The Capital Asset Pricing Model: Theory and Evidence

Author: Fama, French

By Maia

This article argues whether the model’s problem reflect weakness in the theory or in its empirical implementation, the failure of the CAPM in empirical test implies that most application of the model are invalid.

Theory of CAPM

The CAPM model has assumptions about complete agreement between investors, and that there is borrowing and lending for investors, which does not depend on the amount borrowed or lent.

Minimum variance frontier traces combinations of expected return and risk for porfolios of risky assets that minimize return variance at different levels of expected return. With complete agreement about distributions of returns, all investors see the same opportunity set and they combine the same risky tangency portfolio T with risk-free lending or borrowing. This is the value-weight market portfolio of risky assets. Each asset’s weight must be the total market value of all outstanding units of asset divided by the total market value of all risky assets.Beta measures the sensitivity of the asset’s return to variation in the market return.

Critics

Unrestricted risk-free borrowing and lending is an unrealistic assumption. Black developed a model of CAPM without risk-free borrowing or lending. He showed that the market portfolio mean-variance-efficient- can be obtained by allowing unrestricted short sales of risky assets. But the assumption that short selling is unrestricted is as unrealistic as risk-free borrowing. But all interesting models include unrealistic simplifications, thus the model still must be tested against the data.

Early Empirical Tests

-Tests on risk premiums

  1. The regressions consistently find that the intercept is greater than the average risk-free rate and the coefficient on beta is less than the average excess market return.
  2. There is also evidence that the relation of beta and average return is too flat. Fama and French also prove with the test that in real life the relation between beta and average return is much flatter than CAPM predicts. The returns on low beta portfolios are too high, and the returns on high beta portfolios are too low.

-Testing whether market Betas explain expected returns

  1. CAPM implies that differences in expected return across securities and portdolios are entirely explained by market beta. Previous studies, regressions and tests show that the central predictions of CAPM that market betas suffice to explain expected returns and that the risk premium for beta is positive seem to hold.
  2. But the prediction of CAPM that the premium per unit of beta is the expected market return minus risk-free rate is consistently rejected.

Recent tests

Since 1970 evidence mounts that much of the variation in expected return is unrelated to market beta. Researchers argued that there is size effect- average return on small stocks is higher, and then the returns on high E/P stocks (earnings-price) are higher than predicted by CAPM. Also high debt-equity ratios are associated with returns that are too high relative to market betas and moreover, book-to-market equity ratios have high average returns that are not captured by betas.

Fama and French confirm that size, earnings-price, debt-equity and book-to-market ratios add to the explanation of expected stock returns provided by market beta.

Among those who conclude that empirical failures of the CAPM are fatal- two stories emerge. Behavioralists believe that sorting firms on book-to-market ratios exposes investor overreaction to good and bad times.

The second idea is that we need a more complicated asset pricing model. The CAPM has too many unrealistic assumptions. For example, the assumption that investors care only about the mean and variance of the portfolio. It is reasonable that investors also care about how their portfolio return covaries with labor income and future investment opportunities. So an important dimension of risk is missed.

Merton’s Intertemporal Asset Pricing Model (ICAPM) is an extension of CAPM. In this model investors are concerned not only with their end-of-period payoff, but also with the opportunities thy will have to consume or invest the payoff. It requires additional betas for stated variables (labor income, prices of consumption goods, etc). The evidence also shows that the returns of the stocks of small firms covary more with one another than with returns on the stocks of large firms, and returns with high book –to –market value covary more with one another than with low.

Based on this evidence Fama and Frenched proposed three factor model.

In this model SMB- small minus big, is the difference between the returns on diversified portfolios of small and big stocks, HML-high minus low- is the difference between the returns of diversifed portfolios of high and low book-to-market stocks and the ebtas are slopes in the multiple regressions.

From this model the average value of the market premium- 8.3% a year.

SMB= 3.6% and HML=5.0%.

Fama and French find that this model captures much more of the variation than CAPM.

The main shortcoming of three-factor model is its empirical motivation. SMB and HML are not motivated by predictions about concerns of investors, they are just to capture the patterns uncovered by previous work. There is also a “momentum” factor. Stock that do well relatively to the market, continue to do well, and stocks that do poorly,continue to do poorly. This effect is left unexplained by CAPM or three-factor model.

Conclusion

The version of the CAPM developed by Sharpe and Lintner has never been of empirical success. The Black version of the model has some success. But in the late 1970s research begins to uncover variables like size, various price rations and momentum. The problems are serious enough to invalidate most applications of CAPM. In real life the relation between Beta and return is flatter than predicted by Sharpe ratio. We continue to teasch CAPM as an introduction to the fundamental concepts of portfolio theory and asset pricing, but we also want to warn the studens that despite the seducive simplicity, the CAPM empirical problems invalidate use of its implications.

CAMP: Theory and Evidence

By Eugene Fama and Kenneth French

CAMP offers predictions how to measure risk and relation between expected return and risk.

Investors choose “mean-variance-efficient” portfolio:

-minimize the variance, given expected return

-maximize expected return, given variance.

Tests on CAMP are based on three implications:

  1. expected returns on all assets are linearly related to their betas
  2. the beat premium is positive
  3. assets uncorrelated with the market have expected returns equal to the risk-free interest rate

Problems in tests:

  1. estimates of beats for individual assets are no precise
  2. the regression residuals have common source of variation

To mitigate these problems researchers sort securities on beta when forming a portfolio.

The evidence that the relation between beta and average return is too flat is confirmed in time-series tests.=> the return on low beta is too high, the return on high beta is too low.

Important is that time-series and cross-section regression don’t test CAMP because tested is a specific proxy for the market portfolio.

Conclusion:

-CAMP estimates of the cost of equity for the high beta stocks are too high

-CAMP is only an introduction to the fundamental concepts of portfolio theory and asset pricing. It is built by more complicated models such as Merton’s ICAMP (Intertemporal Capital and Asset Pricing Model)

-The return of small firms covary more with one another than with returns on stocks of large firms.

-Betas for global stock market portfolio cannot explain the high average returns observed around the world on stock with high book-to-market or high-earnings price ratio.