Since Treynor (1961, 1962), Sharpe (1964), Lintner (1965), Mossin (1966) and Black (1972) developed the Capital Asset Pricing Model (CAPM), a single factor model, it has been widely used in both academia and industry. Early empirical studies find, however, that the CAPM cannot explain several market anomalies30, including firm size (Banz, 1981), the book-to- market ratio (Stattman, 1980), the earnings-to-price ratio (Basu, 1983), firm leverage (Bhandrari, 1988), long-term return reversals (De Bondt & Thaler, 1985, 1987) and momentum returns (Jegadeesh & Titman, 1993).
Addressing some of these anomalies (size, leverage, E/P and B/M), Fama and French (1992), compare their explanatory powers together with betas in cross-sectional regressions. They find that size and B/M have the strongest relation to returns, while other variables (including beta) have none. Then, in a follow-up study, Fama and French (1993) expand the single factor CAPM by adding the size factor (SMB) and the value factor (HML). Using the model, the authors show that the two additional factors can capture the cross-sectional differences in expected returns on stocks and bonds beyond what the CAPM predicts. For
30 According to Schwert (2003), market anomalies refer to empirical results that are not consistent with the
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instance, the three-factor model is able to explain more than 90% (OLS R2) of cross-sectional changes in expected returns, while the CAPM can only capture 70%, for the US stock market data that they examine. The subsequent research on various stock markets, thus, switched from the CAPM to the Fama-French three-factor model. Their results indicate that the latter is able to explain, on average, 96% (an average OLS R2) of the cross-sectional variations in expected returns.31 The successes of the Fama-French three-factor model have, therefore, made it increasingly popular among academics and practitioners. Fama and French (1993, 1996) suggest that the size and value factors proxy for the priced distress factor. In particular, pursuing value strategies that buy a portfolio of stocks with persistently low sales and earnings records (i.e., high distress) and sell a portfolio of stocks with persistently high sales and earnings records (i.e., low distress) is fundamentally riskier and, therefore, requires compensation for bearing this risk. DeBondt and Thaler (1987), Lakonishok, Shleifer and Vishny (1994) and Haugen (1995) offer another reason for the value premium, based on the overreaction hypothesis. The search for the reasons why the size premium exists has, however, been unsuccessful (see, e.g., Chan & Chen, 1991; Perez-Quiroz & Timmermann, 2000; Lettau & Ludvigson, 2001).
Fama and French (1996) concede that their three-factor model is unable to explain the well-documented momentum effect. In view of this, Carhart (1997) adds a fourth factor to the model to reflect momentum. The author finds that the momentum factor also plays a significant role in explaining expected returns, suggesting that momentum is yet another important market anomaly that the CAPM and the Fama-French three-factor model fail to capture. There are several different explanations for the existence of the momentum. Barberis, Shleifer and Vishny (1998) use behavioural models to show that investor underreaction, or
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overreaction, to firm specific news is a possible explanation of momentum anomaly. Daniel, Hirshleifer and Subrahmanyam (1998) and Barberis et al. (1998) suggest that investors failing to incorporate new information into their investment under the irrational theory may lead to the momentum phenomenon. Hong and Stein (1999) and Chordia and Shivkumar (2002) attribute momentum to macroeconomic factors.
Amihud and Mendelson (1986) pioneer the studies on the role of liquidity in asset- pricing models and find that liquidity, which was previously regarded as a firm specific characteristic, is related to the cross-section of asset returns. Several researchers also suggest that liquidity variation and uncertainty constitutes some undiversifiable systematic risk, which needs to be compensated for (Chordia, Roll & Subrahmanyam, 2001; Hasbrouck & Seppi, 2001; Huberman & Halka, 2001). Amihud (2002) and Bekaert, Harvery and Lundblad (2003) find evidence that liquidity has predictive power for stocks’ future returns. Acharya and Pedersen (2005) incorporate transaction cost, which is a very important determinant of liquidity, into the CAPM framework and reveal that the liquidity-adjusted asset pricing model performs better in explaining return variations. Pastor and Stambaugh (2003) use a five-factor model, adjusting for Fama-French’s three factors and the momentum factor. Their results imply that sensitivity to market-wide shifts in liquidity may also be a priced risk factor, since stocks with a high “liquidity beta” have high average returns. This liquidity factor appears to be distinct from the market, size, value and momentum, hence it is an independent source of risk. Liquidity betas are, however, highly unstable and there is substantial variation in the corresponding premium.
In fact, most of the factors in the above-reviewed multi-factor models, such as the market portfolio, SMB and HML, behave in the way that the risk factors from the Arbitrage
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Pricing Theory (APT) model would behave (these risk factors are systematic and cannot be diversified away).32 The APT model hinges on the premise that arbitrage opportunities should not be present in efficient financial markets and that, in order to prevent arbitrage, an asset’s expected returns must depend (linearly) on its sensitivity to a sufficient number (n) of systematic risks (Ross, 1976a, 1976b). The absence of arbitrage opportunities is possible only if market participants are able to take offsetting positions in close economic substitutes in order to enforce the law of one price. The chief obstacles to arbitrage in these cases are short- sale constraints. Thus, where short sales are practiced, there is no need to include the no- shorting factor defined above as the n+1th common factor. Many asset markets in the real world are, however, inefficient because of short-selling restrictions among all market frictions. As such, the no-shorting factor should be added to the model so that arbitrage opportunities across assets will vanish. Without doing so, the validity of the above-reviewed multi-factor asset-pricing models when applied to markets with short-selling restrictions would be impaired by the presence of arbitrage opportunities.