginning in January 1868, we

compute betas (pre-ranking) for all stocks using the past 24 to 60 months of returns data.

We sort stocks into decile portfolios based on the pre-ranking betas (univariate sort).

Portfolio 1 contains stocks with the lowest betas, while portfolio 10 contains stocks with

the highest betas. The post-ranking value-weighted and equally weighted return for each

month is calculated for each portfolio. New estimates of pre-ranking betas are calculated

in December each year, and the portfolio formation is repeated. We account for the

possible time-variation in betas by rebalancing stocks in each year. Monthly portfolio

58

formation for each year yields 552 monthly returns for each decile portfolio. This process

is followed for all three beta estimates , andMM V dim .

Table 3.1: Time Series Mean (%), Standard Deviation (%), and Post-ranking Betas of Decile portfolios formed from pre-ranking betas in Jan. 1868-Dec. 1913

Table 3.1 reports the average excess return (time series), standard deviation, and the post-

ranking betas of the ten portfolios. From Panel A, when both pre-ranking and post-

ranking betas are estimated with the market model, beta does not exhibit any relationship

with average returns. The average returns do not show any pattern as beta progressively

increases from low to high beta portfolios. The result does not change when we consider

Low 1 2 3 4 5 6 7 8 9 High10

0.34 0.13 0.18 0.45 0.45 0.25 0.32 0.23 0.09 0.26

3.91 2.14 1.93 2.88 3.14 3.22 3.68 3.82 4.71 6.67

0.68 0.45 0.53 0.82 1.10 1.19 1.49 1.60 1.94 2.68

0.17 0.18 0.09 0.12 0.40 0.36 0.27 0.16 -0.06 0.05

3.17 1.22 1.62 2.02 2.82 2.90 3.06 3.34 4.07 5.66

0.62 0.33 0.41 0.67 1.01 1.21 1.33 1.45 1.80 2.48

0.18 0.30 0.28 0.26 0.20 0.30 0.35 0.23 0.26 0.32

3.02 3.12 2.33 2.64 3.00 3.07 3.61 4.12 5.13 6.38

0.71 0.64 0.61 0.95 1.26 1.23 1.48 1.71 2.14 2.49

0.06 0.33 0.17 0.32 0.18 0.26 0.30 0.03 0.14 -0.05

1.63 3.35 1.50 1.95 2.79 2.45 3.08 3.56 4.52 5.48

0.39 0.58 0.45 0.75 1.13 0.98 1.32 1.56 1.92 2.32

0.25 0.23 0.26 0.43 0.37 0.25 0.30 0.23 0.20 0.17

3.59 2.32 2.04 3.08 3.09 3.22 3.68 4.70 5.09 5.58

0.92 0.93 0.92 0.97 1.10 1.19 1.45 1.58 1.57 1.55

0.20 0.13 0.12 0.19 0.36 0.36 0.20 0.17 0.06 0.01

2.79 1.24 1.47 2.34 2.71 2.90 3.36 3.39 4.35 4.66

0.80 0.81 0.81 0.86 0.99 1.21 1.36 1.37 1.41 1.39

series portfolio excess returns and the corresponding excess market returns.

Market Model (Value Weighted)

Dimson Betas(Equally Weighted)

Vasicek Betas(Value Weighted)

Mean (%)

Standard Deviation(%)

Beta

Mean (%)



Beta

At the beginning of each year, stocks are sorted based on pre-ranking betas. The pre-ranking betas are estimated with

Beta


Panel A

Mean (%)


Beta

Market Model (Equally Weighted)

Mean (%)


Beta

Beta

Panel B

Mean (%)

Dimson Betas(Value Weighted)

Vasicek Betas(Equally Weighted)

market model (β MM ), Vasicek's adjustment (β V ) model and the Dimson's model with one month lag (β dim ). The Fama-

MacBeth breakpoint technique is used to assign stocks to decile portfolios. Portfolio 1 contains the lowest betas and Portfolio

10 contains the highest betas. Mean (%) is the time series average of the portfolio excess returns for the entire period.We

compute time series Standard Deviation(%) of the post-ranking excess returns. Betas are estimated by using the long time

Mean (%)

Panel C

59

the value-weighted portfolio excess returns. Estimating betas with the Dimson and

Vasicek methods in Panels B and C does not establish the relationship between beta and

expected returns. The most striking of all is that the post-ranking betas almost surely

follow the ordering of the pre-ranking betas (except the first, second, and the sixth decile

portfolios). The univariate beta sorting results confirm Fama and French (1992) findings.

They use Dimson adjusted betas to establish a flat relationship between beta and average

return. We can also compare our result to the evidence of Reinganum (1981) who finds

no relationship between beta and average return in the period 1964-1979.

3.2.1 The Cross-Sectional Regressions

As stated in chapter one, the standard approach to test the validity of the CAPM is

sorting and FM (1973) cross-sectional regression. In this subsection, we use FM cross-

sectional regression to test the robustness of the above sorting result. The FM approach

also provides a straightforward procedure to test whether the reward for bearing beta risk

(risk premium) is equal to the excess market returns (the return of the market less the risk

free rate) as implied by Sharpe, Lintner, and Mossin‟s version of the CAPM. The method

also considers the noisy nature of portfolio or stock returns by running monthly cross-

sectional regressions of beta-sorted portfolio returns on betas. That is,

0 1jt ft t t jt tR R (11)

where 0t and 1t are the regression intercept and slope for month t respectively. jt is

the beta estimated from the full-sample portfolio returns. The slope coefficient from each

regression is treated as the reward per unit of the beta risk in that month (risk premium).

The time series average of the monthly coefficient is the average reward for bearing the

beta risk. The standard deviation of the monthly time series of slopes is used to perform a

60

t-test, whether the average slope is statistically significant from zero, in other words,

whether the beta risk is priced on average. To mitigate a possible error-in-variable

problem, the result in Chapter 2 (Section 2.4) shows that we can rely on the portfolio

betas. Fama and French (1992) also rely on full window portfolio betas to mitigate the

error-in-variable problem. Moreover, it is common to rely on large sample size statistics

to draw inferences. This curbs the argument that the test can be incorrect if the size of the

sample is not large enough for the asymptotic results to provide a good approximation.

We adopt the method by Fama and French (1992) to estimate full window portfolio

betas. The only difference is that we replicate Ibbotson et al. (1997) method and use the

portfolio betas for the cross-sectional regression instead of assigning the portfolio beta to

individual stocks in the portfolio each year. As in the previous section, we sort stocks

based on their estimated pre-ranking betas (Market model betas, Vasicek betas, and

Dimson betas) and form portfolios each year. Portfolio 1 contains the lowest beta stocks

while portfolio 10 contains the highest beta stocks. We form equally weighted and value-

weighted portfolios from the beta-sorted group of stocks each month. We repeat the

process each year to account for time variations in betas. This will produce 552 monthly

returns of decile portfolios (post-ranking returns). The post-ranking betas are estimated

by using the post-ranking long time series' returns of the decile portfolios. We repeat the

process for the various estimates of betas , ,MM V dim .

The post-ranking beta serves as the input for equation (11) to perform the cross-sectional

regressions. Each month, we regress the post-ranking excess returns of the decile

portfolios on their corresponding beta (post-ranking) estimates.

61

Table 3.2: Average time series slopes from the Fama-MacBeth Cross-Sectional Regressions in Jan. 1868-Dec. 1913

Eventually, we obtained 552 cross-sectional regressions for each estimate of beta. After

performing the monthly cross-sectional regressions, the time series mean of the slope

coefficients is tested for statistical significance. The significance of the average slope is

tested by using heteroskedastic and autocorrelation consistent standard errors (Newey

t-test

Intercept βMM βdim βV H0:Slope=(R m-R f)

Panel A: Equally Weighted Portfolio

0.30% -0.02% 1.41

(2.49) (-0.17)

0.24% 0.02% 0.93

(1.87) (0.14)

0.42% -0.12% 1.05

(1.57) (-0.45)

Panel B: Value Weighted Portfolios

0.24% -0.06% 2.16

(2.92) (-0.48)

0.30% -0.11% 2.63

(3.41) (-0.81)

0.28% -0.10% 0.94

(1.19) (-0.34)

Panel C: Individual Stocks

0.29% -0.01% 1.47

(2.37) (-0.16)

0.26% 0.02% 1.16

(2.10) (0.29)

0.36% -0.06% 1.55

(2.70) (-0.41)

monthly cross-sectional regression of post-ranking portfolio

excess returns on post-ranking beta estimates. It also shows

the hypothesis test of mean slope (risk premium) equal to the

average excess market returns as implied by the Sharpe-Lintner

βMM =Market Model beta, β V =Vasicek beta and β dim =Dimson's

CAPM. Newey West adjusted t-statistics are in parentheses.

This table reports average time series slopes and intercepts from

beta with one month lag.

62

and West (1987) correction with default lag of int (1

4T ), where T is 552). We also adopt

the Shanken‟s correction factor discussed in Chapter one for the computation of t-

statistics. This is to eliminate the possible error-in-variable biased induced by the

estimated betas.

Table 3.2 reports the average intercepts, slopes, and their corresponding t-statistics in

parentheses. As shown by the sorting method, Panel A indicates that the market model

post-ranking beta estimated with equally weighted portfolio returns does not provide a

significant relationship with returns. Estimating pre-ranking and post-ranking betas with

the Vasicek and Dimson methods does not establish the beta-return relationship.

Specifically, in Panel A, the mean estimated slope for the market model beta is negative,

and it is only 0.17 standard errors from zero. The negative slope is quite surprising as it

goes against the notion of positive risk premium (CAPM). Fama and French (1992) had a

negative slope for beta when placed together with size in the cross-sectional regression.

The average slope using the Dimson beta is 0.02% with a t-statistic of 0.14. The

estimated mean slope with the Vasicek beta is also not significant.

The values in the last column show the t-statistics from the hypothesis test of average

slope (risk premium) equals the average excess market return as implied by the CAPM.

In Panel A, the hypothesis cannot be rejected at the 5% level, regardless of how beta is

estimated. However, it may be possible that the result is influenced by small stocks, since

equally weighted portfolios give undue weight to small stocks. Therefore, in Panel B, we

use value-weighted portfolios for the estimation of post-ranking betas and in the cross-

sectional regression. The average slope of all the beta estimates in the cross-sectional

regression is not significantly different from zero. Most strikingly, the hypothesis of

63

equality between the average slope and the average excess market return is rejected at the

5% level for the market model and the Dimson betas. In Panel C, we follow the

traditional FM (1973) rolling window approach by using individual pre-ranking betas in

the cross-sectional regression. This is a predictive test since the pre-ranking betas are

estimated over a period prior to the period over which the cross-sectional regression is

performed. The results do not support the CAPM for the three beta estimates.

Although, portfolio betas are used for cross-sectional regression, others believe that

portfolios may conceal important information contained in the individual stock betas. For

example, Ang, Liu and Schwarz (2008) show that the slope coefficient (risk premium) of

cross-sectional regression can be estimated more precisely using individual stocks

instead of portfolios because creating portfolios reduces the cross-sectional variation in

betas. As a result, we apply the Fama and French (1992) approach of estimating full

window portfolio beta and assigning the portfolio beta to the individual constituent

stocks of the portfolio in the cross-sectional regression. This serves as a robustness check

of the results in Table 3.2.

Table 3.3 reports the average cross-sectional regression slopes for both equally weighted

and value-weighted portfolio betas assigned to individual stocks. The market model beta

and the Vasicek beta estimate still maintains the negative non-significant relationship

with average returns. A detailed look at Panel A shows that the Dimson beta is weak in

explaining average returns (average slope of 0.02% but with a t-statistic of only 0.17).

Using value-weighted portfolios (Panel B) to estimate post-ranking betas does not

establish the beta return relationship. This confirms Fama and French (1992) result; they

assert that beta is flat in relationship with average returns for post-1960s USA data.

64

Surprisingly, in all cases the hypothesis that the mean slope is equal to the mean excess

market return is not rejected. The positive average slope of the Dimson beta cross-

sectional regressions (Table 3.3, Panel A) calls for a detailed look into its time series'

behavior with the excess market returns. In addition, the average intercept is marginally

significant, and it is close to the average risk-free rate as postulated by CAPM. To

investigate the evolution of the slope coefficient and the excess market return through

time,

Table 3.3: Average Time Series Slopes from Fama-French Cross-Sectional Regression in Jan. 1868-Dec. 1913

t-test

Intercept βMM βdim βV H0:Slope=(R m-R f)

Panel A: Fama-French approach (eq)

0.29% -0.02% 1.40

(2.45) (-0.17)

0.24% 0.02% 0.89

(1.81) (0.17)

0.42% -0.12% 1.03

(1.54) (-0.44)

Panel B: Fama-French approach (vw)

0.29% -0.02% 1.39

(2.54) (-0.18)

0.24% 0.03% 0.89

(2.04) (0.19)

0.41% -0.12% 0.97

(1.56) (-0.42)

enthesis.

vw=value weighted. Newey- West adjusted t-statistics are par-

excess market returns. βMM =Market Model beta, βV =Vasicek

beta and βdim = Dimson beta with one lag. eq=equally weighted

In this table, we assign the post-ranking portfolio beta to the

individual stocks in the portfolio. Portfolios are rebalanced

annually. Mean slope and their corresponding t-tstatistic is

reported in parenthesis. We also report the tstatistic for the

test of hypothesis of the mean slope equal to the average

65

Figure 3.2: Sixty months moving average of the cross-sectional slopes and excess market returns using Dimson beta estimates

Surprisingly, there seems to be a close correlation between the slopes and the excess

market returns for much of the period except between the years (1880, 1885) and (1907,

1913).

Table 3.4: Sub-period look into estimated slopes and excess market returns

Figure 3.2 presents a five-year moving average of the estimated slopes and excess market

returns. The graph shows that the relationship between beta and expected returns varies

with time. In Table 3.4, we report sub-period average slope and intercept from the Fama

1870 1875 1880 1885 1890 1895 1900 1905 1910 1915-0.015

-0.01

-0.005

0

0.005

0.01

0.015

year

slo

pes/e

xcess m

ark

et

retu

rns

slope

excess market returns

Intercept Slope

0.15% 0.02%

(0.75) (0.09)

0.32% 0.03%

(3.15) (0.21)

H0:Slope=Avg.(R m-R f)

t-test

sub-periods

0.09

(Avg. R m -R f =0.04%)

Jan. 1868-Dec. 1893

Jan. 1894-Dec. 1913

(Avg. R m -R f =0.20%)

2.04

In this table, Dimson's beta estimated from equally weighted

portfolios is used in the cross-sectional regressions for the two

sub-periods. Avg. =Average. Newey West t-statistic in parenthesis.

66

and French (1992) cross-sectional regressions using the Dimson beta. The last column

shows the t-statistics for the test of equality of the average slope and average excess

market return. For the first sub-period, the average excess market return (0.04%) is very

close to the average slope (0.02%). The null hypothesis of the equal average cannot be

rejected. In contrast, the null hypothesis that the average slope is equal to the average

excess market returns is rejected (t-statistic of 2.04) in the second sub-period as the

difference in magnitude confirms (0.03% average slope and 0.20% average excess

market returns). Chan and Lakonishok (1993) document similar results with post-1920

Amex and NYSE data and caution researchers and practitioners not to rush into

discarding beta. The average slope is significantly less than the average excess market

return (a difference of about 0.17%).

Expected Returns, Beta, and the Size Effect 3.3

This section examines the well-known size effect on the 19th

century BSE. That is, the

propensity for large stocks to have consequent lower returns than small stocks. Early

works of Banz (1981), Reinganum (1981), (1983), Chan, Chen and Hsieh (1985), and

Chan and Chen (1988) first documented the size effect in modern data. Fama and French

(1992) present evidence that size and book-to-market combine to capture the cross-

sectional variation in average stock returns in the period 1963-1990. Subsequently, Fama

and French (1993) build a three-factor model, which uses the excess market returns, size,

and book-to-market factors. The finance literature uses the three-factor model as a

benchmark model to measure long-run abnormal returns and many other factors. This

shows that researchers and practitioners have accepted size as an important characteristic

to explain the cross-sectional behavior of long-run stock returns. On the contrary, a

67

recent paper by Horowitz, Loughran and Savin (2000) presents evidence against the size

effect in the USA market. It conjectures the magnitude of size effect is not robust when

the transaction costs and very small stocks (the removal of stocks with market

capitalization less than $5 million) are taken into account. Schwert (2003) uses US

monthly returns data between the year 1962 to 2002 to document that the size effect

disappears after 1981. With historical data, Grossman and Shore (2006) do not find any

presence of the size effect on UK data between the years 1870 to 1913. This would imply

size is not a systematic risk factor. We present similar evidence on the 19th

century BSE

covering the same period.

Each year, we sort (univariate sort) stocks based on their size (or market capitalization) at

December of the prior year and then split them into decile portfolios. The market

capitalization is measured as the price of stock multiplied by shares outstanding. Again,

FM breakpoint method is employed to group the stocks into decile portfolios. As in the

previous sections, the smallest size stocks are put in decile one, and the largest size

stocks are put in decile ten. Portfolios are rebalanced each year to capture changes in

their constituent stock market capital over time. Monthly portfolio returns are calculated

as the value-weighted and equally weighted averages of the individual stock returns

within each of the ten portfolios. We compute the relative percentage size of a portfolio

as the time series average of the cross-sectional sum of the market size of the stocks in

the portfolio divided by the sum of the size of stocks in our sample. That is, if tn is the

number of stocks in a portfolio for the month t , tN is the number of stocks in the cross-

section of our sample for the month t . T is the number of years. The relative percentage

of markets size is computed as

68

1

1

1

1% Market Size = 100 ,

t

t

n

itTi

Nt

jt

j

Size

TSize

Table 3.5: Beta Estimate and Mean Excess Return for the BSE equally weighted size portfolios, Jan. 1868- Dec. 1913

Two beta estimates of the size portfolios are calculated using equation (9) and (10) in the

previous section. Table 3.5 reports the beta estimates and the average excess returns of

the ten-size portfolios during the period 1868 to 1914. It is well known in empirical

finance that small stocks have both a higher beta and average return than large stocks.

However, this is not the case when size portfolios are value weighted in our sample.

Column 3 reveals that equally weighted portfolio 1 has an extreme average excess return

(1.12%) which is almost three times the next largest excess return (0.38% from portfolio

6). The negative relation between size and returns is concentrated in the first decile

Size Portfolio % Market Size EW(%) VW(%) βMM β dim βMM β dim EW(%) VW(%)

1 0.35 1.12 0.01 1.61 1.89 1.43 1.56 6.16 5.26

2 0.94 0.29 0.14 1.37 1.45 1.26 1.42 4.45 3.86

3 1.60 0.10 0.10 1.16 1.30 1.16 1.28 3.43 3.37

4 2.43 0.14 0.16 1.43 1.54 1.41 1.52 3.65 3.57

5 3.56 -0.06 0.01 1.09 1.16 1.10 1.16 2.77 2.73

6 5.02 0.38 0.52 1.43 1.46 1.61 1.67 3.93 5.16

7 7.04 0.12 0.10 1.16 1.17 1.16 1.17 2.71 2.67

8 10.06 0.20 0.21 1.35 1.36 1.35 1.38 2.97 2.91

9 15.56 0.16 0.19 1.12 1.13 1.12 1.13 2.45 2.43

10 53.46 0.17 0.15 0.88 0.84 0.79 0.74 1.84 1.68

-0.95 0.14

t-statsitics (-3.74) (0.63)

F-statistics with the first decile 4.04

F-statistics without the first decile 0.79

3 and 4. Relative market size is reported in column 2. We also report the Dimson and market model betas for the

In this table, stocks are ranked each year based on their size at the end of the prior year. They are then grouped

deciles for portfolio formation. Portfolio one contains the smallest size stocks, portfolios ten contains the largest

size stocks. Portfolios are rebalancec each year.Average excess returns of the decile portflios are reported in column

EW V W Standard DeviationRp -R f

mean of hedge portfolio (%)

decile portfolios. We also retport the standard deviation of the portfolio return series. The Fstatistic for the test

of hypothesis of equal mean of the porftolio returns is also reported.We test the hypothesis with and without the 1st

decile portfolio. EW=equallyweighted and VW=value weighted.

69

portfolio as the average excess return sharply drops from portfolio 1 to portfolio 2. As the

data source has been well checked for outliers, the extreme excess returns of 1.12%

recorded for the first size decile is not due to data error. Not able to study the events in

1880, 1890 and 1905, the stocks in the lowest size portfolio exhibit very high returns in

these years. In addition, the relative market capitalization (0.35%) of these stocks shows

that they are likely so illiquid that it would have been difficult to profit from buying

them. Looking at the F-statistics, the null hypothesis of equal average returns is rejected

at the 1% significant level when the first decile is included in the test. Excluding the first

decile portfolio fails to reject the hypothesis. In addition, the effect disappears when

stocks are value weighted in the portfolios. The average excess return of the equally

weighted hedge portfolio (mean excess return of -0.95% and t-statistic -3.74) shows that

the size effect exists in our data. Surprisingly, the value increases to 0.14% (t-statistic of

0.63) for the value-weighted hedge portfolio.

Table 3.6: Equally weighted portfolios excess returns without the first-size decile group

R p -R f (EW%)

1 0.28

2 0.10

3 0.11

4 -0.05

5 0.39

6 0.12

7 0.17

8 0.21

9 0.19

10 0.14

mean of hedge portfolio -0.14

t-statsitic (-0.80)

Size Portfolio

70

Recently, Fama and French (2008) used USA data from 1963 to 2004 to document that

the size effect owes much of its power to micro caps and that it is marginal for small and

big caps. As mentioned earlier, Grossman and Shore (2006) find similar results for the

UK market in the same period of our study.

For robustness, we eliminate the stocks in the first-size decile each year and perform the

size sorting analysis. As shown in Table 3.6, the size effect disappears when we

eliminate the first decile portfolio (portfolio with relative market size of about 0.35%)

before the size portfolio formation every year. This corroborates Horowitz et al. (2000),

who find no size effect in the period from 1963 through to 1981 when they eliminate

firms with less than $5 million in market value on the USA market.

Figure 3.4 plots the MM MM and the Dimson dim betas with the one-month lag

for each equally weighted size portfolio. Clearly, the difference between the MM and

dim progressively gets smaller as stock size gets larger.

Figure 3.3: Size Portfolio betas

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1 2 3 4 5 6 7 8 9 10

Be

ta

Size Portfolio

Market Model Betas

Dimson Betas

71

This shows that small stock betas are underestimated when estimated with the market

model. This might be due to non-synchronous trading as chapter two reveals that some

stocks show lead or lag relationship with the market returns. Ibbotson et al. (1997) find

similar results on the USA market between the years 1926 and 1994. They recommend

the inclusion of lagged information of market returns in the estimation of beta. We also

recommend the use of the Dimson beta with the one-month lag when estimating betas for

small stocks in our sample. This is to curb the possible underestimation of small-stock

beta. There is a clear negative correlation (-0.79 with a p-value of 0.0065) between size

and portfolio beta (Figure 3.4).

3.3.1 Fama-MacBeth Cross-Sectional Regressions to Test the Size Effect

In order to support the above evidence on size effect, we resort to the FM cross-sectional

regression method adopted by Ibbotson et al. (1997). We regress the cross-section of

excess returns for a given month on the beta estimate (full window beta estimate) and

natural logarithm of size by using an extension of equation (11):

0 1 2 1

ln Sizejt ft t t jt t tjtR R

(12)

where 0t , 1t and 2t are the regression intercept and slopes for month t , respectively.

t is the full period estimate of beta for portfolio. In our sample, the previous section

reveals that size is cross-sectionally correlated with beta. In addition, Chan and Chen

(1988) argue that as size serves as a proxy for betas, they expect the betas of size

portfolios to be strongly correlated cross-sectionally with size. However, when both

characteristics are included in a regression, the correlation will increase the standard

errors of the estimates, and this will make the outcomes murky for interpretation. Fama

72

and French (1992) show that when portfolios are formed on size alone, there is evidence

of a positive relationship between average return and beta (CAPM). The correlation

between size and beta makes the test on size portfolios unable to disentangle the effect of

size and betas on average returns.

We show that when equally weighted portfolios are built on size alone, there is support

for CAPM. However, allowing the variations in beta that are unrelated to size, it breaks

the effect of size and beta even on equally weighted portfolio excess returns. We achieve

this by conditional double characteristics sorting. Specifically, we first sort stocks based

on size and then sort within each size group on pre-ranking beta. We find a strong

relation between size and average excess return but no relation between beta and average

return for equally weighted portfolios. The size effect disappears when stocks are value-

weighted in portfolios. The size effect does not exist when we eliminate the first-size

decile portfolio in the analysis each year.

As in the sorting method, we form decile size portfolios. This is to confirm the effect of

the correlation between size and beta on the beta-return relationship. To separate the

effect, we sort stocks into three size groups each year. Each size group is then sorted into

five groups based on their pre-ranking MM or dim beta estimates. The equally and

value-weighted return for each portfolio is computed for each month of the following

year. The conditional double-sorting portfolio formation is repeated at the end of each

year. The procedure generates fifteen size-beta portfolios for each beta estimate. For all

portfolio formations, we use the FM breakpoint technique. Post-ranking betas are

estimated with post-ranking returns over the entire period from 1868 through to 1914.

Each month, we regress portfolio excess returns on beta and the natural log of size by

73

using equation (12). The full period post-ranking betas are used in the cross-sectional

regressions. Size is determined at the end of the year before the portfolio formation year.

Table 3.7: Average time series slopes and intercept from the Fama-MacBeth cross-sectional regression: Jan 1868-Dec. 1913

Intercept βMM β dim ln (Size) Intercept βMM β dim ln (Size)

-1.06% 1.05% -0.23% 0.31%

(-3.62) (3.46) (-0.83) (1.12)

-0.88% 0.86% -0.10% 0.20%

(-3.50) (3.43) (-0.45) (0.86)

2.12% -0.13% -0.34% 0.03%

(2.56) (-2.63) (-0.47) (0.79)

-0.42% 0.85% -0.03% -2.00% 0.62% 0.09%

(-0.40) (2.87) (-0.55) (-1.72) (1.74) (1.71)

-2.05% 1.08% 0.06% -2.45% 0.62% 0.12%

(-1.72) (3.50) (0.97) (-1.81) (1.76) (1.86)

Panel B1: Size-β mm Portfolios Panel B2: Size-βmm Portfolios

0.26% 0.01% 0.29% -0.12%

(2.18) (0.09) (2.72) (-0.91)

1.63% -0.09% -0.36% 0.03%

(2.08) (-2.05) (-0.56) (0.91)

1.69% -0.03% -0.09% -0.03% -0.12% 0.02%

(2.35) (-0.20) (-2.18) (-0.05) (-0.89) (0.61)

Panel C1: Size-β dim Portfolios Panel C2: Size-β dim Portfolios

0.17% 0.08% 0.27% -0.09%

(1.35) (0.56) (2.51) (-0.67)

1.69% -0.10% -0.22% 0.02%

(2.09) (-2.06) (-0.32) (0.63)

1.64% 0.01% -0.09% 0.10% -0.09% 0.01%

(2.17) (0.07) (-2.10) (0.15) (-0.64) (0.31)

EQUALLY WEIGHTED VALUE WEIGHTED

Panel A1: Size Portfolios Panel A2: Size Portfolios

ing betas are used in the cross-sectional regression. t-statistics are in parenthesis.

This will yield 15 size-beta equally and value weighted portfolios. In all portfolio formations we use the FM

break point. Estimate post-ranking betas by using the full period post-ranking excess returns. Post rank-

and value weighted portfolio returns are computed each month in the year. The joint effect of size and

beta is seperated by first forming three size portfolios and splitting each size group into five beta groups.

Each year, we sort stocks into ten portfolios based on their size at the end of the prior year. Equally

74

Table 3.7 reports the time series averages of the slopes and intercept of the regression.

The time series standard deviations of the slopes and the intercepts are used to test

whether the average is significantly different from zero. We use Newey and West (1987)

heteroskedastic autocorrelation corrected standard errors for the computation of the t-

statistics (reported in parentheses). The Shanken‟s adjustment factor is also adopted in

the computation of the t-statistics.

The values in Panel A1 show that the CAPM is valid for equally weighted univariate

size-sorted portfolios. Both MM and d im are positively related to excess return when

placed alone in the cross-sectional regression. Size is negatively related to excess returns.

When size and any of the beta estimates are placed simultaneously as independent

variables, only the beta estimate is significantly related to excess returns. Interestingly,

size is sometimes positively but insignificantly related to excess returns when placed

simultaneously with beta in the regressions. This is contrary to Ibbotson et al. (1997)

result, where size is significant when placed together with market model betas in the

regression. When equally weighted portfolios are formed on size alone, both the market

model and the Dimson beta with the one-month lag can predict returns at the expense of

size.

The implication of the CAPM requires that the average cross-sectional regression

intercept will not be significantly different from zero. However, from Panel A1, the

average intercept is significantly negative when MM and the Dimson‟s betas are used in

the cross-sectional regressions. The negative intercept becomes significantly positive

when size is placed alone as a regressor in the cross-sectional regression. The average

75

intercept is not significantly different from zero when the MM and Dimson‟s betas are

placed together with size in the cross-sectional regression.

Panels B1 and C1 show the cross-sectional regression slope and intercept for conditional

double-sorted size-βMM and size-βdim portfolios respectively. Both betas are no more

significantly related to returns, whether placed alone or with size in the regressions.

There is a statistically significant relationship in size to excess returns, whether placed

alone or with any of the beta estimates. This is in support of Fama and French (1992)

evidence that the conditional double-sort portfolio (size-beta sort) allows variations in

beta that are unrelated to size and would break the combined of size and beta on

expected returns. Therefore, size will be related to average returns, but beta will not. It is

worthy to note the significance of the intercepts. These show that beta and size cannot

combine to capture the cross-sectional variation in stock returns.

Most interestingly, when the value-weighted portfolios are used in the analysis (be it

univariate size sorting or conditional double size-beta sorting), beta or size is not

significantly related to the average excess return (See Table 3.7, Panels A2, B2, and C2).

This suggests that the result from the equally weighted portfolio is due to the influence of

small stocks since it assigns equal weights to all stocks in portfolio formations and in the

cross-sectional regressions. This confirms the sorting result in Table 3.5; size effect does

not exist when stocks are value weighted in portfolios. We repeat the above analysis by

adopting Fama and French (1992) method. At the end of each year, the post-ranking

betas estimated with the full period post-ranking returns will be assigned to each stock in

the portfolio. Assigning full period post-ranking betas to stocks does not mean a stock‟s

76

beta is constant, as stocks can move across portfolios with yearly rebalancing. The

method uses the information available for individual stocks in the cross section.

Table 3.8: Average Time Series Slopes and Intercepts from the Fama-French Cross-Sectional Regressions: Jan. 1868-Dec. 1913

Intercept βmm β dim ln (Size) Intercept β mm β dim ln (Size)

-1.05% 1.04% -0.54% 0.65%

(-3.58) (3.44) (-2.57) (2.79)

-0.87% 0.85% -0.48% 0.58%

(-3.46) (3.42) (-2.58) (2.76)

2.63% -0.16% 2.63% -0.16%

(3.15) (-3.29) (3.15) (-3.29)

1.51% 0.37% -0.12% 2.43% 0.06% -0.15%

(1.34) (1.22) (-2.07) (2.44) (0.26) (-2.88)

1.16% 0.38% -0.10% 2.86% -0.10% -0.17%

(0.86) (1.20) (-1.43) (2.62) (-0.46) (-2.91)

Panel B1: Size-βmm Portfolios

0.31% -0.03% 0.26% 0.00%

(2.53) (-0.27) (2.27) (0.03)

2.63% -0.16% 2.63% -0.16%

(3.15) (-3.29) (3.15) (-3.29)

2.70% -0.07% -0.16% 2.77% -0.07% -0.16%

(3.54) (-0.59) (-3.39) (3.57) (-0.50) (-3.48)

Panel C1: Size-β dim Portfolios

0.21% 0.04% 0.17% 0.08%

(1.58) (0.28) (1.44) (0.54)

2.63% -0.16% 2.63% -0.16%

(3.15) (-3.29) (3.15) (-3.29)

2.69% -0.05% -0.16% 2.78% -0.05% -0.16%

(3.52) (-0.35) (-3.47) (3.55) (-0.37) (-3.55)







break point. Estimate post-ranking betas by using the full period post-ranking excess returns. We assign

post-ranking betas to the constituent stocks in the portfolio. Portfolios are rebalanced each year. t-statis-

tics are in parenthesis.

Panel B2: Size-βmm Portfolios

Panel C2: Size-β dim Portfolios

77

Table 3.8 reports the average slopes and intercepts of the cross-sectional regressions

using equally weighted and value-weighted portfolios to estimate the post-ranking betas.

The values in parentheses are the Newey West adjusted t-statistics for the test of a

hypothesis of the average slope or intercept significantly different from zero. From Panel

A1, when the full-period equally weighted portfolio returns used to estimate post-ranking

betas are formed on size alone, both MM and dim have a strong relation with returns

when placed alone in the regression. They lose their relationship when placed together

with size in the regression. This indicates that beta, which is correlated with size, serves

as a proxy for size when placed alone in the regression. From Panels B1 and C1,

conditional double-sorting returns based on size and betas break the hold up between size

and beta. It can be seen that beta has no relationship with excess return when it is placed

alone or together with size. The result is similar when value-weighted post-ranking

returns are used to estimate post-ranking betas (See Panels A2, B2 and C2).

For robustness, we repeat Fama and French (1992) cross-sectional analysis, but exclude

stocks in the first-size decile each year. As in the sorting method, Table 3.9 does not

show the significant relationship between betas and expected returns when placed alone

or combined with size for single-sorted size portfolios in panel A1. In Panels B1 and C1,

double sorting stocks to form portfolios will not establish the relationship between betas,

size, and returns. When value-weighted portfolio returns are used in the analysis, size and

beta have no relationship with return as shown in panels A2, B2, and C2. This shows that

any size effect present in our data is driven by a small group of stocks with an average

relative market size of about 0.35%.

78

Table 3.9: Average Time Series Slopes and Intercepts from the Fama-French Cross-Sectional Regressions without the First-Size Decile: Jan. 1868-Dec.1913

Intercept β mm β dim ln (Size) Intercept βmm β dim ln (Size)

-0.21% 0.31% -0.17% 0.28%

(-0.92) (1.25) (-0.85) (1.37)

-0.10% 0.21% -0.11% 0.22%

(-0.50) (0.98) (-0.65) (1.24)

0.20% 0.00% 0.20% 0.00%

(0.28) (-0.07) (0.28) (-0.07)

-1.39% 0.54% 0.06% -0.88% 0.37% 0.04%

(-1.27) (1.83) (1.09) (-0.89) (1.55) (0.77)

-1.65% 0.51% 0.08% -1.22% 0.37% 0.06%

(-1.30) (1.67) (1.22) (-1.10) (1.61) (1.05)

Panel B1: Size-βmm Portfolios Panel B2: Size-βmm Portfolios

0.28% -0.09% 0.28% -0.10%

(2.70) (-0.74) (2.82) (-0.72)

0.20% 0.00% 0.20% 0.00%

(0.27) (-0.06) (0.27) (-0.06)

0.34% -0.10% 0.00% 0.52% -0.10% -0.02%

(0.55) (-0.79) (-0.10) (0.86) (-0.76) (-0.41)

Panel C1: Size-β dim Portfolios Panel C2: Size-β dim Portfolios

0.28% -0.08% 0.27% -0.08%

(2.57) (-0.62) (2.73) (-0.60)

0.20% 0.00% 0.20% 0.00%

(0.27) (-0.06) (0.27) (-0.06)

0.41% -0.09% -0.01% 0.55% -0.09% -0.02%

(0.68) (-0.67) (-0.22) (0.91) (-0.67) (-0.49)


break point. Estimate post-ranking betas by using the full period post-ranking excess returns. We assign

post-ranking betas to the constituent stocks in the portfolio. Portfolios are rebalanced each year. t-statis-

tics are in parenthesis.






79

Conclusion 3.4

We used sorting and the cross-sectional regression method to investigate whether the

CAPM model is valid in the period before World War I. We find no support for the

CAPM in the 19th

century BSE. Estimating beta with the market model, Dimson model,

and Vasicek model does not establish the cross-sectional relationship between expected

returns and the beta.

However, when we use equally weighted size portfolios in the cross-sectional

regressions, we find the relationship between excess returns and size or beta. There is a

negatively significant relationship of size to excess returns (size effect), but beta does not

relate to excess returns, when placed at the same time as regressors in the cross-sectional

regression. This is due to a strong correlation existing between size and beta. We find

that conditional double-sorting portfolios by size and then by beta breaks the effect

between size and beta on excess returns. As a result, the average slope of the cross-

sectional regression of returns on betas becomes insignificant when placed alone in the

regression or combined with size. We recommend researchers estimate betas with the

Dimson method with a one-month lag since small-stock betas are underestimated when

estimated with the market model with this data.

Further investigation reveals that the size effect in our data is mainly due to small stocks

with relative market size of about 0.35% of the total market size. Eliminating these small

stocks destroys the relationship between excess returns, beta, and size. Both the sorting

and the cross-sectional regression methods reveal that the size effect disappears when the

value-weighted portfolios are used in the regression.

80

CHAPTER 4

4 DOES THE MOMENTUM EFFECT EXIST IN THE 19TH

CENTRURY?

Fama and French (2008) document that the momentum or relative strength strategy

produces an average return that is robust and significant across different size categories

of stocks. The strategy buys stocks that have performed well in the past 6 to 12 months

and sells stocks that have performed poorly in the same period. It produces significant

profit in the following 6 to 12 months. However, most studies testing the returns

momentum effect in 6 to 12-month horizons use post-World War II (WWII) data from

the USA, Europe and Emerging Markets (see Jegadeesh and Titman (1993),

Rouwenhorst (1999), Nijman, Swinkels and Verbeek (2004) and etc.). In this chapter, we

use our pre-World War I BSE data to test the presence and source of momentum effect

between the years 1868 and 1914. This will serve as an out-of-sample and robustness test

of the post-WWII momentum profits documented.


Jegadeesh and Titman (1993) document that portfolios or stocks that have performed

well in the past 3 to 12 months often continue to deliver high returns in the subsequent 3

to 12 months. Their result confirms the pervasive, positively significant, lag-predictable

patterns of stock returns documented by Jegadeesh (1990). Subsequent to this, there has

been extensive literature published confirming the robustness of the momentum effect.

For example, Rouwenhorst (1998) documents the momentum effect in 12 European

equity markets. Though researchers and practitioners have subscribed to the view that the

momentum strategy yields a significant profit, the source of the momentum profit poses a

81

strong challenge in the literature. The literature attributes the source of the profit to cross-

sectional variation in expected returns, data mining bias, the state of the market and the

behavioral biases of investors.

To examine the possibility that the profit can be explained by the cross-sectional

variation in expected returns, Jegadeesh and Titman (1993) compute momentum profit

within size and beta-based sub-samples with lower dispersion in expected returns. They

find that the profit is not necessarily smaller in the sub-samples. Based on this result,

they conclude that the momentum profit is not due to the cross-sectional variation in

expected returns. On the contrary, Conrad and Kaul (1998) and Bulkley and Nawosah

(2009) argue that the momentum profit is due to the cross-sectional variation in the

expected returns, but not to autocorrelation in stock returns. Autocorrelation is the

correlation between two returns observations of the same returns series at different times

(time series pattern in stock returns). The cross-sectional variation of expected returns

explaining momentum implies that the returns of the momentum portfolio will be

positive on average in any post-ranking period. However, Jegadeesh and Titman (2002)

attribute the results found by Conrad and Kaul (1998) to a small sample bias in their

empirical test and bootstrap experiments. The bias is due to the likelihood of drawing

with replacement, the same returns observation in the formation and the holding periods.

Jegadeesh and Titman (2002) adopt sampling without replacement to mitigate the bias

selection of a particular observation and realized that the cross-sectional variations in

expected returns contribute very little of the momentum profits.

While some argue that the momentum profit is due to cross-sectional variations in

expected returns, others believe the profits may be due to data mining. To counter the

82

data mining explanation, Jegadeesh and Titman (2001) extend the data from the period

1965-1989 to 1998 and perform an out-of-sample test. Extending the data enables them

to assess whether the result in the period 1965-1989 is merely due to chance. In addition,

it will allow them to assess whether investors have changed their investment strategies

and if the profit of the momentum strategy does not exist anymore, especially for large

size stocks, which are easier and less expensive to trade. However, they find that the

momentum effect still exists in their extended data, and that the profit found in Jegadeesh

and Titman (1993) is therefore not likely to be a data mining bias. They find momentum

in the first 12 months after portfolio formation. However, the cumulative return in

months 13 to 60 after portfolio formation is negative (return reversal), which is consistent

with the behavioral theories.

On the relationship between the state of the market and momentum, Cooper et al. (2004)

apply the behavioral theory of Daniel et al. (1998) to predict the differences in

momentum profit across different market states, like a bull versus a bear market, as

aggregate overconfidence should be greater following market gains. They find that

momentum profits depend on the state of the market. Likewise, Chabot et al. (2009) use

19th

century data (Victoria Era) from the UK to document the dependence of momentum

profit on the state of the market, when a three year lag in average return is used to define

market states.

It is imperative that executing the momentum strategy involves frequent trading. Despite

the existence of momentum profits on different markets and in different time periods,

Lesmond, Schill and Zhou (2004) argue that when transaction costs are considered,

momentum profit is just an illusion. This is because the strategy tends to pick stocks that

83

have a high trading cost. Frequent trading in these high cost stocks will prevent gainful

strategy execution.

The literature also shows that momentum is strong in industry portfolios than individual

stocks. For example, Moskowitz and Grinblatt (1999) document a strong and persistent

industry momentum effect that cannot be explained by size, value, individual stock

momentum, the cross-sectional dispersion in expected returns and possible

microstructure effects. In contrast, Nijman et al. (2004) documents that the momentum

profits on the European markets are mainly due to individual stock effects. Since the

primary motive of this chapter is to investigate whether momentum profit exists in the

19th

BSE, future research can be conducted on this data to determine whether the

momentum profit is due to individual stock or industry effect.

In this chapter, we investigate whether a 3 to 12-months momentum effect existed in the

19th

century and early part of the 20th

century BSE using the methodology similar to

Jegadeesh and Titman (1993). The only difference is that Jegadeesh and Titman (1993)

used decile portfolios in their analysis, while we use quintile portfolios in order to have a

sufficient number of stocks in our portfolios. We find investors can earn significantly

positive returns over 3 to 12-month holding periods when they adopt the momentum

strategy. The result is not influenced by forming the portfolios just after the formation

period or by skipping one month after the portfolio formation period. Finding a

momentum effect in the 19th

century casts additional doubt on the data-mining

explanation for momentum.

84

A detailed look into an extensively researched momentum strategy (6 months formation

period and 6 months holding period) on the 19th

century BSE reveals that the strategy

tends to pick small size stocks. However, further tests also suggest that momentum exists

in beta and large size subsamples. Unlike Jegadeesh and Titman (1993), (2001) who find

negative momentum profit in January (a reversal) each calendar year, we do not record a

January reversal in the 19th

century BSE. The momentum strategy yields a positive return

in all months throughout the year. Sub-period analysis also shows that momentum profit

is robust in all ten-year sub-periods, except the years between 1878 and 1887.

When we replicate the post-holding period event analysis documented by Jegadeesh and

Titman (2001), we find a strong short-term momentum profit in the first 12 months and

long run reversal, two years after portfolio formation. There is no return reversal in the

first month after the portfolio formation. There is evidence of a sharp rise in profit in the

first year, but the profit declines and reverses to become negative in the second to fifth

year after the portfolio formation, as in the US. We can conclude that in the 19th

century,

the profit does not remain positive after 12-month holding periods, as claimed by Conrad

and Kaul (1998). We also investigate the momentum profit across market states, as it

may be consistent with many behavioral explanations. We follow Cooper et al. (2004) to

predict the cyclicality of the momentum profit across different market states. We find

that momentum profit depends on the state of the market when three years lagged value

market weighted returns are used to define market states.

The rest of the chapter is organized as follows: we explain and compute the returns of the

various combinations of momentum strategies in Section 4.2. In Subsection 4.2.1, we

will focus on a six-month formation/ six-month holding period strategy. This strategy has

85

been extensively researched in the literature to represent the other strategies. We

compute average returns (equally weighted and value weighted), and the average market

capitalization of the quintile momentum portfolios. We document the returns of the

strategy in size and beta based sub-samples in Subsection 4.2.2. Section 4.3 investigates

seasonality in the momentum profits across calendar months and ten-year sub-periods. In

section 4.4, we investigate the source of the momentum profit by studying the

characteristics of the momentum profit after the 12-month holding period. We study the

momentum profit across different market states in section 4.5. Section 4.6 concludes our

findings.

Momentum Trading Strategies and their Returns 4.2

As in the previous chapters, this chapter uses the 19th

century BSE data, consisting of

monthly prices, total returns (returns adjusted for stock splits and dividends), and

outstanding shares listed in Brussels between the years 1868 and 1913. As can be seen

from Figure 4.1, the number of stocks in our sample varies from 71 in 1868 to 513 in

1913. The number of stocks increases sharply from 1890 to 1913. The momentum

strategy and its profitability are constructed in this section as follows: At every given

month , we rank stocks in ascending order based on their previous

(formation period) compound returns. Based on these rankings, five equally weighted

and value weighted portfolios are formed. In order to obtain sufficiently diversified

portfolios, we form quintile portfolios instead of the decile portfolios formed by

Jegadeesh and Titman (1993) and Bulkley and Nawosah (2009). The weights are

determined by the market capitalization of each stock in the portfolio at the end of the

portfolio formation.

t monthsP

86

Figure 4.1: Number of common stocks in our sample for the momentum studies

Figure 4.2: Time line of sample periods

Formation Period Holding Period

t-P t t+Q

The bottom quintile portfolio is called “Loser," and the top quintile portfolio is called

“Winner.” The momentum strategy is to buy the winner portfolio and sell the loser

portfolio in each month . The strategy holds the position for (holding

period). Either the holding period is immediately after the formation period, or we skip

one month after the formation period. Figure 4.2 shows the various periods we

considered in the strategy. We update our portfolio formation every month. Various

combinations of P and Q are considered, where P and Q equal three, six, nine and twelve

months. This yields 16 strategies each for equally weighted and value-weighted portfolio

formation. We calculate holding period returns from the same month in which the stocks

were ranked in order to form portfolios. Specifically, the strategy that selects stocks

0

100

200

300

400

500

600

1860 1870 1880 1890 1900 1910 1920

Nu

mb

er

of

Sto

cks

year

t monthsQ

87

based on the past P-months return and holds it for Q-months is known as a P/Q strategy.

For a comparative purpose, we also calculate returns for skipping one month between the

formation period and the holding period. This will be referred to as P/Q/1 strategy.

Specifically, we construct 6/6 strategy as follows: at the end of each month we sort

stocks in our sample based on their past six month returns (month -6 to month -1) and

group the stocks to form five portfolios based on the ranks. Portfolios are held for six

months (month 0 to month 5) following the ranking months. In order to improve the

power of our test, in all the portfolio formations, we replicate the overlapping portfolio

method adopted by Jegadeesh and Titman (2001). That is, for the 6/6 strategy, the

winning portfolio in month t will contain the top quintile of stocks ranked over the

previous t-5 to t, t-6 to t-1, t-7 to t-2, and it will continue until t-11 to t-6. To illustrate

this on the calendar months, the return in December of the winning portfolio will contain

the top quintile of stocks ranked over the previous June to November, the previous May

to October, and it will continue over the period from January to June. We form equally

weighted and value-weighted quintile portfolios from the returns of stocks that coexist in

the same ranking. We resort to the Fama-MacBeth method for the portfolio break points.

Table 4.1 presents the monthly average returns of the equally weighted and value-

weighted portfolios of the various strategies, over the period from January 1868 to

December 1913 on the BSE. In Panel A, we report both the equally weighted and value-

weighted average returns for strategies with holding periods starting immediately after

portfolio formation. In Panel B, we report equally weighted and value-weighted average

portfolio returns for strategies with holding periods of one month after the portfolio

formation.

88

For each cell in Table 4.1, we report the average returns of the winner, the loser and the

zero cost (winner minus loser) portfolios of the various strategies. The t-statistics based

on Newey-West heteroskedasticity and autocorrelation-adjusted standard errors are

shown in parentheses. For all strategies, the average return of the value weighted zero-

cost portfolio is higher than the equally weighted zero-cost average return. This suggests

that momentum on the 19th

century BSE is mainly due to large size (market capital)

stocks. In Panel A, the average return of the equally and value-weighted zero-cost (W-L)

portfolios for all strategies are positive and significant, except the equally weighted

average return of the 3/3 strategy, which is marginally significant. In Panel B, the

average returns of the equally and value weighted zero-cost portfolio for all strategies are

positive and significant, except the equally weighted 12/12/1 strategy, which is

marginally significant.

The most profitable zero-cost strategy selects stocks based on their previous 6 month

returns and holds the portfolio for 6 months. It yields 0.71% and 0.75% per month for the

equally weighted zero-cost portfolio, when portfolios are formed immediately and one

month after the formation period respectively. For the value-weighted portfolio

formations, it yields 1.06% each for both 6/6 and 6/6/1 strategies. This is contrary to the

results found by Jegadeesh and Titman (1993), where the most profitable strategy was a

12/3 strategy. The 9/3 strategy, with an equally weighted portfolio formation, yields

almost the same profit as the 6/6 equally weighted strategy (0.70% per month). However,

the profit for the latter strategy declines (0.69 % per month) when there is a time lag

between the portfolio formation period and the holding period.

89

Table 4.1: Profitability of momentum Strategies on BSE (Jan.1868-Dec. 1913)

Formation Period Portfolio

EQ VW EQ VW EQ VW EQ VW EQ VW EQ VW EQ VW EQ VW3 Winner 0.81% 0.75% 0.87% 0.79% 0.89% 0.82% 0.90% 0.80% 0.87% 0.79% 0.90% 0.81% 0.92% 0.83% 0.88% 0.78%

(4.32) (4.76) (5.44) (6.10) (6.41) (7.31) (7.10) (7.72) (4.69) (5.12) (5.82) (6.60) (6.83) (7.67) (7.09) (7.57)Loser 0.53% 0.15% 0.44% 0.11% 0.39% 0.06% 0.37% 0.06% 0.48% 0.12% 0.40% 0.08% 0.35% 0.03% 0.36% 0.06%

(2.54) (0.95) (2.31) (0.71) (2.13) (0.42) (2.20) (0.48) (2.29) (0.71) (2.04) (0.51) (1.88) (0.22) (2.12) (0.48)W-L 0.29% 0.60% 0.44% 0.68% 0.51% 0.76% 0.52% 0.74% 0.39% 0.67% 0.51% 0.73% 0.57% 0.80% 0.52% 0.72%

(1.73) (4.08) (3.40) (5.40) (4.58) (7.56) (5.56) (8.69) (2.37) (4.32) (4.09) (5.93) (5.22) (8.16) (5.78) (8.53)

6 Winner 1.04% 0.98% 1.04% 0.98% 1.00% 0.94% 0.91% 0.85% 1.07% 0.99% 1.04% 0.98% 0.97% 0.91% 0.88% 0.81%(6.61) (6.86) (7.50) (7.95) (7.72) (8.27) (7.43) (7.79) (6.99) (7.13) (7.58) (7.98) (7.49) (7.92) (7.12) (7.33)

Loser 0.40% -0.05% 0.33% -0.07% 0.33% -0.04% 0.38% 0.04% 0.33% -0.08% 0.30% -0.08% 0.33% -0.02% 0.40% 0.07%(1.68) (-0.26) (1.52) (-0.41) (1.69) (-0.26) (2.16) (0.25) (1.35) -0.38 (1.35) (-0.44) (1.68) (-0.16) (2.29) (0.50)

W-L 0.64% 1.04% 0.71% 1.06% 0.67% 0.98% 0.53% 0.82% 0.74% 1.06% 0.75% 1.06% 0.64% 0.93% 0.48% 0.74%(3.75) (5.99) (4.84) (7.44) (5.73) (8.89) (5.37) (8.63) (4.28) (6.44) (5.32) (8.02) (5.78) (9.05) (5.10) (8.29)

9 Winner 1.04% 0.99% 0.99% 0.94% 0.92% 0.87% 0.86% 0.80% 1.03% 0.97% 0.95% 0.90% 0.88% 0.83% 0.83% 0.77%(7.02) (7.18) (7.25) (7.51) (7.20) (7.46) (7.05) (7.23) (6.89) (7.12) (6.92) (7.22) (6.81) (7.04) (6.72) (6.86)

Loser 0.35% -0.12% 0.37% -0.02% 0.42% 0.07% 0.46% 0.14% 0.33% -0.08% 0.38% 0.03% 0.44% 0.12% 0.48% 0.17%(1.49) (-0.62) (1.77) -0.135 (2.25) (0.44) (2.76) (0.97) (1.43) -0.414 (1.85) (0.19) (2.42) (0.77) (2.91) (1.23)

W-L 0.70% 1.11% 0.62% 0.96% 0.50% 0.80% 0.40% 0.67% 0.69% 1.05% 0.57% 0.87% 0.44% 0.71% 0.35% 0.60%(4.36) (7.25) (4.66) (7.72) (4.63) (7.92) (4.31) (7.41) (4.46) (7.12) (4.43) (7.29) (4.19) (7.25) (3.88) (6.72)

12 Winner 0.94% 0.90% 0.89% 0.84% 0.84% 0.79% 0.80% 0.75% 0.91% 0.87% 0.86% 0.81% 0.81% 0.76% 0.78% 0.72%(6.17) (6.49) (6.35) (6.57) (6.44) (6.64) (6.44) (6.59) (5.95) (6.26) (6.06) (6.23) (6.16) (6.32) (6.17) (6.28)

Loser 0.47% 0.06% 0.52% 0.15% 0.55% 0.20% 0.58% 0.23% 0.49% 0.12% 0.55% 0.19% 0.58% 0.23% 0.60% 0.25%(2.05) (0.33) (2.56) (0.87) (3.07) (1.31) (3.49) (1.67) (2.17) (0.63) (2.72) (1.15) (3.23) (1.57) (3.63) (1.88)

W-L 0.47% 0.84% 0.37% 0.70% 0.29% 0.60% 0.23% 0.52% 0.42% 0.75% 0.31% 0.62% 0.24% 0.53% 0.18% 0.47%(2.92) (5.42) (2.81) (5.50) (2.66) (5.65) (2.35) (5.46) (2.71) (5.02) (2.46) (5.04) (2.25) (5.14) (1.89) (4.97)

weighed by their market capital, one month before the holding period. EW= Equally Weighted and VW= Value Weighted.Panel A: Holding Period Panel B: Holding Period

3 6 9 12 3 6 9 12

This table reports the returns from momentum strategy based on BSE returns data. Each month t, stocks a ranked based on P-months compound returns. Q-months return are calculated based on the ranking. Equally weighted and value weighted quintile portfolios are formed. The top quintile is called "Winner" portfolio and the bottom quintile is called "Loser" portfolio. The zero-cost (Winner-Loser) portfolio is the portfolio formed by going long on the winner and short on loser portfolios. In Panel A, portfolios areformed immediately after the portfolio formation and in Panel B they are formed one month after the portfolio formation. Different values of P and Q are shown

in the second row and first column respectively. The monthly average of the three portfolios are reported with their Newey-West heteroskedastic and autocorrelation adjusted

standard error t-statistics. We adopt the Fama- MacBeth break point method in the portfolio formation. W=Winner and L=Loser. For the value weighted portfolios, stocks are

90

All equally weighted strategies yield profits around 0.50%, regardless of the holding

period and of the one-month lag between the formation period and holding period. It is

out of the ordinary to note that the positive average returns of the equally weighted loser

portfolios are usually significant (except the 6/3, 6/6, 6/9, 9/3, 9/6, 6/3/1, 6/6/1, 6/9/1,

9/3/1 and 9/6/1 strategies, which are marginally significant). This shows that the positive

returns of the zero cost portfolios are mostly due to the positive significant returns of the

winner portfolios and positive significant returns of the loser momentum portfolios. In

effect, 19th

century investors who would find it difficult to go short on loser portfolios

could have profited from the momentum effect by going long on the winner portfolios. In

contrast, the average return of the value weighted loser portfolio for all the strategies is

not significant, may even be negative sometimes.

The strategy that has been extensively researched in the literature is the 6/6 strategy.

After confirming that momentum strategies of all combinations would yield significantly

positive returns on the 19th

century BSE, the rest of the chapter will focus on the 6/6

strategy (this strategy will be analyzed, and the result will be used to represent the other

strategies that comprise formation and holding periods ranging from three to twelve

months).

4.2.1 Expected Returns and Average Size of Quintile Portfolios

Table 4.2 shows the portfolios‟ average returns (equally weighted and value weighted)

and average market capitalization (price multiplied by the shares outstanding) of the

quintile portfolios. As before, we construct portfolios by adopting the overlapping

method. For equally weighted portfolios, the average returns increase from the losing

91

portfolio to the winning portfolio, but there is a marginal drop in average returns from the

loser portfolio to the second portfolio.

Table 4.2: Average Returns and Average Size of Quintile Momentum Portfolios

In contrast, the average return of the value-weighted portfolios monotonically increases

from the losing portfolio to the winning portfolio. The values in the last column of the

Table indicate that past losing and winning portfolios pick stocks that have low market

capital on the average. This result is consistent with the findings of Jegadeesh and

Titman (1993) and Chabot et al. (2009).

4.2.2 Momentum Profit within Size and Beta-based Subsamples

In order to investigate whether the profit from the momentum strategy is not confined to

any particular group of stocks, we follow Jegadeesh and Titman (1993) to examine the

profitability of the strategy on subsamples. We group stocks into subsamples based on

the beta and size. Size may serve as a proxy for liquidity and beta for volatility. The

subsample analysis of the momentum profit also provides evidence about the source of

the momentum profit. It tests whether the momentum profit is due to the cross-sectional

Average MarketCapitalization

Portfolio EQ VW (Million Belgium Franc)

Loser 0.33% -0.07% 3.802 0.26% 0.11% 9.23

3 0.51% 0.43% 11.764 0.76% 0.70% 11.28

Winner 1.04% 0.98% 7.50

W-L 0.71% 1.06% -

Average returns of the values weighted quintile portfolios.

weighted. The sample period is January1868 to December 1913. Market capital is in millions. W=Winner , L=loser, EQ=Average returns of the equally weighted portfolios and VW is the

This table reports the average returns and average market capital of the quintile portfoliosof 6 /6 months momentum strategy. The market capital is the price times the number of shares outstanding. Average market capital is the average of the holding period market

capitals of the stocks in each portfolio. Quintile portfolios are equally weighted and value

92

variations in expected returns or predictable patterns in the time series of stock or

portfolio returns. If the profit is due to the cross-sectional variations in expected returns,

the profit will be reduced in the subsamples, as the dispersion of the cross-section of

expected returns is lower in the subsamples than in the full sample. If the momentum

profit is due to predictable patterns in individual stock returns, then the subsamples will

yield positive profits, as will the entire sample.

Table 4.3: Portfolio Returns of the Momentum Strategies with Size and Beta Subsamples

Table 4.3 presents the average return of momentum portfolios, momentum profits and the

difference in the mean of the full sample profit and each sub-sample profit. Portfolios are

Portfolio All Micro Small Big β1 β2 β3

Loser 0.33% 1.01% -0.04% 0.09% 0.31% 0.42% 0.53%(1.52) (3.19) (-0.19) (0.69) (1.72) (2.14) (1.80)

2 0.26% 0.47% 0.35% 0.41% 0.32% 0.41% 0.39%

(2.03) (2.17) (3.01) (3.96) (3.89) (3.37) (1.89)

3 0.51% 0.58% 0.60% 0.54% 0.48% 0.64% 0.58%(4.58) (3.61) (5.22) (5.48) (8.63) (5.56) (3.16)

4 0.76% 0.92% 0.75% 0.70% 0.74% 0.80% 0.77%(6.85) (5.92) (6.34) (7.61) (8.05) (7.23) (4.36)

Winner 1.04% 1.30% 0.98% 0.82% 0.98% 1.06% 1.06%(7.50) (7.12) (7.07) (7.02) (7.93) (7.69) (5.69)

W-L 0.71% 0.29% 1.01% 0.73% 0.67% 0.64% 0.53%(4.84) (1.17) (7.55) (6.26) (5.09) (4.16) (2.84)

Difference - 0.42% -0.30% -0.02% 0.04% 0.07% 0.18%- (2.86) (-3.35) (-0.18) (0.32) (0.68) (1.77)

months. The overlapping method is employed in the portfolio formation. Loser/winner portfolio is the equally weighted portfolio of stocks in the lowest/top quintile when stocks are ranked over the previous six months returns. We adopt Fama Macbeth method

portfolio formation to estimate betas. The last two rows show the difference in mean

This table reports the average monthly returns of portfolios formed based on size andbeta subsamples. Portfolios are formed based on six month returns and held for six

Average Monthly Returnssample period is January 1968 to December 1913. W=Winner and L=Loser

subsamples. Size is determine at the beginning of each formation period. We estimate betas for stock returns prior to the portfolio formation period. Dimson's method one month lag is applied to stocks with at least 24 month returns within the five years prior to

and their Newey West tstatistics between full sample profit and each subsample profit.The

for all portfolio breakpoints. "Micro" contains the smallest stocks, "Small" contains the next

smallest and "Big" contains the largest stocks. β1, β2 and β3 the lowest to the highest beta

93

formed based on the 6/6 strategy. The momentum strategy is applied on beta and size

subsamples. Size is determined at the end of each formation period. We estimate beta by

using the Dimson method with a one-month lag. The analysis includes stocks with at

least 24-month returns within five years before the formation month.

Clearly, the momentum strategy is profitable in all subsamples except the “Micro” size

subsamples. This indicates that the profit does not exist for the “Micro” size subsample

of stocks. The values in the last two rows show the average of the difference in profit

between the full sample momentum profits and the sub-sample momentum profits. The t-

statistics for the test of a hypothesis that the difference is equal to zero is reported in

parentheses. The nonexistence of momentum in the “Micro” is mainly due to the extreme

average return recorded by its loser portfolio (average return of 1.01% with a t-statistic of

3.19). Not finding momentum in our micro size stocks support Hong, Lim and Stein

(2000) results. They used NYSE and AMEX data between 1980 and 1996 to document

that momentum does not exist in their smallest size decile stocks. On the contrary, the

result does not support Jegadeesh and Titman (1993) and Chabot et al. (2009), who find

momentum profit in all the small size subsamples. The result also deviates from Fama

and French (2008) who find significantly positive momentum profit for small stocks. As

in our sample, it is positive but not significant. Like Chabot et al. (2009) we do not find a

strong relationship between size and momentum profit. However, it is worthy to note the

high profit (the profit of 1.01% with t-statistics of 7.55) for the “Small” size sub-sample.

Chabot et al. (2009) also find the largest momentum profit for the middle size group.

Consistent with the previous chapter, the beta subsamples show no significant difference

in profit from the full sample. The “Big” size sub-sample also shows no significant

94

difference in the mean with the full sample. The difference in momentum profits between

the full sample and the subsamples (except the “Micro” and “Small” size subsamples)

indicates that the cross-sectional difference in the expected returns of the stocks may not

determine the momentum profits. If anything, the predictable patterns in individual stock

returns may contribute to the momentum profits in the beta sub-samples, as the profit is

not reduced significantly in these groups. It is important to note that the profit of the

“Big” size sub-sample is mainly due to the buy side of the transaction rather than the sell

side. The expected return of the past winner portfolio is significantly positive, and the

average return of the past loser portfolio is not statistically significant. This implies that

even when investors are not allowed to short stocks, they can still earn a momentum

profit by buying winners.

Seasonality and Sub-period Analysis of the Momentum Profit 4.3

We are motivated to look into the seasonal patterns in momentum profits, as Jegadeesh

and Titman (1993) document positive momentum profits in all calendar months except

January. Jegadeesh and Titman (2001) also confirm the January reversal (negative)

returns in later data. However, the reversal becomes marginal when they exclude stocks

with a price lower than $5 per share and stocks in the smallest decile in their sample.

Therefore, they infer that most of the negative profits recorded in the month of January

by Jegadeesh and Titman (1993) are due to small and low priced stocks, which are likely

to be difficult to trade. Table 4.4 reports the momentum profits in all calendar months on

the Brussels stock exchange between January 1868 and December 1913. This will test

the possible seasonal effect of the momentum profits in the 19th

century.

95

Table 4.4: Seasonality in momentum profits

Figure 4.3: Average returns of the momentum profit in all calendar months

It also shows the percentage of positive profits in all the calendar months. Again, we

form momentum portfolios based on the 6/6 strategy. The zero-cost portfolio is the

winning portfolio minus the losing portfolio return in each month. We also report the

Months Jan. Feb. Mar. Apr. May June July Aug. Sep. Oct. Nov. Dec. Feb-Dec Fstats

All 0.87% 0.94% 0.97% 0.70% 0.76% 0.72% 0.52% 0.49% 0.50% 0.63% 0.65% 0.76% 0.70% 0.41(4.02) (4.61) (3.95) (2.72) (2.95) (2.73) (1.39) (1.46) (1.73) (2.80) (2.69) (3.96) (8.84)

76 78 74 74 78 80 78 76 72 67 65 67 74

Micro 0.66% 0.39% 0.47% 0.37% 0.52% 0.35% 0.21% 0.17% 0.38% 0.34% 0.16% 0.34% 0.34% 0.11(2.08) (1.15) (1.18) (0.85) (1.36) (0.84) (0.46) (0.42) (0.96) (0.96) (0.42) (1.03) (3.11)

65 65 63 59 61 63 67 61 59 54 52 50 59

Small 1.07% 1.29% 1.30% 0.89% 0.96% 0.96% 0.87% 0.88% 0.66% 0.75% 0.93% 0.96% 0.95% 0.65(3.91) (5.45) (4.89) (3.04) (3.42) (3.51) (3.14) (2.97) (2.25) (4.10) (5.37) (4.31) (11.78)

85 85 83 72 85 80 83 80 78 72 87 76 80

Big 0.92% 0.93% 0.90% 0.69% 0.56% 0.56% 0.56% 0.59% 0.62% 0.89% 1.00% 0.94% 0.75% 0.81(3.81) (4.32) (4.23) (3.28) (2.68) (3.08) (2.68) (3.49) (3.41) (6.40) (5.44) (5.26) (12.18)

85 83 83 76 76 89 85 80 85 89 87 85 83

For all months in the period 1868-1913, this table reports the average momentum profit, their related t-statistics and the percentageof momentum profits that are positive in calendar month. The momentum portfolios are formed based on past 6 months returnsand held for 6 months. The equally weighted portfolio is formed from the lowest past return decile and is called Loser. The

equally weighted portfolio returns formed from the past return top rank quintile stocks is called Winner. The zero cost portfolio is the Winner minus Loser portfolio. The average return, related t-statistic and the percentage of positive profits is also reported foreach size subsample."Micro" contains the smallest stocks, "Small" contains the next smallest stocks and "Big" contains the largest size stocks. Size is determined at the end of each portfolio formation period. Newey West standard error adjusted tstatistics are in

parenthesis.The last column report the F-statistics for the test of hypothesis of equal average profits in the various calendar months.

This figure reports the average returns of the momentum profit by calender month.

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%

Jan. Feb. Mar. Apr. May June July Aug. Sep. Oct. Nov. Dec.

Mo

me

ntu

m P

rofi

ts

96

average return, corresponding t-statistics and the percentage of positive momentum

profits in each calendar month for size subsamples. Size is determined at the end of each

portfolio formation period. “Micro” is the lowest tercile group for size, “Small” is the

middle tercile group for size, and “Big” is the highest tercile group for size. We compute

the F-statistics in the last column under the null hypothesis that the average returns on the

zero cost portfolios are equal in all calendar months.

The results from the 19th

century BSE do not support the negative momentum profit

found on the USA market by Jegadeesh and Titman (1993) and Jegadeesh and Titman

(2001). The winner portfolio returns exceed the loser portfolio returns in all months. This

is supported by a significant percentage of positive momentum profits in all calendar

months. Specifically, January records the third highest momentum profit (0.87% average

return, with t-statistic of 4.02 and 76% positive profits) after February and March. The

absence of the January effect on 19th

century BSE is not surprising, as Chabot et al.

(2009) record similar results in almost the same period (Victorian Era) in the UK. They

argue that investors, as of that time, were not taxed on capital gains and that the tax year

does not end in December. The same reason applies to the BSE. The F-statistics in the

last column indicate that the null hypothesis of equal profit in all calendar months cannot

be rejected for the entire sample and the size sub-samples. This shows that there is no

significant evidence of difference in average momentum profit for the calendar months.

As shown in Figure 4.3, the profit decreases gradually from January to August but picks

up again from September to December. Jegadeesh and Titman (1993) also recorded the

lowest profit in August. Comparing the profits in all calendar months for the various size

subsamples, the “Micro” size group records the lowest profits in all months. Table 4.5

97

documents the zero-cost portfolio for the 6/6 month strategy in ten-year sub-periods and

the last five years before World War I. This table shows that the momentum strategy

yields positive significant profit in all sub-periods except in the period 1878 to 1887,

although still positive.

Table 4.5: Sub-period Analysis of Momentum Profit

This table reports the average monthly returns of the zero-cost portfolios in ten year subpe-

Sample Month 1868-1877 1878-1887 1888-1897 1898-1908 1908-1913All 0.55% 0.19% 1.05% 1.13% 0.59%

(1.91) (0.48) (5.60) (4.89) (4.03)

All Jan. 0.96% 0.29% 0.60% 1.96% 0.33%(1.88) (0.84) (3.60) (4.55) (3.99)

Feb.-Dec. 0.51% 0.18% 1.09% 1.05% 0.62%(3.96) (0.81) (11.21) (6.54) (6.87)

All 0.17% -0.16% 1.22% 0.30% 0.26%(0.29) (-0.32) (3.48) (0.68) (1.00)

Micro Jan. 0.50% 0.06% 0.87% 1.68% -0.11%(0.52) (0.08) (2.18) (2.18) (-0.57)

Feb.-Dec. 0.14% -0.18% 1.25% 0.17% 0.30%(0.58) (-0.72) (7.02) (0.66) (1.73)

All 0.54% 0.43% 1.17% 1.76% 0.87%(2.58) (1.29) (6.17) (7.88) (9.08)

Small Jan. 0.67% 0.52% 0.76% 2.42% 0.90%(1.55) (3.16) (2.46) (3.94) (4.65)

Feb.-Dec. 0.53% 0.42% 1.21% 1.70% 0.86%(4.82) (2.09) (9.56) (11.43) (9.86)

All 0.75% 0.31% 0.72% 1.23% 0.83%(2.57) (1.26) (6.73) (6.13) (7.10)

Big Jan. 1.28% 0.36% 0.34% 1.86% 0.69%(3.25) (1.73) (0.95) (3.27) (2.66)

Feb.-Dec. 0.70% 0.30% 0.76% 1.17% 0.85%(6.36) (2.09) (11.75) (8.33) (11.45)

riods and the last five years before World War I. The zero-cost portfolios are formed basedon six month past returns and held sixm months. We sorts stocks in ascending order based

on past six months returns and equally weighted portfolios are formed from lowest qui-ntile stocks group. This group is called the sell portfolio and equally weighted portfolios formed from the top quintile group of stocks is called Winner portfolio. The zero cost portfo-lio is the winner minus loser portfolios.The average return of the zero-cost portfolio formed

using size-based subsamples of stocks within sub-periods is also reported."Micro" is the sub-

sample which contains the smallest stocks and "Big" contains the largest size stocks. Newey west standard error adjusted tstatistics is reported in parenthesis. The sample period is Jan. 1968- Dec. 1913.

98

When the strategy is applied to the middle and largest size subsamples, it produces

significantly positive profits in all sub-periods except in the periods 1878 and 1887. It is

important to note the significant average returns in January and outside January for

“Micro” size subsamples in 1888 and 1897 period. This shows that there is a momentum

profit for small stocks in this ten-year sub-period. This may counter the assertion that

momentum profit does not exist in small stocks for the entire period (the assertion is not

robust over time). If we base our research on this ten-year period, we may find

momentum profit for all size subsamples, and small stocks will contribute to the greater

part of the momentum profit across the entire sample period. Except for the periods

1868-1877, 1878-1887 and 1888-1897, there is a significant positive profit for January

and outside January in all the periods for the “Small” and the “Big” size subsamples.

Post holding Period Momentum Profits 4.4

The support for short-term reversal, intermediate term continuation and long run post-

holding period reversal of momentum profits has been extensively documented in the

literature (Jegadeesh and Titman (1993), Conrad and Kaul (1998), Jegadeesh and Titman

(2001) and Chabot et al. (2009)). In effect, there seems to be strong evidence of past

losers exceeding past winners in the first month after portfolio formation (short-term

reversal). In addition, past winners continue to exceed the past losers for two to twelve

months after portfolio formation (intermediate term continuation), and past losers will

reverse to exceed past winners over three to five years. The behavioral explanation of

momentum indicates that the time series' variation in individual stock or portfolio returns

contributes to momentum profit. That is, the time series‟ abnormal holding period return

(momentum) is due to investor delay in overreaction to information, which pushes the

99

prices of winners (losers) above (below) their fundamental values. Upon returning to

their senses, investors force the prices to revert to their fundamental values. However,

Conrad and Kaul (1998) argue that the cross-sectional variation in expected returns

generates momentum profit. Empirical evidence presented by Bulkley and Nawosah

(2009) support the assertion. Conrad and Kaul (1998) hypothesize that stock prices

follow a random path with various drifts, and that every stock has a unique drift. They

show that the difference in unconditional drifts across stocks explains the momentum

profits. Since the predictability under this hypothesis is based on the difference in

unconditional drifts across stocks, but not on the variation in the time series of prices for

individual stocks in any particular period, the profits from the momentum strategy will

continue to remain positive in any post formation period. To differentiate between the

behavioral bias hypothesis and the Conrad and Kaul (1998) hypothesis, we examine the

returns of the momentum portfolios, in the periods following the holding periods

considered in the previous sections. That is, if momentum profits are completely due to

behavioral biases, we expect profit to be reduced to zero overtime, and if possible,

reverse its sign. On the other hand, if the profit is due to cross-sectional variation in

expected returns, the profit should continue to increase after the formation period with

time.

Table 4.6 presents the average monthly returns for the first five years after portfolio

formation. From Panel A, across all stocks, the winner portfolio returns drop from 0.91%

in the first year to 0.46% in the fifth year. In contrast, the loser portfolio increases from

0.38% in the first to 0.86% in the fifth year, more than double its value in the first year.

The profit in the second year is approximately the same for the winner and the loser

100

portfolios. From the third year to the fifth year, the zero-cost (winner minus loser)

portfolio profit becomes significantly negative, as the loser portfolio returns exceed the

winner portfolio in these periods. The strongly significant average returns of -0.31%

from the second through the fifth year confirms the return reversal.

Table 4.6: Long Horizon Momentum Profits

Month Months Months Months Months Months Months

Portfolios 1 1-12 13-24 25-36 37-48 49-60 13-60Panel A: All

0.50% 0.53% -0.02% -0.27% -0.46% -0.40% -0.31%

(2.66) (5.37) (-0.23) (-2.90) (-4.95) (-4.29) (-6.83)

0.99% 0.91% 0.64% 0.53% 0.46% 0.46% 0.59%

(5.65) (7.43) (4.64) (4.34) (3.72) (3.97) (8.76)

0.50% 0.38% 0.66% 0.80% 0.92% 0.86% 0.90%(2.03) (2.16) (4.07) (4.54) (5.35) (5.11) (10.09)

-0.02% 0.30% -0.23% -0.52% -0.73% -0.59% -0.53%(-0.06) (1.94) (-1.70) (-3.62) (-5.37) (-4.61) (-7.83)

1.24% 1.13% 0.81% 0.64% 0.54% 0.52% 0.73%(5.43) (7.15) (4.18) (4.08) (3.50) (3.25) (8.41)

1.26% 0.83% 1.03% 1.15% 1.26% 1.11% 1.27%(3.41) (3.46) (4.85) (4.95) (5.88) (5.43) (10.79)

called "loser portfolio". Zero-cost portfolio is the winner minus loser portfolios. We

repeat the portfolio formation for size subsamples. "Micro" is the lowest size group,

"Small" is the middle size group and "Big", the largest size group. Size is the marketcapitalization of stock and is determined at the end of portfolio formation. Newey

This table reports monthly average momemtum profit for zero-cost, winner and loser portfolios, one to five years after portfolio formation. Portfolios are formed

based on past six months returns. Stock are sorted based based on the pased six

months returns and equally weighted portfolio is formed from the lower and the upper quintile group of stocks. The portflio formed from the upper group of stocks is called the "winner portfolio" and the portfolio formed from the lower group is

West standard error adjusted tstatistics are reported in parenthesis. The sample

period is Jan. 1868 to Dec. 1913.

Zero-cost Portfolio

Winner Portfolio

Loser Portfolio

Winner Portfolio

Loser Portfolio

Panel B: Micro Zero-cost Portfolio

101

Figure 4.4: Cumulative Returns for Five years after portfolio formation

It is important to note that there is no short-term return reversal in the 19th

century BSE,

as the momentum profit one month after portfolio formation is positively significant

(0.50% with t-statistic of 2.66). Figure 4.4 depicts the cumulative momentum profits for

Table 4.6 Continued

Month Months Months Months Months Months Months

Portfolios 1 1-12 13-24 25-36 37-48 49-60 13-60

0.90% 0.77% 0.27% -0.02% -0.25% -0.18% -0.09%(4.85) (8.02) (2.76) (-0.23) (-2.46) (-1.59) (-1.81)

0.82% 0.78% 0.58% 0.48% 0.46% 0.46% 0.53%(4.64) (6.56) (4.81) (4.13) (3.37) (4.16) (7.91)

-0.08% 0.01% 0.31% 0.51% 0.71% 0.63% 0.62%(-0.36) (0.06) (2.09) (3.11) (4.01) (3.54) (7.42)

0.70% 0.61% 0.17% 0.10% -0.13% -0.21% -0.03%(4.22) (8.27) (2.31) (1.59) (-2.04) (-2.76) (-0.95)

0.82% 0.76% 0.51% 0.50% 0.43% 0.44% 0.50%(5.03) (7.29) (4.62) (4.61) (4.30) (4.32) (8.28)

0.12% 0.15% 0.34% 0.40% 0.56% 0.65% 0.54%(0.83) (1.39) (3.14) (3.74) (4.73) (5.09) (7.74)

Panel D: Large Zero-cost Portfolio

Winner Portfolio

Loser Portfolio

Winner Portfolio

Loser Portfolio

Panel C: Small Zero-cost Portfolio

-0.30%

-0.20%

-0.10%

0.00%

0.10%

0.20%

0.30%

0.40%

0.50%

0.60%

0.70%

0.80%

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

Cu

mu

lati

ve R

etu

rns

Event Months

Figure 4.4: Cumulative Returns for five years after portfolioformation

102

five years after portfolio formation. For our 1868 to 1913 periods, the graph shows that

the momentum profit increases monotonically from the first month to the seventh month.

The profit declines from the seventh month to the twelfth month, when it falls below its

first month value. As shown in Table 4.6, the momentum profits become negative around

the second year after portfolio formation, but the negative profit is not strong enough to

offset the positive profit recorded in the first year. This keeps the cumulative profits

above zero until the fourth year, in which the negative profits exceed the positive profits.

Therefore, the cumulative profit falls below zero on the fourth year after portfolio

formation. In effect, there is a strong return reversal from the second to the fifth year

after portfolio formation on the 19th

century BSE. This result is consistent with the

behavioral explanation found on the USA market by Jegadeesh and Titman (2001).

However, similar analysis on size subsamples (Panels B, C and D) shows that the strong

long-term return reversal recorded for all stocks is mainly due to the lower long run

return reversal in the “Micro” size group of stocks. For the “Micro” size stocks in Panel

B, the first month after portfolio formation records an insignificantly negative

momentum profit. The momentum profit one year after portfolio formation is significant

(0.30% with a t-statistic of 1.94). There is a strong return reversal from the second to the

fifth year (-0.53, t-statistic of -7.83). From Panels C and D, the first year records a very

strong momentum profit, but the profit reverses from the second year to the fifth year,

and it is not significant (-0.09 and -0.03 with t-statistics of -1.81 and -0.95 respectively).

The evidence that the return reversal draws its power from small size stocks cautions us

to interpret the behavioral model explanation of momentum with care. In general, the

result is still not consistent with the argument by Conrad and Kaul (1998) either.

103

The Momentum profit and the Market State 4.5

In this section, we investigate whether the condition of the state of the market can

determine the profitability of the momentum strategy. As indicated in Cooper et al.

(2004), the behavioral theory can be extended to predict differences in momentum profit

across the state of the market. The confidence of a group of investors is expected to be

higher following market gains (Daniel et al. (1998) and Gervais and Odean (2001)). The

upwards adjustment of market prices will tend to be attributed unduly to investor skill.

This will result in greater aggregate overconfidence, as aggregate investors hold the long

positions in the equity market. The high overconfidence in following up markets will

trigger strong overreactions, and it will eventually lead to short-run momentum. We

follow Cooper et al. (2004) and Chabot et al. (2009) in defining two market states: for

each month t, the UP (DOWN) market is when the lagged three-year value weighted

market return is positive (negative). We compute average momentum profits across

market states by taking the momentum profit (winner minus loser quintiles) for each

formation month, and taking the average across all formation months that qualify for a

particular market state. Our sample period is still January 1868 to December 1913. For

each month t, we sort stocks into a quintile portfolio based on the past six-month return.

We adopt the portfolio-overlapping method in all portfolio formations. We do not skip

one month between the formation period and the holding period, since the previous

section shows no sign of return reversal in the first month after the formation period. The

Fama and MacBeth (1973) breakpoint method is used to form portfolios. The holding

period profits are computed for three horizons: t to t +5, t to t +11 and t +12 to t +59.

104

Table 4.7: The Momentum profit and the Market State

Table 4.7 reports the mean of the momentum profit for both UP and DOWN markets in

the period January 1868 to December 1913. In order to verify whether the number of

months used to define the market state has any influence on the results, we investigate

the profit of the 6/6 strategy on three (one year, two years, three years, etc.) different

definitions of the market state.7 For brevity, we report the UP and DOWN market

momentum profit for the three-year definition of market state. In Panel A, for the 6 and

12 months holding periods, the UP market momentum profits are significant, and are all

above 0.60%. Cooper et al. (2004) and Chabot et al. (2009) find similar results. The

DOWN market in panel B shows that momentum profit for 6 and 12 month holding

periods are not significantly different from zero, when the three year lagged value

weighted returns index is used to define the market state. To corroborate the

7 The result is not robust when less than 3 years return is used to define the market states.

Market States DefinitionN

Mean Momentum profit

t-statistics

market. The sample period is January 1868 to December 1913.

4240.88%(7.42)

4240.65%(7.61)

markets. Newey-West t-statistics are in parenthesis. N is the number of observation for each state of the

Months t to t +5 Months t to t +11 Month t +12 to t +59

Market States Definition

Mean Momentum profitN

Holding Periods

This table reports momentum profits for the UP and DOWN market states. The momentum portfolio is formedbased on past six month returns and held for six months. Each month, stocks are sorted in ascending order based on past six months returns. Equally weighted quintile portfolios are formed. The First quintile portf-

olio is called the loser portfolio and the top quintile is called the Winner portfolio. The profit of the mo-mentum portfolio (winner minus loser quintiles) is cumulated across the holding periods : months t to t+5, t to t +11 and t+12 to t+59 if t -1 is the end month of the formation period. Market is classified asUP (DOWN) if the value weighted market index over the period t -36 to t -1 is positive (negative).We

report the mean monthly profits, Panel A and B reports the momentum profit following UP and DOWN

Panel A: UP market states3-years

4.28 4.59 3.65

128

0.15%(0.37) (0.62) (-4.85)

Panel B: Down market states

Panel C: Test of Equality of the Mean Momentum profit (UP=DOWN)

1283-years

0.15%

376-0.27%(-6.07)

128

-0.43%

105

unconditional results from Lee and Swaminathan (2000), Jegadeesh and Titman (2001)

and Cooper et al. (2004), we find that UP market momentum profit significantly reverses

over the long run. The average momentum profits are significantly below -0.20% over

the holding period of 13 to 60 months. We also find significant long-run reversal for

DOWN markets. Cooper et al. (2004) find similar results, and they assert that long run

reversals are not solely due to corrections of prior momentum.

In Panel C, we test the hypothesis of equals in the mean of the momentum profit between

the UP and DOWN markets. The hypothesis is rejected at 5% for the five-year holding

period horizons considered after portfolio formation. Chabot et al. (2009) did not find a

significant difference in the mean between the UP and DOWN momentum profits.

106

Conclusion 4.6

We investigate the trading strategy that buys past return winners and sells past return

losers (momentum trading strategy) over the period of January 1868 to December 1913.

There is convincing evidence that the momentum strategy is profitable. For instance, the

6/6 strategy that we study in detail here yields an average profit of about 8.52% and

12.7% per annum, for equally and value-weighted portfolios, respectively. Finding

momentum profits in the 19th

century provide some evidence that the profits found for

the post-World War II US market are not mainly due to data snooping biases. Detailed

analysis of the 6/6 strategy on beta and size subsamples shows that momentum profit is

not confined to particular beta subsamples. We find no momentum profit for small size

stocks. Except for the small size sample, the momentum profits for beta and large size

samples are not significantly different from the full sample profit.

Investigating the momentum profit for each calendar month shows that the negative

January momentum profit found on the USA market by Jegadeesh and Titman (1993),

(2001) is not in the 19th

century BSE. January records the third highest momentum profit

relative to the other months of the year. The momentum profit is not robust across our

sample period, as a ten-year sub-period analysis indicates that the profit is not strong in

the first twenty years of our sample. The profit is marginally significant or not significant

in the first and the second ten years respectively. Unsurprisingly, the marginal profit

recorded in the first ten years is mainly due to the middle and the large size groups of

stocks, since the average momentum profit for the small size group is insignificant.

To investigate the source of momentum profit, we resort to the Jegadeesh and Titman

(2001) approach to examine the returns of the momentum portfolios in the post-holding

107

period. We study post-holding period returns to differentiate between the assertion by

Conrad and Kaul (1998) and behavioral explanations presented by Barberis, Shleifer and

Vishny (1998), Daniel et al. (1998) and Hong and Stein (1999). Conrad and Kaul (1998)

assert that the momentum profit is due to the cross-sectional differences in expected

returns, not to the time series' pattern in asset returns. Therefore, the momentum strategy

will continue to yield positive returns in all periods after the holding period. The

behavioral explanations suggest that, if momentum profit is completely due to under

reaction to information, the returns of the momentum portfolio will decay to zero.

Conversely, if the profit is due to lagged overreaction, the momentum portfolio will

possibly reverse in sign before decaying down to zero overtime. Our evidence supports

the Jegadeesh and Titman (2001) results, and suggests that the profit of the momentum

portfolio in the 13 to 60 months after the portfolio formation is significantly negative (-

0.31 with t-statistics of -6.83). This evidence supports the behavioral explanations and

clearly rejects the Conrad and Kaul (1998) assertion. Further study of the size

subsamples revealed that the negative profit recorded in the months 13 to 60 after

portfolio formation is mainly contributed by the small groups. This suggests that the

support for the behavioral explanations of the momentum profit should be interpreted

with caution, although the result is still not consistent with the Conrad and Kaul (1998)

assertion.

We also test if momentum profit and long-run reversal in the cross-section of stock

returns depend on the state of the market. Cooper et al. (2004) document that the Daniel

et al. (1998) behavioral theory can be extended to predict differences in momentum profit

across states of the market, like UP and DOWN markets, as aggregate overconfidence

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should be greater following market gains. For each month between 1868 and 1913, we

define the state of the market as UP (DOWN), if the lagged three-year returns of the

value weighted market index are positive (negative). The 6 month formation and 6 to 12

month holding period strategies are solely profitable in the periods of market gains, when

three year lagged value weighted returns are used to define the market state. Specifically,

from 1868 to 1913, the average monthly momentum profit for UP market states is

significantly positive (0.88% and 7.42 t-statistic, 0.65% and 7.62 t-statistics for both 6

and 12 months holding periods respectively). In contrast, the DOWN markets in the same

period record insignificant positive momentum profits of 0.15% (t-statistic of 0.37 and

0.62 for both 6 months and 12 months holding periods). We also find that the momentum

profit in the UP market states is reversed in the long term.

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CHAPTER 5

5 THE COMBINED EFFECT OF DIVIDEND YIELD, SIZE,

TOTAL RISK AND MOMENTUM (1868-1913 EVIDENCE)8

In the previous chapters, stock returns do not show a positive relationship with beta

(CAPM) in the 19th

century BSE data. However, the winners (losers) over the past 3 to

12 months predict the subsequent 3 to 12 month winners (losers) for the 19th

century BSE

data (momentum). Size seems to have a relationship with average returns in our data.

However, the relationship is completely driven by extremely small stocks, accounting for

about 0.35% of the total market capitalization. In this chapter, we use the 19th

century

BSE data to study the predictive pattern of stock returns based on size, momentum, total

risk and dividend yield. The next section explains the motivation for repeating size and

momentum and choosing total risk and dividend yield. By studying the predictive power

of these characteristics on stock returns in a new database, we provide out-of-sample

evidence that may address the data-mining critique. The results may also provide

evidence on the combined effect of different characteristics on the cross-section of stock

returns.


The Capital Asset Pricing Model (CAPM) of Sharpe (1964), Lintner (1965) and Mossin

(1966) provides a particularly appealing way to look at the cross-section of expected

returns. The model implies that expected returns are a linear function of the stock‟s beta

coefficient, i.e. the regression slope of the stock‟s return on the market return. It

8 Different versions of this chapter have been presented at conferences: the 14

th Conference for Swiss

Society for Financial Market Research (SGF), 8th

April, 2011, Zurich Switzerland and (Blind Reviewed).

Eastern Finance Association 2011 Annual Meetings, 15th

April, 2011, Savannah- Georgia, USA (Blind

Reviewed)

110

measures the security‟s systematic risk, which is the only part of its total risk that should

be rewarded in the market. Although initially the model was corroborated empirically

(e.g. Fama and MacBeth (1973)), its prediction is not borne out in more recent empirical

research, as summarized in Fama and French (1992). Not only is there no longer a

positive relation between beta and average stock returns, the returns are also found to be

related to other firm or stock characteristics, such as size (market capitalization) and its

book-to-market ratio. Later research adds even more characteristics that are associated

with average returns. For instance, Fama and French (2008) dissect the return patterns

based on momentum, asset growth, profitability, net stock issues and accruals, as well as

size and book-to-market.

These patterns beg explanation. One possibility is that the characteristics are proxies for

exposure to common risk factors, which then leads to the question of which factors

should be studied and how to measure them. Another explanation is that they reflect

irrational investor behavior that a rational investor could exploit. This then raises the

issue of to what extent these patterns are tradable, as the patterns are often stronger for

smaller and less liquid stocks and exploitation involves high portfolio turnover. For

instance, Hanna and Ready (2005) demonstrate the vulnerability of some patterns to

turnover-induced transaction costs. Finally, the patterns could be illusory or simply found

thanks to collective data dredging (see e.g. Schwert (2003)), in which case the patterns

should not be discernable in new datasets.

In this chapter, we shed some light on this issue by studying cross-sectional patterns in

Belgian stock returns for the period of 1868-1914. This unique and high-quality data set

provides a genuine out-of-sample testing environment. In chapter 1, we tested the

111

predictive power of the beta coefficient for average stock returns. We find that, similar to

the post-1969 U.S. results of Fama and French (1992), the relation in pre-World War I

Belgian data is flat. We pay particular attention to the computation of beta, as 19th

century stock markets were less liquid than their modern counterparts, but to no avail.

Also, within the largest group of stocks, representing on average about 96% of stock

market capitalization, beta and size are of no importance in explaining average returns.

We now turn our attention to the test of the presence of some repeated and other

characteristic effects, namely size, momentum, total risk and dividend yield. We repeat

size in order to investigate whether the relationship between stock returns and the other

firm characteristics will not be confined to the extremely small stocks. In addition, Fama

and French (1992) show that book-to-market and size are the most important stock

characteristics related in the cross-section to average returns. As we do not have

accounting information, we cannot include the book-to-market ratio, but we do include

the size (market capitalization) of the firm in our analysis. Given the evidence that the

size effect seems to have attenuated since the publication of Banz (1981) (see Schwert

(2003)), additional robustness analysis, using a new and independent dataset may shed

light on the explanation of the size effect. Horowitz et al. (2000) list three potential

explanations: (a) data mining; (b) the increased popularity of passive investments, which

would have driven up prices of large companies; (c) the awareness of investors after

publication of the research results has eliminated the profit opportunities. As index funds

did not exist in the 19th

century, finding a size effect would favour the awareness

explanation, whereas not finding a size effect is more consistent with the data mining

argument.

112

Since Jegadeesh and Titman (1993) published their article on momentum, or short to

medium term past returns, this type of stock prediction has received a prominent place in

empirical asset pricing. Although it is still not clear why momentum is positively related

to future average returns, it is complementary to the size and book-to-market effects

(Fama and French (1996)). Also, Jegadeesh and Titman (2001) have updated their

previous results and still consistently observe the momentum effect in the years 1965 to

1998, making it less likely that it is due to data mining. Fama and French (2008) use a

different measure of momentum in their dissection of the anomaly test and find

momentum to be positively related to the average return. We follow Fama and French

(2008) to repeat momentum in the analysis. Including this characteristic in our tests

yields additional out-of-sample evidence.

Furthermore, there has recently been a debate on the usefulness of idiosyncratic or total

volatility to predict average returns in the cross-section. Theoretically, Merton (1987)

argues that when investors do not or cannot hold the entire market portfolio due to

various exogenous reasons, idiosyncratic risk and total risk should be priced. On this

note, Malkiel and Xu (2006) find that portfolios of stocks with high idiosyncratic

volatility have higher returns than portfolios with low volatility stocks. In contrast, Ang

et al. (2006) find a negative relation between average returns and idiosyncratic volatility.

In addition, Blitz and Van Vliet (2007) based on Sharpe Ratio and alpha from the Fama-

French three factor model document a negative relationship between excess returns and

total volatility on global markets. However, Bali and Cakici (2008) show that the

relationship between total risk and excess return is induced by methodology and the

predominance of small illiquid stocks in the sample. Screening stocks using liquidity and

113

price filters destroys the relation. In addition, in the 19th

century, stocks were expensive

relative to the average daily wage (see Scholliers (1997)). The above literature measures

idiosyncratic risk as the standard deviation of the errors in the Fama and French (1993)

three-factor model. However, we cannot compute the value factor in the Fama-French

model as the accounting data has not been digitalized in our data. In addition,

idiosyncratic risk estimated from the standard deviation of the error term in Fama-

French‟s three-factor model may introduce error-in-variable complications in the cross-

sectional regression.

On this note, we considered total risk to minimize the error inherent in the estimation of

risk. Investors might not be able hold the market portfolio due to the high prices of stocks

relative to the daily wage. Therefore, total risk could also be priced to compensate

rational investors for their inability to hold the market portfolio. Total risk, which is the

main arbitrage risk, may also prevent arbitrageurs from exploiting mispricing

opportunities on the market. Therefore, total risk will have a positive relationship with

mispricing (arbitrage limit theory). Given this debate and the household income situation

in the 19th

century, we decide to include total risk in our list of characteristics. We follow

Blitz and Van Vliet (2007) to measure total risk as the standard deviation of the past two

to five years excess returns.

Lastly, we would have investigated the relationship between book-to-market value and

the cross-section of stock returns in the 19th

century BSE, following Fama and French

(1992). However, as we do not have data on the book-to-market value of equity, we

follow Grossman and Shore (2006) and use dividend yield as the best available proxy for

value. In addition, the investigation on the interaction between dividend yield (as a

114

measure of value) and momentum has recently been documented in the literature. For

example, Asness (1997) documents a negative correlation between momentum and

dividend yield. This implies investment in high value stocks, and to some extent entails

investment in poorly performing stocks and vice versa. Similarly, Gwilym, Clare, Seaton

and Thomas (2009) use independent double-sort quintile portfolios to document that the

momentum strategy yields a significant return among the lower value quintile, and the

value strategy is less effective within the highest momentum quintile. They advise value

investors to stay away from high momentum firms until they exhibit at least some

relative strength compared to the general market. On historical data, Grossman and Shore

(2006) also record that a negative relationship exists between dividend yield and

momentum. In view of this, we also investigate the relationship between momentum and

dividend yield in the 19th

century BSE. Moreover, as it has been shown in the literature

that small firms find it necessary or desirable to pay dividends in the earlier periods, we

also investigate the relationship between size and dividend yield in the 19th

century BSE.

In addition, we investigate the effect of the relationship between dividend yield and total

risk on the average returns.

The rest of the chapter is organized as follows: The next section describes the

measurement of the characteristics. In section 5.3, descriptive statistics of the

characteristic sort portfolios are studied. Section 5.4 describes the average returns of the

single-sort and independent double-sort portfolios. We use the FM cross-sectional

regression method to confirm the sorting result in section 5.5. We conclude the chapter

with section 5.6.

115

Measures of Characteristics 5.2

We follow two paths to establish the importance of the characteristics: portfolio sorting

(mainly single-sort and independent double-sort) and FM cross-sectional regressions. To

study the pervasiveness of any pattern, we divide our sample into three groups based on a

characteristic and investigate the effect of dividend yield separately in each group.

As in chapter 3, our sample starts in 1868 and Figure 3.1 illustrates our motivation. As

part of our analysis relies on portfolio sorts (sometimes with double sorting), a minimum

of stocks in the cross-section is needed. Thanks to a change in legislation in 1867, it

became much easier to set up a company, and the number of listed firms increased

accordingly. Portfolios are constructed in January of each year based on information

available by the end of December of the previous year. More specifically, to be included

in the analysis, the stock has to comply with the following requirements:

1. In order to obtain some accuracy in the estimation of total risk, a minimum of 24

out of the 60 months‟ return observations are required.

2. Six months‟ return data in the previous year is necessary to compute our

momentum measure (discussed below).

We use excess return, which is computed as the difference between the realised return

and the risk-free rate used in chapter three.

In order to study the relationship between dividend yield, size, total risk and momentum,

we form yearly portfolios. Unlike Asness (1997), we pay more attention to zero-dividend

stocks, as they account for, on-average, more than a quarter of the stocks in the cross-

section each year. Figure 5.1 shows the percentage of stocks in the cross-section that did

not pay dividends each year.

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Figure 5.5.1: Percentage of Zero-dividend paying stocks and their Relative Market Capital: Jan. 1868- Dec.1913

It is clear from the figure that about 45% of the stocks in the cross-section did not pay

dividends in 1880 and or in 1903. On average, about 28% of stocks did not pay

dividends across the period of our study. This tends to be smaller stocks compared with

those that pay dividends. The relative market capitalization of these firms does not

exceed 20% across the period of our study. The result is not surprising, as Gwilym et al.

(2009) and Grossman and Shore (2006) record that small stocks do not pay dividends on

the contemporary and historical UK markets respectively. We treat the zero-dividend

stocks as a group, rather than incorporating them into the lowest dividend group of

stocks. We do this because both Keim (1985) and Morgan and Thomas (1998) had a

comparable return between the zero-dividend firms and the highest dividend yield firms.

In effect, a “U-shaped” relationship between dividend yield and return. Each year, in

order for a stock to be part of this analysis in the following year, it must have at least 6

months of return data to facilitate the computation of the momentum characteristic.

As before, each year, we measure the size (market capitalization) as price multiplied by

shares outstanding in December of the year before the portfolio formation. Momentum is

0

5

10

15

20

25

30

35

40

45

50

1860 1870 1880 1890 1900 1910 1920

Pe

rce

nta

ge

year

Relative Market Capitalization

% Zero-Dividend Paying stocks

117

measured as the compound return from June to November of the previous year. We are

motivated to use the six-month compounded return, as the 6/6 strategy emerges as the

most profitable strategy in chapter 4. Fama and French (2008) rely on the most profitable

strategy in Jegadeesh and Titman (1993) to compute the 12-month compound return as a

momentum measure. Total risk is the standard deviation of the past 24 to 60 months

excess returns. Finally, each year, we measure the dividend yield as the sum of all

dividends paid in the past 12 months, divided by the price in December of the year. As

Annaert et al. (2004) observe seasonality in dividend yield, summing dividend over a

full year removes any seasonal patterns in dividend payments, and the current price level

is used to incorporate the most recent information in the stock prices.

Each year, we separately sort stocks into three groups based on size, momentum or total

risk. We use the FM break-point method in all stock groupings. The lowest size group is

called „Micro‟ cap stocks. The second group is called „Small‟ cap stocks and the largest

size group is called „Big‟ cap stocks. For total risk and momentum, we place the lowest

total risk (momentum) in group 1 and the highest in group 3. In the same year, we

separately sort stocks based on dividend yield. Zero-dividend paying stocks are placed in

one group. The rest is then sorted into three groups based on their dividend yield. The

stocks that pay the lowest dividends are in group 1 and the highest dividend paying

stocks are in group 3. We follow Lakonishok, Shleifer and Vishny (1994) and Fama and

French (1996) to form 12 (for example, Micro/D/P= 0, Micro/1, Micro/2, Micro/3,

Small/D/P=0, Small/1, Small/2, Small/3, Big/D/P=0, Big/1, Big/2, Big/3) sets of

portfolios from the intersections of dividend yield sorts and other characteristic sorts.

These are the independent double-sort portfolios. We repeat the portfolio formations for

118

dividend sorts and the size, momentum or idiosyncratic risk sort. Sorting on two

characteristics will test the marginal effect of each characteristic on average excess

returns.

Descriptive Summary Statistics of the Characteristics 5.3

In this section, we report the summary statistics of the twelve sets of portfolios formed on

size-dividend yield, momentum-dividend yield and idiosyncratic risk-dividend yield. We

also report the univariate sort on the various characteristics.

5.3.1 Size-Dividend yield double sorts

Table 5.1 reports the summary statistics of the characteristics for the 12 portfolios formed

from the intersections of the size sort and dividend yield sort stocks. We also report

separate univariate sort portfolios for size and dividend yield. Between 1868 and 1914,

our sample contains 84 to 518 different firms, which results in an average of 240 stocks

traded every year (see Panel A and Figure 3.1). On average, there are seven or more

stocks in every independent double-sorted portfolio. The number of „Micro‟ stocks that

do not pay dividends in the last 12 months exceeds the number of total stocks that pay

dividends. It is not surprising to see fewer numbers of „Big‟ stocks that do not pay

dividends (seven stocks on the average).

In panel B, the average relative market capitalization of each portfolio is reported. The

first column indicates that the „Big‟ portfolio accounts for the largest percentage of

money invested in the stock market, representing, on average, 81% of total stock market

capitalization. On the contrary, the „Micro‟ portfolio accounts for less than 4% of stock

market capitalization. The remaining stocks represent only 15% of market capitalization.

For the double-sorted portfolios, it is surprising to see more money invested in „Micro‟

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Table 5.1: Summary statistics for Size-Dividend double-sorts

Market D/P= 0 1 2 3 Market D/P= 0 1 2 3

Market 72 56 56 56 8.96 43.96 29.67 17.42

Micro 80 46 8 10 16 3.67 1.52 0.47 0.65 1.02

Small 79 19 19 20 22 15.22 3.10 3.86 3.97 4.28

Big 80 7 30 26 18 81.11 7.00 29.50 26.00 17.67


Market 0 3.31 5.00 8.58 12.65 5.90 5.10 6.44

Micro 5.31 0 3.15 5.05 10.34 11.54 14.58 8.86 6.72 7.59

Small 5.05 0 3.25 5.00 7.62 6.96 9.86 6.65 5.27 6.50

Big 4.50 0 3.37 4.99 7.01 5.06 7.58 4.84 4.39 5.24


Market 0.49 10.30 5.09 2.63 226 1006 893 802

Micro 0.63 -2.08 7.75 4.83 2.00 244 134 364 409 364

Small 5.86 5.84 10.22 4.90 2.48 606 311 644 716 725

Big 7.33 7.49 10.66 5.39 3.48 1259 668 1376 1226 1330

Market D/P= 0 1 2 3

Market 2.55 15.69 10.84 6.19

Micro 0.94 0.71 1.29 1.30 1.16

Small 3.92 3.59 4.23 3.96 3.87

Big 20.40 12.29 26.01 19.83 14.25

Panel A: Average Number of stocks Panel B: Relative Market Cap

Panel C: Dividend Yield (% ) Panel D : Annual time series average of Total risk(% )

Panel E:Annual time series Momentum(% ) Panel F: Annual Average of Price (Belgian Franc)

Panel G:Annual time series average Size (*10^6)

are then used to create a set of 12 portofolios (Micro/D/P= 0, Micro/1, Micro/2, Micro/3, Small/D/P= 0, Small/1, Small/2, Small/3, Big/D/P= 0, Big/1,

Big/2 and Big/3.We compute the annual average number of stocks in each portfolio. The annual average relative market capital of the stocks in each

portfolio is reported. Dividend Yield is measured as the sum of all dividends paid in the year before year t divided by the current price.Total risk is

the standard deviation of the past 24 to 60 months excess returns. Momentum is measured as the compound returns for six months before the

In this table we show summary statistics of some characteristic identified to capture the cross-section of stock returns. At the beginning of January

for each year t, we sort stocks into three groups (Micros, Small and Big) based on their size (price time's shares outstanding) at the end of the

previous year. We seperately sort the stocks in the same year based on their dividend yield in the previous year. No dividend paying stocks are

assigned one group. The rest of the stocks is splitted into three groups in order of magnitude of their dividend yield. The lowest dividend paying

stocks are place in 1 and the highest dividend paying stocks are place in 3. The intersections of the stocks in the size-sort and dividend-sort

t .We also report the annual averages for univariate sorted characteristic on the market. The sample period is January 1868 -December 1913.

120

zero-dividend paying stocks as compared to the various dividend-paying stocks. This

might be due to the high number of zero dividend paying stocks in the micro size group

(see Panel A). Unsurprisingly, less money is invested in zero-dividend paying „Big‟

stocks. Among the dividend paying „Big‟ stocks, the average market capital for the

highest dividend paying stocks is lower. For the „Small‟ group of stocks, the zero-

dividend paying stocks have slightly lower market capital than the dividend paying

stocks.

Panel C shows the average dividend yield of the univariate sort on size. It also shows the

dividend yield for the 12 size-dividend yield double-sorted portfolios. The first column

shows very small reduction in dividends as size increases. Among the double-sorted

dividend paying stocks, there is a positive relationship between the lowest dividend yield

stocks and size. On the contrary, the relationship is less negative for the middle and the

highest dividend paying stocks.

In panel D, there is a strong correspondence between total risk and size. As the first

column shows, total risk monotonically reduces as size increases. This relationship

persists in all double-sorted size-dividend yield portfolios. It is worthy to note the high

total risk recorded for zero-dividend paying stocks. For the univariate sort on dividend

yield, the relationship between total risk and dividend yield is „U-shaped‟ among

dividend paying stocks. The „U-shaped‟ relationship persists in all size groups.

Panel E of Table 5.1 shows the average annual past performance (momentum) of the

univariate size and dividend yield sort portfolios. For univariate size sorts, the first

column shows that size increases with momentum. The positive relationship persists in

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all columns of size-dividend yield double-sorted portfolios. The zero-dividend paying

stocks performed poorly in the past six months, compared to the dividend paying stocks.

The poor performance may be due to „Micro‟ zero-dividend stocks, as they record an

average momentum of -2.08%. It is important to note the strong negative relationship

between momentum and dividend yield among dividend paying stocks. This confirms

the Asness (1997) results and is consistent with the phenomena that value stocks are

stocks that performed lower in the past 6 to 12 months, and vice versa.

Panel F reports the annual average price of the size and dividend yield sorted portfolios.

Unsurprisingly, there is a positive relationship between size and price in both single and

double sort portfolios. It is clear that zero-dividend paying stocks have the lowest price.

This persists for all size groups. This confirms the results of Grossman and Shore (2006),

who found that stocks that do not pay dividends tend to have lower market capitalization

and price.

Finally, panel G reports the average size (in millions) of the stocks in each portfolio

across the period of the study. It is obvious to observe the zero-dividend paying stocks

recording the lowest size in the 19th

century BSE. Size seems to show a negative

relationship with the dividend yield (single sort among dividend paying stocks). Detailed

analysis of the double-sort portfolios reveals that the “Small” and the “Big” stocks

contribute to the negative relationship.

5.3.2 Momentum-Dividend yield double sorts


from the intersections of the momentum sort and dividend yield sort stocks. We also

report univariate sort portfolios on momentum, and again on the dividend yield. As in the

122

previous section, between 1868 and 1914, our sample contains 84 to 518 different firms,

which result in an average of 240 stocks traded every year (see Panel A and Figure 3.1).

On average, there are twelve or more stocks in every double-sorted portfolio. The

number of stocks that performed poorly in the last six months (displaying low

momentum) and do not pay dividends in the past 12 months exceed the dividend-paying

stocks in each portfolio. For the middle momentum group, zero-dividend stocks are less

than the numbers that pay dividends.

In panel B, the average relative market capitalization of each portfolio is reported. The

first column indicates that the middle-momentum portfolio accounts for the largest part

of money invested in the stock market, representing, on average, 45% of total stock

market capitalization. On the contrary, the lowest momentum portfolio accounts for less

than 22% of stock market capitalization. The remaining high momentum stocks represent

only 33% of the market capitalization. For the double-sorted portfolios, it is not

surprising to see less market capital for zero-dividend paying stocks in all momentum

categories. For single-sort dividend paying stocks, the amount of money invested in the

various portfolios decreases as dividend yield increases. This is also true for all

categories of double-sort portfolios. Among the dividend paying portfolios, the middle

momentum portfolios show a higher amount of investment than the other portfolios. On

the contrary, the middle momentum records the lowest amount among the zero-dividend

paying portfolios.

Panel C shows the average dividend yield of the univariate sort on momentum. It also

shows the dividend yield for the 12 momentum-dividend yield double-sorted portfolios.

The first column shows a slight increase in dividend yield as momentum increases to the

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Table 5.2: Summary statistics for Momentum-Dividend yield double sorts


Market 72 56 56 56 8.96 43.96 29.67 17.42

1 80 37 12 12 19 21.62 3.55 7.11 5.97 4.99

2 79 13 20 25 21 45.32 2.35 21.11 14.63 7.23

3 80 22 23 19 16 33.05 3.06 15.73 9.07 5.19


Market 0 3.31 5.00 8.58 11.74 5.31 4.55 5.75

1 4.78 0 3.29 4.99 8.55 9.29 12.96 6.20 5.71 6.98

2 5.45 0 3.33 5.03 7.32 5.95 10.48 5.16 4.50 5.73

3 4.62 0 3.33 4.98 8.56 8.30 13.29 6.56 5.78 6.85


Market 0.49 10.30 5.09 2.63 226 1006 893 802

1 -16.11 -22.63 -9.29 -9.25 -12.63 468 174 829 830 591

2 2.86 2.77 3.21 2.97 2.60 839 308 1064 942 874

3 26.91 37.08 26.76 18.08 21.20 808 261 1061 911 946

Market D/P= 0 1 2 3

Market 2.55 15.69 10.84 6.19

1 5.49 1.94 11.48 8.75 5.25

2 11.55 3.70 19.74 12.63 7.10

3 8.35 2.86 13.97 9.58 5.84


for each year t, we sort stocks into three groups (1, 2 and 3) based on their momentum ( compound returns in prior six month ) at the end of the

previous year. The lowest momentum stocks are assigned group 1 and the highest assigned group 3. We seperately sort the stocks in the same

year based on their dividend yield in the previous year. No dividend paying stocks are assigned one group (D/P=0). The rest of the stocks is spl-

itted into three groups in order of magnitude of their dividend yield. The lowest dividend paying stocks are place in 1 and the highest dividend

paying stocks are place in 3. The intersections of the stocks in the momentum-sort and dividend-sortare then used to create a set of 12 portofolios

(1/D/P= 0, 1/1, 1/2, 1/3, 2/D/P= 0, 2/1, 2/2, 2/3, 3/D/P= 0, 3/1, 3/2 and 3/3).We compute the annual average number of stocks in each portfolio.

The annual average relative market capital of the stocks in each portfolio is reported. Dividend Yield is measured as the sum of all dividends paid in

the year before year t divided by the current price. Total risk is the standard deviation of the past 24 to 60 months excess returns. Momentum

is measured as the compound returns six months before the t .We also report the annual averages for univariate sorted characteristic

on the market. The sample period is January 1868 -December 1913.


Panel C: Dividend Yield (% ) Panel D : Annual time series average of Total risk(% )

Panel E:Annual time series Momentum(% ) Panel F: Annual Average of Price (Belgian Franc)

Panel G:Annual time series average Size (*10^6)

124

middle portfolio. Dividend yield increases slightly with momentum in the lowest double-

sorted dividend paying stocks. On the contrary, the relationship is „cup-shaped‟ and „U-

shaped‟ for the middle and the highest-dividend paying portfolios.

In panel D, the second column shows a very high total risk for the zero-dividend paying

portfolios. This is sometimes almost twice the value of the total risk for the dividend

paying portfolios in each momentum category. Surprisingly, the total risk for the middle

momentum portfolios is the lowest. The total risk for high and low momentum portfolios

is almost the same for all dividend yield groups. This is surprising, as one would expect

the stocks that performed well in the past to have lower total risk than stocks that

performed poorly in the past.

Panel E of Table 5.2 shows the average annual past performance (momentum) of the

univariate and double-sort momentum and dividend yield portfolios. As in the previous

section, for the univariate sort, it is important to note the strong negative relationship

between momentum and dividend yield among dividend-paying stocks. The double-sort

portfolios reveal that the strength of the negative relationship is due to the low and the

middle momentum portfolios.

The average price for the univariate sort and double sort portfolios are reported in panel

F. As before, the prices for zero-dividend paying portfolios are low, sometimes one-third

of the price of their dividend paying counter parts (univariate sort). This persists in all

double-sort momentum groups. For the univariate sorts, there is a negative relationship

between average price and dividend yield among dividend paying stocks. The double-

125

sort portfolios indicate that the negative relationship pulls its strength from the middle

portfolios.

Finally, we show the average size of the single and double-sort portfolios in panel G.

Clearly, the zero-dividend paying stocks are the small size stocks. For the univariate sorts

on dividend yield, the zero-dividend paying portfolio has an average size that is less than

that of the dividend paying portfolios. This persists in all double-sort portfolios. The

negative relationship between size and dividend yield in dividend-paying portfolios is

obvious for both single and double-sort portfolios.

5.3.3 Total risk-Dividend yield double sorts


from the intersections of the total risk sort and dividend yield sort stocks. We also report

the univariate sort for total risk and dividend yield. As in the previous section, between

1868 and 1914, our sample contains 84 to 518 different firms, which result in an average

of 240 stocks traded every year (see Panel A and Figure 3.1). On average, there are five

or more stocks in every double-sorted portfolio. Looking at the rows of the double-sorts,

the number of high-risk zero-dividend stocks exceeds (sometimes by 8 times) the

dividend paying stocks. This is not surprising, as the small stocks are more likely the

high-risk stocks (see Table 5.1).

In panel B, we report the relative amount of money invested in each double-sort total

risk-dividend yield portfolio. For the univariate total risk sorts (first column), there is a

negative relationship between the amount of money invested in each portfolio and its

risk. Perhaps smaller firms are simply less diversified and therefore have a higher total

risk. The double-sort portfolios show that the negative relationship between the amount

126

Table 5.3: Summary statistics of total risk- dividend yield double sorts


Market 72 56 56 56 8.96 43.96 29.67 17.42

1 80 5 24 31 20 61.84 1.47 31.85 21.01 7.51

2 79 15 21 18 25 25.31 2.99 7.90 7.00 7.41

3 80 52 10 6 12 12.85 4.50 4.21 1.65 2.49


Market 0 3.31 5.00 8.58 11.74 5.31 4.55 5.75

1 5.55 0 3.52 4.98 7.03 3.13 3.65 2.84 3.05 3.58

2 6.65 0 3.17 5.03 8.00 6.31 6.71 6.31 6.13 6.19

3 2.68 0 2.99 5.04 9.90 14.06 15.35 12.57 11.07 11.46


Market 0.49 10.30 5.09 2.63 226 1006 893 802

1 3.29 -1.86 4.97 3.71 2.25 902 450 1096 917 792

2 4.17 -2.49 8.13 6.17 3.00 808 336 949 914 885

3 6.35 1.77 22.53 9.92 2.90 406 170 857 659 534

Market D/P= 0 1 2 3

Market 2.55 15.69 10.84 6.19

1 15.54 5.36 25.17 14.07 7.99

2 6.53 3.85 8.16 7.65 5.91

3 3.32 1.88 7.42 4.20 3.48

divided by the current price. Total volatility is the standard deviation of the past 24 to 60 months excess returns. Momentum is measured

as the compound returns for six months before the t . We also report the annual averages for univariate sorted characteristic on the market.

The sample period is January 1868 -December 1913


Panel C: Dividend Yield (% ) Panel D: Annual time series average of Total risk(% )

Panel E:Annual time series momentum(% ) Panel F: Annual Average of Price (Belgian Franc)


for each year t, we sort stocks into three groups (1,2 ans 3) based on their total risk (standard deviation of excess returns) at the end of the

previous year. The lowest total risk group are assigned group 1 and highest group 3. We seperately sort the stocks in the same year based on their

dividend yield in the previous year. No dividend paying stocks are assigned one group. The rest of the stocks is splitted into three groups in

order of magnitude of their dividend yield. The lowest dividend paying stocks are place in 1 and the highest dividend paying stocks are place

in 3. The intersections of the stocks in the size-sort and dividend-sort are then used to create a set of 12 portofolios (1/D/P= 0, 1/1, 1/2, 1/3, 2

/D/P= 0, 2/1, 2/2, 2/3, 3/D/P= 0, 3/1, 3/2 and 3/3.We compute the annual average number of stocks in each portfolio. The annual average relative

market capital of the stocks in each portfolio is reported. Dividend yield is measured as the sum of all dividends paid in the year before year t

Panel G:Annual time series average size (*10^6)

127

of investments and total risk is completely due to the dividend paying stocks. In fact, the

relationship is positive for zero-dividend paying stocks. A negative relationship is clearly

visible between dividend yield and the amount of investments. This relationship is

mainly due to the low total risk stocks.

In panel C, dividend payment does not show any sign of increasing or decreasing with

risk (column one). This is reflected in all double-sorted portfolios. In Panel D, total risk

does not show any sign of decrease or increase in the univariate sort dividend yield

portfolios. An exception is the total risk of the zero-dividend portfolio. The double-sort

portfolios show that the high risk recorded by the univariate sort zero-dividend portfolio

draws its power from the highest total risk portfolios.

Panel E reports the past performance of the total risk-dividend yield double-sort

portfolios. We also report the univariate sort portfolio characteristics. Momentum

increases as the firm‟s specific risk also increases for univariate sort portfolios. The

positive relationship is reflected in the lowest and the middle dividend yield portfolios.

As in the previous sections, the negative relationship between dividend and momentum

are prevalent in both single-sort and double-sort portfolios (among dividend paying

portfolios). The lowest momentum recorded by the zero-dividend paying portfolios is

also apparent.

As before, the price for zero-dividend portfolios remains smaller (Panel F). There is a

negative relationship between price and total risk (first column). The negative

relationship persists in zero-dividend, low and middle dividend yield portfolios. As

128

before, the negative relationship between price and dividend yield are still present in the

univariate sort. The negative relationship is persistent in all double-sort portfolios.

Finally, size shows a negative relationship with firm-specific risk (Panel G, column one).

The negative relationship continues to exist in all double-sorted portfolios. As in the

previous sections, size decreases as dividend yield increases among the dividend paying

stocks. This relationship persists in all dividends paying double-sort portfolios. The

average size for zero-dividend paying stocks is lower compared to their dividend-paying

counterparts.

From the previous sections, there is enough evidence to conclude that zero-dividend

stocks had low past performance, small market capitalization, low price and high total

risk in the 19th

century. This is consistent with the notion that dividends play an

important role in communicating to investors in the early capital markets; they can

assume that the small size and high-risk firms that do not pay dividends are distressed

(see Baskin and Miranti (1997), Cheffins (2006) and Cheffins (2008)). Alternatively,

this may be security for smaller, riskier, lower-priced and younger firms that may have

chosen not to pay a dividend because they were newly established and had more growth

prospects. Often, growth firms in their early lives have low or zero payouts ratios, with

the hope of returning more earnings back to investors at maturity.

To investigate the robustness of the relation among the suggested characteristics, we

compute the cross-sectional correlation matrix for each year. In Table 5.4, we report the

time-series averages of the bivariate correlations. We perform a hypothesis test on the

time series average to test whether it is significantly different from zero. We also include

129

realized annual returns in the matrix. We indeed retrieve the negative correlations

between total risk on the one hand and dividend yield and size on the other hand. Both

are significantly different from zero at the 1% level. Likewise, size and momentum are

significantly positively related.

Table 5.4: Annual Time Series Average of the correlation between the entire characteristic and Average return

This is also visible in panel E of Table 5.1. It is not surprising to see the positive

relationship between size and dividend yield, as the relationship would be influenced by

the high number of zero-dividend stocks (see sections 5.3.1-5.3.3). The dummy variable

is correlated with all the other characteristics except the average returns. Investigating the

correlations with realized returns in the last line of Table 5.4, we notice that all are small

in magnitude. Only two are significantly different from zero at the 5% level: the negative

Dummy DY In(Size) σεi Mom AR

Dummy

DY 0.609

***

In(Size) 0.503 0.187

** **

σεi -0.509 -0.268 -0.570

*** *** ***

Mom 0.139 0.027 0.157 -0.015

** ***

AR -0.001 -0.005 -0.072 0.037 0.071

** **

log of size, σɛi = total risk, DY = dividend yield, Mom = momentum. We also report

stocks.

a dummy variable which is 1 for zero-dividend stocks and 0 for dividend paying

cance at 1 % , ** = signifincance at 5 %. AR=average returns, In(Size) = natural

Note : This table shows the time series averages of the bivariate annual cross-

sectional correlation between the various characteristics define to explain average

returns. We test the hypothesis that, the time series average of the bivariate corre-

lation is equal to zero.The significance of the test are in parenthesis. *** = signifi-

130

correlation with size and the positive correlation with past returns. We now turn to more

formal testing of any predictive relation between stock characteristics and future returns.

Average Excess Returns on Portfolio Sorts 5.4

In this section, we investigate the relationship between stock characteristics and excess

returns using tercile portfolios. As before, we sort the stocks for each year into tercile

groups based on a specific characteristic (size, momentum and total risk) observed the

previous December. We sort stocks separately based on the dividend yield in the

previous year. We assign zero-dividend stocks to one group. The rest of the stocks are

divided into terciles. Twelve sets of portfolios are formed from the intersection of stocks

from the dividend yield sort group and the size, momentum or total sort groups. We then

hold these portfolios for the entire year and compute monthly returns. We compute

portfolio returns either using equal weights or value weights. Both weighting schemas

are complementary: with equal weights, the smaller stocks dominate, whereas the large

caps stand out with value weights. In addition, we form portfolios on univariate sort

characteristics and hold the position for one year. The FM breakpoint is used in all

portfolio formations. Repeating the portfolio formations each month yields 552 portfolio

returns in our sample period. We report the average excess returns and their

corresponding Newey-West autocorrelation, heteroskedastic standard-error adjusted t-

statistics for each portfolio. We also report the difference in average excess returns and

their t-statistics for the highest and the lowest terciles characteristic portfolios (hedge

portfolio). For the dividend yield, we show the difference in average excess returns for

the highest dividend-paying portfolios on the one hand, and the lowest and zero-dividend

paying portfolio on the other hand. The results are reported in Table 5.3.

131

Table 5.5: Equal and Value-weighted portfolios excess returns (%) of double-sorted characteristics

Market D/P= 0 1 2 3 3-0 3-1 Market D/P= 0 1 2 3 3-0 3-1

Panel A: Sorting on Size and Dividend Yield

Market 0.27 0.14 0.34 0.26 -0.01 0.12 1.33 1.43 3.59 2.19 -0.05 1.23

Micro 0.47 0.53 0.00 0.53 0.17 -0.36 0.11 2.73 2.21 0.02 3.15 1.17 -1.58 0.50

Small 0.22 -0.11 0.21 0.27 0.48 0.62 0.26 1.74 -0.48 1.48 2.63 2.00 2.19 1.10

Big 0.19 0.00 0.14 0.33 0.22 0.35 0.08 1.91 -0.02 1.43 3.09 1.69 2.06 0.74

Big-Micro -0.28 -0.28 -0.65 0.07 -0.20 0.05 -2.20 -2.20 -2.86 0.34 -1.36 0.33

Market 0.01 0.19 0.38 0.42 0.42 0.24 0.04 2.50 4.36 3.03 2.70 1.94

Micro 0.16 0.03 0.04 0.53 0.06 0.03 0.01 1.16 0.13 0.25 2.98 0.46 0.17 0.08

Small 0.35 0.01 0.26 0.33 0.71 0.70 0.46 2.75 0.06 1.89 3.32 2.43 2.20 1.54

Big 0.25 0.09 0.19 0.38 0.33 0.24 0.14 3.15 0.49 2.54 4.18 2.64 1.43 1.37

Big-Micro 0.09 0.06 0.14 -0.15 0.27 0.83 0.31 0.86 -0.93 1.95

EW Mean Monthly Returns(%) t-statistics for EW

VW Mean Monthly Returns(%) t-statistics for VW

dividends in the past one year are assigned one group. The rest of the stocks is split into three groups based on their dividend yield. The stocks in the

intersections of dividend sorts and the Size, Momentum, and Idiosyncratic sorts are grouped to form equally and value weighted portoflios. For the size

and dividend yield sort, we have the following 12 portfolios, Micro/D/P= 0, Micro/1, Micro/2, Micro/3, Small/D/P= 0, Small/1, Small/2, Small/3, Big/D/P= 0,

Big/1, Big/2 and Big/3. Similar portfolio formations are repeated for Momentum and Idiosyncratic risk. Size is measured as the price times the number of

shares outstanding in December of the year before portfolios formations. Momentum is the measured as the compound returns of the stock six month

the portfolios formation year. Total risk is the standard deviation of the past 24 to 60 months excess returns. Dividend yield is the sum of all

dividends paid in the year before the protfolio formation divided by the price at December of the same year. We also report the univariate sort on Divide-

nd Yield, Size, Momentum and Total risk. Portfolios are formed annually. We report the Newey-West Heteroskedastic autocorellation adjsuted

t-statistic for the average excess return for each portfolio. The sample period is Jan. 1868- Dec. 1913.

EW= Equally Weighted, VW= Value Weighted

At the beginning of January for each year t , the 19th centrury BSE stocks are allocated to three groups based on their sorted size (market capitalization),

Momentum and Idiosyncratic Risk in the previous year t-1. The BSE stocks are also sorted on dividend yield and grouped into 4. Stocks which do not pay

132

Table 5.5 continued


Panel B: Sorting on Momentum and Dividend Yield

Market 0.27 0.14 0.34 0.26 -0.01 0.12 1.33 1.43 3.59 2.19 -0.05 1.23

1 0.17 0.30 0.02 0.14 -0.13 -0.43 -0.14 1.16 1.39 0.11 0.86 -0.72 -1.84 -0.70

2 0.26 -0.18 0.13 0.36 0.42 0.59 0.29 2.86 -0.72 1.44 3.67 3.95 2.46 2.93

3 0.60 0.60 0.44 0.62 0.56 -0.01 0.12 4.21 2.20 3.35 4.73 4.44 -0.06 1.11

3-1 0.43 0.25 0.42 0.49 0.69 3.05 0.91 2.38 2.78 3.75

Market 0.01 0.19 0.38 0.42 0.42 0.24 0.04 2.50 4.36 3.03 2.70 1.94

1 -0.09 -0.28 -0.21 0.14 0.11 0.39 0.32 -0.72 -1.53 -1.18 0.95 0.42 1.39 1.09

2 0.21 -0.22 0.16 0.31 0.36 0.58 0.21 2.86 -0.94 2.07 3.31 3.30 2.64 2.03

3 0.56 0.39 0.53 0.60 0.63 0.24 0.10 4.69 1.76 4.13 4.78 4.63 1.25 0.81

3-1 0.66 0.67 0.74 0.46 0.52 4.90 3.05 3.89 2.64 1.85


Panel C: Sorting on Total risk and Dividend Yield

Market 0.27 0.14 0.34 0.26 -0.01 0.12 1.33 1.43 3.59 2.19 -0.05 1.23

1 0.29 -0.35 0.17 0.36 0.42 0.77 0.25 4.07 -1.30 2.39 4.74 2.91 2.69 1.78

2 0.19 0.13 0.18 0.23 0.20 0.07 0.02 1.58 0.68 1.27 1.69 1.61 0.43 0.15

3 0.39 0.40 0.07 0.90 -0.06 -0.45 -0.13 1.92 1.59 0.38 3.47 -0.29 -1.94 -0.61

3-1 0.10 0.75 -0.10 0.54 -0.47 0.56 2.17 -0.57 2.29 -2.31

Market 0.01 0.19 0.38 0.42 0.42 0.24 0.04 2.50 4.36 3.03 2.70 1.94

1 0.21 -0.23 0.16 0.31 0.30 0.53 0.15 3.29 -0.81 2.68 3.84 1.67 1.65 0.82

2 0.23 0.11 0.23 0.25 0.29 0.18 0.06 1.86 0.60 1.58 1.78 2.24 1.15 0.53

3 0.08 -0.14 -0.07 0.82 -0.04 0.10 0.03 0.43 -0.61 -0.36 2.99 -0.20 0.48 0.15

3-1 -0.13 0.08 -0.23 0.51 -0.34 -0.86 0.25 -1.22 2.05 -1.44

EW= Equally Weighted, VW= Value Weighted





133

In panel A, average excess returns and t-statistics for the sorting on size and dividend yield

are shown. When sorting on dividend yield across all stocks, there is no obvious pattern in

equally weighted portfolio returns. There is no significant difference in average returns of the

highest and the lowest dividend yield portfolios (12 basis points with t-statistic of 1.23). The

difference in average returns of the zero-dividend yield and highest dividend yield portfolio is

not significant.

We find high returns for zero-dividend stocks, which is consistent with Grossman and Shore

(2006) and Gwilym et al. (2009). For value-weighted portfolios, there is a monotonic

increase in average excess returns for univariate-sort dividend yield portfolios. The difference

in the average excess returns of the highest and the lowest dividend yield portfolios is 24 basis

points, with a t-statistic of 1.94. The profit improves when the investor goes long on the high

dividend yield and short on the zero-dividend yield portfolios. The difference in average

excess return increases to 42 basis points with the t-statistic of 2.70. This shows that

weighting stocks by their market capital in portfolio formations, a strategy that goes long on a

high-dividend yield portfolio and short on a low-dividend yield portfolio, results in a

significantly positive profit. The result is consistent with the findings for the UK market by

Dimson, Marsh and Staunton (2002) and Grossman and Shore (2006).

For equally weighted double-sort portfolios, among the size groups, „Small‟ and „Big‟ stocks

show a significantly positive difference in the highest and the zero-dividend yield portfolios.

Average returns increase monotonically from zero-dividend yield stocks to the highest

dividend yield stocks (except the middle dividend paying portfolio in „Big‟ stocks). The

positive significant difference disappears among the dividend yield stocks. It is obvious that

the size effect exists in the cross-section of the stocks. However, the effect obtains its power

from the „Micro‟ and zero-dividend yield stocks. These are the securities for distressed firms,

as they have low prices and negative past performance (see Tables 5.1 to 5.3). For value-

134

weighted portfolios, within the „Small‟ size groups, the dividend yield shows a strong positive

relationship with the average excess returns. Surprisingly, the positive relationship between

dividend yield and average returns disappear in the „Big‟ size group. It is not surprising to see

the size effect disappear when stocks are value-weighted to form portfolios. This confirms the

result from Chapter 3. The result adds credence to the view that the initial evidence for the

size effect is due to data mining.

In Panel B, double-sort portfolios are formed based on dividend yield and momentum. In

Table 5.1, dividend yield is negatively related to momentum; however, momentum is

positively related to average returns (Chapter 4). In view of this, one would expect

momentum to be an additional predictor of returns holding the dividend yield constant, and

vice versa. Panel B confirms momentum as a predictor of future returns. An exceptional case

is the insignificant average excess return, spread between the high momentum portfolio and

the lower momentum portfolio, for zero-dividend yield portfolios. The spread becomes

significant when stocks are value-weighted. In general, there is a strong momentum effect and

a significant dividend yield effect when stocks are value-weighted.

For the double-sort portfolios, the spread between the average excess returns of the high and

low dividend yield portfolios in the momentum tercile groups is not always significant. The

dividend yield only shows a linear pattern with average excess returns in the middle

momentum group for equally weighted portfolios. The average excess return for the hedge

portfolio is 29 basis points, with a t-statistic of 2.93. This value increases to 59 basis points

when the zero-dividend yield portfolio is used to compute the hedge portfolio. The positive

relationship between dividend yield and average excess return in the middle momentum

portfolios is robust to the weighting scheme used to form portfolios. The relationship still

exists for value-weighted portfolios. The notable exception is the negative spread in average

excess returns for the lowest and the highest momentum groups in equally weighted

135

portfolios, which becomes positive when stocks are value-weighted. Surprisingly, the value-

weighted portfolios average excess return spread for the largest momentum stocks is not

significant (the average excess return spread of 10 basis points with a t-statistic of 0.81). The

results show that among dividend yield stocks, the relationship between dividend yield and

average excess return in the middle momentum group is strong. However, the relationship

becomes stronger when zero-dividend yield stocks are considered. This finding supports those

of Gwilym et al. (2009), who found a strong relationship between dividend yield and average

excess returns among dividend-paying stocks in their quintile momentum portfolios. On zero-

dividend yield stocks, Grossman and Shore (2006) have shown that stocks that do not pay

dividends and have performed poorly in the past have very high future returns, while stocks

that do not pay dividends and have a high past return have lower future returns. We record

opposite results on the 19th

BSE when stocks are equally weighted, and are even stronger

when stocks are value-weighted. This shows that, for stocks that do not pay dividends, past

performance is most likely to determine future returns.

We now turn to total risk. The evidence presented in panel C does not show clear patterns.

There does not seem to be a monotonous relation between total risk and average returns,

neither in the entire market, nor across the dividend yield quartile, regardless of how returns

are weighted. When focusing on the hedge portfolios, the only difference that is statistically

significant is the middle dividend-yield portfolio, where high total risk translates into high

average excess returns. The difference is 54 and 51 basis points per month, 2.29 and 2.05

standard deviations from zero for equally weighted and value-weighted portfolios,

respectively. Our result does not support Blitz and Van Vliet (2007), who argue based on

Sharpe Ratio and alpha to confirm a negative relationship between total risk and average

excess returns on international markets. However, the results confirm Bali, Cakici, Yan and

Zhang (2005), which show that the positive relationship between total risk and expected

136

returns documented by Goyal and Santa-Clara (2003) is driven by small stocks (traded on

NASDAQ, in their case). Looking across dividend yield groups, there is no statistically

significant result in the hedge portfolios, be it equally weighted or value weighted. However,

we repeat that the absence of a monotonous pattern across the total risk portfolios in the entire

market, as well as the lack of any significant results for the high dividend yield portfolios,

indicates that total risk is not a pervasive characteristic of price in the 19th

century BSE

market. Generally, there is no total effect.

The Cross-Sectional regressions 5.5

From Table 5.4, it is clear that our characteristics are cross-sectionally correlated. In order to

study the marginal effects of the characteristics, we resort to the FM cross-sectional

regression method.

Every month, we do a regression of the cross-section of individual stock excess returns on the

characteristics proposed to explain the average excess return. We update characteristics

annually in January, based on information available at the end of December. The fact that

characteristics are recomputed every year introduces some time variations. The full usage of

the available individual stocks ensures the maximum utilization of information about the

cross-sectional behavior of individual stocks, which might have been lost when portfolios are

formed. We run the cross-sectional regression equation of the form

(13)

where is the excess return with , the return on the individual stocks in the month

t, and is the short-rate used as a proxy for the risk-free rate. DYj,t-1 is the dividend yield

estimated in the previous year.

(price times shares outstanding) is the size of a stock

in December of the year before, and is the total risk measured as the standard deviation

0 1 1 2 1 3 1 4 1 5 1DY Size Mom Dum , , , , ,ln ,jt ft t t j t t j t t j t t j t t j t jtR R

jt ftR R jtR

ftR

, 1Size j t

, 1j t

137

of the past 24 to 60 months excess returns. is the momentum estimated as the

compound gross return from June to November of the year before portfolio formation. Dumj,t-

1 is the dummy variable which takes the value 1 for zero-dividend yield stocks and 0 for

dividend paying stocks. From Figure 5.1, the number of zero-dividend stocks constitutes

about 28% of the stocks in the cross-section each year. To eliminate the effect of zero-

dividend stocks on the dividend yield-excess return relationship, one has to delete these stocks

or add a dummy variable. The dummy variable takes a value of 1 when a stock does not pay

dividends, and 0 for all other stocks. Deleting the zero-dividend stocks has the disadvantage

of reducing the cross-sectional information on stocks. The advantage of using the dummy

variable is to allow full usage of the cross-sectional information on individual stocks. In

addition, using the dummy variable allows a direct measurement and a test of significance of

the difference in behavior of the excess returns in the zero-dividend stocks. is the

vector of regression coefficients and the regression error. We also estimate the regression

with subsets of the characteristics. The estimation of the cross-sectional regression every

month yields 552 time series for regression coefficients. The time-series average of the slope

coefficients is the estimated premium earned for the different exposures. The averages are

tested for statistical significance using heteroskedastic autocorrelation corrected standard

errors. We use the Newey and West (1987) correction with T1/4

lags.9

The average of the coefficients and their corresponding Newey-West standard error adjusted

t-statistic (parenthesis) is reported in Table 5.6. In Panel A, model 1 confirms the positive

(negative) relationship between momentum (size) and average excess returns. The importance

of size is consistent with the post WWII-USA evidence presented by Fama and French

(1992). The significance of the size premium is also consistent with our equally weighted

9 We used , where T is 552, the number of months in our sample.

, 1Mom j t

0 5, ,t t

jt

1 4int T

138

portfolio sorts. This is not surprising, as the regression observations are unweighted, giving

undue importance to the „Micro‟ size stocks. We return to this issue in the next section. Total

risk does not show a significant relationship with average returns (average

Table 5.6: Cross-Sectional Regression of Excess Returns on Dividend Yield, Size, Total Risk and Momentum

Dividend Total Dividend

Model Intercept Yield Size Risk Momentum Dummy

1 1.88% -0.15% 0.51% 0.71%

(2.74) (-4.13) (0.38) (2.21)

2 1.81% 0.51% -0.15% 0.63% 0.69%

(2.66) (0.37) (-4.10) (0.47) (2.14)

3 2.58% -1.64% -0.18% 1.13% 0.54% -0.41%

(3.63) (-0.82) (-4.81) (0.82) (1.63) (-2.60)

Subperiods

Jan.1868-Dec. 1877 -0.08% -6.23% 0.04% 4.35% 0.03% -0.89%

(-0.05) (-1.83) (0.55) (1.06) (0.03) (-2.46)

Jan. 1878-Dec. 1887 6.22% 4.80% -0.34% -0.49% -0.83% -0.27%

(2.85) (0.68) (-3.08) (-0.16) (-1.04) (-0.61)

Jan. 1888-Dec. 1897 1.64% -0.21% -0.18% -1.60% 1.78% 0.16%

(1.31) (-0.06) (-2.66) (-0.61) (3.08) 0.55

Jan. 1898-Dec. 1907 3.19% -4.42% -0.25% -0.22% 1.10% -0.58%

(2.66) (-1.57) (-3.39) (-0.11) (2.26) (-1.94)

Jan. 1908-Dec. 1913 1.68% -2.37% -0.15% 4.65% 0.61% -0.48%

(1.63) (-0.75) (-2.64) (1.47) (1.35) (-1.65)

Panel A

Panel B

is Jan. 1868- Dec. 1913.

This table reports the coefficients of the monthly cross-sectional regressions of the excess return on the characte-

ristic.The characteristics identified in this regression are dividend yield size, momentum and idiosyncratic risk. We

also consider a dummy variable for dividend paying and zero-dividend paying stocks in the last 12 months before

the portfolios formation year. The dummy variable is assigned a value is assigned a value of 1 for zero-dividend

paying stocks and 0 for dividend paying stocks. Each year, the characteristics are measured based on the inform-

ation available prior to the year. Size is measured as price times number of shares outstanding. Momentum is comp-

uted as 6 months compound returns prior to the regression year. Dividend yield is the sum of dividends paid in the

last 12 months dividend by the current price. Total risk is the standard deviation of the past 24 to 60 months excess

returns.The interactions between size, momentum and dividend dummy are considered. Newey-West autocorrelation

and heteroskedastic adjusted t-statistics are in parentheses.We compute characteristics each year.The sample period

139

coefficient is 0.51 with a t-statistic of only 0.38). This confirms the sorting result, as for the

entire market, the average total risk hedge portfolio is 10 basis points with a t-statistic of 0.56.

Model 1 in Panel A confirms the positive relationship between past returns and future returns

in the equal and value weight sorts. Adding dividend yield to the regressors in model 2 shows

that the dividend yield does not relate to excess returns. The average coefficient is 0.51% with

a t-statistic of 0.37. This is not surprising, as the cross-sectional regression gives equal weight

to all stocks, and it confirms the results for equal weight sorts on dividends. The momentum

and size premiums are still significant in model 2. Including the dividend yield and its dummy

in regression model 3 reveals a negative insignificant relationship between dividend and

average excess returns. However, the dummy variable has a negative significant relationship

with average returns. This shows that there is a negative significant difference in average

returns between the zero-dividend and dividend paying stocks. Specifically, zero-dividend

paying stocks have an average excess return less than the dividend paying stock. The value -

0.41 is significant at a 5% level. The intercepts in models 1 to 3 are significantly different

from zero, and it is far greater than the risk-free rate.

As a further check on the form of these relationships, we run the regression in model 3 on five

(four ten-year and a five-year sub-periods) non-overlapping sub-periods between 1868 and

1914. The result in Panel B shows that most periods support the overall results in model 3.

The relationship between size and average excess returns does not persist in all sub-periods.

Size is not related to excess returns in the first ten-year period. Momentum seems to pull its

power from the last twenty-five years of the study. Dividend yield does not show a significant

relationship in any of the sub-periods. The effect of the dummy variable is not always

significant in the sub-periods. Table 5.6 confirms the result from the sorting method for

equally weighted portfolio formations.

140

5.5.1 Pervasiveness of the Cross-Sectional Relationships

From a broad economic point of view, for a characteristic to be accepted and to explain the

cross-section of the returns, its effect should be market-wide. The danger with the cross-

sectional regression approach is that illiquid, small stocks drive the results, as the observations

are not weighted. Recent evidence shows that some characteristics are not pervasive. For

example, Bali and Cakici (2008) documents that the relationship between total volatility and

the expected stock returns are not robust, but depend on the (i) weighting scheme used to

compute average portfolio returns, (ii) the frequency of the return data used to estimate total

volatility and, (iii) the breakpoints used to sort stocks into quintiles. Likewise, Horowitz et al.

(2000) indicate that when firms with less than $5 million in value are excluded, the size effect

is considerably reduced and becomes statistically insignificant. Using equally weighted

portfolios and ignoring transaction costs therefore overstates the size effect. This seems to be

consistent with Schwert (2003). He reports that the abnormal performance of the Dimensional

Fund Advisors (DFA) US 9-10 Small Company Portfolio, which invests in the two lowest

decile of stocks by market value, has been close to zero since 1982. Also, Fama and French

(2008) report that the asset growth anomaly is prevalent in their so-called small and micro

stocks.

We investigate whether our results suffer from this caveat by separately running the Fama-

MacBeth analysis for our „Micro‟ and large („Small‟ plus 'Big‟) stocks. Table 5.7 reports the

time series averages of the monthly cross-sectional regression coefficients. First, the evidence

for size is not consistent across size groups (model 1). It appears that the microcap group,

which represents, on average, only 3.67% of market capitalization (Panel B), drives the

negative relationship between size and average return.

Unsurprisingly, total risk does not have a relationship with average excess returns in the large

stocks (Panel A). In model 2, introducing the dividend yield in the regressions further reduces

141

the importance of total risk. It is still negative for the large stocks, but is statistically

insignificant. These conclusions do not change when the dividend yield dummy is included in

the regression. As an expectation, dividend yield has a consistent significant positive

relationship with average excess returns in the large stocks. The average coefficient of the

dummy variable is no more significant.

Table 5.7: Cross-Sectional regression of Excess Returns on Dividend Yield, Size, Total Risk and Momentum of Size subsamples

Panel B confirms that the size effect pulls its strength from the „Micro‟ stocks. The strength of

the dividend yield effect and the momentum effect is concentrated in the large stocks, which

Dividend Total Dividend

Model intercept Yield Size Risk Momentum Dummy

3 -0.86% -0.06% -2.46% 2.23%

(-1.13) (-1.54) (-1.42) (6.68)

4 -1.15% 5.55% -0.05% -1.41% 2.12%

(-1.63) (2.04) (-1.36) (-0.95) (6.53)

5 -1.42% 8.36% -0.03% -1.41% 1.98% 0.09%

(-2.16) (1.64) (-0.99) (-0.88) (6.06) (0.38)

1 9.02% -0.64% 0.09% 0.05%

(4.66) (-4.68) (0.04) (0.10)

2 8.96% -0.59% -0.63% 0.00% -0.01%

(4.62) (-0.28) (-4.59) (-0.00) (-0.02)

3 10.27% -4.06% -0.69% 0.74% -0.26% -0.57%

(5.06) (-1.35) (-4.84) (0.36) (-0.51) (-2.16)

paying stocks. Each year, the characteristics are measured based on the information available prior to the year.

Size is measured as price times number of shares outstanding. Momentum is computed as 6 months compound retur-

ns prior to the regression year. Dividend yield is the sum of dividends paid in the last 12 months dividend by the

current price. Total risk is the standard deviation of the past 24 to 60 months excess returns.The interactions between

size, momentum and dividend dummy are considered. Newey-West autocorrelation and heteroskedastic adjusted

t-statistics are in parentheses.We compute characteristic each year.The sample period is Jan.1868- Dec.1913.

Panel A (Small and Big)

Panel B (Micro)

This table reports the coefficients of the monthly cross-sectional regressions of the excess return on the characte-

ristic without the Micro size stocks. We seperately perform similar analysis on Micro stock.The characteristics iden-

tified in this regression are dividend yield size, momentum and idiosyncratic risk.We also consider a dummy vari-

able for dividend paying and zero-dividend paying stocks in the last 12 months before the portfolios formation year.

The dummy variable is assigned a value is assigned a value of 1 for zero-dividend paying stocks and 0 for dividend

142

accounts for about 96% of market capital. The dummy variable contributes its effect in the

„Micro‟ stocks. Table 5.7 confirms the results from the sorting method, as the value-weighted

dividend sort portfolios seem to have the positive relationship with average excess returns.

The result is not surprising, as Elton and Gruber (1983) obtained similar results on the USA

market between the years 1927 and 1976, using NYSE data. Finally, the results for

momentum are quite consistent across size groups. In all models, we find a positive

relationship between past returns and average realized returns. The premium for momentum

significantly ranges from 1.98% to 2.23% (compared to 0.54% and 0.71% from the full

sample regressions).

143

Conclusion 5.6

Since beta fails to explain the cross-section of stock returns in the 19th

century BSE, we

document the cross-sectional relationship between average excess returns and size, total risk,

momentum and dividend yield. We investigate these relationships with completely out of

sample data in the 19th

and first few years of the 20th century from the Brussels Stock

Exchange. We also investigate the pervasiveness of the cross-sectional relationships across

different size groups. We use sorting and cross-sectional regressions in the analyses.

Unsurprisingly, we find a significantly negative relationship between size and expected

returns. However, further investigation reveals that the negative significant relationship

between average return and size is completely driven by our „Micro‟ stocks, accounting for

about 3.67% of the market capitalization. There is no consistent pattern to be found for total

risk. The momentum effect, on the other hand, does not exist in zero-dividend yield stocks but

strong in dividend paying stocks for equally weighted sorts (average regression coefficient

with t-statistics not less than two standard errors from zero). Momentum can explain average

excess returns of stocks, which account for about 96% of the market capital („Small‟ and

„Big‟ stocks groups).

Dividend yield is negatively related to momentum and each of them is positively related to

excess returns. Further investigation reveals that the relationship between excess return and

dividend yield does not exist among „Micro‟ group, which are mostly zero-dividend yield

stocks. The relationship is significant in „Small‟ and „Big‟ stocks.

144

6 CONCLUSION

“The behavior of the aggregate U.K stock markets before World War I is similar in many ways to that

of the modern US markets. The relative size of the market and the relative numbers of large and small

stocks are also similar. However, the cross section of stocks looks quite different in the two samples”

Grossman and Shore (2006)

In this doctoral thesis, we answered the following research questions:

Is beta (systematic risk) stable, unbiased and robust to outliers in the 19th century BSE?

Does the CAPM provide a good description for expected returns in the 19th century BSE?

Does size affect the cross-section of stock returns on the 19th

century BSE market?

Does the momentum effect exist in the 19th century? If it exists, what is its source?

Does total risk predict returns on the 19th century BSE?

Does dividend yield predict returns on the 19th century BSE?

What is the marginal effect of the above characteristics on the cross-section of stock returns?

This doctoral dissertation answered the above questions, thereby contributing to the existing

literature on the cross-sectional predictability of stock returns. More specifically, we

examined the robustness of the cross-sectional predictability of stock returns. The study used

the 19th

and the first few years of the 20th

century Brussels stock exchange data. To this end,

we conducted four empirical studies to answer the above research questions. These studies

covered the assessment of betas (the main inputs in the CAPM), testing of the CAPM and the

effects of size, the presence and source of momentum and the combined effects of size,

momentum, dividend yield and total risk on the cross-section of stock returns.

We found that market model betas for individual stocks were poor predictors of future betas.

Predictability was improved by adjusting betas with Blume and Vasicek‟s autoregressive

methods. Grouping stocks to form portfolios also improved beta stability. On the 19th

century

145

BSE, non-synchronous trading effects were not prevalent. This may have been due to the

measurement interval of returns, as monthly returns were used to compute betas. We also

found that the iterative re-weighted least square method, which accounts for outliers in the

estimation of beta, produced betas that were not significantly different from the market model

betas, in terms of predictive accuracy. By studying the behavior of betas in the 19th

century,

we produced sufficient evidence of how betas should be adjusted for instability and bias when

testing the CAPM. Overall, our results also suggested that betas on the 19th

century BSE were

biased and not stable, as in the post-World War II period.

In the second study, we examined the validity of the CAPM for the 19th

century BSE. We also

investigated whether size effects determined cross-sectional variation in stock returns. First,

sorting and cross-sectional regression methods were used to investigate the relationship

between asset beta and the cross-section of stock returns. We found no relationship between

beta and average excess return for the various estimates of beta. Our results indicated that the

CAPM is not a valid model for capturing cross-sectional variations in stock returns on the 19th

century BSE. The results also confirmed Fama and French (1992) finding that beta has a flat

relationship with the cross-section of average returns in the US market. Second, we adopted

sorting and cross-sectional regression methods to test the cross-sectional relationship between

size and average excess return. We found a strong relationship between size and average

excess return on the 19th

century BSE. To this end, size could have been used to capture the

cross-sectional variation of stock returns on the 19th

century BSE. This would have confirmed

results from Banz (1981), Reinganum (1981), (1983), Chan et al. (1985) and Chan and Chen

(1988) and Fama and French (1992). However, the relationship was not cross-sectionally

robust. Detailed investigation confirmed that the size effect drew its power from a small group

of stocks accounting for about 0.35% of market capital. The size effect disappeared when

these stocks were omitted. In effect, we could not rely on size as a cross-sectional predictor of

146

returns on the 19th

century BSE, as it was confined to a group of stocks representing a small

fraction of market wealth. Our results implied that size should not be considered a systematic

proxy for risk, which corroborated Horowitz et al. (2000) findings for the US market between

1963 and 1981. The results also confirmed the findings of Fama and French (2008), who used

US data from 1963 to 2004 to document that the size effect owes much of its power to micro

caps and that it is marginal for small and big caps. In our data, the size effect did not exist for

small and large stocks.

The third study investigated the relationship between the short-term past performance of

stocks (momentum) and their future short-term performance. We found that momentum

existed in stocks, which constituted, on average, more than 90% of market wealth. Our

finding that large stocks had momentum showed that momentum could be used as a firm

attribute when predicting returns in the cross-section of the 19th

century BSE. The presence of

momentum on the 19th

century BSE also provided evidence that the momentum profit found

in post-WWII US and other markets was not due to data snooping bias. We further

investigated the source of momentum profit in the 19th

century and found that profit reversed

two to five years after portfolio formation. This evidence supported Jegadeesh and Titman

(2001) results, and it is contrary to that of Conrad and Kaul (1998). Therefore, the cross-

section of expected returns cannot explain the momentum profit. However, investigating the

momentum profit in size sub-samples showed that post-holding period reversal was mainly

due to “Micro” size stocks. Therefore, the Jegadeesh and Titman (2001) behavioral

explanation of momentum profit should be interpreted with caution. Extensions of behavioral

theory have postulated that investors‟ aggregate overconfidence is high following market

gains. This compelled us to test whether momentum profit in the cross-section of stocks

depended on the state of the market. We found that momentum depended on the state of the

market when a three-year lagged return was used to define the state of the market.

147

Dependence of momentum on market state for the 19th

century BSE added to the behavioral

explanation of momentum profit. This result was not surprising, as it corroborated Cooper et

al. (2004) and Chabot et al. (2009) results on the contemporary US and Victorian Era UK

markets, respectively.

In the last study, we examined the combined effects of size, momentum, total risk and

dividend yield on average returns. We included size to investigate whether the other effects

were confined to small and illiquid groups of stocks. Given its importance, momentum was

also included, to investigate the marginality of its effect in the presence of other

characteristics. In addition, we did not compute momentum as we did in the third study (i.e.

did not use the portfolio-overlapping method). Here, we measured momentum as the

compound return of individual stocks over six-month periods. We used six months compound

returns, because the six formation and six month holding period strategy has been the most

profitable in previous studies. As stated earlier, following Basu (1983), Rosenberg, Reid and

Lanstein (1985) and Fama and French (1992), we would have added price-earnings ratio or

book-to-market ratio as a measure of value or growth. However, data for the computation of

price-earnings and book-to-market ratios were not available for the 19th

century BSE. As a

result, dividend and price, which were readily available, were used to compute dividend yield,

which serves as a proxy for value. We considered total risk, as investors might not have been

able to hold the market portfolio, due to transaction cost constraints. Therefore, total risk

could also be priced to compensate rational investors for their inability to hold the market

portfolio. In this case, total risk was useful in explaining the cross-section of stock returns.

We found that the size-effect that existed in the 19th

century was driven by our so-called

“Micro” stocks, of which more than 50% had a zero-dividend yield, negative momentum, low

price and very high total risk. Low price, coupled with low momentum, high total risk and no

dividend payment, may point to firms that were distressed. Total risk did not show any

148

consistent relationship with average return. This confirmed Bali and Cakici (2008) finding

that (i) the interval of return measurement used to estimate risk (ii) the portfolio breakpoint

method (iii) the weighting scheme use to compute portfolio returns and (iv) using liquidity

and price filters to screen stocks determines the existence and significance of the cross-

sectional relationship between risk and expected returns.

Among dividend paying stocks, momentum was negatively related to dividend yield.

However, each was positively related to excess stock return for our large stocks. These

results were not different from what Asness (1997) and Gwilym et al. (2009) documented

recently in the US and UK markets, respectively.

Based on the predictability of stock market returns, we found several similarities between

contemporary stock markets and the 19th

century Brussels Stocks Exchange. Specifically,

CAPM was not valid for the 19th

century BSE, as it is with current markets. At first sight,

there seem to be evidence for the size effect, but the effect disappears when stocks in the

lowest size decile are eliminated on the 19th

century BSE. The findings on size effect confirm

Fama and French (2008) results, who conjectured that the effect draws its power from micro

stocks on the recent US market. The momentum effect existed on the 19th

century BSE, as on

contemporary markets. Total risk did not show any consistent relationship with average

excess returns on the 19th

century BSE. Similar results are found for contemporary markets,

where positive, negative and no relationships have been found between total risk and average

excess return (see Ang et al. (2006), Bali and Cakici (2008), Ang, Hodrick, Xing and Zhang

(2009), Fu (2009)). Dividend yield showed a positive relationship with average returns on the

historical BSE. A similarly positive relationship also existed in the current UK and US

markets (as in Asness (1997) and Gwilym et al. (2009)). The positive relationship between

dividend yield and expected returns shows the presence of value effect on the 19th

century

BSE as the dividend yield is used to represent value.

149

Although any inference across historical periods and systems must be interpreted with care,

the similarities that we found with the 19th

century BSE mostly supported the conclusions of

current research on the cross-sectional predictability of stock returns. Specifically, not finding

the relationship between expected return and beta in our data, we confirm the doubt placed on

the CAPM in the contemporary markets. In this research, size effect is not market wide but

rather found in small size stocks. This indicates that the effect is not due to market

inefficiency as confirmed in the contemporary markets. Therefore, we rule out size as a

predictor of the cross-section of expected return of securities. Total risk should not be

considered as a predictor of the cross-section of stock returns and limit to arbitrage in our

data. This is because the total risk does not show a consistent relationship with average

returns. Furthermore, returns from the dividend yield effect are not positively related to total

risk.

Our findings on momentum effect, dividend yield effect and the interactive effect of these two

on the 19th

century BSE revealed the robustness of these characteristics as predictors of the

cross-section of stock returns across time. In view of this, we see momentum and value as the

main predictors of the cross-section of stock returns. Even though the environment in which

the historical market operated has changed so much in relation to the contemporary market,

value and momentum turn out to be the common characteristics that can predict returns.

Back to Chapter 1, we differentiate between characteristics that are consistent predictors of

returns and those that are due to data snooping or statistical artifacts. Specifically, in this

dissertation, we reveal that characteristic such as size, total risk, momentum and dividend

yield are not time series and cross-sectionally robust in predicting stock returns.

150

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157

NEDERLANDSTALIGE SAMENVATTING

In dit proefschrift bestuderen we cross-sectionele patronen in aandelenrendementen, gebruik

makende van een volledig onafhankelijke databank gebaseerd op gegevens van de Brusselse

Beurs (BSE: Brussels Stock Exchange) tijdens de 19de

eeuw en de eerste jaren van de 20ste

eeuw. Deze dataset laat ons toe de invloed te bestuderen op aandelenrendementen van sterk

variërende omstandigheden in de economische en institutionele omgeving. De tijdsperiode die

deze dataset bestijht, vermijdt mogelijke kritiek op datamining. Met deze data:

Testen we de validiteit van het CAPM.

Daarenboven testen we of andere kenmerken een verklaring kunnen bieden voor de

cross-sectionele variatie in aandelenrendementen.

Op het moment van het schrijven van dit proefschrift was de boekhoudkundige en

transactiedata van de BSE nog niet gedigitaliseerd voor de 19de

eeuw. Daarom was het niet

mogelijk de verklaringskracht van boekhoudkundige gerelateerde kenmerken voor

aandelenrendementen te onderzoeken. Daarentegen onderzoeken we of grootte

(marktkapitalisatie), momentum (voorbije korte termijn rendementen), totaal risico

(bedrijfsspecifiek risico) en dividendrendement (als indicator voor de waarde van de activa,

net zoals de book-to-market ratio) de aandelenrendementen cross-sectioneel kunnen

voorspellen.

Er werden vier empirische studies uitgevoerd aan de hand van de BSE data uit de 19de

eeuw

en het begin van de 20ste

eeuw. In studie 1 behandelen we de beoordeling van de bèta. In

studie 2 testen we de validiteit van het CAPM en het grootte-effect. De derde studie test het

momentum-effect. De gecombineerde impact van grootte, momentum, totaal risico en

dividendrendement op de cross-sectionele aandelenrendementen wordt behandeld in studie 5.

158

In de eerste studie focussen we op de beoordeling van de bèta. Bèta is de belangrijkste

inputvariabele van het CAPM. Het is een geschatte variabele die mogelijk gemeten wordt met

een bepaalde statistische fout, waardoor de testresultaten van het CAPM vertekend kunnen

zijn. De instabiliteit, vertekening en niet-robuustheid naar outliers toe van bèta zijn dan ook

belangrijke onderzoekstopics geworden sinds de ontwikkeling van het CAPM. In deze studie

onderzoeken we de relatieve prestatie van de verschillende methodes om de bèta te schatten,

gebaseerd op hun vermogen om de erop volgende bèta te voorspellen. Meer specifiek

vergelijken we de bèta‟s van het marktmodel met bèta‟s die geschat werden door de auto-

regressieve technieken van Blume (1971) en Vasicek (1973).

We tonen aan dat de individuele bèta‟s van het aandelenmarktmodel niet stabiel zijn. De

voorspelbaarheid van deze bèta‟s kan worden verbeterd door het vormen van portefenilles

met ten minste tien of meer aandelen. Opvallend genoeg zijn er geen significante verschillen

in de verklarende nauwkeurigheid tussen de Blume en Vasicek aangepaste bèta‟s. Wanneer

er gebruik gemaakt wordt van de Dimson-methode om de bèta‟s te schatten, blijken een klein

aantal aandelen rendementen te hebben die een voorsprong (lead) of achterstand (lag) habben

op de marktrendementen. Om rekening te kunnen houden met outliers werden iterative

reweighted least square (IRLS) technichen gebruikt om de bèta‟s te schatten. De bèta‟s van

de IRLS zijn klein qua grootte in vergelijking met de bèta‟s van het marktmodel, maar hebben

wel dezelfde verklarende nauwkeurigheid als het marktmodel.

In de derde studie werd er gebruik gemaakt van de sorteermethode en de Fama en MacBeth

(1973) (FM) cross-sectionele regressiemethode om te kunnen onderzoeken of het CAPM

geldig is op data van vòòr de Eerste Wereldoorlog. Er werd eveneens getest of het grootte-

effect (de neiging van kleine aandelen om hogere rendementen te hebben dan grote aandelen)

reeds in de 19de

eeuw aanwezig was op de BSE.

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De sorteermethode en de FM cross-sectionele regressiemethode leveren geen empirische

bewijskracht voor het CAPM. We tonen eveneens aan dat de relatie tussen de bèta en de

rendementen varieert doorheen de tijd. De nulhypothese die de gelijkheid van de geschatte

hellingen veronderstelt van de cross-sectionele regressie en de abnormale marktrendementen

wordt niet verworpen in de periode 1868-1893. Daarentegen wordt door gebruik te maken van

de op grootte gesorteerde portfolio‟s (met gelijk gewicht) in de cross-sectionele regressie, een

verband vastgesteld tussen bèta en abnormaal rendement met bèta als enige verklarende

variabele (het CAPM is geldig). De voorwaardelijke dubbele sorteermethode die toegepast

wordt door Fama en French (1992) scheidt echter het effect van bèta en grootte op de

verwachte rendementen. Deze methode maakt de gemiddelde cross-sectionele helling van de

bèta niet significant, zowel wanneer ze met als zonder de grootte in de regressie wordt

geplaatst.

We vinden dat grootte negatief gerelateerd is aan abnormale rendementen. Er bestaat een

significant negatief verband met grootte (grootte-effect), maar de bèta is niet gerelateerd aan

abnormale rendementen wanneer beide variabelen worden opgenomen in de cross-sectionele

regressies. Een gedetailleerde analyse van de data onthult dat het grootte-effect voornamelijk

wordt veroorzaakt door de kleinere aandelen, die meetellen voor slechts 0.35% van de totale

marktkapitalisatie. Wanneer deze kleine aandelen buiten beschouwing worden gelaten wordt

er geen relatie gevonden tussen abnormale rendementen enerzijds en bèta‟s of grootte

anderzijds. Zowel de sorteermethode als de cross-sectionele regressie onthult dat het grootte-

effect verdwijnt wanneer de aandelen op waarde worden gewogen bij het vormen van de

portefenilles. Samenvattend wil dit zeggen dat het CAPM niet geldig is voor de BSE tijdens

de 19de

eeuw. Door het schatten van de bèta‟s met het marktmodel en de Dimson en Vasicek

methodes zal het model niet tot stand gebracht worden. Het grootte-effect bestaat, maar is

160

voornamelijk toe te schrijven aan een kleine groep van aandelen die slechts een klein

percentage van de totale marktkapitalisatie vertegenwoordigen.

In de vierde studie onderzoeken we of een momentum-strategie een abnormale winst kan

realiseren op de 19de

-eeuwse BSE. De momentum-strategie houdt in dat aandelen worden

gekocht (verkocht) die sterk (zwak) gepresteerd hebben in de laatste 3 tot 12 maanden. Er

bestaat overtuigend bewijs dat deze strategie winstgevend is op de 19de

-eeuwse BSE. Het

vinden van een momentum-effect in deze periode bevestigt de bewering dat momentum-

winsten gevonden op markten in de periode na de Tweede Wereldoorlog, niet enkel toe te

schrijven zijn aan vertekeningen door data-snooping. Een gedetailleerde analyse onthult dat

het momentum-effect niet bestaat in de groep van kleine aandelen. Een bijkomende analyse

met betrekking tot de momentum-winsten in elke kalendermaand toont aan dat de winst

positief was voor elk van deze maanden. Een omkening in januari (January reversal effect)

dat gevonden wordt op naoorlogse Amerikaanse markten kan niet gevonden worden op de

19de

-eeuwse BSE. In feite laat de maand januari zelfs de vierde hoogste momentum-winsten

optekenen in vergelijking met de andere maanden van het jaar. We vinden dat de momentum-

winsten niet sterk zijn in de eerste twintig jaar die we bestudeerden.

Teneinde de oorzaak na te gaan van de momentum-winsten hebben we gebruik gemaakt van

de Jegadeesh en Titman (2001)-benadering om de rendementen te bestuderen van de

momentum-portrfenilles in de post-holdingperiode. De momentum-rendementen keren om in

het tweede tot vijfde jaar na de holdingperiode. Verder onderzoek toont aan dat deze

omkering voornamelijk veroorzaakt wordt door kleine aandelen. We hebben eveneens getest

of de momentum-winsten en de lange termijn ommekeer in de cross-sectie van

aandelenrendementen afhankelijk is van de markttoestand. We vonden dat de 6-maanden

formatiestrategie en de 6- tot 12-maanden holdingperiodestrategie enkel winstgevend waren

in perioden van marktwinsten.

161

In de vijfde studie onderzoeken we of grootte, momentum, total risico en dividendrendement

de cross-sectie van aandelenrendementen kunnen verklaren in de periode 1868-1913. Grootte

en momentum worden opnieuw in de analyse opgenomen om de standvastigheid en de

gecombineerde impact van deze kenmerken te testen op de cross-sectie van abnormale

rendementen. Het sorteren op grootte test eveneens of het effect van de andere

karakteristieken niet enkel van toepassing is op de groep van kleine en illiquide aandelen. Het

totaal risico voor elk aandeel wordt gemeten als de standaardafwijking van de residuen van

het Dimson-model voor het schatten van de bèta‟s van de aandelen. In elk jaar is het

dividendrendement van een aandeel gelijk aan de som van alle dividenden betaald tijdens de

laatste 12 maanden gedeeld door de eindejaarsprijs. We onderzochten de standvastigheid van

de relaties over alle dividendrendement-, grootte-, totaal risico en momentum-groepen heen.

De sorteermethode en FM cross-sectionele regressie methodes werden toegepast. We

bevestigen dat grootte een significant negatief verband heeft met abnormale rendementen.

Echter, wanneer deze analyse op groepen van verschillende grootte wordt uitgevoerd, komt

aan het licht dat dit negatieve verband volledig is toe te schrijven aan zeer kleine aandelen die

meetellen voor slechts 3.67% van de totale marktkapitalisatie. Dit bevestigt de bevinding dat

het grootte-effect voornamelijk toe te schrijven is aan de eerste deciel grootte-portefenille,

waarvan deze zeer kleine aandelen deel uit maken. We hebben geen consistente verbanden

gevonden voor totaal risico. Momentum toont een consistent positief verband met abnormale

aandelenrendementen, die meetellen voor 96% van de totale marktkapitalisatie. Verder

vonden we een negatief verband tussen dividendrendement en momentum bij dividend-

betalende aandelen, maar elk van hen is positief gerelateerd aan gemiddelde abnormale

rendementen. Dividendrendement en momentum zijn positief gerelateerd aan gemiddelde

abnormale rendementen bij onze grote aandelen, die meetellen voor ongeveer 96% van de

totale marktkapitalisatie.

162

Hoewel elke conclusie over historische periodes en verschillende systemen heen met enige

voorzichtigheid geïnterpreteerd moet worden, bevestigen de gelijkenissen met de 19de

-eeuwse

BSE de conclusies van actueel onderzoek naar cross-sectionele voorspellingen van

aandelenrendementen. Meer specifiek bevestigen we, door het niet vinden van een verband

tussen verwachte rendementen en de bèta in onze data, de twijfel die rust over het CAPM in

de hedendaagse markten. In dit onderzoek is het grootte-effect niet van toepassing op de

gehele markt, maar eerder op de kleine aandelen. Dit toont aan dat het effect niet te wijten is

aan marktinefficiëntie zoals bevestigd wordt in hedendaagse markten. Daarom sluiten we

grootte uit als een voorspeller van de cross-sectie van verwachte rendementen van effecten.

Totaal risico mag niet beschouwd worden als een voorspeller van de cross-sectie van

aandelenrendementen en is slechts beperkt tot een arbitrage rol in onze data. Dit is omdat

totaal risico geen consistent verband toont met de gemiddelde rendementen. Bovendien zijn

rendementen van het dividendrendement-effect niet positief gerelateerd aan totaal risico.

Onze bevindingen in verband met het momentum-effect, dividendrendement-effect en het

interactie-effect van beide op de 19de

-eeuwe BSE tonen de robuustheid van deze kenmerken

aan als voorspellers van de cross-sectie van aandelenrendementen doorheen de tijd. Afgaande

hierop beschouwen we momentum en waarde als de belangrijkste voorspellers van de cross-

sectie van aandelenrendementen. Ook al veranderde de omgeving waarin deze historische

markten actief waren enorm in vergelijk met de huidige marktomstandigheden, waarde en

momentum blijken de gemeenschappelijke kenmerken te zijn die rendementen kunnen

voorspellen.

We maken dus een onderscheid tussen karakteristieken die consistente voorspellers zijn voor

rendementen en deze die toe te schrijven zijn aan data-snooping of statistische artefacten. In

het bijzonder onthullen we in dit proefschrift dat karakteristieken zoals grootte, totaal risico,

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momentum en dividendrendement niet robuust zijn in tijdzeeksen en cross-secties in de

voorspelling van dividendrendementen.

cross-sectional predictability of stock returns: pre-world war i evidence

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