Stock markets in the United States and foreign countries exhibit a strong weekly seasonal, an empirical regularity for which no theoretical explanation has been found. One's belief in this phenomenon would be strengthened if it is known to also occur in capital markets separated from those in the United States by distance, institutional arrangements, and culture.

The empirical distributions of price changes for speculative assets (e.g., common stocks, bonds, etc.) measured over calendar time yield a higher frequency of observations near the mean and at the tails than would be expected for a normal distribution. The sample kurtosis is almost always greater than 3—the value expected for a normal distribution—and the distributions are commonly characterized as fat-tailed and peaked (i.e., leptokurtic).

It is clear from several previous empirical studies that diversification reduces portfolio return variability and that the reduction of variability appears very quickly. The purpose of this paper is to reexamine the question of how diversification affects the distribution of portfolio returns. There is no doubt that increasing the number of securities in a portfolio will reduce the nonmarket related return variability. However, there are several areas of controversy. For example, it should be recognized that the term “variability” can have different definitions. Furthermore, the ability of diversication to eliminate independent elements of the variability of return is important only if this reduction can be incorporated into predictions of future risk. In addition, the method of portfolio formation may determine the extent to which diversification enables portfolio managers to more accurately assist future risk.

This paper examines the validity of two widely used methods for forming conditional predicted portfolio returns. The first method relies on a one-period, mean-variance theory of equilibrium expected return, sometimes referred to as the “capital asset pricing model” (CAPM). The second method is based upon a proposal by Markowitz [14] and is called the [market model] (MM).

The “market model” of capital asset pricing theory posits that the oneperiod return on an asset is a linear function of the one-period return on a “market factor” plus the effect of factors that are unique to that asset. The coefficients of the model, estimated using realized returns, can be used for predicting asset returns conditional on market returns, and the slope or “beta” coefficient provides an estimate of the asset's risk. Although the market model has been applied to a wide variety of capital market studies and is now being applied by practitioners for assessing asset risk, very little research has been undertaken to discover the determinants of the beta coefficient.