More Evidence on the Distribution of Security Returns

THE SHARPE [18], Lintner [131 and Mossin 1151 capital asset pricing model has provided important insights into such substantive economic issues as capital budgeting, the cost of capital and investment performance. One of the key assumptions in the model is that security returns follow a stable symmetric distribution. The purpose of this paper is to provide additional evidence on the validiity of this assumption. Capital asset pricing models can be derived by assuming that investors are risk adverse and have quadratic utility of wealth functions.' While this assumption is mathematically convenient, it has the unappealing implication that the marginal utility of wealth is negative above some wealth level. Tobin [201 has shown that if asset returns are normally distributed then variance is the proper measure of risk. Thus, the capital asset pricing models are usually based on the assumption that security returns are normally distributed. Serious examination of this assumption began with Fama [5] who analyzed the distribution of the thirty stocks that make up the Dow Jones Industrial Average. His results suggested that security returns are "fat-tailed" or have kurtosis. This evidence casted doubts on the viability of assuming security returns are normally distributed and lead Fama and others to investigate more further the distribution of security returns. There are at least two reasons for this research. First, portfolio theory is sensitive to charges in distributional assumptions. If the distribution of security returns is not stable under addition, it is hard to envision a theory of how to combine securities optimally into portfolios. Second, this research is needed to answer the question of what distribution should be used when testing hypotheses based on security returns. These data have been used to test the efficient market hypothesis, the effect of government regulation and the impact of changes in accounting techniques among other things.2 Thus, both on theoretical and empirical grounds, the question of what distribution security returns follow is important.