Fama and French Factors in Australia

Michael A. O’Brien∗

UQ Business School

The University of Queensland

Qld Australia 4072

Phone: +61 7 3346 9327

e-mail: m.obrien@business.uq.edu.au

October 2007

Abstract

This study analyses the size and book to market effects and the ability of the Fama and

French (1993) three factor model to explain the cross-section of returns. Previous studies in

Australia have suffered from data limitations due to the difficulty in obtaining a comprehensive

series of accounting data. This study overcomes these limitations by hand collecting accounting

information on over 98% of all listed companies during the period 1981 to 2005. This study

finds that the Fama and French (1993) model provides increased explanatory power in explaining

the cross-section of returns in Australia when compared to the Capital Asset Pricing Model

(CAPM). In contrast to previous Australian studies this is due to both size and book to market

effects playing a role in asset pricing.

∗I wish to thank my advisers Tim Brailsford, Clive Gaunt and Jamie Alcock who have provided constructive insights,

David Forster who has provided valuable managerial advice and skills during the construction of the database and Alina

Hale with constructive comments. The author gratefully acknowledge financial assistance provided by Dimensional

Fund Advisors (DFA) Australia and the Australian Research Council through ARC Linkage Grant (LP0453913)

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Preface

Title of Thesis: Risk and Growth in Australia: Are SMB and HML Proxies for Extreme Risk?

Advisers: Professor Tim Brailsford, Dr Clive Gaunt and Dr Jamie Alcock.

Numerous studies have documented the ability of financial variables to explain the cross-section of

returns. These variables include market capitalisation, past stock returns, earnings yield, leverage

and book to market ratios. Bringing this evidence together Fama and French developed a three factor

model to explain the cross-section of returns. This model has been highly successful in explaining

the cross-section of returns but as it is an empirical model the reason why it has preformed so well

is unknown. In Australia only a few studies have analysed whether book to market ratios or the

Fama and French three factor model can explain the cross-section of returns. This thesis attempts to

rectify these gaps by analysing the book to market ratio in Australia and test the Fama and French

model over a 25 year period. One reason for the lack of studies is due to the lack of a comprehensive

accounting data in Australia. To rectify this accounting data is hand collected from annual reports

over the period 1981 to 2005. The thesis also adds to the debate on why the Fama and French factors

can explain asset returns by seeing whether they proxy for risk associated with extreme downside

movements.

The thesis is structured as follows:

• Chapter 1: Introduction.

• Chapter 2: Data.

• Chapter 3: Value and Growth Anomalies.

• Chapter 4: Disentangling Size from Momentum in Australian Stock Returns.

• Chapter 5: Fama and French Factors in Australia.

• Chapter 6: Asymmetries and the Fama and French Factors.

• Chapter 7: Conclusion.

The following study is based on Chapter 5.

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1 Introduction

Over the last twenty-five years several studies have documented the ability of certain variables to

explain the cross-sectional variation in returns which can not be explained by the Capital Asset

Pricing Model (CAPM).1 These variables include past stock returns (De Bondt and Thaler, 1985,

1987; Jegadeesh and Titman, 1993, 2001), size (Banz, 1981; Brown, Keim, Kleidon, and Marsh,

1983; Reinganum, 1981), earnings yield (Basu, 1977, 1983; Jaffe, Keim, and Westerfield, 1989),

leverage (Bhandari, 1988) and book to market value (Chan, Hamao, and Lakonishok, 1991; Fama

and French, 1992; Rosenberg, Reid, and Lanstein, 1985). Bringing this evidence together Fama

and French (1992) found that size and book to market values are the variables with the strongest

relationship to returns and that many of the other variables explanatory power vanished. Building on

this work Fama and French (1993) propose an empirically driven asset pricing model that captured

the returns to the size and book to market premiums by forming two mimicking factors, small

minus big (SMB) and high minus low (HML). By including these two factors with the market risk

premium they show that the three factor model captures the majority of the common variation in

returns. Subsequently the model has become the benchmark of asset pricing models, and subsequent

studies have tried to understanding why the factors explain the cross-sectional variation of returns.

Three main explanations are proposed. First, the variables are proxies for underlying risk in the

market (Davies, Fama, and French, 2000; Fama and French, 1993, 1995, 1996, 1998) in the spirit

of the Arbitrage Pricing Theory (APT) (Ross, 1976) or the Intertemporal Capital Asset Pricing

Model (ICAPM) (Merton, 1971, 1973). Second, that they are capturing behaviourial biases of the

investors and inefficiencies in the market (Daniel and Titman, 1997; Daniel, Titman, and Wei, 2001;

Lakonishok, Shleifer, and Vishny, 1994; LaPorta, Lakonishok, Shleifer, and Vishny, 1997; Skinner

and Sloan, 2002; Teo and Woo, 2004). Third, that they are a result of data-snooping (Black, 1993a,b;

Kothari, Shanken, and Sloan, 1995; Lo and Mackinlay, 1990).

In Australia a number of market anomalies have also been reported, including past stock returns

(Demir, Muthuswamy, and Walter, 2004; Durand, Limkriangkrai, and Smith, 2006b; Gaunt and

Gray, 2003; Hurn and Pavlov, 2003) and size (Beedles, Dodd, and Officer, 1988; Brown, Keim,

Kleidon, and Marsh, 1983; Durand, Juricev, and Smith, 2007; Gaunt, Gray, and McIvor, 2000).

These studies are generally consistent with US evidence, indicating that these variables may be

proxies for systematic risk or behavioural bias. Unfortunately few studies have studied how earnings

yield (Allen, Lisnawati, and Clissold, 1998), leverage and book to market effects (Gaunt, 2004;

Gharghori, Chan, and Faff, 2006; Halliwell, Heaney, and Sawicki, 1999) influence stock returns in

Australia. One of the reasons for this paucity of research in this area has been due to the lack

of a comprehensive accounting database in Australia. This has also meant that there are only

a few studies that have tested the Fama and French (1993) three factor model in Australia and1Black (1972); Lintner (1965a,b); Mossin (1966); Sharpe (1964)

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that these studies have generally focused on the mid to late 1990’s when accounting data is more

available (Durack, Durand, and Maller, 2004; Durand, Limkriangkrai, and Smith, 2006a; Gaunt,

2004; Gharghori, Chan, and Faff, 2006; Halliwell, Heaney, and Sawicki, 1999). The few studies

generally find that the three factor model has higher explanatory power compared to the CAPM in

explaining the cross-section of returns in Australia, but this is primarily driven by the SMB factor.

This result must be viewed with caution because of two reasons. First, the co-efficent on the SMB

factor is negative in some studies (Faff, 2001, 2004) and positive in others (Durack, Durand, and

Maller, 2004; Durand, Limkriangkrai, and Smith, 2006a; Gaunt, 2004; Gharghori, Chan, and Faff,

2006) even though similar time periods are studied. Second, these studies only cover 35% of the

market, on average, because book values of the other companies were unavailable. This could lead

to in-correct formation of the HML factor leading to its insignificance in these studies.

The purpose of this study is three fold. First, to significantly increase the coverage of accounting

information in Australia, and to expand this coverage into the 1980’s. Previous studies in Australia

have had limited access to accounting variables limiting the scope and potentially influencing the

results of these studies. This study hand collects accounting information from over 98% of all

companies that produced an annual report over the period 1981 to 2005. This is a significant

increase over previous studies in Australia and allows a through investigation into the size and value

premiums in Australia.

By increasing the coverage and expanding the time period of previous studies we address the second

purpose of this study, which is in response to Lo and Mackinlay (1990) who argue that results of

asset pricing tests need to be examined out-of-sample to ensure that data snooping has not occurred.

The primary location to test the Fama and French (1993) three factor model has been the US, with

only limited studies performed outside the US (Bagella, Becchetti, and Carpentieri, 2000; Daniel,

Titman, and Wei, 2001; Fama and French, 1998). These international studies generally find that

the Fama and French (1993) three factor model has increased explanatory power over the CAPM.

By analysing the size and value premium in a relatively unexplored data set we can form a more

comprehensive understanding of whether the model success is a result of data-snooping.

The final motivation for this research is to broaden the debate on the appropriate asset pricing

model to be used in Australia. Australian research on the CAPM and competing asset pricing

models have found that competing models provide additional power over the CAPM in explaining

the cross-section of returns, but they do not produce drastic improvements over the CAPM. Data

limitations and the length of the period studied has also generated doubt regarding the appropriate

model to apply. By increasing the time period and coverage of companies in the sample we will allow

a more informed debate to develop on the appropriate asset pricing model to use.

Consistent with overseas evidence, results indicate that returns in Australia are positively related

to book to market values. Results also indicate that small firms earn a premium over large firms,

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but there is a strong non-linearity between size and returns. This non-linearity causes stocks in

the middle size portfolios to under-perform both the stocks in the small and large portfolios. We

further analyse the SMB and HML factors in Australia and find that there is a strong June and

July seasonality in the SMB factor consistent with previous evidence in Australia (Brown, Keim,

Kleidon, and Marsh, 1983; Durand, Juricev, and Smith, 2007). We also find an unusually large

negative return in the HML factor occuring in 1989, which seems to be driven by severe distress in

value stocks leading into 1989 and extremely large negative returns from a few large stocks in the

value portfolio. The results indicate a low correlation between the market risk premium and the two

factors, indicating that they are capturing other underlying risk or behaviourial bias.

We then compare the CAPM against the Fama and French (1993) three factor model over the

period 1982 to 2006. These results demonstrate that the Fama and French (1993) model explains

a significantly higher proportion of the cross-section of returns in Australia when compared to the

CAPM. In contrast to previous studies in Australia we find that both the SMB and HML are

influential in explaining the cross-section of returns. These results also indicate that the Fama and

French (1993) model can not explain the under-performance of middle size portfolios and can only

explain, on average, 70% of the cross-section of returns.

The remainder of this paper is organised as follows. Section 2 reviews the international and Aus-

tralian literature relevant to this research. Section 3 presents the data and discusses our testing

framework. Section 4 analyses the SMB and HML factors in Australia, while Section 5 presents our

results. Section 6 summaries and concludes.

2 Literature Review

The capital asset pricing model (CAPM) is the foundation for most asset-pricing models in finance.

This model specifies that expected return is the product of the risk free rate and the expected

premium for risk. The expected risk premium is a function of the asset’s covariance with the market

return. This model provided the finance community with an elegant method to value risky assets.

Unfortunately the model relies on a number of assumptions including; using a single period model,

perfect information and frictionless markets. Since these restrictions are unrealistic in financial

markets new theoretical models were developed that relaxes some of these assumptions. Fama (1970)

extends the original CAPM into an intertemporal setting and demonstrates that if preferences and

future investment opportunity sets are constant, then an intertemporal utility maximiser can be

treated as if they have a single period utility function. This means that an intertemporal CAPM has

the same structure as the single-period model. However, these assumptions on the utility maximiser

are restrictive. Merton (1971, 1973) demonstrates that if opportunity sets are stochastic then an

intertemporal CAPM (ICAPM) would be a linear multi-factor model. Ross (1976) develops a new

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approach on how to value risky assets. His model, the Arbitrage Pricing Theory (APT), is developed

from a statistical charateristic of returns. This model assumes that there are a common component to

stock returns plus an idiosyncratic component (Cochrane, 2005). Using the principle of diversification

and arbitrage Ross (1976) demonstrate that the idiosyncratic component should not be priced.

Hence, the expected returns of each stock will be determined by its covariance with each common

component or “factor.” Therefore the model proposes that the expected return on an asset will be a

linear function of k factors. The model does not specifically state what these factors are, but using

factor analysis and economic arguments these factors could be selected and the model tested.

Despite being theoretically elegant, the CAPM has preformed poorly in empirical studies probably

because its assumptions are not meet in financial markets. Early empirical studies indicate that the

security market line is flatter than predicted (Black, Jensen, and Scholes, 1972; Fama and MacBeth,

1973). Subsequent research indicates that other factors are successful in explaining the proportion of

excess returns not explained by beta. Banz (1981); Reinganum (1981) demonstrate that the size of a

stock has explanatory power in explaining the cross-section of expected returns. These studies finds

that average returns on small stocks are higher than large stocks given the stock’s respective beta.

Bhandari (1988) analyses the debt/equity ratio. The debt/equity ratio could be related to the risk

of a stock, but the CAPM argues that the leverage effect should be captured by beta. In contrast

to the predictions of the CAPM, Bhandari (1988) finds a positive relationship between debt/equity

ratio and returns. Basu (1983) finds that high earnings/price ratio (E/P) stocks earn a statistically

significant positive return after controlling for beta and size. Chan, Hamao, and Lakonishok (1991)

find that in the Japanese market similar anomalies occur with the book to market ratio (B/M) and

cash flow yields have a significant positive impact on expected returns. While Chen, Roll, and Ross

(1986); Roll and Ross (1980) suggest that economic variables influence excess return. De Bondt and

Thaler (1985, 1987) demonstrate that stock returns over three to five years have explanatory power

over future returns. These studies demonstrates that stocks that have out performed the market,

over the last three to five years, subsequently under perform the market. In contrast, stocks that

have under performed the market, over the last three to five years, subsequently out perform the

market. Jegadeesh and Titman (1993, 2001) demonstrate that returns over 3 to 12 months also have

predictive power over future returns with winner portfolios continuing to outperform stocks that had

underperformed. This evidence indicates that stocks are priced with factors other than beta.

The empirical failure of the CAPM, with evidence suggesting that other factors can explain a pro-

portion of excess returns, lead to the development of empirically driven multi-factor models based

on the theoretical arguments of the APT and ICAPM. Ball (1978) proposes that yield surrogates,

such as E/P and dividend yields, are correlated with returns because they proxy for underlying risks

not accounted for by traditional risk measures. Using this argument Fama and French (1992, 1993)

analysed yield surrogates, size and B/M in an attempt to develop an empirically driven model. Fama

and French (1992) demonstrate that average stock returns are not positively related to their market

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betas when portfolios are formed on size and beta. These results indicate that size and B/M play

a significant role in explaining the cross-section of expected returns, while yield surrogates do not

add explanatory power once size and B/M effects are taken into account. Fama and French (1993)

extend Fama and French (1992) by creating two portfolios based on market capitalisation and B/M

ratios that they call SMB (small minus big) and HML (high minus low). These portfolios are de-

signed to proxy for the underlying factor that drives the size and B/M effect. They demonstrate

that the market risk premium, SMB and HML play an important role in explaining the cross-section

of expected returns for stocks. Using this model they subsequently show that the model can explain

the size, book to market, earnings yield, leverage and long term reversal anomalies, but it can not

explain medium term momentum (Fama and French, 1996).

The success of the Fama and French (1993) three factor model lead to a number of studies analysing

why it works. Three major explanations have emerged. First, that the factors SMB and HML

are additional risk factors in the spirit of the ICAPM (Merton, 1971, 1973) or APT (Ross, 1976).

A number of studies argue that the success of the model in explaining a majority of the market

anomalies is proof that they are proxies for underlying risk (Davies, Fama, and French, 2000; Fama

and French, 1995, 1996). Studies have also indicated that SMB and HML are can predict future

GDP in some countries (Liew and Vassalou, 2000) and that consumption wealth ratio is related

to the SMB and HML factor (Lettau and Ludvigson, 2001). Second, that behaviourial bias in

investors and market inefficiency leads to these persistent anomalies in the market (Daniel and

Titman, 1997; Daniel, Titman, and Wei, 2001; Lakonishok, Shleifer, and Vishny, 1994; LaPorta,

Lakonishok, Shleifer, and Vishny, 1997; Skinner and Sloan, 2002; Teo and Woo, 2004). Third, that

data-snooping has lead to the success of the model (Black, 1993a,b; Kothari, Shanken, and Sloan,

1995; Lo and Mackinlay, 1990).

2.1 Australian Evidence

In Australia, tests of the CAPM and its implications in Australia have found similar results to that

observed overseas. Earlier studies suggested support for the CAPM (Ball, Brown, and Officer, 1976)

but anomalies similar to overseas evidence are also prevalent in Australia. These regularities have

included seasonalities (Brailsford and Easton, 1991; Officer, 1975), medium term momentum (Demir,

Muthuswamy, and Walter, 2004; Durand, Limkriangkrai, and Smith, 2006b; Gaunt and Gray, 2003;

Hurn and Pavlov, 2003) and the size anomaly (Beedles, Dodd, and Officer, 1988; Brown, Keim,

Kleidon, and Marsh, 1983; Durand, Juricev, and Smith, 2007; Gaunt, Gray, and McIvor, 2000).

This lead to tests of multi-factor models which suggested mixed support for the APT (Faff, 1988).

In contrast, there has been only limited studies on the book to market (Gaunt, 2004; Gharghori,

Chan, and Faff, 2006; Halliwell, Heaney, and Sawicki, 1999), earnings yield (Allen, Lisnawati, and

Clissold, 1998) and other leverage anomalies. The lack of studies in Australia on B/M, earnings

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yield and leverage has been due to the difficulty in obtaining a comprehensive series of accounting

data. This lack of accounting information has also resulted in only limited studies on the Fama and

French model.

Halliwell, Heaney, and Sawicki (1999) was the first study that replicated the Fama and French (1993)

methodology in Australia using data from an eleven year period (1981 to 1991). The study only

collected, on average, accounting data on 350 companies per year. over the eleven year period there

existed, on average, 1370 companies per year, meaning only 26% of the total number of companies are

covered. As the authors acknowledge, this lack of accounting data means that the sample is heavily

skewed towards larger stocks, potentially influencing the results. Their study reports evidence of

premiums to small firms and high book to market firms, though it is not as strong or as consistent as

overseas studies. Their tests of the three factor model indicate that the SMB factor is significant and

positively related to size. In contrast to overseas studies there is little evidence that the HML factor

is significant in explaining the cross section of returns. Overall their results indicate that the Fama

and French (1993) model provide marginal improvement over the CAPM in Australia in explaining

the cross-section of returns. Further this improvement is solely due to the SMB factor.

Faff (2001, 2004) provides further evidence for the three factor model in Australia using ‘off the

shelf’ style indexes to construct the SMB and HML factors. Faff (2001, 2004) uses four Australian

equity style indexes provided by the Frank Russell Company. These indexes are the the ASX/Russell

Value 100, ASX/Russell Growth 100, ASX/Russell Small Value and the ASX/Russell small Growth

index. Faff (2001) examines the three factor model over the period 1991 to 1999 which provides an

external validity test of the Halliwell, Heaney, and Sawicki (1999) study. This study finds strong

support for the three factor model, but there is a significant negative size premium, rather than the

expected positive premium. Faff (2001) argues that this result is consistent with the recent evidence

of the reversal of the size premium (Dimson and Paul, 1999; Horowitz, Loughran, and Savin, 2000).

In contrast to Halliwell, Heaney, and Sawicki (1999) the study finds stronger support for the HML

factor being a priced factor in Australia. Faff (2004) re-examines the three-factor model over the

the period 1996 to 1999 using daily returns. Similar results are observed to his previous study and

the premium on the SMB factor is again negative.

Gaunt (2004) tests the Fama-French model in Australia over a ten year period spanning 1991 to

2000. The sample has an average of 650 companies, while the average number of companies during

the 10 year period studied was 1310. This is a significant increase in coverage over Halliwell, Heaney,

and Sawicki (1999), but only 50% of the market is considered. The methodology also means that

the sample is skewed towards larger more establish firms. Gaunt (2004) demonstrates the negative

association between size and returns with the smallest quintile of firms being the driver of the results,

with the other size quintiles having similar returns. His study also has the strongest evidence of high

book to market stocks earning a premium over low book to market stocks in Australia. The regression

results using the Fama and French (1993) model are generally consistent with Halliwell, Heaney, and

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Sawicki (1999), with the market risk premium and SMB being highly significant and positive. In

contrast to Halliwell, Heaney, and Sawicki (1999) Gaunt (2004) results demonstrate that HML plays

a role in explaining the cross-section of returns, although its role is minor when compared to the

market risk premium and SMB. He also demonstrates that the Fama and French (1993) three-factor

model provides increased explanatory power over the CAPM.

Durack, Durand, and Maller (2004) uses a similar time period to Gaunt (2004) to study the per-

formance of the conditional CAPM (Jagannathan and Wang, 1996) against the Fama and French

(1993) three-factor model. The sample used in this study is significantly smaller than Gaunt (2004)

study and has access to only 264 companies book value per year on average. This implies that only

20% of all companies are included in the formation of the HML factor. Results indicate that the

three factor model outperforms the conditional CAPM. The result seems to be primarily driven by

the important role SMB plays in the Australian market. However, the results for the HML factor are

inconclusive and again suggests that HML is not priced. These results leads Durack, Durand, and

Maller (2004) to suggest further research is required on the book to market anomaly in Australia.

Durand, Limkriangkrai, and Smith (2006a) re-analyse the period and data studied by Durack, Du-

rand, and Maller (2004) and tests whether US or Australian factors are better at explaining the

cross-section of assets returns. They find that the SMB factor is highly significant and positive,

but that the HML is generally insignificant. However when the US factors are used more HML

co-efficient’s are found to be significant. This would suggest that HML may play a role in Australia,

although why only the US HML and not the Australian HML is priced has not been studied. Gen-

erally, using the US factors instead of the Australian factors leads to lower explanatory power in the

model and more noisy estimates, suggesting that local factors are important.

Recently Gharghori, Chan, and Faff (2006) analysed whether the Fama and French (1993) factors

proxy for risk or behaviourial bias. The study covers the period 1992 to 2003, but the number of

companies that are covered ranges from 35% to 50% and are skewed towards larger more established

companies. Similar to Gaunt (2004) the results indicate a strong relationship between book to market

and returns. The test of whether the factors are compensation for differences in risk or are capturing

behaviourial bias indicate some support for the risk based argument. Results also indicate that the

HML factor, in particular, is a proxy for underlying risk, while the results from the SMB factor are

inconclusive. Overall Gharghori, Chan, and Faff (2006) suggest that a longer more extensive data

set is required for this research.

The confusing results in testing the Fama and French three factor model on Australia data, in par-

ticular the lack of evidence of why the Australian HML and SMB factor is in-consistently priced,

suggests that more studies of the model are required. The conflicting results, even when using simi-

lar time-periods, may indicate that the short time periods analysed and substantial data limitations

could be influencing the results. In particular, all previous studies have had limited access to ac-

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counting data meaning that less than half of all firms in the market are included when forming book

to market portfolios. Overall the number of companies covered in the Australian studies has been

around 35% of the total firm population. By hand collecting book values, this study is the first

Australian study to comprehensively analyse the book to market anomaly.

3 Data and Methodology

3.1 Data

Previous studies in Australia on the book to market anomaly has suffered because of a lack of quality

accounting data. To rectify this problem this study hand collects accounting information from annual

reports for the period 1981 to 2005. Company annual reports were catalogued and stored by the

Australian Stock Exchange (ASX) and its forebears until the late 1990s. These reports are stored

in each state library throughout Australia and are the primary source of our annual reports for the

period 1981 to 1997. We have further collected hard and electronic copies of annual reports from

companies to supplement and extend the period of reports beyond 1997. This has been accomplished

through a variety of methods including accessing reports directly from the companies, either through

their website or directly requesting a copy. This allows us to then match the accounting data

to readily available price data sources including the Australian Graduate School of Management

(AGSM) Centre for Research in Finance (CRIF) database. Table 1 records the number of annual

reports collected, the number of companies that did not produce an annual report during the year,

the number of companies that we can not find an annual report for and the number of companies

with price data in CRIF. This indicates that we have been able to collect data from approximately

98% of all companies that produced an annual report during the time period considered. This is a

substantial increase over previous studies in Australia where accounting information coverage was

always less than 50% (Gaunt, 2004) and in most cases less than 25% (Durack, Durand, and Maller,

2004; Durand, Limkriangkrai, and Smith, 2006a; Halliwell, Heaney, and Sawicki, 1999) of companies

listed.

From the annual reports the following information is collected to allow us to calculate book values;

• total value of equity,

• outside equity interests,

• value of preference shares capital,

• future tax benefits.

Following Fama and French (1992, 1993) we define book value as the total value of equity minus

outside equity interests, the value of preference shares capital and future tax benefits. Consistent

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Table 1

Number of annual reports collected per year

Year Number of annual Number of firms Number of firms Number of unique

reports collected that did not produce that produced an firms in CRIF

an annual report annual report but

can not be found

1981 835 73 111 1019

1982 855 72 61 988

1983 846 81 49 976

1984 892 81 39 1012

1985 976 145 31 1152

1986 1190 167 42 1399

1987 1572 206 49 1827

1988 1624 231 33 1888

1989 1437 369 27 1833

1990 1272 327 15 1614

1991 1135 245 5 1385

1992 1037 185 5 1227

1993 1054 128 2 1184

1994 1155 70 3 1228

1995 1167 64 2 1233

1996 1164 88 3 1258

1997 1155 98 27 1280

1998 1181 83 21 1285

1999 1227 118 17 1362

2000 1337 136 10 1483

2001 1371 118 7 1496

2002 1384 117 7 1508

2003 1410 116 1 1527

2004 1522 128 0 1650

2005 1634 132 0 1766

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with previous studies companies, with negative book value are dropped from the sample. We then

match the book values to market capitalisation information from the AGSM-CRIF database. To be

consistent with previous literature and to avoid any look ahead bias, because the release of accounting

information is later than the balance date on the annual report, we only use accounting information

that is at least 6 months old. For example, when we are calculating book values for December 1982

only accounting information released prior to and including 30 June 1982 can be used. Book to

market ratio is then calculated as the book value dividend by the market capitalisation following

the methodology in Fama and French (1992, 1993). For example, if a company has a balance date

of 31 December and we are calculating book to market value in December 1982. We use the book

value from the annual report with a balance date of 31 December 1981 and use the stocks market

capitalisation as of 30 June 1982.

Throughout the study price and market capitalisation information from the AGSM-CRIF database

is utilised. The AGSM-CRIF database contains monthly prices, market capitalisation dividends,

adjustments for capitalisation changes and returns for all Australian Stock Exchange (ASX) listed

stocks. This database also contains the monthly 13-week treasury note yield and the value-weighted

monthly market return of all stocks in the database. In this study we remove all property trusts2

and investment funds from the database. Using our accounting information and the AGSM-CRIF

database allows us to to analyse the CAPM and the Fama and French (1993) three factor model

for the period 1982 to 2006. This sample period covers the combined periods studied by Durack,

Durand, and Maller (2004); Durand, Limkriangkrai, and Smith (2006a); Gaunt (2004); Gharghori,

Chan, and Faff (2006); Halliwell, Heaney, and Sawicki (1999) and extends these studies to 2006.

This significantly extends the previous Australian studies to a 25 year period.

3.2 Portfolio Construction

To test the CAPM and Fama and French (1993) model we follow the portfolio formation technique of

Fama and French (1993) and construct 25 portfolios. First, each December all stocks in our sample

are ranked by their book to market value and each stock is assigned to one of five book to market

portfolio, where each portfolio contains an equal number of stocks. The first portfolio (growth)

contains the first 20% of stocks with the lowest book to market value. The next 20% of stocks are

assigned to portfolio 2. The process continues with the last portfolio (value) containing the last 20%

of stocks who on average have the highest book to market value.

Independently, the sample is ranked by market capitalisation at year end and assigned to one of five

size groups, where each portfolio contains an equal number of stocks. Portfolio 1 (big) contains the

first 20% of stocks and contains the stocks with the largest market capitalisation. Portfolio 2 contains

the next 20% of stocks. We continue this process with portfolio 5 (small) containing the last 20% of2These are similar to REIT’s in the USA

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stocks with the lowest market capitalisation. Thus each stock is assigned to one size portfolio and to

one book to market portfolio, giving a total of 25 size-book to market portfolios. Each portfolio is

then held for the next twelve months and equal-weighted and value-weighted returns are calculated.

At the end of the holding period the procedure is repeated. As a result of the above procedure we

have a series of 300 monthly returns covering the period January 1982 to December 2006 for the 25

size-book to market portfolios.

Table 2

Characteristics of Portfolios

This table presents the average number of companies, mean and median market capitalisation and

mean book to market values of the 25 size-book to market portfolios. The 25 size-book to market

portfolios are formed by first ranking all stocks in the sample by their book to market values and

assigning each stock to one of five book to market portfolio where each portfolio contains an equal

number of stocks. Independently all stocks are ranked by their market capitalisation and assigned to

one of five size portfolio with each portfolio containing an equal number of stocks. The intersection of

the five book to market portfolios and the five size portfolio leads to the creation of our 25 portfolios.

Panel A: Number of Companies

Growth 2 3 4 Value

Big 52 53 43 25 10

2 39 42 41 38 23

3 33 35 39 40 38

4 30 31 33 42 48

Small 29 23 29 39 65

Panel B: Mean Market Capitilisation ($ millions)

Growth 2 3 4 Value

Big 1,894.6 2,095.8 1,516.6 1,055.7 1,358.1

2 69.5 69.3 67.0 69.0 65.5

3 19.7 19.8 19.4 19.3 18.8

4 7.6 7.7 7.5 7.5 7.4

Small 2.6 2.8 2.7 2.7 2.5

Panel C: Median Market Capitilisation ($ millions)

Growth 2 3 4 Value

Big 1,640.2 1,811.0 1,396.5 782.5 713.3

2 67.3 77.7 69.5 74.6 58.9

3 20.4 20.6 19.5 21.5 20.1

13

Table 2

(continued)

4 7.8 7.8 7.8 7.9 7.4

Small 2.4 2.7 2.7 2.7 2.6

Panel D: Mean Book to Market Values

Growth 2 3 4 Value

Big 0.31 0.60 0.88 1.27 2.98

2 0.30 0.60 0.89 1.27 7.26

3 0.28 0.60 0.90 1.31 3.71

4 0.28 0.61 0.89 1.30 2.99

Small 0.26 0.60 0.90 1.31 4.94

Table 2 provides summary information for each of the 25 size-book to market portfolios. Panel A

reports the average number of companies within each of the 25 size-book to market portfolios. These

results clearly demonstrate that growth stocks are over-represented in the big quintile with 28% of

stocks classified as growth also being classified as big. As we move down the growth quintile this

percentage declines with only 16% of growth stocks being classified as small. In contrast value stocks

are under-represented in the big quintile with 6% of stocks classified as value being big, while 35%

of stocks classified as value are also classified as small. This result, which suggests that value stocks

are on average smaller than growth stocks, is confirmed by Panel B and Panel C which report the

mean and median market capitalisation respectively. These Panels indicate that the mean (median)

market capitalisation of growth stock within the big quintile is $1,894.6 million ($1,640.2 million),

while the value stocks have a substantially lower market capitalisation of $1,358.1 million ($713.3

million). On average, value companies are smaller than growth companies which is similar to prior

Australian and overseas evidence (Fama and French, 1993; Gaunt, 2004; Halliwell, Heaney, and

Sawicki, 1999). It is also consistent with the argument that value stocks are under stress and are in

industries that are in decline, causing a fall in their market capitalisation, while growth companies

have been growing rapidly causing market capitalisation to increase.

Panel D of Table 2 reports the average book to market value of each portfolio. The result demonstrate

that the average book to market value is fairly consistent across the five size quintiles within each

book to market quintile, i.e. the growth quintile has an average book to market ratio of 0.29, with

big growth having the highest average of 0.31 and small growth having the lowest at 0.26. The

only exception is the value classification where the average is 4.38, with big-value having the lowest

average of 2.98 and portfolio 2-value having the highest average of 7.26. This higher variability is

being driven by a few companies with extremely large book to market values.3 If these stocks are3All companies with extremely large book to market values are being re-checked to confirm their book and market

14

removed from the calculations the variability is substantially reduced with the average within the

value classification falling to 3.27 and the largest average occurring in small-value with 3.76, and

the lowest being 2-value with 2.90. Overall the portfolio construction procedure has achieved its

objective of controlling for unwanted intra-quintile variability.

We now turn to the performance of the 25 size-book to market portfolios, and five value minus

growth (VMG) portfolios within each size quintile. The VMG portfolios are formed as the difference

between the return of the value portfolio less the return on the growth portfolio within each size

quintile. Table 3 reports the average monthly return of the size-book to market portfolios. Panel

A reports the equal-weighted portfolio returns while Panel B reports the value-weighted portfolio

returns.

The results indicate that the growth portfolio within each size quintile earns the lowest return. As

we move towards the value portfolio returns steadily increase with the value portfolio earning the

highest return. The F -test and Kruskal-Wallis test both indicate that there are significant differences

across the portfolio returns within each size portfolios, with the exception being the small quintile,

where there is evidence of no significant difference between the mean and median monthly returns.

Focusing on the VMG portfolio, the results clearly demonstrate a premium to value firms across each

size quintile with the average monthly return of the five VMG portfolios being 1.3%. This result

is consistent for both equal and value-weighted returns and indicates that size has effectively been

neutralized across the portfolios within each size quintile. The highest value premium is observed

in size quintile three with the lowest occurring in the small quintile. This strong premium to value

stocks is consistent with previous Australian studies of Gaunt (2004); Gharghori, Chan, and Faff

(2006) and is larger than overseas evidence, where the premium is usually around 0.55% in the US

(Fama and French, 1993, 1996) when portfolio and returns are calculated in a similar way.

Table 3 also reports the standard deviation of returns for each of the portfolios. These results

indicate that the five different book to market portfolios have similar volatility in returns within the

big quintile. As we move down the the size quintiles the results start to change with the growth

portfolio having a higher volatility compared to the value portfolio. There is also strong evidence

of higher volatility in returns as size declines. Among the various arguments for this finding is the

observation that small stocks typically have a lower price per share. This implies that small stocks

are more likely to display higher volatility because a small change in price leads to a larger percentage

change.

values.

15

Tab

le3

Ret

urn

sto

25si

ze-b

ook

tom

arke

tpor

tfol

ios

Pre

sent

edar

eth

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lym

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(VM

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whe

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(%)

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alue

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-0.2

340.

644

0.79

90.

777

1.18

11.

415

-4.7

2**

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5**

2-0

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0.09

90.

152

0.26

40.

261

1.21

5-3

.75

**-2

.54

*

3-2

.252

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78-0

.314

0.00

40.

030

2.28

2-7

.69

**-4

.33

**

4-1

.361

-0.3

44-0

.558

-0.0

53-0

.360

1.00

0-2

.46

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l0.

290

0.44

01.

015

0.69

30.

946

0.65

6-1

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4

F-s

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3.66

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2.71

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23

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G

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6.48

55.

138

4.78

45.

217

5.89

15.

194

26.

828

5.20

05.

181

4.84

16.

497

5.61

5

37.

914

6.59

65.

701

5.13

96.

268

5.13

7

410

.341

8.38

27.

375

6.65

97.

246

7.04

4

Smal

l10

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10.1

549.

140

8.06

77.

800

6.21

1

16

Tab

le3

(con

tinu

ed)

Pan

elB

:V

alue-

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ghte

dR

eturn

s

Mea

nM

onth

lyRet

urns

(%)

Gro

wth

23

4V

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VM

GF

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0.22

40.

653

0.83

40.

913

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11.

097

-2.9

3**

-2.4

7*

2-0

.877

0.10

50.

171

0.29

30.

352

1.23

0-3

.94

**-2

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**

3-2

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26-0

.282

0.07

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049

2.27

8-7

.74

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**

4-1

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-0.3

04-0

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13-0

.366

1.06

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.63

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0.08

80.

723

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569

0.79

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F-s

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6.71

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Big

5.62

75.

535

5.24

76.

102

6.83

06.

495

26.

628

5.22

45.

165

4.77

86.

070

5.40

8

37.

809

6.33

35.

441

4.95

36.

164

5.09

9

410

.103

8.18

57.

210

6.40

57.

231

7.01

3

Smal

l10

.657

10.3

619.

218

8.16

47.

856

6.61

9

17

3.3 Testing Framework

The CAPM can be expressed as:

E(ri) = βi[E(rm)], (1)

while Fama and French (1993) proposes the following three-factor model;

E(ri) = βi[E(rm)] + siE(SMB) + hiE(HML). (2)

Where E(ri) is the expected excess return on asset i, E(rm) is the expected excess return on the

market portfolio, E(SMB) is the expected return on the mimicking portfolio for the size factor and

E(HML) is the expected return on the mimicking portfolio for the book to market factor. These

models can be converted into their empirical counterpart where expected returns are replaced by ex

post versions of the market portfolios and Fama and French factors which takes the form;

rit = αi + βirmt + εit i = 1, · · · , N, (3)

and

rit = αi + βirmt + siSMBt + hiHMLt + eit i = 1, · · · , N. (4)

Where rit is the excess return on asset i in time t. rmt is the excess return of the market. SMBt

is the return on the mimicking size portfolio and HMLt is the return on the mimicking book to

market portfolio. αi, βi, si and hi are regression coefficients, εit and eit are the error terms and N

is the number of test assets. Equation 3 indicates that the CAPM is a restricted three-factor model

where the restrictions are si = hi = 0.

While there are a number of different ways to test the CAPM and the Fama-French three factor

model this study will use the generalised method of moments (GMM) technique. This method has

several advantages; first, it relaxes the assumption that excess returns are independent and identically

distributed (i.i.d.) normal. Second, it allows all asset parameters to be estimated simultaneously.

Third, we can derive a statistic to test that all the pricing errors are jointly equal to zero, which

is equivalent to the Gibbons, Ross, and Shanken (1989) (GRS ) statistic but allows the errors to be

cross-correlated, autocorrelated and heteroskedastic. Fourth, we can utilise the D-statistic of Newey

and West (1987) to test whether the restriction si = hi = 0 is true.4

In the case of the CAPM empirical model (equation 3) there are 2N sample moment conditions.

First, that the mean regression error term is equal to zero,

E[εit] = 0 ∀i = 1, · · · , N.

Second, that the regression error is orthogonal to the market return,

E[εitrmt] = 0 ∀i = 1, · · · , N.

4For further details on the GMM technique and its uses in testing asset pricing models see Cochrane (2005).

18

As the system has 2N unknown parameters the system is just-identified and the estimated parameters

are equivalent to their ordinary least square (OLS) counterparts.

Similarly, in the Fama and French three factor model (equation 4) there are 4N sample moment

conditions. The first 2N are identical to the CAPM moment conditions. The final two moment

conditions are that the SMB and HML factors are orthogonal to the regression error term:

E[eitSMBt] = 0 ∀i = 1, · · · , N

E[eitHMLt] = 0 ∀i = 1, · · · , N.

As the CAPM is a restricted three-factor model with the restriction si = hi = 0, this restriction can

be tested by forming the following D-statistic which has a χ2 distribution;

TgT (φ̂r)′S−1gT (φ̂r)− TgT (φ̂u)′S−1gT (φ̂u) ∼ χ24N−2N . (5)

Where gT (φ̂r) and gT (φ̂u) are the empirical moment condition vectors for the restricted and unre-

stricted model respectively, S−1 is the optimal weighting matrix and T is the number of observations.

A complete model of excess returns should also result in the pricing errors to be equal to zero. This

can be tested using

α̂′var(α̂)−1α̂ ∼ χ2N , (6)

where α̂ is the estimated intercept and var(α̂)−1 is the variance covariance matrix of the estimated

intercept terms.5

4 Construction and Attributes of the Fama and French Factors

An essential component of testing and analysing the Fama and French three-factor model is the

construction of the SMB and HML factors. The factor SMB captures the premium that small stocks

earn over large stocks, while HML captures the premium that value stocks earn over growth stocks.

It is still debatable what these premiums are capturing, with the two major arguments being that

they are proxies for underlying economic risk (Fama and French, 1995, 1996, 2006, 2007), or that they

are capturing a behavioural bias in investors (Daniel and Titman, 1997; Daniel, Titman, and Wei,

2001; Durand, Juricev, and Smith, 2007; Lakonishok, Shleifer, and Vishny, 1994). Whatever they

are capturing, the size and value premium are proxies for economic risk or behavioural bias and the

fluctuations in the premiums allows us to better understand how assets are priced. As an example,

when HML increases investors will demand a higher return on assets with a strong weighting on the

HML factor. As structures, breadth and depth of markets vary around the world, manifestations

of the size and value premium could also occur in different ways. Hence, when creating the factors5For full details of this test statistic see Cochrane (2005) pp 231-235.

19

Table 4

Portfolios used in the formation of SMB and HML in the USA market

This table demonstrates the interaction of the two size portfolios and three book to market portfolio

lead to the formation of six size book to market portfolios

Book to Market portfolio

30% 40% 30%

50% big big big

Size growth middle value

portfolio 50% small small small

growth middle value

we need to take into account these differences and tailor the factors accordingly. We also need to

remember that fluctuations in these factors rather than the absolute value of the factors are the

major determinant in explaining the cross-section of asset returns.

Fama and French (1993) propose that SMB and HML be formed by ranking all stocks on the New

York Stock Exchange (NYSE) by market capitalisation and assigning all stocks (including those listed

on the NASDAQ stock market and American Stock Exchange (AMEX)) with a market capitalisation

higher than the median NYSE market capitalisation into the big portfolio and all other stocks into

a small portfolio. Independently all NYSE stocks are ranked on book to market values. Any stock

containing a negative book to market value are excluded. The first 30% of stocks with the lowest

book to market ratios are then assigned to the growth portfolio. The next 40% of stocks based on

book to market value are assigned to the middle portfolio and finally the last 30% of stocks are

assigned to the value portfolio. This leads to all stocks being assigned to one of two size portfolio

and one of three book to market portfolio giving a total of six portfolios (see Table 4 for details).

These portfolio are held for twelve months and returns are value-weighted. After twelve months the

process is repeated. The SMB factor is then formed by calculating the average return of the three

small portfolios (small growth, small middle and small value) and subtracting the average of the

three big portfolios (big growth, big middle and big value). Similarly the HML factor is formed by

calculating the average return of the two value portfolios (big value and small value) and subtracting

the average return of the two growth portfolios (big growth and small growth). This methodology has

subsequently been used in countless studies including Campbell (1996); Campbell and Vuolteenaho

(2004); Carhart (1997); Chan, Jegadeesh, and Lakonishok (1995, 1996); Conrad and Kaul (1998);

Daniel and Titman (1997); Daniel, Titman, and Wei (2001); Davies (1994); Fama and French (1995,

1996, 1998, 2006, 2007); Jagannathan and Wang (1996); Jegadeesh and Titman (2002); Kim (1995,

1997); LaPorta, Lakonishok, Shleifer, and Vishny (1997); Lettau and Ludvigson (2001) and Zhang

(2005)

20

To determine whether this is an ideal method for capturing the size and value premium in Australia

we need to understand where the size and value premium occurs in Australia. Table 5 reports the

mean return, market capitalisation and book to market value of portfolios formed on size and book

to market values in Australia. The ten size portfolios are formed by ranking all stocks by market

capitalisation at the end of December each year and assigning an equal number of companies into one

of ten size portfolio. Portfolio 1 contains the 10% of stocks with the largest market capitalisation,

portfolio 2 contains the next 10% of stocks (i.e. those ranked between 10% and 20%) as determined

by market capitalistion. This process continues for all the portfolios, with portfolio 10 containing

the 10% of all stocks with the smallest market capitalisation. A similar process is followed for book

to market portfolios. First all stocks are ranked by their book to market value as at December each

year. Then each stock is assigned to one of ten book to market portfolio with the first 10% of stocks

with the lowest book to market value being assigned to portfolio 1, the next 10% of stocks are then

assigned to portfolio 2. This process continues for all the portfolios with portfolio 10 containing the

last 10% of stocks with the highest book to market values. The portfolios are then held for twelve

months and value-weighted logarithmic returns calculated each month. The process is repeated each

year resulting in a series of 300 monthly returns for ten size portfolios and ten book to market

portfolios covering the period January 1982 to December 2006.

Table 5 highlights a number of important issues that we must take into consideration when forming

factors that attempt to capture the premium to small and value companies. First, as we move

from the largest stocks to the smallest stock the returns initially decline, reaching a minimum for

portfolios 5 through 7 and then increases until we reach the smallest decile. If we take the difference

between the small and big portfolio there is a premium of approximately 0.52% per month. This

U-shape pattern in average returns is in contrast to the US market where there is a steady increase

in returns from the largest to smallest portfolio when portfolios are formed on size (Banz, 1981;

Fama and French, 1992; Reinganum, 1981). Second, returns to portfolios formed on book to market

ratios indicate that the returns for growth stocks are lowest and it increases as we move towards

value stocks. The only anomaly from this pattern is portfolio 10 which has a lower return than

portfolio 9. If we take the difference between portfolio 10 and portfolio 1 we find a value premium

of 0.73% per month. This result is more consistent with previous evidence from the US (Barber and

Lyon, 1997; Fama and French, 1992). Third, there is evidence that the size and value premiums may

be correlated with the smallest stocks on average having a higher book to market value. This can

be seen with size portfolio 10 having the highest book to market value of 3.1 and book to market

portfolio 10 which has the lowest market capitalisation of $62.2 million. This is consistent with

overseas evidence that small companies generally have higher book to market values compared to

big companies (Fama and French, 1992).

Results from Table 5 indicate that although small stocks earn a premium, this premium is not

linear. This would indicate that if we formed the factors using the original Fama and French (1993)

21

Table 5

10 size and book to market portfolios

The table reports the monthly mean return, market capitalisation and book to market value of ten

size and ten book to market portfolios in Australia for the period January 1982 to December 2006.

The size portfolios are formed by ranking all stocks by market capitalisation and assigning each

stock to one of ten size portfolio with each portfolio containing an equal number of stocks. Portfolio

1 contains the first 10% of stocks with the biggest market capitalisation, while portfolio 10 contains

the last 10% of stocks with the smallest market capitalisation. Similarly, all stocks are ranked by

their book to market value and assigned to one of ten book to market portfolio. Portfolio 1 contains

the first 10% of stocks with the lowest book to market values, while portfolio 10 contains the last

10% of stocks which have the highest book to market values.

Size Portfolios Book to Market Portfolios

Portfolio Returns Market Book to Returns Market Book to

Capitalisation Market Capitalisation Market

($ millions) Value ($ millions) Value

1 0.738 3,144.1 0.722 -0.305 437.0 0.189

2 0.362 262.0 0.851 0.394 709.7 0.390

3 0.010 88.8 0.961 0.528 718.2 0.534

4 -0.106 42.2 1.843 0.716 530.6 0.669

5 -0.664 23.4 1.460 0.839 463.2 0.812

6 -0.569 14.0 1.375 0.730 314.8 0.968

7 -0.619 8.9 1.279 0.852 207.4 1.161

8 -0.497 5.6 1.510 0.726 145.2 1.428

9 -0.011 3.4 1.634 1.101 88.4 1.870

10 1.256 1.6 3.093 0.424 62.2 6.524

22

methodology we may not capture the size premium. Whether this affects our results will depend on

how the factor fluctuates. If it fluctuates in a similar way to the size premium and the underlying

economic phenomenon then even though the premium is not on average the same, we will still

be able to better understand how the cross-section of assets are priced. Taking into consideration

the underlying regularities in the Australian market three different methods are used to form the

factors. First, we follow the methodology of Fama and French (1993) except that breakpoints for

portfolio allocation is determine by the Australian market and portfolios are formed in December.

The factors formed using this methodology are called SMB 2x3 and HML 2x3. Second, following

previous Australian studies and some overseas studies (Durack, Durand, and Maller, 2004; Durand,

Limkriangkrai, and Smith, 2006a; Liew and Vassalou, 2000) we form SMB and HML in the following

manner. Each December we rank all stock by their market capitalisation and assign them to one of

three size portfolios. The first portfolio (big) contains the first 30% of stocks and contains the biggest

stocks. The middle portfolio contains the next 40% of stocks ranked by market capitalisation. Finally

the small portfolio contains the last 30% of stock and contains the smallest stocks. Independently

all stocks are ranked by their book to market value and assigned to one of three book to market

portfolios. The first 30% of stocks are assigned to the growth portfolio which contains stocks with

the lowest book to market values. The middle portfolio contains the next 40% of stocks ranked

by their book to market value. The last 30% of stocks are assigned to the value portfolio which

contains the stocks with the highest book to market value. This leads to the formation of nine

portfolios as outline in Panel A of Table 6. Each portfolio is then held for 12 months and value-

weighted logarithmic returns are calculated. At the end of 12 months the process is repeated. SMB

3x3 is formed by taking the average of the three small portfolios (small growth, small middle and

small value) and subtracting the average return of the three big portfolios (big growth, big middle

and big value) each month. Similarly HML 3x3 is formed as the average return of the three value

portfolios (large value, middle value and small value) less the average of the three growth portfolios

(large growth, middle growth and small growth). Third, in December we rank all stocks by market

capitalisation and assign each stock to one of five size portfolio. The big portfolio contains the first

20% of stocks with the largest market capitalisation. Portfolio 2 contains the next 20% of stocks by

market capitalisation. This process continues with the last portfolio (small) containing the last 20%

of stocks which have the smallest market capitalisation. As with the previous two methodologies

we independently assign each stock to one of three book to market portfolio. As with the previous

methodologies the 30% of stocks with the lowest book to market value are assigned to the growth

portfolio, the next 40% of stocks are assigned to the middle portfolio and the final 30% of stocks are

assigned to the value portfolio. This leads to each stock being assigned to one of fifteen portfolios

as outlined in Panel B of Table 6. Each portfolio is then held for 12 months and value-weighted

logarithmic returns are calculated. At the end of 12 months the process is repeated. SMB 5x3 is

formed by taking the average of the three small portfolios (small growth, small middle and small

value) and subtracting the average return of the three big portfolios (big growth, big middle and big

23

value) each month. Similarly HML 5x3 is formed as the average return of the five value portfolios

(large value, 2 value, 3 value, 4 value and small value) less the average of the five growth portfolios

(large growth, 2 growth, 3 growth, 4 growth and small growth).

Panel A of Table 7 reports the average monthly returns of the 3 different methods of constructing

the factors in Australia. We also construct one further SMB factor called SMB 10. SMB 10 is

formed by ranking all stocks each December by market capitalisation and assigning each stock into

one of ten size portfolio where each portfolio contains an equal number of stocks. Portfolio 1 (big)

contains the 10% of stocks with the largest market capitalisation and portfolio 10 (small) contains

the 10% of all stocks with the smallest market capitalisation. SMB 10 is then calculated as the

value-weighted logarithmic return of the small portfolio less the value-weighted logarithmic return of

the big portfolio. We also report the average monthly return to the market risk premium in Australia

(MRP) which is calculated as the value-weighted monthly market return less the 13-week treasury

note yield with both extracted from the AGSM-CRIF price relative file, the US market risk premium

(USMRP), the US SMB factor (USSMB) and the US HML factor (USHML). The US market risk

premium and factors are obtained directly from the data library in Ken French’s webpage.6 Panel

B of Table 7 also reports the correlation coefficients between each of the factors.

6The address of the website is http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data library.html.

24

Table 6

Alternative Methods to forming SMB and HML

This table demonstrates the alternative methods of assigning stocks to either one of nine size book

to market portfolios (Panel A) or one of fifteen size book to market portfolios (Panel B). These

assignments are used to form various SMB and HML factors

Panel A: 3x3 portfolio formation

Book to Market portfolio

30% 40% 30%

30% big big big

growth middle value

Size 40% middle middle middle

portfolio growth middle value

30% small small small

growth middle value

Panel B: 5x3 portfolio formation

Book to Market portfolio

30% 40% 30%

20% big big big

growth middle value

20% 2 2 2

growth middle value

Size 20% 3 3 3

portfolio growth middle value

20% 4 4 4

growth middle value

20% small small small

growth middle value

25

Tab

le7

Ret

urn

sto

Fac

tors

Pan

elA

pres

ents

the

mea

n,m

edia

n,st

anda

rdde

viat

ion

t-st

atis

tic

and

z-va

lue

ofm

onth

lyva

lue-

wei

ghte

dre

turn

sof

diffe

rent

HM

Lan

dSM

B

fact

ors

for

the

peri

od19

82to

2006

.T

heco

rrel

atio

nco

effici

ents

betw

een

each

fact

oris

repo

rtin

Pan

elB

.SM

B2x

3an

dH

ML

2x3

was

form

ed

follo

win

gth

em

etho

dof

Fam

aan

dFr

ench

(199

3).

SMB

3x3

and

HM

L3x

3is

form

edby

assi

gnin

gea

chas

set

into

one

ofth

ree

size

port

folio

and

one

ofth

ree

book

tom

arke

tpo

rtfo

lio.

SMB

3x3

isth

enfo

rmed

asth

eav

erag

ere

turn

ofth

eth

ree

smal

lpor

tfol

ios

less

the

aver

age

retu

rn

ofth

eth

ree

big

port

folio

s.H

ML

3x3

isth

enfo

rmed

asth

eav

erag

ere

turn

ofth

eth

ree

valu

epo

rtfo

lios

less

the

aver

age

retu

rnof

the

thre

e

grow

thpo

rtfo

lios.

SMB

5x3

and

HM

L5x

3is

form

edby

assi

gnin

gea

chas

set

into

one

offiv

esi

zepo

rtfo

lioan

don

eof

thre

ebo

okto

mar

ket

port

folio

.SM

B5x

3is

then

form

edas

the

aver

age

retu

rnof

the

thre

esm

allp

ortf

olio

sle

ssth

eav

erag

ere

turn

ofth

eth

ree

big

port

folio

s.H

ML

5x3

isfo

rmed

asth

eav

erag

ere

turn

ofth

efiv

eva

lue

port

folio

sle

ssth

eav

erag

eof

the

five

grow

thpo

rtfo

lios.

SMB

10is

form

edby

rank

ing

alls

tock

sby

mar

ket

capi

talis

atio

nan

das

sign

ing

each

stoc

kto

one

ofte

nsi

zepo

rtfo

lios

whe

reea

chpo

rtfo

lioha

san

equa

lnum

ber

ofst

ocks

.

The

big

port

folio

cont

ains

the

10%

ofst

ocks

wit

hth

ela

rges

tm

arke

tca

pita

lisat

ion,

whi

leth

esm

allp

ortf

olio

cont

ains

the

10%

ofst

ocks

wit

h

the

low

est

mar

ket

capi

talis

atio

n.SM

B10

isfo

rmed

asth

ere

turn

ofth

esm

allpo

rtfo

liole

ssth

ere

turn

ofth

ebi

gpo

rtfo

lio.

We

also

repo

rt

the

aver

age

retu

rnof

the

mar

ket

risk

prem

ium

(MR

P)

inA

ustr

alia

,whi

chis

calc

ulat

edas

the

valu

e-w

eigh

ted

mon

thly

mar

ket

retu

rnle

ssth

e

13-w

eek

trea

sury

note

yiel

dw

ith

both

bein

gex

trac

ted

from

the

AG

SM-C

RIF

pric

ere

lati

vefil

ean

dth

eU

Sm

arke

tri

skpr

emiu

m(U

SMR

P),

US

HM

L(U

SHM

L)

and

US

SMB

(USS

MB

)w

hich

was

sour

ced

from

Ken

Fren

ch’s

web

page

.

**an

d*

deno

tesi

gnifi

canc

eat

the

1%an

d5%

leve

lsre

spec

tive

ly.

Pan

elA

:Ret

urns

Mea

nM

edia

nSt

anda

rdt-

stat

isti

cz-

valu

e

Dev

iati

on

HM

L2x

30.

916

0.85

23.

362

4.72

**-4

.94

**

HM

L3x

30.

867

0.97

53.

203

4.69

**-4

.93

**

HM

L5x

30.

959

0.66

73.

044

5.46

**-5

.41

**

SMB

2x3

-1.2

33-1

.224

5.12

7-4

.16

**-4

.42

**

SMB

3x3

-0.9

10-1

.235

6.67

7-2

.36

*-3

.14

**

SMB

5x3

-0.4

86-1

.066

7.40

3-1

.14

-1.9

8*

26

Tab

le7

(con

tinu

ed)

SMB

100.

518

-0.0

957.

751

1.16

-0.5

3

MR

P0.

392

0.96

64.

907

1.38

-2.9

5**

USM

RP

0.67

81.

045

4.34

32.

70**

-3.4

4**

USS

MB

0.08

6-0

.125

3.27

90.

46-0

.02

USH

ML

0.46

20.

425

3.11

02.

57*

-2.6

9**

Pan

elB:C

orre

lation

coeffi

cien

t

HM

L2x

3H

ML

3x3

HM

L5x

3SM

B2x

3SM

B3x

3SM

B5x

3SM

B10

MR

PU

SMR

PU

SSM

BU

SHM

L

HM

L2x

31.

000

HM

L3x

30.

892*

*1.

000

HM

L5x

30.

862*

*0.

927*

*1.

000

SMB

2x3

-0.3

20**

-0.4

07**

-0.4

62**

1.00

0

SMB

3x3

-0.3

13**

-0.4

31**

-0.4

85**

0.96

5**

1.00

0

SMB

5x3

-0.2

92**

-0.3

95**

-0.4

66**

0.94

3**

0.97

7**

1.00

0

SMB

10-0

.128

*-0

.251

**-0

.326

**0.

885*

*0.

911*

*0.

922*

*1.

000

MR

P-0

.209

**-0

.182

**-0

.266

**-0

.083

-0.0

69-0

.086

-0.1

21*

1.00

0

USM

RP

-0.1

36*

-0.1

46*

-0.1

80**

-0.0

66-0

.053

-0.0

66-0

.069

0.54

0**

1.00

0

USS

MB

-0.0

79-0

.084

-0.1

29*

0.06

80.

058

0.04

30.

058

0.23

7**

0.19

4**

1.00

0

USH

ML

0.17

9**

0.19

2**

0.19

9**

0.02

2-0

.003

0.02

30.

052

-0.1

78**

-0.5

06**

-0.4

28**

1.00

0

27

Starting with the HML factors we see that the three methodologies produce similar average monthly

returns with the highest being HML 5x3 with 0.959% per month and the lowest being HML 3x3 with

0.867% per month. This average monthly return is statistically different from zero with the average

t-statistic being 4.96 and is similar to the return reported in Gharghori, Chan, and Faff (2006)

and citetHalliwelletal:1999:ARJ. The average monthly return for the USHML factor is significantly

lower with a return of 0.462% per month. The extremely large HML factor indicates that the value

premium is not only statistically significant but economically significant in the Australia equities

market. The results also indicate that the standard deviation of returns of the three Australian

HML factors and USHML are very similar with the Australian factors having an average of 3.203%

and USHML having a standard deviation of 3.110%. Turning to the correlation coefficients, the

results demonstrate that the three Australian HML factors are highly correlated with an average

correlation coefficient of 0.894. Surprisingly the correlation between the USHML and the Australian

HML factors are quite low with an average correlation of 0.190 although it is still statistically

significant. This result would indicate that to properly test the Fama and French (1993) model

in Australia that factors formed on Australia information is essential. The results taken together

suggest that the three methods of forming the HML factor in Australia produce very similar results

and our choice of methodology will have little impact on the results. To further examine whether

the time-series behaviour of the different formation procedures are similar we calculate the average

monthly return during each year and the average monthly return for each month of the year for the

three HML factors. These results are reported in Figure 2 and 1 respectively. This will also allow

us to check for market seasonalities in the HML factor.

Figure 1 plots the average return each month and indicate that the three formation methodologies

lead to similar result with all three portfolios following a similar trend. Figure 1 also suggest that

there is no evidence of a monthly seasonality in the HML factor. Figure 2 demonstrates that the

three methodologies lead to similar outcomes with all three portfolios having similar average monthly

returns each year. The results demonstrate one clear anomaly during the 25 year period, 1989. In

1989 there is clear evidence of severe underperformance by value stocks with the HML 2x3 factor

earning an average monthly return of -4.98% during the year. HML 3x3 and HML 5x3 also have

extremely large loses at an average of -3.41% and -2.73% per month respectively. We investigated

these extreme negative returns further and two important features surfaced. First, the average book

to market ratio in the value portfolios were substantially higher at the start of 1989 than during the

rest of the sample. For example, the average book to market value for large value and small value

in the 2x3 portfolio formation procedure in December 1988 is 6.57 against an average of 3.36 during

the full period studied. This result suggests that value stocks were under extreme financial distress

leading into 1989. This is further confirmed by the fact that the percentage of companies delisting

during the year nearly doubles. Second, the extreme negative result is being driven by a few large

value companies suffering extremely large loses during the year. This includes one company suffering

28

-2.0

-1.0

0.0

1.0

2.0

January February March April May June July August September October November December

Month

Av

era

ge

Re

turn

(%

)

HML 2x3

HML 3x3

HML 5x3

Figure 1

Average Monthly Return for various HML factors

monthly returns of -101.2%, -86.0%, -58.0% and -32.5%, which had a value-weight of 5.55%.7 While

another company with a value-weight of 17.74% had monthly returns of -64.19%, -32.85%, -19.63%

and -12.72%. The extreme negative return being driven by a few large companies is confirmed

by calculating equal-weighted logarithmic returns for 1989 and the average return for HML 2x3

increases to -1.91% HML 3x3 to -1.95% HML 5x3 to -1.78%. This result suggests that value stocks

did particularly badly in 1989 and were in severe distress leading into to 1989, but the extremely

negative number is being driven by a few companies. As such to test the robustness of our results we

should include a 1989 dummy variable in the regressions. Overall, the results are supportive of the

conclusion that the three methods produce similar time-series behaviour in the HML factor indicate

the exact formation technique will be unimportant.

Turning to the SMB factors. The first thing that we have found is that the average monthly return

for the three methodologies is negative. The SMB 2x3 factor has the lowest average monthly return

of -1.23%, which is statistically significant, while SMB 5x3 has the highest at -0.486% which is

statistically insignificant. In contrast the SMB 10 factor has a positive average monthly return of

0.518%, although it is statistically insignificant. These results are not surprising given the results

reported in Table 5, which shows a non-linear relationship between size and average returns in the7As could be expected this company was delisted during the year of 1989

29

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

Date

Av

era

ge

Mo

nth

ly R

etu

rn (

%)

HML 2x3 HML 3x3

HML 5x3

Figure 2

Average Monthly Return for various HML factors each year

Australian equity market. It is interesting that the USSMB also has a very low average monthly

return of 0.086% which is insignificantly different from zero. These results support recent evidence

that the size premium has been declining in equity markets in recent years (Barber and Lyon,

1997; Dimson and Paul, 1999), with the only evidence of the size premium in Australia being

extremely small stocks that have extremely low liquidity. The SMB factors in Australia also have a

standard deviation that is approximately double the HML factors and 37% larger than the market

risk premium. As expected, the standard deviation of SMB 10 and SMB 5x3 are the highest with

7.75% and 7.4% respectively, while SMB 2x3 has the lowest standard deviation of 5.13%. Among

the various arguments for this finding is the observation that small stocks typically have a lower

price per share. This implies that small stocks are more likely to display higher volatility because

a small change in price leads to a larger percentage change. This argument is supported by our

results which demonstrate that as we increase the number of divisions in the data, higher standard

deviations occur. Turning to the correlation coefficients, the results indicate that the four Australian

SMB factors are highly correlated with each other with an average correlation coefficient of 0.934. As

with the HML factor, the Australian SMB factors have a very low correlation with the USSMB with

an average correlation coefficient of 0.057. This result confirms that factors formed on Australian

information is essential for testing the Fama and French (1993) model.

30

-5.0

-3.0

-1.0

1.0

3.0

5.0

7.0

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

Date

Avera

ge M

on

thly

Retu

rn (

%)

SMB 2x3 SMB 3x3

SMB 5x3 SMB 10

Figure 3

Average Monthly Return for various SMB factors each year

The high correlation coefficients between the four different ways of forming the SMB factor in

Australia suggest that the choice of formation methodology may not influence our results when we

test the Fama and French (1993) model. This is because the fluctuations, rather than the average

monthly return of the factor, is the major determinant in its role in explaining the cross-section

of asset returns. To further analyse this issue and to check for market seasonalities in the SMB

factor we calculate the average monthly return during each year and the average monthly return

for each month of the year for the four SMB factors. These results are reported in Figure 3 and 4

respectively. Figure 3 again demonstrates the high correlation and volatility in returns for the SMB

factor in Australia. Although there are a number of years that have a large negative average return

(including 1988, 1997 and 2001), there are just as many years with very large positive average return

(including 1993, 1996, 1999 and 2003). We therefore conclude there is little evidence of any abnormal

year in the SMB factor. In contrast Figure 4 demonstrates strong seasonalities in the SMB factor

in Australia. The result demonstrates a large negative return in June which is followed by a large

positive return in July. This result is consistent with the tax-loss hypothesis explaining the small

firm effect (Brown, Keim, Kleidon, and Marsh, 1983; Keim, 1983). Unfortunately this can not be the

complete explanation because there is evidence of a strong positive return in January. These results

are consistent with earlier findings on the size premium in Australia (Brown, Keim, Kleidon, and

Marsh, 1983; Durand, Juricev, and Smith, 2007) and suggests that in our empirical test that a June,

31

-7.0

-5.0

-3.0

-1.0

1.0

3.0

5.0

7.0

January February March April May June July August September October November December

Month

Av

era

ge

Re

turn

(%

)

SMB 2x3

SMB 3x3

SMB 5x3

SMB 10

Figure 4

Average Monthly Return for various SMB factors

July and possibly a January dummy variable should be included in robustness checks. Overall, the

time-series behaviour of the four different ways of forming the SMB factor are similar and indicate

that the three methods will have similar explanatory power in explaining the cross-section of asset

returns. We are inclined to support the SMB 5x3 factor because it has the highest average monthly

return and is closest in capturing the size premium in Australia.

The results in Table 7 also indicate that the HML factors and SMB factors have a moderate corre-

lation between them with the average correlation being -0.356. This is similar, although lower, to

the correlation between the USSMB and the USHML which has a correlation of -0.428. This result

suggests that robustness checks that separate out the factors in the regressions may be required. It

also indicates a low correlation between the factors and the MRP in Australia with the correlation

between the Australian HML averaging -0.219 while the SMB and MRP has an average correlation

of -0.090. This suggests that the factors are proxies for economic risk or behaviourial bias which are

independent of the market risk premium.

Results in this section show that the Australian equity markets display different regularities than

their North American cousins. This suggests that the construction of the SMB and HML factor may

need to be tailored to take into account these differences. We propose three different methodologies

to form SMB and HML factors in Australia. The HML factors all demonstrate very similar average

32

monthly returns and are highly correlated with each other thus it would seem that it will not matter

how we form the HML factor in Australia. In contrast, the SMB factors differ substantially in their

average monthly returns, although they are all highly correlated with each other and demonstrate

similar time-series properties. We are inclined to support the SMB 5x3 factor because it has the

highest average monthly return and thus captures the size premium better than the other two

methodolgies. Given this information we believe the most appropriate factors to use in Australia

are the HML 5x3 and SMB 5x3. To test our assumptions we will also use the SMB 2x3 and HML

2x3 in our tests of the Fama and French (1993) model.

5 Results

The results from estimating equation 3 to explain portfolio excess returns are reported in Table

8. For brevity we only report the results using the value-weighted returns.8 As expected, Table 8

indicates that market risk tends to be higher for low book to market portfolios (growth) and decline

as we move toward higher book to market portfolios (value). This result is consistent with Fama and

French (1993) and Gaunt (2004); Halliwell, Heaney, and Sawicki (1999). Contrary to expectation,

the results also indicate that the small portfolios exhibit similar market risk to the big portfolios

and on average the reported β’s are less than one.

If the CAPM explained the returns of the 25 size-book to market portfolios the intercepts should

not be significantly different from zero. Results indicate that the majority of the intercept terms

are statistically different from zero. This result is supported by the GRS statistics being statisti-

cally significant, indicating we should reject the null that all intercepts are jointly equal to zero.

Surprisingly the results suggest little evidence of the size effect with the small portfolios generally

earning an adjusted return less than their equivalent big portfolio, although all the intercept terms

within the small quintile are insignificantly different from zero. This result needs to be considered

with caution because this appears to be a result of the low explanatory power of the model for the

portfolios within the small quintile. This is demonstrated in a number of ways, first, the adjusted R2

of the portfolios within the small quintile averages only 21% compared to the average of 68% for the

five portfolios within the big quintile. Second, the intercept terms are generally larger in absolute

terms for the portfolios within the small quintile compared to the portfolios within big quintile; but

the intercept terms are insignificant for the portfolios within the small quintile but significant for the

portfolios within the big quintile. This result indicates that the variability around the estimates for

the portfolios within the small quintile are substantially larger. It also reinforces the non-linear re-

lationship between size and returns in Australia with the intercept terms of the middle size quintiles

being substantially lower than any of the portfolios within the big or small quintiles.

8The equal-weighted return results are similar and can be obtained from the author upon request.

33

Tab

le8

Reg

ress

ions

resu

lts

from

the

CA

PM

The

tabl

epr

esen

tsth

ere

sult

sfr

omre

gres

sing

the

300

exce

ssm

onth

lyre

turn

sof

each

ofth

e25

size

-boo

kto

mar

ket

port

folio

son

exce

ss

mar

ket

retu

rns.

The

25si

ze-b

ook

tom

arke

tpo

rtfo

lios

are

form

edby

usin

gin

depe

nden

tso

rts

base

don

mar

ket

capi

talis

atio

nan

dbo

okto

mar

ket

valu

esdu

ring

the

peri

od19

82to

2006

.T

hefo

llow

ing

tim

e-se

ries

regr

essi

onis

esti

mat

ed;

r it=

αi+

βir

mt+

ε it

i=

1,···,

N.

Whe

rer i

tis

the

retu

rnon

port

folio

iin

mon

tht

less

the

13w

eek

trea

sury

note

yiel

dan

dr m

tis

the

valu

e-w

eigh

ted

mar

ket

mon

thly

retu

rn

less

the

13w

eek

trea

sury

note

yiel

d.B

oth

the

mar

ket

retu

rnan

dth

e13

wee

ktr

easu

ryno

tyi

eld

are

extr

acte

dfr

omth

eC

RIF

pric

ere

lati

ve

file.

The

syst

emis

esti

mat

edus

ing

the

GM

Mte

chni

que

wit

hth

efo

llow

ing

mom

ent

rest

rict

ions

E[ε

it]=

0,E

[εitr m

t]=

0∀i

=1,···,

N.

The

t-st

atis

tic

for

the

regr

essi

onco

effici

ents

uses

HA

Cst

anda

rder

rors

.T

head

just

edR

2ar

eca

lcul

ated

for

each

equa

tion

inth

esy

stem

.W

e

also

repo

rtth

eG

ibbo

ns,R

oss,

and

Shan

ken

(198

9)(G

RS

)te

stst

atis

tic

and

anad

just

edχ

2st

atis

tic

(see

equa

tion

6)th

atad

just

edth

eG

RS

stat

isti

csfo

rcr

oss-

corr

elat

eder

rors

.

**an

d*

deno

tesi

gnifi

canc

eat

the

1%an

d5%

leve

lsre

spec

tive

ly.

Coeffi

cien

tt-

stat

isti

c

αi

Gro

wth

23

4V

alue

Gro

wth

23

4V

alue

Big

-0.8

620

-0.4

531

-0.2

196

-0.1

612

0.32

23B

ig-5

.19

**-3

.71

**-1

.18

-0.5

90.

79

2-1

.951

0-0

.910

4-0

.841

2-0

.694

8-0

.671

82

-5.5

9**

-3.8

2**

-3.2

3**

-3.1

2**

-1.9

9*

3-3

.325

6-1

.633

8-1

.255

6-0

.871

2-0

.969

63

-7.8

9**

-4.1

7**

-4.1

1**

-2.9

7**

-2.9

1**

4-2

.574

6-1

.359

7-1

.538

5-1

.065

4-1

.409

74

-4.4

1**

-2.7

7**

-3.4

8**

-2.6

4**

-3.3

5**

Smal

l-1

.308

9-0

.959

7-0

.294

3-0

.634

2-0

.441

4Sm

all

-1.9

2-1

.49

-0.5

3-1

.25

-0.9

1

βi

Gro

wth

23

4V

alue

Gro

wth

23

4V

alue

Big

1.01

891.

0699

0.93

730.

9896

0.79

68B

ig25

.00

**42

.34

**14

.66

**17

.74

**9.

98**

20.

9880

0.84

050.

8310

0.76

950.

8611

211

.23

**23

.71

**20

.43

**14

.13

**10

.93

**

31.

0464

0.82

060.

7339

0.65

790.

8466

311

.36

**13

.60

**16

.40

**18

.45

**16

.58

**

41.

1646

0.94

350.

7838

0.67

800.

9125

48.

39**

9.87

**8.

75**

11.2

7**

14.6

0**

34

Tab

le8

(con

tinu

ed)

Smal

l1.

0073

0.92

280.

8441

0.74

690.

8266

Smal

l8.

27**

5.79

**7.

24**

7.53

**12

.57

**

Adj

R2

Gro

wth

23

4V

alue

Big

0.78

840.

8943

0.76

040.

6313

0.32

24

20.

5333

0.61

650.

6149

0.61

040.

4738

30.

4289

0.40

000.

4308

0.41

510.

4445

40.

3164

0.31

620.

2807

0.26

570.

3763

Smal

l0.

2114

0.18

760.

1985

0.19

720.

2625

GR

Sχ

2

11.0

3**

269.

80**

35

Consistent with Fama and French (1993); Gaunt (2004) and Halliwell, Heaney, and Sawicki (1999)

there is evidence of abnormal returns monotonically increasing from the lowest book to market

portfolios (growth) to the highest book to market portfolios (value). This result is consistent across

all five size quintiles and reinforces the evidence of a strong value premium in Australia. Overall the

explanatory power of the CAPM is relatively low with the average R2 of the 25 equations within the

system being 43.9%. The model particularly struggles to explain the returns of the portfolios within

the value quintile, and portfolios within the small quintile.

Table 9 presents the estimates from estimating equation 4 when SMB 2x3 and HML 2x3 are used.

The results now indicate a strong abnormal performance is present for small firms, even after the

effects of SMB and HML are taken into account, with a strong non-linearity still present in the size-

effect. This is demonstrated with the average intercept of the portfolios within the big quintile being

slightly negative. As we move down the size quintile the average intercepts declines in value and

then increases as we reach the portfolios within the small quintile where the intercepts are positive,

though insignificant.

The results also indicate that the value premium has substantially disappeared. This is demonstrated

by similar intercepts for the growth and value portfolios within each size quintile, e.g. small growth

having an intercept 0.46 while small value has an intercept of 0.45. This suggests that the value

premium is now being captured by the HML factor. This is supported by evidence in Table 9 that

the HML factor does possess explanatory power, particularly for the portfolios with high average

book to market values (portfolio 3, 4 and value). Contrary to Halliwell, Heaney, and Sawicki (1999)

and the mixed evidence in Gaunt (2004) this evidence is the strongest, so far in Australia, that HML

possesses explanatory power. As expected, the results indicate a linear relationship between HML

and book to market values, with growth portfolios having a negative or very low loading and as we

move towards value portfolios this loading steadily increases.

Consistent with Fama and French (1993, 1996); Gaunt (2004) and Halliwell, Heaney, and Sawicki

(1999) there is evidence of a monotonic relationship between size and the SMB factor. This is

demonstrated by the steady increase in loading on the SMB factor as we move from the big to small

size quintile. There is also some evidence of an increased loading on SMB as we move from value to

growth portfolios. These results all indicate that SMB is a very important factor in the Australian

market.

36

Tab

le9

Reg

ress

ions

resu

lts

from

the

thre

efa

ctor

model

The

tabl

epr

esen

tsth

ere

sult

sfr

omre

gres

sing

the

300

exce

ssm

onth

lyre

turn

sof

each

ofth

e25

size

-boo

kto

mar

ket

port

folio

son

exce

ssm

arke

tre

turn

s.

The

25si

ze-b

ook

tom

arke

tpo

rtfo

lios

are

form

edby

usin

gin

depe

nden

tso

rts

base

don

mar

ket

capi

talis

atio

nan

dbo

okto

mar

ket

valu

esdu

ring

the

peri

od

1982

to20

06.

The

follo

win

gti

me-

seri

esre

gres

sion

ises

tim

ated

r it=

αi+

βir

mt+

s iS

MB

t+

hiH

ML

t+

e it

Whe

rer i

tis

the

retu

rnon

port

folio

iin

mon

tht

less

the

13w

eek

trea

sury

note

yiel

d,r m

tis

the

valu

e-w

eigh

ted

mar

ket

mon

thly

retu

rnle

ssth

e13

wee

k

trea

sury

note

yiel

d.S

MB

tis

the

retu

rnon

the

mim

icki

ngsi

zepo

rtfo

lioan

dH

ML

tis

the

retu

rnon

the

mim

icki

ngbo

okto

mar

ket

port

folio

.B

oth

mim

icki

ngpo

rtfo

lios

are

form

edus

ing

two

size

and

thre

ebo

okto

mar

ket

port

folio

split

s.T

hesy

stem

ises

tim

ated

usin

gth

eG

MM

tech

niqu

ew

ith

the

follo

win

gm

omen

tco

ndit

ions

;E

[εit]=

0,E

[εitr m

t]=

0,E

[eitS

MB

t]=

0,E

[eitH

ML

t]=

0∀i

=1,···,

N.T

het-

stat

isti

cfo

rth

ere

gres

sion

coeffi

cien

ts

uses

HA

Cst

anda

rder

rors

.T

head

just

edR

2ar

eca

lcul

ated

for

each

equa

tion

inth

esy

stem

.W

eal

sore

port

the

Gib

bons

,R

oss,

and

Shan

ken

(198

9)

(GR

S)

test

stat

isti

c,an

adju

sted

χ2

stat

isti

c(s

eeeq

uati

on6)

that

adju

sted

the

GR

Sst

atis

tics

for

cros

s-co

rrel

ated

erro

rsan

dth

eN

ewey

and

Wes

t(1

987)

D-s

tati

stic

.

**an

d*

deno

tesi

gnifi

canc

eat

the

1%an

d5%

leve

lsre

spec

tive

ly.

Coeffi

cien

tt-

stat

isti

c

αi

Gro

wth

23

4V

alue

Gro

wth

23

4V

alue

Big

-0.5

943

-0.4

557

-0.2

489

-0.6

243

-0.5

119

Big

-3.2

7**

-3.1

4**

-1.0

1-2

.10

*-1

.01

2-1

.248

8-0

.620

8-0

.633

9-0

.631

5-0

.703

12

-3.9

8**

-3.0

2**

-2.6

2**

-2.5

7*

-1.8

7

3-2

.181

1-0

.828

7-0

.732

1-0

.530

0-0

.582

43

-7.3

1**

-3.2

8**

-3.0

9**

-2.4

6*

-2.5

2*

4-0

.917

9-0

.160

7-0

.572

4-0

.363

5-0

.958

64

-2.3

1*

-0.5

0-2

.01

*-1

.89

-3.8

4**

Smal

l0.

4645

0.68

961.

0620

0.43

120.

4528

Smal

l1.

121.

593.

07**

1.34

1.75

βi

Gro

wth

23

4V

alue

Gro

wth

23

4V

alue

Big

0.95

551.

0520

0.94

841.

0709

0.91

81B

ig24

.25

**34

.35

**12

.04

**22

.96

**5.

97**

21.

0281

0.90

790.

8920

0.83

200.

9811

214

.40

**27

.68

**19

.43

**14

.48

**13

.60

**

31.

1094

0.89

880.

8180

0.75

890.

9807

320

.07

**20

.54

**16

.62

**23

.41

**21

.73

**

41.

2653

1.05

080.

9132

0.82

791.

1056

414

.12

**15

.33

**12

.51

**20

.23

**21

.80

**

Smal

l1.

1488

1.06

301.

0114

0.90

431.

0120

Smal

l15

.06

**9.

08**

10.9

2**

11.3

6**

21.9

9**

37

Tab

le9

(con

tinu

ed)

s iG

row

th2

34

Val

ueG

row

th2

34

Val

ue

Big

-0.0

909

-0.0

698

0.02

570.

0499

-0.0

059

Big

-1.9

2-2

.98

**0.

580.

86-0

.06

20.

5464

0.41

870.

3483

0.27

310.

4389

29.

29**

8.01

**6.

28**

5.36

**4.

71**

30.

8812

0.74

900.

6137

0.57

550.

7270

313

.81

**14

.59

**12

.76

**12

.24

**11

.26

**

41.

3120

1.08

041.

0338

0.96

360.

9874

414

.89

**18

.10

**18

.02

**19

.74

**12

.94

**

Smal

l1.

5323

1.45

781.

3966

1.19

611.

2063

Smal

l18

.93

**14

.91

**14

.88

**12

.07

**18

.60

**

hi

Gro

wth

23

4V

alue

Gro

wth

23

4V

alue

Big

-0.3

874

-0.0

834

0.06

190.

5379

0.85

09B

ig-4

.51

**-2

.07

*0.

885.

04**

3.18

**

2-0

.048

50.

2185

0.21

640.

2718

0.57

362

-0.4

73.

25**

2.60

**4.

06**

5.06

**

3-0

.090

50.

0956

0.21

840.

3589

0.49

853

-0.8

81.

323.

01**

5.32

**5.

34**

4-0

.086

00.

0992

0.28

120.

4666

0.75

384

-0.4

70.

982.

46*

6.66

**6.

13**

Smal

l0.

0656

0.10

140.

3273

0.37

930.

5681

Smal

l0.

510.

652.

88**

3.59

**6.

47**

Adj

R2

Gro

wth

23

4V

alue

Big

0.83

260.

8980

0.76

030.

7069

0.48

70

20.

7170

0.76

180.

7169

0.68

930.

6226

30.

7765

0.74

450.

7233

0.71

990.

7613

40.

7685

0.75

190.

7664

0.78

380.

8094

Smal

l0.

7388

0.68

730.

7472

0.69

740.

8027

GR

Sχ

2D

-tes

t

8.99

**14

1.28

**15

639*

*

38

As discussed in Section 4 our preferred methodology in forming the SMB and HML factors in

Australia is to use SMB 5x3 and HML 5x3. Table 10 reports the results from estimating equation

4 when SMB 5x3 and HML 5x3 are used. As expected, the results are similar to those reported in

Table 9 and again indicate that the exact methodology in forming the factors is immaterial. The

results demonstrate that there is a monotonic relationship between size and the SMB factor with

the loading on SMB factor increasing as we move from the portfolio in the big to small quintile.

Results also indicate a monotonic relationship between book to market value and HML, with the

loading on HML increasing as we move from portfolios in the growth quintile to portfolios in the

value portfolios.

The results still demonstrate a non-linear relationship between abnormal returns and size with the

intercept terms declining as we move from the portfolio in the big quintile through quintile 2 and 3

and then increasing as we go from quintile 3 until we reach the portfolios within the small quintile.

In contrast, the relationship between book to market and abnormal returns has substantially been

removed.

The results from Tables 9 and 10 indicate that the Fama and French (1993) three factor model

explains a significantly higher proportion of the variation in returns in Australia when compared

to the CAPM. This can be seen in the average adjusted R2 for each equation in the system, with

the three factor model having an average adjusted R2 of 73% compared to the CAPM average of

44%. In particular is the increased explanatory power of the three factor model in explaining the

returns of portfolios in the small quintile where the average R2 has risen from 21% to 77%. The

D-test also indicates that we should reject the null that the coefficients on SMB and HML are equal

to zero. This substantial increase in explanatory power of the Fama and French (1993) model over

the CAPM in explaining the cross-sectional variation in returns is similar to the evidence presented

in Fama and French (1993), although the US evidence suggests the three factor model explains a

higher proportion of returns. Though the results are supportive of the Fama and French (1993)

three factor model the model still struggles to explain a number of the portfolio returns, particularly

the portfolio big value. The results also indicate that the vast majority of the intercept terms are

significantly different from zero which is confirmed by the GRS statistic. The large and significant

intercept terms generally occur in the middle size quintiles. This is consistent with previous evidence

of a non-linear relationship between size and returns and indicates that some other unknown factor

is driving this under performance. Overall, these results indicate that although the Fama and French

(1993) model is superior to the CAPM in explaining the cross-section of average stock returns in

Australia it is not a complete model and still leaves the non-linear relationship between size and

returns unexplained.

39

Tab

le10

Reg

ress

ions

resu

lts

from

the

thre

efa

ctor

model

The

tabl

epr

esen

tsth

ere

sult

sfr

omre

gres

sing

the

300

exce

ssm

onth

lyre

turn

sof

each

ofth

e25

size

-boo

kto

mar

ket

port

folio

son

exce

ssm

arke

tre

turn

s.

The

25si

ze-b

ook

tom

arke

tpo

rtfo

lios

are

form

edby

usin

gin

depe

nden

tso

rts

base

don

mar

ket

capi

talis

atio

nan

dbo

okto

mar

ket

valu

esdu

ring

the

peri

od

1982

to20

06.

The

follo

win

gti

me-

seri

esre

gres

sion

ises

tim

ated

r it=

αi+

βir

mt+

s iS

MB

t+

hiH

ML

t+

e it

Whe

rer i

tis

the

retu

rnon

port

folio

iin

mon

tht

less

the

13w

eek

trea

sury

note

yiel

d,r m

tis

the

valu

e-w

eigh

ted

mar

ket

mon

thly

retu

rnle

ssth

e13

wee

k

trea

sury

note

yiel

d.S

MB

tis

the

retu

rnon

the

mim

icki

ngsi

zepo

rtfo

lioan

dH

ML

tis

the

retu

rnon

the

mim

icki

ngbo

okto

mar

ket

port

folio

.B

oth

mim

icki

ngpo

rtfo

lios

are

form

edus

ing

five

size

and

thre

ebo

okto

mar

ket

port

folio

split

s.T

hesy

stem

ises

tim

ated

usin

gth

eG

MM

tech

niqu

ew

ith

the

follo

win

gm

omen

tco

ndit

ions

;E

[εit]=

0,E

[εitr m

t]=

0,E

[eitS

MB

t]=

0,E

[eitH

ML

t]=

0∀i

=1,···,

N.T

het-

stat

isti

cfo

rth

ere

gres

sion

coeffi

cien

ts

uses

HA

Cst

anda

rder

rors

.T

head

just

edR

2ar

eca

lcul

ated

for

each

equa

tion

inth

esy

stem

.W

eal

sore

port

the

Gib

bons

,R

oss,

and

Shan

ken

(198

9)

(GR

S)

test

stat

isti

c,an

adju

sted

χ2

stat

isti

c(s

eeeq

uati

on6)

that

adju

sted

the

GR

Sst

atis

tics

for

cros

s-co

rrel

ated

erro

rsan

dth

eN

ewey

and

Wes

t(1

987)

D-s

tati

stic

.

**an

d*

deno

tesi

gnifi

canc

eat

the

1%an

d5%

leve

lsre

spec

tive

ly.

Coeffi

cien

tt-

stat

isti

c

αi

Gro

wth

23

4V

alue

Gro

wth

23

4V

alue

Big

-0.5

315

-0.4

199

-0.2

786

-0.6

701

-0.3

086

Big

-2.4

5*

-2.8

7**

-1.0

8-1

.94

-0.5

3

2-1

.422

0-0

.908

3-0

.885

1-0

.966

0-1

.326

62

-4.2

2**

-3.7

7**

-3.0

7**

-3.6

8**

-3.6

2**

3-2

.704

9-1

.339

1-1

.238

3-1

.123

9-1

.311

13

-7.6

2**

-4.5

8**

-4.4

9**

-4.4

5**

-4.9

9**

4-1

.629

7-0

.962

8-1

.366

2-1

.199

1-1

.999

74

-3.4

7**

-2.6

1**

-3.9

6**

-4.4

5**

-5.9

9**

Smal

l-0

.492

4-0

.433

5-0

.136

7-0

.778

9-0

.783

6Sm

all

-1.3

4-1

.15

-0.4

3-2

.47

*-3

.35

**

beta

iG

row

th2

34

Val

ueG

row

th2

34

Val

ue

Big

0.95

081.

0551

0.95

211.

0819

0.89

37B

ig21

.03

**35

.61

**11

.47

**20

.93

**6.

02**

20.

9588

0.89

140.

8785

0.85

241.

0361

217

.46

**23

.78

**16

.09

**14

.86

**15

.44

**

31.

0455

0.86

110.

8060

0.77

781.

0038

318

.79

**19

.20

**13

.44

**20

.40

**22

.84

**

41.

1613

1.01

310.

8878

0.82

801.

1459

417

.91

**15

.03

**13

.74

**17

.34

**19

.05

**

Smal

l1.

0895

1.05

271.

0188

0.95

581.

0675

Smal

l16

.27

**11

.63

**11

.80

**13

.21

**26

.17

**

40

Tab

le10

(con

tinu

ed)

s iG

row

th2

34

Val

ueG

row

th2

34

Val

ue

Big

-0.0

745

-0.0

475

0.02

650.

0525

-0.0

227

Big

-1.7

4-2

.95

**0.

731.

09-0

.29

20.

2798

0.25

590.

2023

0.19

660.

3486

25.

64**

5.68

**4.

42**

4.48

**4.

09**

30.

4951

0.43

980.

3749

0.39

680.

5115

38.

68**

9.57

**7.

84**

8.65

**8.

68**

40.

7441

0.66

760.

6594

0.64

320.

6928

49.

34**

10.9

7**

13.8

4**

12.4

6**

9.98

**

Smal

l1.

0684

1.07

351.

0008

0.92

880.

9297

Smal

l21

.84

**19

.59

**18

.35

**15

.62

**22

.52

**

hi

Gro

wth

23

4V

alue

Gro

wth

23

4V

alue

Big

-0.3

544

-0.0

526

0.06

880.

5193

0.60

65B

ig-3

.25

**-1

.17

0.70

4.16

**2.

20*

2-0

.397

70.

1068

0.12

890.

3484

0.78

772

-2.8

8**

1.14

1.20

3.81

**5.

88**

3-0

.395

7-0

.100

90.

1424

0.41

540.

5510

3-2

.93

**-0

.87

1.38

4.40

**5.

14**

4-0

.606

5-0

.103

90.

1119

0.40

390.

8706

4-2

.58

*-0

.78

0.76

4.19

**4.

98**

Smal

l-0

.343

3-0

.057

70.

2714

0.53

610.

7293

Smal

l-2

.27

*-0

.37

2.08

*4.

22**

6.95

**

Adj

R2

Gro

wth

23

4V

alue

Big

0.81

260.

8966

0.76

020.

6796

0.39

29

20.

7157

0.72

620.

6795

0.67

880.

6293

30.

7387

0.68

620.

6509

0.67

090.

7189

40.

7378

0.69

990.

7037

0.70

610.

7413

Smal

l0.

8363

0.78

310.

7754

0.76

980.

8543

GR

Sχ

2D

-tes

t

8.77

**11

6.24

**89

410*

*

41

5.1 Sensitivity analysis

Section 4 demonstrated a strong June and July seasonality in the SMB factor and an abnormal result

in 1989 for the HML factor. To test if these seasonalities or abnormal results affect are analysis, we

adjust equation 4 to take these phenomena into account by adding interactive dummy variables to

the equation and evaluate the following model:

rit = αi + βirmt + siSMBt + hiHMLt+

djunDjunSMBt + djulDjulSMBt + d1989D1989HMLt + eit i = 1, · · · , N. (7)

Where rit is the excess return on asset i in time t. rmt is the excess return of the market. SMBt is

the return on the mimicking size portfolio and HMLt is the return on the mimicking book to market

portfolio. αi, βi, si, hi, djun, djul and d1989 are regression coefficients, eit are the error terms, N is

the number of test assets. Djun, Djul and D1989 are dummy variables that takes the value of one

if the month is June (Djun), if the month is July (Djul), if the year is 1989 (D1989) otherwise the

value is zero. An interactive dummy variable approach is used because the seasonality is specific to

the SMB factor, while the anomalies behaviour in 1989 is specific to the HML factor.

The results from estimating equation 7 are reported in Table 11. These results are consistent with

those reported in Table 10. The results indicate that the June and July seasonal regularity is

captured within the SMB factors and separating out the two effects adds little to the model. This

is demonstrated by insignificant co-efficient values on djun and djul indicating a similar loading on

the SMB factor no matter the time of the year. In contrast, the loading on the HML factor is quite

different in 1989 than for the rest of the time period. Nearly all of the portfolios in 1989 have a

significant positive loading on the HML factor and the loadings are larger than the rest of the time

period. The result is particularly dramatic for the portfolios in the growth and value quintiles. The

loadings on the portfolios within the growth quintile generally goes from a significant negative to

a significant positive loading. For the portfolios in the value portfolio the loadings substantially

increases particularly portfolio big-value whose loading goes from 0.34 to 2.92. These results confirm

that the return in 1989 for the HML factor and the resulting responses in the portfolio returns are

unusual and a control for 1989 is required.

A number of other unreported sensitivity test have also been carried out and indicate that the load-

ings on the factors are relatively constant when the sample is split into two sub-periods, although

individually estimates have higher variability, as expected, because of the lower number of observa-

tions available in the estimation. The results also indicate that both the SMB and HML factors are

significant when the system is run with only one of the factors at a time. As expected the results

indicate that the SMB is essential to explain the difference in returns between the big and small

quintiles, while the HML factor is required to explain the difference in returns between the growth

and value quintiles.

42

Tab

le11

Reg

ress

ions

resu

lts

from

the

thre

efa

ctor

model

The

tabl

epr

esen

tsth

ere

sult

sfr

omre

gres

sing

the

300

exce

ssm

onth

lyre

turn

sof

each

ofth

e25

size

-boo

kto

mar

ket

port

folio

son

exce

ssm

arke

tre

turn

s.

The

25si

ze-b

ook

tom

arke

tpo

rtfo

lios

are

form

edby

usin

gin

depe

nden

tso

rts

base

don

mar

ket

capi

talis

atio

nan

dbo

okto

mar

ket

valu

esdu

ring

the

peri

od

1982

to20

06.

The

follo

win

gti

me-

seri

esre

gres

sion

ises

tim

ated

r it=

αi+

βir

mt+

s iS

MB

t+

hiH

ML

t+

dju

nD

ju

nS

MB

t+

dju

lDju

lSM

Bt+

d1989D

1989H

ML

t+

e it

Whe

rer i

tis

the

retu

rnon

port

folio

iin

mon

tht

less

the

13w

eek

trea

sury

note

yiel

dan

dr m

tis

the

valu

e-w

eigh

ted

mar

ket

mon

thly

retu

rnex

trac

ted

from

the

CR

IFpr

ice

rela

tive

file.

SM

Bt

isth

ere

turn

onth

em

imic

king

size

port

folio

and

HM

Lt

isth

ere

turn

onth

em

imic

king

book

tom

arke

tpo

rtfo

lio.

Bot

hm

imic

king

port

folio

sar

efo

rmed

usin

gfiv

esi

zean

dth

ree

book

tom

arke

tpo

rtfo

liosp

lits.

Dju

n,D

ju

lan

dD

1989

are

dum

my

vari

able

sth

ateq

uals

one

ifth

em

onth

isJu

ne(D

ju

n),

orJu

ly(D

ju

l),o

rth

eye

aris

1989

(D1989)

othe

rwis

eth

edu

mm

yva

riab

leeq

uals

zero

.T

hesy

stem

ises

tim

ated

usin

gth

e

GM

Mte

chni

que.

The

t-st

atis

tic

for

the

regr

essi

onco

effici

ents

uses

HA

Cst

anda

rder

rors

.T

head

just

edR

2ar

eca

lcul

ated

for

each

equa

tion

inth

esy

stem

.

We

also

repo

rtth

eG

ibbo

ns,R

oss,

and

Shan

ken

(198

9)(G

RS

)te

stst

atis

tic.

**an

d*

deno

tesi

gnifi

canc

eat

the

1%an

d5%

leve

lsre

spec

tive

ly.

Coeffi

cien

tt-

stat

isti

cp-v

alue

αi

Gro

wth

23

4V

alue

Gro

wth

23

4V

alue

Big

-0.4

177

-0.4

041

-0.2

615

-0.5

122

0.01

12B

ig-1

.94

-2.8

9**

-1.1

1-1

.83

0.03

2-1

.235

8-0

.738

3-0

.730

8-0

.904

7-1

.308

02

-4.4

2**

-3.7

4**

-2.8

9**

-3.8

2**

-3.6

8**

3-2

.644

8-1

.270

9-1

.093

6-0

.986

2-1

.273

43

-8.9

5**

-4.7

1**

-4.6

2**

-4.8

3**

-5.3

6**

4-1

.295

7-0

.829

1-1

.043

3-1

.154

9-1

.651

74

-3.3

7**

-2.5

6*

-4.2

5**

-4.7

7**

-7.8

1**

Smal

l-0

.307

1-0

.434

5-0

.022

6-0

.586

4-0

.695

3Sm

all

-0.9

8-1

.41

-0.0

8-2

.34

*-3

.84

**

βi

Gro

wth

23

4V

alue

Gro

wth

23

4V

alue

Big

0.94

311.

0518

0.94

901.

0660

0.84

80B

ig22

.66

**40

.98

**13

.58

**25

.14

**8.

82**

20.

9386

0.87

450.

8610

0.84

351.

0265

224

.94

**25

.05

**18

.20

**16

.46

**16

.66

**

31.

0233

0.85

380.

7924

0.76

370.

9894

321

.67

**22

.47

**14

.91

**25

.45

**26

.57

**

41.

1130

0.99

080.

8595

0.81

211.

1069

423

.39

**18

.77

**20

.06

**20

.75

**22

.21

**

Smal

l1.

0711

1.03

900.

9980

0.94

331.

0560

Smal

l18

.42

**14

.52

**14

.46

**18

.01

**27

.38

**

43

Tab

le11

(con

tinu

ed)

s iG

row

th2

34

Val

ueG

row

th2

34

Val

ue

Big

-0.0

921

-0.0

490

0.03

090.

0114

-0.0

371

Big

-2.0

6*

-3.0

7**

0.91

0.28

-0.6

6

20.

2719

0.23

500.

1799

0.17

850.

3085

25.

25**

4.94

**3.

97**

4.03

**3.

68**

30.

4511

0.44

830.

3559

0.38

730.

4561

38.

40**

10.0

0**

7.55

**8.

20**

8.76

**

40.

6557

0.62

160.

6302

0.59

860.

6265

411

.63

**11

.30

**14

.41

**12

.61

**10

.10

**

Smal

l1.

0549

1.04

530.

9642

0.93

980.

9199

Smal

l22

.87

**22

.46

**17

.04

**17

.35

**25

.10

**

hi

Gro

wth

23

4V

alue

Gro

wth

23

4V

alue

Big

-0.3

847

-0.0

721

0.04

600.

4582

0.33

74B

ig-3

.67

**-1

.79

0.53

5.40

**2.

45*

2-0

.513

10.

0234

0.04

190.

3087

0.76

032

-4.6

7**

0.31

0.51

3.62

**5.

71**

3-0

.499

0-0

.152

30.

0769

0.33

820.

5064

3-4

.47

**-1

.36

0.88

5.11

**5.

14**

4-0

.829

1-0

.203

0-0

.032

60.

3410

0.69

044

-4.7

3**

-1.9

7*

-0.3

53.

86**

6.21

**

Smal

l-0

.442

5-0

.122

10.

1732

0.45

450.

6670

Smal

l-3

.60

**-0

.95

1.69

4.64

**7.

98**

dju

nG

row

th2

34

Val

ueG

row

th2

34

Val

ue

Big

0.10

86-0

.034

1-0

.069

10.

1680

-0.3

947

Big

1.73

-0.8

0-1

.10

2.36

*-1

.55

2-0

.110

10.

0259

0.00

500.

0272

0.11

702

-1.4

20.

400.

080.

431.

16

3-0

.046

5-0

.118

30.

0435

-0.0

409

0.15

403

-0.4

1-1

.40

0.56

-0.6

02.

30*

40.

0865

0.05

240.

0425

0.05

870.

1287

40.

490.

620.

570.

751.

58

Smal

l-0

.037

9-0

.066

0-0

.007

2-0

.087

2-0

.047

6Sm

all

-0.4

1-0

.40

-0.0

7-0

.93

-0.7

0

dju

lG

row

th2

34

Val

ueG

row

th2

34

Val

ue

Big

-0.0

041

0.01

73-0

.002

50.

0861

0.10

98B

ig-0

.07

0.46

-0.0

51.

280.

88

20.

0032

0.02

620.

0533

0.06

420.

1770

20.

040.

320.

540.

961.

43

30.

2572

-0.0

308

0.01

920.

0056

0.24

203

2.55

-0.3

00.

190.

082.

09*

40.

3201

0.18

38-0

.011

70.

2189

0.15

954

2.20

1.51

-0.1

52.

80**

2.09

*

Smal

l0.

0036

0.20

300.

1661

-0.1

248

0.03

62Sm

all

0.04

2.22

*1.

45-1

.17

0.31

44

Tab

le11

(con

tinu

ed)

d1989

Gro

wth

23

4V

alue

Gro

wth

23

4V

alue

Big

0.25

330.

2116

0.26

960.

5111

2.92

04B

ig1.

922.

51*

1.64

0.80

2.67

**

21.

2330

0.82

910.

8694

0.37

240.

1670

28.

32**

7.42

**5.

84**

3.08

**0.

76

31.

0045

0.59

530.

6388

0.80

690.

3052

35.

97**

3.82

**2.

21*

4.85

**2.

15*

42.

1339

0.93

061.

4545

0.54

841.

7252

47.

88**

2.75

**3.

89**

3.76

**3.

83**

Smal

l1.

0295

0.63

420.

9583

0.91

320.

6499

Smal

l4.

99**

1.61

1.95

3.47

**1.

63

Adj

R2

Gro

wth

23

4V

alue

Big

0.81

380.

8965

0.76

000.

6846

0.49

51

20.

7310

0.73

570.

6903

0.67

940.

6319

30.

7504

0.68

920.

6543

0.68

050.

7279

40.

7623

0.70

580.

7205

0.71

320.

7698

Smal

l0.

8392

0.78

510.

7801

0.77

520.

8564

GR

S

7.15

**

45

6 Conclusion

While the size and book to market effects and the application of the Fama and French (1993) model

have been extensively documented using US data, there have been few studies on these effects in

Australia. This has been a results of an absence of a comprehensive database containing accounting

information. This lack of a comprehensive database has lead to severe data limitations on previous

studies in Australia, potentially affecting the results. Previous studies in Australia have found only

weak evidence of a value effect being present in Australia, although a size effect is well documented.

In contrast, evidence from the US and other markets suggests that a value premium is common.

A lack of evidence for the value premium in Australia could be the result of data limitation and

previous studies only focusing on relatively short periods of time, generally covering the mid to late

1990’s when accounting information in Australia is more readily available. The previous studies on

the value premium in Australia have had, on average, access to less than 35% of all companies that

produced annual reports. This study is the first to rectify this lack of market coverage by hand

collecting accounting information from over 98% of all companies that produced an annual report.

We also extend the previous studies to cover the period 1982 to 2006.

We present evidence on the size and book to market anomalies that indicate that the size effect

is non-linear in Australia while the book to market effect is linear. These results suggest that

forming the SMB and HML factors following the methodology proposed by Fama and French (1993)

in Australia may not capture the size and book to market anomalies correctly. We analyse three

potential methods for forming the two factors in Australia and conclude that the three methodologies

will give factors that behave in a similar manner, although the preferred methodology in Australia

is to use five size and three book to market independent sorts. These results indicate a large HML

premium in Australia, with earnings on average of 0.959% per month. This result is consistent with

previous studies in Australia (Gharghori, Chan, and Faff, 2006; Halliwell, Heaney, and Sawicki, 1999)

and is larger than the US HML factor which averages 0.462% per month. In contrast, the SMB factor

earns an average monthly return of -0.486%, which is insignificantly different from zero. This result

is consistent with the US SMB factor which earns an average monthly return of 0.086% which is

insignificantly different from zero. These results support recent evidence that the size premium has

been declining in equity markets in recent years (Barber and Lyon, 1997; Dimson and Paul, 1999).

We also demonstrate a strong June and July seasonality in the SMB factor which is consistent

with previous research on the size anomaly in Australia (Brown, Keim, Kleidon, and Marsh, 1983;

Durand, Juricev, and Smith, 2007). We also document that in 1989 the HML factor experienced

a large negative return. This result seems to be driven by value firms experiencing severe distress

leading into 1989, with the average book to market value in 1989 being substantially higher than

other years in the sample. We also document that the result is also influenced by a few large firms

experiencing extremely large negative returns of over 50% for several months in 1989.

46

The current study extends prior Australian studies analysing the Fama and French (1993) model

by combining the periods analysed in Halliwell, Heaney, and Sawicki (1999) and Gaunt (2004) and

extending it by 5 years giving a time period of 25 years. We also significantly increase the number

of companies in our sample. Consistent with prior evidence in the US and Australia (Fama and

French, 1993, 1996; Gaunt, 2004; Halliwell, Heaney, and Sawicki, 1999), our results demonstrate a

strong monotonic relationship between size and the SMB factor. In contrast to previous Australian

evidence there is also a strong monotonic relationship between book to market portfolios and the

HML factor, which is consistent with the US evidence (Fama and French, 1993, 1996). Consistent

with a number of Australian studies (Durack, Durand, and Maller, 2004; Durand, Limkriangkrai,

and Smith, 2006a; Gaunt, 2004) we find that the Fama and French (1993) three factor model provides

significant improvement over the CAPM in explaining the cross-section of portfolio returns. Finally,

in contrast to Durack, Durand, and Maller (2004); Durand, Limkriangkrai, and Smith (2006a); Gaunt

(2004); Halliwell, Heaney, and Sawicki (1999) which find that the bulk of the increased explanatory

power is due to the SMB factor, but consistent with Gharghori, Chan, and Faff (2006) we find that

both SMB and HML factors are important in explaining the cross-section of portfolio returns in

Australia.

Overall our study suggests that the Fama and French (1993) three factor model provides a significant

improvement over the CAPM in explaining the cross-section of portfolio returns. The results also

indicate that the three factor model can not explain the returns of the portfolios in the middle

size quintiles, which earn substantial negative abnormal returns. This result confirms the non-

linear relationship between returns and size. This indicates that to fully explain the cross-section

of portfolio returns in Australia more work is required in understanding the non-linear relationship

between returns and size.

47

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