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CAPM Review
向上 ] [ CAPM Review ] Critical Research ]


Come Together

PART 1.  



One of the major tasks of corporate financial executives is to evaluate investment opportunities. Of the many analytical methods collectively referred as to Modern Portfolio Theory, the Capital Asset Pricing Model (CAPM) is the most widely recognised and applied measure of risk in the investment opportunities.

The essence of the CAPM is the relationship between expected return and systematic risk, and the valuation of security that follows. In other words, a security will be expected to provide a return commensurated with its systematic risk, the risk that can not be eliminated by the diversification. Moreover, the greater the systematic risk of a security, the greater the return the investors will expect from the security. CAPM describes the relationship as the following equation.

E(Ri)  =  Rf  +  bi ´ [ E(Rm) - Rf ]

Where the E(Ri) is the expected rate of return on the asset, Rf is the risk free return, bi is the beta of the asset, E(Rm) is the expected return on the market portfolio.

1.  CAPM indicates the required rate of return is equal to the sum of two terms: the risk free return and the compensation for accepting the asset’s risk. The compensation for taking risk can be expressed as sensitivity of exposure to the systematic risk, bi, multiplied by the expected excess return of the market, E(Rm) - Rf, also called market risk premium.[1]


CAPM underlines that the cross-section of expected excess returns of financial assets must be linearly related to the market betas, with an intercept of zero. The recent empirical examinations have presented some evidences that statistically contradict the hypothesis that the intercept of a regression of excess return of the market is zero (MacKinlay, 1995, pp.4). These empirical examinations categorise the cross-section pattern of stock returns into characteristics such as size[2], leverage, past returns, dividend-yield, earning-to-price ratios (EP) and book-to-market[3] (BE/ME) ratios.[4]  These factors are referred as anomalies because they are not explained by the CAPM.

Fama and French (1993, 1996) examine these anomalies simultaneously and argue that these anomalies are related and the cross-section variation in expected returns can be explained in only two of these characteristics, size and book-to-market ratio. The conventional measure of risk in CAPM, beta, has little use in explaining the cross-section dispersion in expected return while considering the effect of size factor. The three-factor model (Fama and French, 1993, 1996), asserted to capture most the anomalies, argues that the expected return on a portfolio in excess of the risk-free rate[5] is clarified by the sensitivity of its return on the three following factors: the excess return on a broad market portfolio (E(Rm) - Rf), the difference between the return a portfolio of small stocks and the return on a portfolio of large stocks (SMB, small minus big), and the difference between the return on a portfolio of high-book-to-market stocks and the return on a portfolio of low-book-to-market stocks (HML, high minus low). They further states the following equation of expected excess return on portfolio (1996).

E(Ri) -  Rf =  bi ´[ E(Rm) - Rf ] + si ´E(SMB) + hi ´E(HML)[6]

In this model, they find that the high earnings tend to move together with low book-to-market ratio and positive slopes on HML. They also show that the loading on zero cost factor portfolios that is based on size factor (represented as SMB), book-to-market ratios (represented as HML), and a weighted market portfolio together can determine the excess returns of a full set of book-to-market and size sorted portfolio. Moreover, Fama and French (1993, 1996) asserts this model is an equilibrium pricing model and can be treated as the three-factor version of intertemporal CAPM, ICAPM (Merton, 1973) and arbitrage pricing theory, APT (Ross, 1976).

The three-factor model has triggered a number of debates. Fama and French (1996) recognise much of the debate is about the characteristic of distress premium (the average HML return). One critique is that the three-factor model does illustrate the return but it is the investor irrationality that keeps this model from failing to CAPM (Lakonishok, Shleifer, and Vishny, 1994; MacKinlay, 1995). Lakonishok, Shleifer, and Vishny (1994) suggest that the investors are likely to be overly pessimistic if the past records of the firm appear good and overly optimistic if the records appear bad. Thus, the high returns of high book-to-market stocks are generated by the incorrect extrapolation of past earnings growth rate of firms. On the other hand, the low book-to-market stocks are more attractive than value stocks so that the naive investors will increase prices and degrade the expected returns of these securities. Because of this irrational interpretation, the difference between the average return on high and low book-to-market stocks is too large to be considered as the compensation of the risk (Lakonishok, Shleifer, and Vishny, 1994; MacKinlay, 1995).

Another critique associated with the distress premium in average returns asserts the three-factor model is spurious and CAPM still holds true. This critique results from two aspects, data snooping and survivor bias. Black (1993) and MacKinlay (1995) argue that it is the data snooping that generates the CAPM anomalies. This is concerned with that one can always dredge deviation from CAPM, provided by an ex post basis. Moreover, these deviations organised in  a group will be considered statically significant. However, such deviations are merely the consequence that generated by grouping assets with common disturbance terms. MacKinlay (1995) show the nonrisk-based alternative for CAPM is unconstrained to detect therefore it is difficult to quantify and adjust the influence of data snooping bias. The multifactor model on its own can not explain the deviation from CAPM.

The studies about survivor bias assert the data from which generate the deviation for CAPM may have bias in selection. Kothari, Shanken, and Sloan (1995) present the evidence that, provided that betas are measured at the annual interval, the average returns do reflect considerable compensation for beta risk. Furthermore, they argue that the Fama and French’s results are influenced by the combination of survivorship bias in the COMPUSTAT database. The average returns on high book-to-market portfolios of COMPUSTAT database are overstated because COMPUSTAT database is more likely to not to include the distressed firms that fail but the firms that survive (Kothari, Shanken, and Sloan ,1995, p.204). Therefore, they cast the doubt upon the explanatory power of book-to-market equity. However, they identify the evidence of size effect and furthermore assume that the survivor bias may not be the major problem for value-weighed portfolios (pp.220). Moreover, a recent study (Chan, Jegadeesh, and Lakonishok, 1995) has shown the selection bias is not large and therefore contracted Kothari, Shanken, and Sloan’s statements.



PART 2.  



Although CAPM provides a sensible approach for measuring risk and return , it does have it defect. For example, Roll (1977) argues that CAPM is too restrictive due to the doubt of uniqueness of its only risk reference, the market portfolio. He (1977) further asserts that CAPM can not be really tested empirically and it is unable to capture the questions about persistent return differences associated with size, yield, and even the time of year.[7] Arbitrage pricing theory (APT), developed originally by Ross (1976), does not resolve all of these defects but is thought to be the major alternative for the capital asset pricing model (CAPM). The main attempt of APT can be referred as to resolve the problem with testability and anomalous empirical evidence that undermines the static and intertemporal capital asset pricing models. As the CAPM tries to use a single market index to explain the relation between risk and return, APT considers using several factors to identify such relation.

The underlying assumption of APT is that in the competitive financial markets, arbitrage will assure that the riskless assets make no excess return on average (Ross, 1976). He further asserts that systematic risk (pervasive macroeconomic influence, non-diversifiable) can be measured as exposure to a small number of common factors instead of represented by the single common factor such as the rate of return on market portfolio indicated in CAPM. On the other hand, the idiosyncratic risk can be eliminated in the well-diversified portfolio. Therefore, it suggests that risky assets’ value is determined by their returns’ relationship to a set of macro-factors in the economy; and that assets can be differentially sensitive to movement in such factors.[8]


The advantage of APT, compared with CAPM, can be its ability to provide better description of the expected returns on assets. Connor and Korajczyk (1988) estimate and test the pervasive factors influencing asset returns and restrictions implied by the APT. Although their evidences show that neither of the CAPM nor APT can be the perfect model of asset pricing, the APT is consistent with the size-related seasonal effects in asset pricing. They therefore argue that APT can be the reasonable alternative to the CAPM. Such empirical findings that indicate the better performance of APT to CAPM can also be found in Dhrymes’s article (1984). The recent work of Ferson and Korajcyk (1995) also show that the APT capture the great fraction of predictability for all of the investment horizon, even for the long-horizon returns (2 years). Therefore, APT provides a feasible alternative to CAPM as a practical method of risk estimation for the investors.

However, APT does have some disadvantages. The arbitrage pricing theory does not indicate what the underlying factors are and how many factors are needed to form the formula. The pervasive and systematic influences on the asset price are vague in theory – unlike CAPM, which reduces all the macroeconomic variables into one well-defined factor, the return on the market portfolio. The gap between the theory and application can be possibly reduced in searching the empirical factors which can explain the relation between return and risk. Based on their empirical finding, Chen, Roll and Ross (1986) assert the stock returns are priced in accordance with the their exposures to the systematic economic news. The news can be identified and measured as the innovation in stated variables. In other words, they believe that different securities have different sensitivities to the systematic factors and the major sources of security portfolio risk are captured in them. They further claim that there are four factors found to be significant in explaining the expected stock returns. The four factors are the spread between long and short interest rates, expected and unexpected inflation, industrial production, and the spread between high and low grade bonds (1986). Moreover, according to a recent work on the effect of economic forces on UK stock market (Cheng, 1995), the appropriate variables in explaining UK stock market can be categorised into three economic factors. The first economic factor is comprised mainly of market indices. The second economic factor represents mainly the longer leading indicator, lagging indicator, money supply, interest rate, and unemployment rate. The third economic factor consists of the variables of output measures, such as GDP, consumer expenditures on durable goods, industrial production, and short leading indicator.


The benefit of arbitrage pricing theory can be characterised as providing a better explanation of the relation between risk and return. APT’s better performance stems from its using several macroeconomic variables to explain variation in stock return, instead of using single factor as derived from CAPM. Although it is still in need of more empirical evidence to examine its application, APT has been recognised as the most possible alternative for CAPM. However, APT also has its defects. The theory does not indicate what these underlying factors are and how many should be required for the sufficient explanation. APT however needs more research to identify the determinant economic forces behind those statically constructed factors.


[1] The detail of the equation is described in Appendix attached.

[2] Size (ME) can be described as the price of share times number of shares.

[3] Book-to-market ratio can be described as the ratio of the book value of common equity (BE) to its market value (ME).

[4] The size factor was observed by Banz (1981) and Kein (1983), leverage by Bhandari (1988), the past return effect by DeBondt and Thaler (1985) and Jegadeesh and Titman (1993), the EP ratio by Basu (1983), the book-to-market effect by Rosenberg, Rein, and Lanstein (1985). This summary is originally cited in Daniel and Titman (1997).

[5] The excess of the expected return on a portfolio to the risk-free rate can be described as ( E(Ri)  -  Rf ). 

[6] Where [ E(Rm) - Rf ], E(SMB), and E(HML) are expected premiums and the sensitivity factors bi, si, hi  are the slopes in the time-series regression (Fama and French, 1996).

[7] There are also some details about Roll’s critique described in Copeland’s book (1992, pp217).

[8] The equation of APT is further described in Appendix attached.