Empirical research has provided several pieces of evidence that reject the validity of the Sharpe-Linter capital asset pricing model (CAPM). The existence of market
frictions, the presence of irrational investors and inefficient markets may distort the cross-sectional relationship between expected stock returns and market return. This research will discuss the related evidence that has been reported in empirical studies.
2.1 Systematic Risk (Beta)
Beta, or the sensitivity of asset returns to underlying sources of risk, is central to modern finance. Beta has been used by academics and practitioners to model and measure systematic risk. Sharpe (1964) and Linter (1965) found a positive and a linear function between the expected returns on securities and their betas. Miller and Scholes (1972), Black, Jensen, and Scholes (1972), and Fama and MacBeth (1973) all empirically confirmed a positive relationship between mean returns and betas across firms.
Subsequently, Reinganum (1981) found that estimated betas were not systematically related to average returns across New York Stock Exchange and American Stock Exchange securities. In the 1990s, however, much controversy was stirred in the finance literature as if beta completely lacked predictive power for expected returns.
For instance, Fama and French (1992) also found evidence that the relationship between the average return and beta for common stocks was even flatter after the sample periods used in the early empirical work on the CAPM, and that the relationship between beta and the average return was flat, even when beta was the only explanatory variable. Kothari, Shanken, and Sloan (1995) tried to resuscitate the Sharpe-Lintner CAPM by arguing that the weak relationship between the average return and beta came about just by chance. However, the strong evidence that other variables captured the variation in expected return missed by beta made this argument irrelevant. By investigating international findings, Heston, Rouwenhorst, and Wessels (1999) examined the ability of beta and size to explain cross-sectional variation in average returns in 12 European countries. They found that average stock
returns were positively related to beta and negatively related to firm size. The beta premium was in part due to the fact that high beta countries outperformed low beta countries. Within countries, high beta stocks outperformed low beta stocks only in January, but not in other months. The differences in the average returns of the size- and beta-sorted portfolios could not be explained by market risk and exposure to the excess return of small over large stocks (SMB)1.
2.2 Size Effect
The size effect is the most well-known empirical inconsistency of the CAPM.
The size premium for small-cap firms is one of the market anomalies and was originally discovered by Banz (1981). The evidence showed that the stock returns of firms with small-cap market capital (size) had statistically higher returns than firms with large-cap market capital and the CAPM beta could not justify this effect. In the meantime, Reinganum (1981) also found that the size of the firm (as measured by the market value of firm equity) was inversely related to mean returns across firms over the 1963-1977 period, after controlling for the beta. After that, there were several discussions regarding the size effect, and studies such as Chan, Chen and Hsieh (1985) among others argued that small firms had higher returns than large firms because they fluctuated more with economic expansions and contractions. Later, Fama and French (1992) concluded that, in their U.S. sample, the univariate relationship between beta and the average return for the 1941-1990 period was weak and beta did not explain the average return. It was size that captured the differences in the average stock returns.
Berk (1995) provided an explanation for the size effect and argued that firm size
1 SMB, which stands for Small Minus Big, is designed to measure the additional return that investors have historically received by investing in the stocks of companies with relatively small market capitalization. This additional return is often referred to as the “size premium.” A further definition can be seen in Section 4.2 in this paper.
would in general explain the part of the cross-section of expected returns left unexplained by an incorrectly specified asset pricing model. Chen and Zhang (1998) found that returns were higher for small firms in the Taiwan stock market. Besides, further research on the size effect using data from international markets has also been examined. For example, Heston, Rouwenhorst, and Wessels (1995) found evidence of a size effect in European markets by showing that equally-weighted stock portfolios tended to have higher average returns than value-weighted portfolios.
Chui and Wei (1998) showed that the size effect was significant in Pacific-Basin emerging markets apart from Taiwan. Rouwenhorst (1999) showed that the return factors in 20 almost emerging markets were qualitatively similar to those documented in many developed markets: small stocks outperformed large stocks.
2.3 Book-to-Market Equity (BE/ME)
Research since the 1980s has generally found that BE/ME has significant explanatory power to predict the cross-sectional stock returns and that BE/ME has better explanatory ability than firm size. Stattman (1980) documented an association between expected returns and BE/ME, which remained significant after controlling for beta, size, and other firm characteristics (Fama and French, 1992; Lakonishok, Shleifer, and Vishny, 1994). Rosenberg, Reid, and Lanstein (1985) also found a positive and significant relationship between BE/ME and mean returns across firms.
Penman (1991) and Fama and French (1995) found similar evidence of high BE/ME firms being more profitable than high BE/ME firms.
There have also been many international studies examining the explanatory ability of BE/ME. Chan and Chen (1991) also found that BE/ME played an important role in explaining the cross-section of average returns on Japanese stocks.
Miles and Timmerman (1996) reported that BE/ME appeared to be a main factor driving the cross-sectional company returns in the U.K. Roll (1995) analyzed
Indonesian stocks and reported that the value portfolios (high BE/ME) consistently out-performed the growth portfolios (low BE/ME). Chen and Zhang (1998) observed that the difference in returns between high BE/ME firms (risky firms) and low BE/ME firms (low-risk firms) was larger in mature markets than the difference in high-growth markets. Jansen and Verschoor (2004) discovered that the relationship between market returns and the BE/ME ratio was strong in the Czech Republic, Hungary, Poland, Russia, and Hong Kong. As a whole, the evidence provides considerable support for the cross-sectional explanatory power of BE/ME.
A positive relationship between BE/ME and risk is expected for several reasons.
Chan and Chen (1991) and Fama and French (1993) suggested that a distinct “distress factor” helped explain the common variation in stock returns. Poorly performing, or distressed, firms are likely to have high BE/ME ratios. These firms are especially sensitive to economic conditions, and their returns might be driven by many of the same macroeconomic factors (such as variation over time in bankruptcy costs and access to credit markets). In addition, based on the arguments of Ball (1978) and Berk (1995), a firm’s BE/ME might proxy for risk because of the inverse relationship between market value and discount rates. By holding book value constant in the numerator, a firm’s BE/ME ratio increases as expected return, and consequently risk, increases. Alternatively, the BE/ME ratio might provide information about security mis-pricing. The mis-pricing view takes the perspective of a contrarian investor. A firm with poor stock price performance tends to be under-priced and to have a low market value relative to book value. As a result, a high BE/ME is indicative of high future returns as the under-pricing is eliminated. Lakonishok, Shleifer, and Vishny (1994) offered a rationale for the association between past performance and mis-pricing. They disputed the view that investors truthfully extrapolated past growth when evaluating a firm’s prospects. For example, investors tended to be
overly pessimistic about a firm that has had low or negative earnings.
2.4 Value-at-Risk (VaR)
The VaR analysis originated with the variance-covariance model introduced by RiskMetrics that was developed by J.P. Morgan in 1993. However, the variance-covariance approach to calculating risk can be traced back to the early days of modern portfolio theory starting with Markowitz (1959), with which most of today’s risk managers are conversant. This is why this type of VaR model had a lot of applications in the early days. Engle and Manganelli (1999) extended the quantile regression to model the VaR directly instead of modeling the underlying volatility generating process and also introduced the conditional autoregressive Value-at-Risk (CAViaR) model.
More recently, one thing that particularly deserves to be mentioned is that VaR has been found to be an important risk factor for explaining cross-sectional stock returns. Bali and Cakici (2004) found that the maximum likely losses measured by VaR could capture the cross-sectional differences in expected stock returns on the NYSE, AMEX, and Nasdaq stocks for the period from January 1963 through December 2001, while the market beta and total volatility had almost no power whatsoever to explain average stock returns at the firm level. Bali and Cakici (2004) argued that VaR had so far not been regarded as an alternative risk factor that added to the explanation of stock returns. This study has been largely motivated by their strong findings and will follow a similar methodology by applying data from Taiwan that will compare the relative predictive ability (in terms of the