Does The Three Factor Model Explain Capm Anomalies Finance Essay

Surveies have documented several anomalousnesss in mean returns that can non be explained by the individual hazard factor in the CAPM. Consistent with the APT, Fama and French ( 1993, 1996 ) suggest a three-factor theoretical account including risk factors of market, size, and BtM. The theoretical account is claimed to capture much of the cross-sectional fluctuation in mean returns, every bit good as absorb most of the CAPM anomalousnesss. Still, there are other faculty members seeking to farther better this theoretical account. Fama and French interpret their theoretical account as grounds for a distress premium. In contrast to the risk-based account, behavioralists explain the size and BtM anomalousnesss as a consequence of irrational pricing. Criticisms of the three-factor theoretical account are centred on informations excavation and survivorship prejudice. These hypotheses can be tested by utilizing different clip periods, different states, or a holdout sample. Nevertheless, a figure of empirical surveies have shown favorable grounds to back up the three-factor theoretical account.

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The purpose of this research is to reexamine the work that has been done sing the three-factor theoretical account of Fama and French ( 1993, 1996 ) , in effort to analyze whether it can explicate CAPM anomalousnesss. This paper comprises a wide scope of literature survey, including both theoretical and empirical plants.

Asset pricing is an of import subject to analyze. Research workers have documented a figure of anomalousnesss in mean returns that can non be explained by the CAPM. The influential CAPM is challenged by the three-factor theoretical account which is claimed to capture much of the cross-sectional fluctuation in mean returns, every bit good as absorb most of the CAPM anomalousnesss. If this claim is true, the three-factor theoretical account can thereby be lawfully used in any application that requires estimation of expected returns. Hence, it is necessary to analyze the cogency and utility of the theoretical account.

Rather than a individual hazard factor underlying the CAPM, the three-factor theoretical account is consistent with the multifactor arbitrage pricing theory ( APT ) , and it includes three hazard factors of market, size, and book-to-market ratio ( BtM ) . Based on legion surveies that support Fama and French ‘s consequences, most research workers have reached the consensus that stocks with little capitalization and high BtM can gain higher returns ( Davis, 2001 ) . Fama and French ( 1993, 1996 ) construe the empirical success of their theoretical account as grounds for a hurt premium – investors require higher returns for hard-pressed stocks because of more peril. In contrast to the risk-based account, behavioralists explain the size and BtM anomalousnesss as a consequence of mispricing.

Criticisms of the three-factor theoretical account are centred on informations excavation and survivorship prejudice. However, the three-factor theoretical account is once more validated by a figure of empirical surveies demoing grounds over different clip periods, in different states, and in holdout samples.

Finally, it is of import to observe that empirical trials of informations excavation and survivorship prejudices can non work out the critical issue of whether size and BtM are placeholders for common hazard factors, or irrational pricing ( Barber and Lyon, 1997 ) . It suggests that future research should seek to work out this relation with more sophisticated survey designs.

Introduction

The capital plus pricing theoretical account ( CAPM ) and the arbitrage pricing theory ( APT ) are two of import equilibrium plus pricing theoretical accounts that enable us to monetary value hazardous assets ( Copelan et al 2005 ) . Constructing on the portfolio theory of Markowitz ( 1959 ) , Sharpe ( 1964 ) , Lintner ( 1965 ) and Black ( 1972 ) independently developed the CAPM theoretical account, which is appreciated as one of the most of import developments in modern fiscal theory, and makes “ the birth of plus pricing theory ” ( Fama and French 2004:25 ) . The CAPM shows that the equilibrium rates of return on all hazardous assets are a positive additive map of their covariance with a mean-variance-efficient market portfolio. The market portfolio is the lone beginning of systematic hazard that is measured by beta coefficients. In contrast, the arbitrage pricing theory ( APT ) as developed by Ross ( 1976 ) is more general than the CAPM because it allows assorted hazard factors ( non merely the market portfolio ) to explicate plus returns. As the APT does non stipulate the figure of hazard factors, nor does it place the factors, a assortment of multifactor plus pricing theoretical accounts have been developed constructing on the APT model. Though the three-factor theoretical account of Fama and French ( 1993, 1996 ) is non the first multifactor plus pricing theoretical account, it might be the most outstanding one which has besides created immense sums of academic argument.

Get downing in the late seventiess, empirical surveies have documented legion divergences from the CAPM. Several factors sing house features have been identified that seemingly supply more power other than the CAPM betas in explicating mean stock returns. Fama and French ( 1993, 1996 ) refer to these factors as anomalousnesss. It is argued by advocates of multifactor pricing theoretical accounts that with merely one hazard factor, the CAPM does non capture all the factors that affect stock returns.

The three-factor theoretical account has been subjected to considerable theoretical probe and empirical research. The purpose of this research is to reexamine the work that has been done sing the three-factor theoretical account in explicating CAPM anomalousnesss. Particularly, the survey addresses the inquiry of whether Fama and French ‘s three-factor theoretical account can explicate CAPM anomalousnesss. If it can, what are possible accounts? Otherwise, what shortcomings underlying the theoretical account that prohibit its success? Analyzing plus pricing is valuable for doing investing determinations, such as choosing portfolios, measuring the public presentation of managed financess, mensurating unnatural returns in event surveies, and gauging the cost of capital for houses ( Fama and French, 1993 ) . It is hence necessary to reexamine the development of the CAPM and measure the cogency of the three-factor theoretical account as a typical multifactor theoretical account.

This paper comprises a literature survey and efforts to analyze the three-factor theoretical account from both theoretical principle and empirical grounds. The balance of the paper is structured as follows. Section II reviews some of import empirical contradictions of the CAPM ; and so introduces the influential three-factor theoretical account, every bit good as its development with respect of two new multifactor theoretical accounts of Carhart ( 1997 ) and Chen and Long ( 2009 ) . Section III discusses viing accounts for the size and BtM effects that are captured by the three-factor theoretical account. Section IV examines unfavorable judgments of the theoretical account. Section V presents empirical grounds that against those unfavorable judgments. Section VI concludes and proposes possible recommendations for future surveies.

Empirical Contradictions of the CAPM and the Development of the Three-Factor Model

The CAPM implies that market betas suffice to depict the differences in expected returns across assets. However, since the late seventiess, the CAPM appears to be challenged by a figure of surveies, which provide grounds to demo that much of the fluctuation in expected returns is unrelated to betas ( Fama and French, 2004 ) . Banz ( 1981 ) reveals a size consequence: the mean returns on stocks of houses with little market capitalisations are higher than predicted by the CAPM. Basu ( 1977, 1983 ) identifies that houses with high ( low ) earnings-price ratios ( P/E ) have lower ( higher ) returns than expected. DeBondt and Thaler ( 1985 ) find that stocks with low returns during the past three to five old ages would see long-run return reversals. The impulse consequence as found by Jegadeesh and Titman ( 1993 ) shows that stocks with high returns during the past three to twelve months be given to give extra returns in the hereafter. Bhandari ( 1988 ) finds that houses with high purchase are associated with abnormally higher returns in footings of their betas. Rosenberg, Reid and Lanstein ( 1985 ) maintain that stocks with high book-to-market equity ratios ( BtM ) have high mean returns that are non captured by betas. All surveies discussed above dramatis personae uncertainty on the ability of the CAPM to explicate the cross-section of expected returns. Harmonizing to the CAPM, above hazard variables should non be able to explicate mean returns better than betas ( Davis, 2001 ) .

The empirical contradictions of the CAPM motivate Fama and French ( 1992 ) to synthetically measure the explanatory power of beta, size, E/P, purchase, and BtM in the cross-section of mean returns on NYSE, AMEX, and NASDAQ stocks. The return files of non fiscal houses from the Centre for Research in Security Prices ( CRSP ) and COMPUSTAT database are used for the period of 1963-1990. They conclude that size and BtM capture the cross-sectional fluctuation in mean stock returns, whereas market betas reveal small information about norm returns ( ibid. ) .

By utilizing the times-series arrested development attack, Fama and French ( 1993 ) trial 25 stock portfolios formed on size and BtM of value-weighted NYSE, AMEX, and NASDAQ stocks over the 1963-1993 period. The empirical consequences confirm that factors related to size and BtM can explicate the differences in the mean cross-section stocks returns. However, the differences between the mean stock returns and one-month T-bill rates can non be explained by these two factors entirely ; the inclusion of the market factor can explicate this as the market hazard premium links the mean returns on stocks and T-bills ( ibid. ) . Therefore, they conclude that the common fluctuation in stock returns is mostly captured by three factors of market, size and BtM.

Based on this grounds, Fama and French ( 1996, p. 55 ) developed a three-factor theoretical account ( it is a three-factor version of the APT in nature ) . Specifically, the expected return on portfolio I in surplus of the riskless rate is,

E ( Ri ) – Rf = Bi [ E ( RM ) – Rf ] + siE ( SMB ) +hiE ( HML )

where E ( RM ) – Releasing factor is the extra returns on a wide market portfolio. SMB ( little subtraction large ) is the difference between the return on a diversified portfolio of little and big stocks. Similarly, HML ( high subtraction depression ) is the difference between the returns on a diversified portfolio of high BtM and low BtM stocks. The Bi, Si, and hello coefficients measure the sensitiveness of the portfolio ‘s return to three factors ( ibid. ) .

Based on empirical successes in their 1993, 1995 and 1996 surveies, Fama and French ( 1996, p. 50 ) assert that except for the short-run return impulse consequence, the three-factor theoretical account “ captures most of the average-return anomalousnesss of the CAPM ” . As the impulse consequence is left unexplained, Carhart ( 1997 ) develops a four-factor theoretical account by adding one impulse factor to the original three-factor theoretical account. He claims that with the extra impulse factor, the four-factor theoretical account well improves on the mean pricing mistakes of both the CAPM and the Fama-French theoretical account ( ibid. ) . However, it is of import to observe that the four-factor theoretical account portions the same risk-based intuition with the three-factor theoretical account ; both theoretical accounts can non guard off agnosticism from the behavioralists in footings of irrational pricing, which are discussed in the following subdivision.

Several surveies show that except for the impulse consequence, the Fama-French theoretical account still leaves many CAPM anomalousnesss unexplained, such as net incomes surprises, fiscal hurt, net stock issues, and plus growing ( Chen and Zhang, 2009 ) . Based on q-theory, Chen and Zhang ( 2009 ) update the Fama-French theoretical account and suggest a new three-factor theoretical account including the market factor, a low-minus-high investing factor, and a high-minus-low return-on-assets ( ROA ) factor. They test this theoretical account through empirical observation for a wide sample of stocks over the period of 1972 – 2006. Result show that the new theoretical account well outperforms the Fama-French theoretical account as it can explicate many forms anomalous to the original theoretical account ( ibid. ) . However, with similar defects like the Carhart ( 1997 ) theoretical account, the new three-factor theoretical account is soundless on factor effects sing compensation for hazard and behavioral mispricing accounts.

Theoretical Explanations: Rational Hazard or Irrational Pricing?

The economic reading of the Fama and French ‘s three-factor theoretical account is problematic. The first narrative is the risk-based account. The surveies of Fama and French ( 1993, 1996 ) show that there exists covariation in returns related to size and BtM, which are captured by burdens on SMB and HML factors, and beyond the covariation is explained by the market return. It suggests that the three factors in the theoretical account gaining control much of the common fluctuation in portfolio returns that is missed by univariate hazard factor ( betas ) in the CAPM. The CAPM anomalousnesss reflect the fact that size and BtM are placeholders for hurt. Small stocks and high BtM ( value ) stocks have high mean returns because they are hazardous, for which investors require a positive hazard premium.

In contrast to the risk-based account, behavioralists explain the size and BtM anomalousnesss as a consequence of irrational pricing. Lakonishok, Shleifer and Vishny ( 1994 ) suggest that higher returns associated with little stocks and value stocks are due to mispricing. They interpret the BtM anomalousness as investors tend to generalize houses ‘ past public presentation into the hereafter. Therefore, monetary values of growing stocks ( low BtM ) are normally excessively high as a consequence of over-optimistic outlooks. However, these pricing mistakes will finally be corrected, ensuing low returns for growing stocks. Similarly, hard-pressed stocks are undervalued therefore have high returns. Other advocates of this position include DeBondt and Thaler ( 1987 ) , and Haugen ( 1995 ) . The mispricing account implies that investors can increase returns without bearing extra hazards, merely by purchasing value stocks and selling growing stocks ( Davis, 2003 ) . It clearly contradicts the Fama and French ‘s statement because the mean HML return in the three-factor theoretical account that based on rational-pricing is interpreted as a hazard premium for hurt.

Daniel and Titman ( 1997, 1998 ) reject the risk-based account by reasoning that it is features ( e.g. , high versus low BtM ) instead than covariances ( e.g. , factor sensitivenesss ) that determine stock returns. In support of this statement, they provide grounds that for the 1973-1993 period, expected returns do non look to be positively related to the burdens on the three factors in the Fama-French theoretical account after commanding for house features. It follows that there is no return premium associated with any of the three factors as proposed by Fama and French ( Daniel and Titman, 1998 ) . However, their features account is argued to be specific to their instead short sample period. As a longer 1929-1997 period is examined in Davis, Fama and French ( 2000 ) , covariances show more explanatory power than features. Therefore, Davis, Fama and French ( 2000 ) rebut the hypothesis that the BtM feature is compensated irrespective of hazard burdens. Alternatively, the three-factor theoretical account better explains the value premium because expected returns counterbalance hazard burdens ( ibid. ) .

Criticisms: Data Mining and Survivorship Bias

Criticism of the three-factor theoretical account has centred on informations excavation ( or informations spying ) and survivorship prejudice. Black ( 1993 ) and Mackinlay ( 1995 ) contend that CAPM anomalousnesss could be the consequence of informations excavation. The information excavation narrative predicts that the size and BtM effects would vanish in out-of-sample trials. In other words, when analyze another clip period or another information beginning, the three-factor theoretical account will cut down to the CAPM and the three factors will be completed explained by CAPM betas if the information excavation narrative holds ( Fama and French, 1996 ) .

The surveies of Fama and French are further criticised for the COMPUSTAT database that they used. As many stocks with high BtM and little size do non last and are excluded from the COMPUSTAT, their consequences suffer from a sample-selection prejudice. Kothari, Shanken and Sloan ( 1995 ) re-examine the work of Fama and French ( 1993 ) in order to find whether beta and BtM capture the cross-sectional fluctuation in mean returns. Using an alternate Standard & A ; Poor ( S & A ; P ) industry-level informations from 1947 to 1987, they find small relation between BtM and mean returns but significant compensation for beta hazard when measured by one-year instead than monthly informations ( ibid ) . They attribute the contradictions to the survivorship prejudice. They argue that mean returns on high BtM stocks are overstated by the three-factor theoretical account because the COMPUSTAT includes hard-pressed houses that have survived and excludes hard-pressed houses that have failed.

Furthermore, the CAPM is rejected by the three-factor theoretical account based on the grounds that size and BtM are capturing cross-sectional fluctuation in mean returns that can non be explained by betas ( Fama and Gallic 1996 ) . However, it is argued by Levy ( 1997, p. 120 ) that in rejecting the CAPM, Fama and French use “ historical betas as steps of betas based on future returns ” . As the CAPM is concerned about ex ante outlooks and non ex station returns, their empirical findings could non rebut the CAPM ( Laubscher, 2002 ) .

Empirical Evidence Against Criticisms

Harmonizing to Barber and Lyon ( 1997 ) , the informations snooping and sample-selection prejudice hypothesis can be tested by analyzing the Fama-French theoretical account utilizing different clip periods, different states, or a holdout sample. In contrast to above unfavorable judgments for informations spying and sample-selection prejudice, Fama and French ‘s theoretical account is besides supported by a figure of empirical surveies.

Davis ( 1994 ) provides strong grounds to counter-argue the information excavation and survivorship prejudice claims. He maintains that the hurt premium is non specific to the period studied in Fama and French ( 1992, 1993 ) . In support of this statement, he constructs a database of big US industrial houses for the period of 1940-1963, which is “ pre-COMPUSTAT epoch ” and besides precedes the period studied by Fama and French. He finds a strong relation between BtM and cross-section of accomplished stock returns, which agrees with Fama and French ‘s consequences. As Davis ( 1994 ) uses a different database to analyze independent clip periods yet produces consistent consequences, he rejects the unfavorable judgments of the three-factor theoretical account in footings of informations excavation and survivorship prejudice.

Further grounds is provided by Chan, Jegadeesh and Lakonishok ( 1995 ) , demoing that sample-selection prejudice does non hold a important consequence on Fama and French ‘s consequences. They find that the proportion of CRSP companies losing from COMPUSTAT over the 1968-92 period is little ; at most 3.1 per centum can be loosely interpreted as financially hard-pressed houses that are omitted from COMPUSTAT. In add-on, the mean return is non really different between them. They besides construct a dataset of big houses which is free from any choice prejudice from back-filling informations. They conclude that choice prejudice on COMPUSTAT is exaggerated, and the BtM consequence in Fama and French ( 1992, 1993 ) is confirmed for the top 20 per centum of NYSE-Amex stocks.

Barber and Lyon ( 1997 ) through empirical observation test the informations spying issue by analysing the relation between size, BtM ratios, and stock returns for fiscal houses, which are excluded in Fama and French ( 1992 ) . By analyzing the 1973-1994 period, they find that the house size and BtM forms in returns are similar for both fiscal and nonfinancial houses. They besides show grounds that survivorship prejudice on COMPUSTAT information does non significantly affect either size or BtM premiums ( ibid. ) . Since they use a big holdout sample, their consequences seemingly challenge informations snooping and choice prejudices criticisms.

Other surveies based on international grounds besides refute the information prejudice unfavorable judgments. The early survey of Chan, Hamao, and Lakonishok ( 1991 ) paperss a important cross-sectional relationship between BtM ratio and stock returns in the Nipponese stock market from 1971 to 1988. Capaul, Rowley and Sharpe ( 1993 ) observe a similar BtM premium in Japan every bit good as four other developed states during the 1981-1992 period. For a longer clip interval during 1975 to 1995, Fama and French ( 1998 ) find permeant BtM premium in 12 of 13 major markets, every bit good as in emerging markets. In add-on, they claim that with a hazard factor for comparative hurt included, their theoretical account captures the BtM premium in state and planetary returns ( ibid. ) . There is farther grounds in emerging markets documented in more recent surveies that tends to back up the three-factor theoretical account, for illustration, trials of Connor and Sehgal ( 2001 ) in the Indian market, and trials of Tony and Veeraragavan ( 2005 ) in the Chinese market.

Decision

In decision, this research reviews literature sing the three-factor theoretical account, in effort to analyze whether it can explicate CAPM anomalousnesss. Rather than a individual hazard factor underlying the CAPM, multifactor APT theoretical accounts allow assorted hazard factors to explicate plus returns. Surveies have documented several CAPM anomalousnesss. Consistent with the APT, the Fama-French theoretical account that includes three hazard factors of market, size and BtM is claimed to capture much of the cross-sectional fluctuation in mean returns, and besides it seems to absorb most of the CAPM anomalousnesss. Fama and French ( 1993, 1996 ) construe the empirical success of their theoretical account as grounds for a hurt premium, since hazard factors of SMB and HML gaining control independent beginnings of systematic hazard which are missed by the CAPM. In contrast, behavioralists explain the size and BtM premium as a consequence of mispricing. They argue that investors ever make incorrect outlooks and hence misprice distressed stocks. Once pricing mistakes are corrected, returns for these stocks would be high. Criticisms of the three-factor theoretical account are centred on informations excavation and survivorship prejudice. However, these hypotheses can be tested by utilizing different clip periods, different states, or a holdout sample. A big figure of empirical surveies have shown favorable grounds to back up the three-factor theoretical account.

However, empirical trials of informations excavation and the survivorship prejudice can non work out the critical issue of whether size and BtM are placeholders for common hazard factors, or irrational mispricing ( Barber and Lyon, 1997 ) . Future work should seek to work out this relation with more sophisticated survey designs. Additionally, as Fama and French ( 1996 ) point out, their theoretical account might non explicate all plus returns. Therefore, future surveies are suggested to look actively for a richer theoretical account that includes other possible hazard factors. For illustration, liquidness seems to be a priced hazard, which might be the possible way for future survey.

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