Custom Search

4.00%

In an economy in which returns are Gaussian and independent; and in which standard deviation risk is priced; and in which investors hold portfolios similar to the sum portfolio, it can be shown that investors will only price the additive component of standard deviation risk (called the systematic risk) of a risky asset. The remainder of the risk, called 'diversifiable risk', simply cancels out on addition to the sum portfolio.

The only economic theory we have used so far are: (1) standard deviation risk is priced in the economy, (2) the sum portfolio is observable, and (3) investors hold well diversified portfolios similar to the sum portfolio. It is therefore only these aspects of the theory that may be put to empirical tests.

Let us now examine the Fama and French (1992) paper in some detail. The authors collect beta and returns data over a moving window of time from 1962 to 1989 and find no relationship between beta and returns. We would expect to see such a relationship only if the market volatility Sm were constant. This is not the case. Therefore no conclusion may be drawn from their test.

The real question is whether standard deviation risk is priced. And corollary questions; are how should the standard deviation be measured? and is the S&P500 index an adequate proxy for the sum portfolio?

When Fama and French (1992) removed the size effect from the data they may have also removed that which they intended to measure - the beta effect. A failure to find a beta effect in the residuals of the size effect does not imply an absence of a beta effect. There are better ways to find the unique contributions of the two correlated variables. For example, one might first regress beta against size and use these residuals as the unique contribution of beta and then regress size against beta and use those residuals as the unique contribution of size. Alternately, one might look for orthogonal principal components of size and beta.

An added complication in asset pricing research is that some of the empirical models include the PE ratio (PE = stock price over accounting earnings) as an explanatory variable in addition to the risk measure beta. But PE too contains a risk measure. Current financial theory interprets PE as a combination of two effects. Ceteris paribus higher perceived risk would lower the PE ratio and higher perceived growth would raise the PE ratio. Empirical studies are complicated by a high collinearity between PE and beta. There are other problems with asset pricing studies that have to do with the time series nature of the data and the methods by which the concept of risk is rendered and we review these concerns in a later section of this paper.

BRIEF REFERENCES

Banz, Rolf, The relationship between return and market value of common stocks, Journal of Financial Economics, v9 p3, 1981

Black, Fisher, Beta and return, Journal of Portfolio Management, Fall 1993, p8

Brown, Keith, W.B. Harlow, and Seha Tinic, How rational investors deal with uncertainty: reports of the death of the efficient market theory are greatly exaggerated, Financial Management Collection, Fall 1990

Chan, K. C., and Josef Lakonishok, Are reports of beta's death premature?, Journal of Portfolio Management, Summer 1993

Dimson, Elroy, Risk measurement when shares are subject to infrequent trading, Journal of Financial Economics, v7, p197, 1979 (the non-synchronicity problem)

Fama, Eugene, and Kenneth French, The cross section of expected stock returns, Journal of Finance, v47:2, 1992, p427

Fama, Eugene, and James MacBeth, Risk, return, and equilibrium, Journal of Political Economy, 1973, 81, p607

Garman, Mark, and Michael Klass, On the estimation of security price volatilities from historical data, Journal of Business, v53, p67, 1980

Haugen, Robert, and Nardin Baker, Interpreting risk and expected return: comment, Journal of Portfolio Management, Spring 1993, p36 (confirms F-F and rationalizes higher returns for lower ris. the market prices growth stocks too high)

Hsieh, David, Nonlinear Dynamics in Financial Markets, Financial Analysts Journal, July-August 1995, p55

Kolb, Robert, and Ricardo Rodriguez, The regression tendencies of betas, The Financial Review, v24:2 May, 1989, p319 (beta is not stationary)

Krueger, Thomas, and William Kennedy, An examination of the superbowl stock market predictor, Journal of Finance, June, 1990, p691

Markowitz, Harry, Portfolio selection, Journal of Finance, v12, March 1952, p77

Parkinson, Michael, The extreme value method for estimating the variance of the rate of return, Journal of Business, v53, p61, 1980

Reinganum, Marc, A new empirical perspective on the CAPM, Journal of Financial and Quantitative Analysis, v16, p439, 1981

Roll, Richard, A critique of the asset pricing theory's tests, Journal of Financial Economics, March 1977, p129

Schwert, G. W., Why does stock market volatility change over time?, Journal of Finance, Dec 1989, p1115

Sharpe, William, A simplified model for porftolio returns, Management Science, 1962, p277

Sharpe, William, Capital asset prices: a theory of market equilibrium under conditions of risk, Journal of Finance, v19, p425, 1964

Shukla, Ravi, and Vhrles Trzcinka, Research on risk and return: Can measures of risk explain anything?, Journal of Portfolio Management, Spring 1991 (weekly returns, capm just as good as multifactor apt)

Velleman, Paul, Definition and comparison
of robust nonlinear data smoothing algorithms", Journal of the American
Statistical Association, 75, September 1980,

609-615.