International Investment 2005-2006

Professor André FarberSolvay Business SchoolUniversité Libre de Bruxelles

PhD 01-1 |2April 22, 2023

Notions of Market Efficiency

• An Efficient market is one in which:– Arbitrage is disallowed: rules out free lunches– Purchase or sale of a security at the prevailing market price is never a

positive NPV transaction.– Prices reveal information

• Three forms of Market Efficiency• (a) Weak Form Efficiency

• Prices reflect all information in the past record of stock prices• (b) Semi-strong Form Efficiency

• Prices reflect all publicly available information• (c) Strong-form Efficiency

• Price reflect all information

PhD 01-1 |3April 22, 2023

Efficient markets: intuition

Expectation

Time

Price

Realization

Price change is unexpected

PhD 01-1 |4April 22, 2023

Weak Form Efficiency

• Random-walk model:– Pt -Pt-1 = Pt-1 * (Expected return) + Random error– Expected value (Random error) = 0– Random error of period t unrelated to random component of any past

period

• Implication:– Expected value (Pt) = Pt-1 * (1 + Expected return)– Technical analysis: useless

• Empirical evidence: serial correlation– Correlation coefficient between current return and some past return– Serial correlation = Cor (Rt, Rt-s)

PhD 01-1 |5April 22, 2023

S&P500 Daily returns

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08

Return day t

Ret

urn

day

t+1

PhD 01-1 |6April 22, 2023

Semi-strong Form Efficiency

• Prices reflect all publicly available information

• Empirical evidence: Event studies• Test whether the release of information influences returns and when this

influence takes place.

• Abnormal return AR : ARt = Rt - Rmt

• Cumulative abnormal return:• CARt = ARt0 + ARt0+1 + ARt0+2 +... + ARt0+1

PhD 01-1 |7April 22, 2023

Efficient Market Theory

-16-11-6-149

141924293439

Days Relative to annoncement date

Cum

ulat

ive

Abn

orm

al R

etur

n (%

)Announcement Date

PhD 01-1April 22, 2023

Example: How stock splits affect value

05

10152025303540

Month relative to split

Cumulative abnormal return %

-29 0 30

Source: Fama, Fisher, Jensen & Roll

PhD 01-1 |9April 22, 2023

Event Studies: Dividend Omissions

Cumulative Abnormal Returns for Companies Announcing Dividend Omissions

0.146 0.108

-0.72

0.032-0.244-0.483

-3.619

-5.015-5.411-5.183

-4.898-4.563-4.747-4.685-4.49

-6

-5

-4

-3

-2

-1

0

1

-8 -6 -4 -2 0 2 4 6 8

Days relative to announcement of dividend omission

Cum

ulat

ive

abno

rmal

retu

rns

(%)

Efficient market response to “bad news”

S.H. Szewczyk, G.P. Tsetsekos, and Z. Santout “Do Dividend Omissions Signal Future Earnings or Past Earnings?” Journal of Investing (Spring 1997)

PhD 01-1 |10April 22, 2023

Strong-form Efficiency

• How do professional portfolio managers perform?

• Jensen 1969: Mutual funds do not generate abnormal returns

• Rfund - Rf = + (RM - Rf)

• Insider trading

• Insiders do seem to generate abnormal returns

• (should cover their information acquisition activities)

PhD 01-1 |11April 22, 2023

What moves the market

• Who knows?• Lot of noise:

– 1985-1990: 120 days with | DJ| > 5%• 28 cases (1/4) identified with specific event(Siegel Stocks for the Long Run Irwin 1994 p 184)

– Orange juice futures (Roll 1984)• 90% of the day-to-day variability cannot explained by

fundamentals

• Pity financial journalists!

PhD 01-1 |12April 22, 2023

Trading Is Hazardous to Your Wealth(Barber and Odean Journal of Finance April 2000)

• Sample: trading activity of 78,000 households 1991-1997• Main conclusions:

1. Average household underperforms benchmark by 1.1% annually2. Trading reduces net annualized mean returns

Infrequent traders: 18.5% Frequent traders: 11.4%3. Households trade frequently (75% annual turnover)4. Trading costs are high: for average round-trip trade 4% (Commissions 3%, bid-ask spread 1%)

PhD 01-1 |13April 22, 2023

US Equity Mutual Funds 1982-1991(Malkiel, Journal of Finance June 1995)

• Average Annual Return• Capital appreciation funds 16.32%• Growth funds 15.81%• Small company growth funds 13.46%• Growth and income funds 15.97%• Equity income funds 15.66%

• S&P 500 Index 17.52%

• Average deviation from benchmark -3.20% (risk adjusted)

PhD 01-1 |14April 22, 2023

: Excess Return

• Excess return = Average return - Risk adjusted expected return

Risk

Return Expected return

Average return

Risk

PhD 01-1 |15April 22, 2023

Jensen 1968 - Distribution of “t” values for “”115 mutual funds 1955-1964

0

5

10

15

20

25

30

35

-5 -4 -3 -2 -1 0 1 2 3 4

Not significantly different from 0

PhD 01-1 |16April 22, 2023

US Mutual FundsConsistency of Investment Result

Successive Period PerformanceInitial Period Performance Top Half Bottom HalfGoetzmann and Ibbotson (1976-1985)Top Half 62.0% 38.0%Bottom Half 36.6% 63.4%Malkiel, (1970s)Top Half 65.1% 34.9%Bottom Half 35.5% 64.5%Malkiel, (1980s)Top Half 51.7% 48.3%Bottom Half 47.5% 52.5%

Source: Bodie, Kane, Marcus Investments 4th ed. McGraw Hill 1999 (p.118)

PhD 01-1 |17April 22, 2023

Decomposition of Mutual Fund Returns(Wermers Journal of Finance August 2000)

• Sample: 1,758 funds 1976-1994

• Benchmark 14.8%+1%

• Gross return 15.8%

• Expense ratio 0.8%• Transaction costs 0.8%• Non stock holdings 0.4%

• Net Return 13.8%

Stock picking +0.75%No timing abilityDeviation from benchmark +0.55%

Funds outperform benchmark

Not enough to cover costs

Performance evaluation

PhD 01-1 |19April 22, 2023

• Complicated subject• Theoretically correct measures are difficult to construct• Different statistics or measures are appropriate for different types of

investment decisions or portfolios• Many industry and academic measures are different• The nature of active management leads to measurement problems

Introduction

PhD 01-1 |20April 22, 2023

Dollar-weighted returns• Internal rate of return considering the cash flow from or to investment• Returns are weighted by the amount invested in each stock

Time-weighted returns• Not weighted by investment amount• Equal weighting

Dollar- and Time-Weighted Returns

PhD 01-1 |21April 22, 2023

Text Example of Multiperiod Returns

Period Action

0 Purchase 1 share at $50

1 Purchase 1 share at $53

Stock pays a dividend of $2 per share

2 Stock pays a dividend of $2 per share

Stock is sold at $108 per share

PhD 01-1 |22April 22, 2023

Period Cash Flow

0 -50 share purchase

1 +2 dividend -53 share purchase

2 +4 dividend + 108 shares sold

%117.7)1(

112)1(

5150 21

rrr

Internal Rate of Return:

Dollar-Weighted Return

PhD 01-1 |23April 22, 2023

Time-Weighted Return

%66.553

25354

%1050

25053

2

1

r

r

Simple Average Return:

(10% + 5.66%) / 2 = 7.83%

PhD 01-1 |24April 22, 2023

Averaging Returns

Arithmetic Mean:

n

t

t

nrr

1

Geometric Mean:

1)1(/1

1

nn

ttrr

Text Example Average:

(.10 + .0566) / 2 = 7.81%

[ (1.1) (1.0566) ]1/2 - 1

= 7.83%

Text Example Average:

PhD 01-1 |25April 22, 2023

• Past Performance - generally the geometric mean is preferable to arithmetic

• Predicting Future Returns- generally the arithmetic average is preferable to geometric– Geometric has downward bias

Comparison of Geometric and Arithmetic Means

PhD 01-1 |26April 22, 2023

What is abnormal?Abnormal performance is measured:• Benchmark portfolio• Market adjusted• Market model / index model adjusted• Reward to risk measures such as the Sharpe Measure:

E (rp-rf) / p

Abnormal Performance

PhD 01-1 |27April 22, 2023

• Market timing• Superior selection

– Sectors or industries– Individual companies

Factors That Lead to Abnormal Performance

PhD 01-1 |28April 22, 2023

1) Sharpe Index

rp = Average return on the portfolio

rf = Average risk free rate

= Standard deviation of portfolio returnP

Risk Adjusted Performance: Sharpe

P

fP rr

PhD 01-1 |29April 22, 2023

M2 Measure

• Developed by Modigliani and Modigliani

• Equates the volatility of the managed portfolio with the market by creating a hypothetical portfolio made up of T-bills and the managed portfolio

• If the risk is lower than the market, leverage is used and the hypothetical portfolio is compared to the market

PhD 01-1 |30April 22, 2023

M2 Measure: Example

Managed Portfolio: return = 35% standard deviation = 42%

Market Portfolio: return = 28% standard deviation = 30%

T-bill return = 6%

Hypothetical Portfolio:

30/42 = .714 in P (1-.714) or .286 in T-bills

(.714) (.35) + (.286) (.06) = 26.7%

Since this return is less than the market, the managed portfolio underperformed

PhD 01-1 |31April 22, 2023

2) Treynor Measure

rp = Average return on the portfolio

rf = Average risk free rate

ßp = Weighted average ß for portfolio p

Risk Adjusted Performance: Treynor

p

fp rr

PhD 01-1 |32April 22, 2023

Risk Adjusted Performance: Jensen

3) Jensen’s Measure

p= Alpha for the portfolio

rp = Average return on the portfolio

ßp = Weighted average Beta

rf = Average risk free rate

rm = Avg. return on market index port.

])([ pfmfpp rrrr

PhD 01-1 |33April 22, 2023

Appraisal Ratio

Appraisal Ratio = p / (ep)

Appraisal Ratio divides the alpha of the portfolio by the nonsystematic risk

Nonsystematic risk could, in theory, be eliminated by diversification

PhD 01-1 |34April 22, 2023

It depends on investment assumptions

1) If the portfolio represents the entire investment for an individual, Sharpe Index compared to the Sharpe Index for the market.

2) If many alternatives are possible, use the Jensen or the Treynor measureThe Treynor measure is more complete because it adjusts for risk

Which Measure is Appropriate?

PhD 01-1 |35April 22, 2023

• Assumptions underlying measures limit their usefulness

• When the portfolio is being actively managed, basic stability requirements are not met

• Practitioners often use benchmark portfolio comparisons to measure performance

Limitations

PhD 01-1 |36April 22, 2023

Adjusting portfolio for up and down movements in the market• Low Market Return - low ßeta• High Market Return - high ßeta

Market Timing

PhD 01-1 |37April 22, 2023

Example of Market Timing

***

*

**

*

*

*

**

**

******

* ***

rp - rf

rm - rf

Steadily Increasing the Beta

PhD 01-1 |38April 22, 2023

• Decomposing overall performance into components

• Components are related to specific elements of performance

• Example components– Broad Allocation– Industry– Security Choice– Up and Down Markets

Performance Attribution

PhD 01-1 |39April 22, 2023

Set up a ‘Benchmark’ or ‘Bogey’ portfolio• Use indexes for each component• Use target weight structure

Process of Attributing Performance to Components

PhD 01-1 |40April 22, 2023

• Calculate the return on the ‘Bogey’ and on the managed portfolio

• Explain the difference in return based on component weights or selection

• Summarize the performance differences into appropriate categories

Process of Attributing Performance to Components

PhD 01-1 |41April 22, 2023

)(

&

1

11

11

BiBi

n

ipipi

n

iBiBi

n

ipipiBp

n

ipipip

n

iBiBiB

rwrw

rwrwrr

rwrrwr

Where B is the bogey portfolio and p is the managed portfolio

Formula for Attribution

PhD 01-1 |42April 22, 2023

Contributions for Performance

Contribution for asset allocation (wpi - wBi) rBi

+ Contribution for security selection wpi (rpi - rBi)

= Total Contribution from asset class wpirpi -wBirBi

PhD 01-1 |43April 22, 2023

• Two major problems– Need many observations even when portfolio mean and variance are

constant– Active management leads to shifts in parameters making measurement

more difficult• To measure well

– You need a lot of short intervals– For each period you need to specify the makeup of the portfolio

Complications to Measuring Performance

PhD 01-1 |44April 22, 2023

Theory of asset pricing under certainty

Passive Portfolio Management

Professor André FarberSolvay Business SchoolUniversité Libre de Bruxelles

PhD 01-1 |46April 22, 2023

Academic Foundations of Passive Investment

• Portfolio Theory (Markowitz 1952)– Benefits of diversification

• Capital Asset Pricing Model (Sharpe, Lintner)– Relationship between expected return and risk

• Market Efficiency (Fama 1970)– Stock prices reflect all available information.

• Mutual Fund Performance (Jensen 1968)– Professionally managed portfolio seem unable to make consistent

abnormal returns

PhD 01-1 |47April 22, 2023

Portfolio Theory

• Portfolio characteristics– expected return– risk (standard deviation)

• Risk determined by covariances• Efficient frontier• If riskless asset: one optimal

portfolio

• Expected return

Risk

PhD 01-1 |48April 22, 2023

Capital Asset Pricing Model

• Equilibrium model, optimal portfolio = market portfolio• Risk of individual security = beta (systematic risk)• Risk - expected return relationship

E(r) = Risk-free rate + Market risk premium x Beta

Beta

Expected return

1

E(rmarket)

PhD 01-1 |49April 22, 2023

Efficient Market Hypothesis (EMH)

• Strong version:“Security prices fully reflect all available information”

• Weaker version:“Prices reflect information to the point where the marginal benefit of

acting on information (the profit to be made) do not exceed the marginal costs”

(Fama 1991)

PhD 01-1 |50April 22, 2023

EMH (continued)

• A theoretical result: – Bachelier (1900) Théorie de la spéculation – Samuelson (1965) Proof that properly anticipated prices fluctuate

randomly.• A vast empirical litterature

– “weak-form tests”: do past returns provide information?– “semistrong-form”: is public information reflected in stock prices?– “strong-form tests”: do stock prices reflect private information?

PhD 01-1 |51April 22, 2023

Implications of the EMH for Investment Policy

• Technical Analysis• Fundamental Analysis• Active Portfolio Management

– market timing– stock selection

PhD 01-1 |52April 22, 2023

Mutual Fund Performances

• Malkiel (Journal of Finance June 1995)• 239 equity funds 1982-1991• Average excess return

Benchmark Portfolio: Wilshire 5000 S&P500 Net returns -0.93% -3.20% Gross returns 0.18% -2.03%

• Persistence of Fund Performance:– Winner: rate of return > median– Percent Repeat Winners: 51.7%

PhD 01-1 |53April 22, 2023

Mutual Fund Performances (cont.)

• Otten and Barms, WP 2000• 506 European equity funds 1991-1998

No Mean Market Funds Return ReturnFrance 99 10.9 12.7Germany 57 13.9 15.3Italy 37 15.2 14.9Netherland 9 22.0 21.0United Kingdom 304 12.3 14.2

PhD 01-1 |54April 22, 2023

EMH: faith or fact?

• All empirical tests based on asset pricing model:Excess return = Realized return - Expected return

• Any test of the EMH is a joined test• Still looking for the Capital Asset pricing model

– anomalies (calendar, size)– missing factors (book-to-market, value vs growth)– time variation of market risk premium– international diversification

PhD 01-1 |55April 22, 2023

From Theory to Practice

• First index fund: 1971 launched by Wells Fargo (Samsonite pension fund) and American National Bank

• Fidelity vs Vanguard• Benchmarking• Asset classes• Expense ratio• Outliers: talent or luck?

PhD 01-1 |56April 22, 2023

Optimal portofolio with borrowing and lending

Optimal portfolio: maximize Sharpe ratio

M

PhD 01-1 |57April 22, 2023

Capital asset pricing model (CAPM)

• Sharpe (1964) Lintner (1965)• Assumptions

• Perfect capital markets• Homogeneous expectations

• Main conclusions: Everyone picks the same optimal portfolio• Main implications:

– 1. M is the market portfolio : a market value weighted portfolio of all stocks

– 2. The risk of a security is the beta of the security:• Beta measures the sensitivity of the return of an individual security to the

return of the market portfolio• The average beta across all securities, weighted by the proportion of each

security's market value to that of the market is 1

PhD 01-1 |58April 22, 2023

Market equilibrium: illustration

Wealth Risk free asset

MarketPortfolio

Firm 1 Firm 2 Firm 3

Optimal portfolio 100% 20% 50% 30%

Alan 10 -10 20 4 10 6

Ben 20 -5 25 5 12.5 7.5

Clara 30 15 15 3 7.5 4.5

Market 60 0 60 12 30 18

PhD 01-1 |59April 22, 2023

Capital Asset Pricing Model

Expected return

Beta

Risk free interest rate

Rj

RM

1βj

jFMFj RRRR )(

PhD 01-1 |60April 22, 2023

Inside CAPM

PhD 01-1 |61April 22, 2023

Arbitrage Pricing Theory

• Starts from statistical characterization of returns• Consider one factor model for stock returns:

• Rj = realized return on stock j

• E(Rj) = expected return on stock j• F = factor – a random variable E(F) = 0• εj = unexpected return on stock j – a random variable

• E(εj) = 0 Mean 0

• cov(εj ,F) = 0 Uncorrelated with common factor

• cov(εj ,εk) = 0 Not correlated with other stocks (=key assumption)

jjjj FRER )(

PhD 01-1 |62April 22, 2023

Diversification

• Suppose there exist many stocks with the same βj.• Build a diversified portfolio of such stocks.

• The only remaining source of risk is the common factor.

FRER jjj )(

PhD 01-1 |63April 22, 2023

Created riskless portfolio

• Combine two diversified portfolio i and j.• Weights: xi and xj with xi+xj =1• Return:

• Eliminate the impact of common factor riskless portfolio

• Solution:

FxxRExREx

RxRxR

jjiijjii

jjiiP

)())()((

0 jiii xx

ji

jix

ji

ijx

PhD 01-1 |64April 22, 2023

Equilibrium

• No arbitrage condition:• The expected return on a riskless portfolio is equal to the risk-free rate.

Fjji

ii

ji

j RRR

j

Fj

i

Fi RRERRE )()(

At equilibrium:

PhD 01-1 |65April 22, 2023

Risk – expected return relation

jFj RRE )(

FM RRE )(

Linear relation between expected return and beta

For market portfolio, β = 1

Back to CAPM formula:

jFMFj RRERRE )()(

PhD 01-1 |66April 22, 2023

Generalization

• The approach can easily be generalized to several factors

N

jkjkjj FRER )(

PhD 01-1 |67April 22, 2023

Empirical challenges

• Explaining the cross section of returns

• Explaining changes in expected returns

PhD 01-1 |68April 22, 2023

Beta

NoDu

Durb

Oil

Chem

Manu

Telc Util

ShopMone

Other

MktPort

RF

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

18.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60

Beta

Ave

rage

retu

rn

NoDuDurbOilChemManuTelcUtilShopMoneOtherMktPortRF

PhD 01-1 |69April 22, 2023

Average return vs market beta for 25 FF stock portfolios 1926-2004

Mkt

RF

S1S2

S3S4

S5

GovB

CorpB

BM1

BM2

BM3

BM4

BM5

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

-0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

Beta

Mea

n re

turn

Size S: S1 smallest - S5 biggest B/M: BM1 lowest - BM5 highest

Average monthly returns Small BigLowB/M 0.91 1.01 1.08 1.01 0.92 0.99 1.29 1.33 1.26 1.10 0.92 1.18 1.50 1.46 1.30 1.30 1.03 1.32 1.69 1.51 1.40 1.35 1.11 1.41HighB/M 1.83 1.64 1.53 1.46 1.34 1.56 1.45 1.39 1.32 1.24 1.07

PhD 01-1 |70April 22, 2023

Size and B/M

12

34

5

Low B/M

S2

S3

S4

High B/M

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

mean

monthly return

%

Size

Value

Low B/MSeries2Series3Series4High B/M

Small

Big

PhD 01-1 |71April 22, 2023

Small BigAv.Ret. 1.45 1.39 1.32 1.24 1.07St.Dev. 9.47 7.59 7.03 6.70 6.45Beta 1.35 1.17 1.15 1.13 1.05

SIZE

Low HighAv.Ret. 0.99 1.18 1.32 1.41 1.56St.Dev. 7.38 6.91 6.75 7.10 8.85Beta 1.17 1.12 1.10 1.13 1.32

B/M

Based on monthly data 192607 200411

File: 25_Portfolios_5x5_monthly.xls

PhD 01-1 |72April 22, 2023

Fama French

Fama French Factors - Annual

-60

-40

-20

0

20

40

60

80

1927

1930

1933

1936

1939

1942

1945

1948

1951

1954

1957

1960

1963

1966

1969

1972

1975

1978

1981

1984

1987

1990

1993

1996

1999

2002

RM SMB HML

PhD 01-1 |73April 22, 2023

Predictability: Interest Rates and Expected Inflation

Sample period (Sample Size) γ

1831-2002 (2,053) -2.073(-3.50)

1831-1925 (1,136) -3.958(-4.58)

1926-1952 (324) 0.114(0.03)

1953-1971 (228) -5.559(-2.57)

1972-2002 (357) -1.140(-1.08)

Schwert, W., Anomalies and Market Efficiency,WP October 2002 http://ssrn.com/abstract_id=338080

tftmt RR

PhD 01-1 |74April 22, 2023

Predictability: D/P

Price/dividend ratio

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

100.00

1926

1928

1930

1932

1934

1936

1938

1940

1942

1944

1946

1948

1950

1952

1954

1956

1958

1960

1962

1964

1966

1968

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

PhD 01-1 |75April 22, 2023

Predictability

Nobs 77

R(t+1)=a+b*R(t)+e(t+1)Mean StDev Slope Standerror t R²

Stock 0.1190 0.2050 0.03 0.1154 0.27 0.001Tbill 0.0421 0.0350 0.92 0.0465 19.79 0.838Excess 0.0769 0.2083 0.04 0.1155 0.31 0.001

Excess(t+x) = a + b (D/P)(t) + eHorizon1 year 4.17 1.60 2.61 0.0822 year 8.13 2.26 3.60 0.1473 years 11.27 2.62 4.30 0.2004 years 13.69 2.95 4.64 0.2285 years 15.02 3.21 4.67 0.233

PhD 01-1 |76April 22, 2023

ER(+5)=a+b*(D/P)(t)+e

-1

-0.5

0

0.5

1

1.5

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

D/P

Exce

ss R

etur

n +5

PhD 01-1 |77April 22, 2023

Econometrician wanted…Excess Return + 5 : Residuals

-1.5

-1

-0.5

0

0.5

1

1.5

1926

1928

1930

1932

1934

1936

1938

1940

1942

1944

1946

1948

1950

1952

1954

1956

1958

1960

1962

1964

1966

1968

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998