ABSTRACT Complete diversification is the rational investment strategy for a risk averse individual in a homogeneous securities market who considers only the first two moments of return. Observed behavior of market participants, however, demonstrates that the majority of individual investors hold imperfectly diversified portfolios. The purpose of the present study is to examine one potential cause for this behavior which does not rely on imperfection in the capital market. Specifically, we show that given the existence of, and investor preference for, positive skewness, a rational investor may hold an optimal limited number of homogeneous risk assets.

Studies of horse race betting have empirically established a long shot anomaly; that is, low‐probabiliy, high‐variance bets (long shots) provide low mean returns and high‐probability, lowvariance bets provide relatively high mean returns. Because bettors willingly accept low‐return, high‐variance bets, researchers conclude that bettors are risk lovers. In this study, we show that the data are at least as consistent with risk aversion as they are with risk loving when one explicitly considers the skewness of bet returns. Because the variance and skewness of bet returns are highly correlated, bettors may appear to prefer variance when it is skewness that they crave.