What is CAPM, and is it valid to use in modern financial markets? In this paper, the writer will discuss the CAPM in an argumentative approach, and show alternative models with a practical test of the CAPM and its other extension theories, to answer these questions.
Overview:
Capital Assets Pricing Model (henceforth, CAPM) was founded by William Sharp (1964) and John Lintner (1965). It is recognized as the first theory in the field of assets pricing, and because of what Sharp accomplished in order to develop such a theory, he obtained a NOPIL prize in 1990 (Fama & French, 2004). The idea of CAPM is made on the base of portfolio theory. Therefore, it was used to determine the capital's cost and measure portfolio performance.
Portfolio theory and CAPM:
Investors generally look to maximize their wealth, and they are risk-averse. As one expect that to gain more addition return the risk would be increasing or in case of risk decreasing, the return would be decreasing as well. Therefore, there is a question of whether it is possible for investors to maximize the return and minimize the risk level at the same time (Dimson & Mussavian, 1999).
Markowitz (1952) developed the portfolio selection model that essentially answers this question. This model seeks to maximize the expected return in any level of risk. The main idea is that the portfolio total risk can be decreased, provided that additional asset's return is not positively correlated with the return of existing assets in the portfolio. The implication found is that the risk is not the portfolio total risk for an additional security in the portfolio, but "its contribution to the riskiness of a portfolio" (Dimson & Mussavian, 1999, p. 1748). Therefore, the portfolio that has a highest expected return with any level of risk, or a lowest risk level with an expected return represents a point on an "efficient frontier".
Tobin (1958) extended Markowitz's model to prove how investors can invest in different assets classes, and he identified his framework as, "breaking down the portfolio selection problem into gates at different level of aggregation-allocation first among, and then within, asset categories "(p. 85). Tobin's framework is known as the "separation theory". The theory explains that investors will be holding best selected risky portfolio with a risk-free rate asset.
However, regardless of Tobin's development on the model, it needs a huge number of estimates to apply it in practice by financial institutes at this time. Due to the difficulty that has been faced with associating estimations with the portfolio selection model, Sharpe (1963), advanced the model with a simplified portfolio analysis. He assumed that there is a linear relationship between broad market return and assets return, and the asset return can be distinguished by its variance and mean . Sharpe's model has fewer estimates than that required in the optimized portfolio model; therefore, by applying the estimates, which calculate only three parameters per security and the market return variance , the risk measurement has become less problematic (Dimson & Mussavian, 1999). After developing the portfolio, Sharpe (1964) formalized the model, with continuing work of Lintner (1965) and Mossin (1966), who also separately developed the model, "all three authors used the Tobin-Markowitz mean-variance model of portfolio selections as the 'demand side' of an equilibrium approach to the determination of assets pricing" (Buiter, 2003, p.587). Their model is CAPM, it is also known as the Sharpe-Linter-Mossin (SLM), and it explains the relationship between the risk and the expected return, and how assets are priced in financial markets.
CAPM assumptions:
CAPM has several assumptions. Firstly, it assumes that the financial market is perfect and all of its assets are perfectly divisible. Moreover, investors in the market are price takers, there are no transaction costs or tax allocations, and there is no limit to the amount of borrowing and allowing for shot selling. Secondly it assumes that investors can get risk-free rate in case of lending and borrowing. Thirdly, all investors seem to to exhibit risk reverse, as they are interested in maximizing the utility for one period of time. Lastly, it assumes that investors are equal in their expectations.
The CAPM equation, also known as security market line (SML), is:
= + = +
Where : The expected return on asset i
: The risk free rate
: The expected return on market portfolio.
: Beta, which is the measure of "systematic risk" of the asset i
The equation states that the asset has a positive relationship with the return and the risk premium of the market. The expected return on asset i is determined by market risk premium, the risk-free rate and its beta, only in cases of equilibrium.
Empirical tests of CAPM:
Many researchers have tested CAPM to prove the validity of its expectations of future securities and market returns. There have been a large number of hypothesis tests implied by the CAPM.
Sharpe and Cooper (1972) tested the CAPM , they used all stocks in New York stock exchange (NYSE) for the periods between 1931-1967. They examined all stock betas based on the return of five-years prior. After that, they divided the portfolios to ten equal weighted based on the beta values of the individual securities. Then, they recalculated betas yearly and used them to rebalance the portfolios. Sharpe and Cooper then did a regression test of the expected return for portfolios on their beta, and concluded that beta explains a fundamental proportion of the variation in the cross-sectional stock return, with of 95%. However, they discovered that the estimated intercept term was bigger than the actual risk-free rate, which contradicts the prediction of the CAPM.
Another CAPM test was conducted by Miller and Schools (1972), who studied the NYSE stock from 1954-1963. They found that the estimated slope of the market premium was only 0.042, which was smaller than the expected 0.165. In addition, they found that the estimated intercept term was 0.127, not zero as expected. In other words, they concluded that low-beta stocks likely to show positive alphas, whereas high-beta stocks likely to show negative alphas. Therefore, the results appear to be conflicting with the prediction of CAPM.
Generally, the early empirical tests that were conducted on the CAPM seem to contradict the prediction of CAPM, as the intercept term appears to be different from zero and the slope of the model is different from the market return. However, many researchers have shown that the CAPM is an acceptable model of returns, such as Blume and Friend (1973), who tested the CAPM they used stocks of NYSE over the period ranging from 1955-1968. They divided the sample into three periods (i.e. 1955-1959, 1960-1964 and 1965-1968). They rejected the model, as the estimated intercept term looked considerably greater than the actual risk-free rate for the first two periods and smaller in the third period. However, their results have supported the linearity prediction of the CAPM, because the slopes of are insignificant in five of the six regressions. But, their rejection was likely caused by the violation of the short- selling assumption.
Critiques on the CAPM tests:
The conclusions drawn by researchers in support of CAPM and the empirical tests of CAPM were attacked by what it is known as "Roll's critique". Roll (1977) claimed that the conclusion made related to CAPM's prediction might be invalid. Roll showed that beta calculated in the portfolio mean return matches the linearity condition, despite the actual return generating process, in any data sample. Therefore, the results of the early tests on CAPM are tautological, in that similar results could be obtained regardless of how the securities are priced to their risk.
Then, Roll (1977) declared that the only testable hypothesis regarding the CAPM is "the market portfolio is mean-variance efficient" (p.130). Roll declared that in order to test the model prediction and the linear relationship between the beta and return , the mean-variance efficient market portfolio condition must be holds, and it should not be tested alone. Roll also mentioned that the test of CAPM is more critical in case of choosing the proxy of the market portfolio, as the theory requires that it must apply the true market portfolio (which comprises all individual assets in the global financial markets), which is complicated to apply it in practice. This has made researchers think about making a proxy portfolio, which is the broad market index. However, the theory of market portfolio that Roll pointed out has several problems. First, the proxy market portfolio might be efficient whereas the true market portfolio is not. Second, the proxy market portfolio might be inefficient, but then it would be unnecessary to imply the true market portfolio is also inefficient. Roll concluded that if the true market portfolio is unknown, the CAPM cannot be tested.
Extensions of the CAPM and alternatives asset-pricing models:
7.1 Intertemporal CAPM:
Several studies and research projects have attempted to extend the CAPM. One of CAPM's limitations involves its highly simplified assumptions. For example, investors only make decisions over one single time period. It is, therefore, unlikely to hold. In practice, investors rebalance their portfolio holdings. In particular, Merton (1973) developed what it called Intertemporal CAPM (ICAPM), which permits holding periods that are permitted to change over time, and assumes that investors can maximize their return during their lifetime. The major implication of this model that a number of betas are needed to set the expected return, and the number of betas equal to one (i.e. the broad market factor).
7.2 Consumption CAPM:
In another attempt to simplify the Merton's model (ICAPM), Breeden (1979) developed the Consumption CAPM (CCAPM), which had a beta that was based not on aggregate market portfolio, but on aggregate consumption. The main implication in this model was that only one single beta is required to capture the expected return.
7.3 Fama-French three-factor model:
Since the studies and development of the CAPM, those studies concluded that it does not perform well in explaining securities returns. As in many cases of these studies, both slope and alpha have been reported to be statistically different from the hypothesized values. In addition, there are many "anomalies" that have appeared when the CAPM is implied in cross-sectional expected return tests. One of the anomalies is the size effect mentioned by Banz (1981), who examined the size effect of the NYSE stocks beween 1936-1977. The results indicated that small size companies (measured by market equity) appeared to have higher risk-adjusted (measured by beta) average annualized return of 19.8 than the large sized firms. Another anomaly documented by Stattman (1980), was the book-to-market effect, where the high book-to-market ratio companies have a higher average return than the low book-to-market ratio companies. Other anomalies include the leverage effect, where the firms with high leverage tend have a higher return (Bhandari, 1988); and the earning/price effect (E/P), where stocks with a high E/P seem to have a higher return (Basu, 1983).
Fama and French (1992) empirically investigated how the market beta, E/P, size, leverage and book-to-market equity clarify the cross-sectional average return of all non-financial NYSE, AMEX and NASDAQ stocks over the period ranging from 1962-1989. They classed the stocks first into size deciles, based on the firms' previous year market equity values. Then, they into beta deciles based on pre-ranking beta estimates. Then, they applied a cross-sectional regression technique. Their results indicated that market beta appeared to be insignificant. Furthermore, the results showed that when E/P and leverage effects were significant, they were counted by book-to-market and the size factors. Generally, these outcomes imply that only book-to-market and size variables are needed to explain the cross-sectional return of the stocks. Therefore, this contradicts the major prediction of the CAPM.
However, Fama and French (1993) found that beta was significant and that its effect was neither subsumed by book-to-market nor size effects. The results suggest an asset-pricing model, which is referred to as, ' Fama-French three-factors model.'
Fama and French (1996) conducted an empirical test of the three-factor model using NASDAQ, AMEX and NYSE stocks over the period from 1963-1993. The model appeared in this test to capture a number of anomalies that CAPM did not. The three-factor model proved that stocks with a positive HML slope have a higher return than growth stocks. However, the model did not explain the short-term momentum return.
Conclusion
In general, the early studies of the CAPM seem to support the model's prediction. However, the intercept term appears different from the predicted value. A number of alternative models developed the CAPM. Currently, the most prominent asset-pricing model is the Fama-French three-factor model. This model includes two anomalies that differ from the CAPM: book-to-market and the size factors. The performance of the model was later confirmed by their early studies (1993-1995-1996). However, the writer believes that the CAPM will still be the base from which all developed models start, at least from a theoretical viewpoint. But the question remains regarding the capability of the CAPM in remaining applicable for long time as a foundational theory.
