A New Explanation for Underdiversification

Contrary to the prediction of the standard portfolio diversification theory, most investors invest a large fraction of their stock investment in a small number of stocks and less wealthy investors invest in even fewer stocks. We provide a new and somewhat surprising explanation that it can be exactly the need for risk reduction that causes underdiversification. The two key assumptions are that investors require a nonnegative subsistence consumption at which the marginal utility is finite and do not buy on margin or short sell. We show that investors always underdiversify when wealth is low and investors with CRRA or mean-variance preferences may always underdiversify no matter how wealthy they are. Furthermore, investors select stocks only by expected returns and covariances, but any higher moments such as variance and skewness are irrelevant. In addition, less wealthy and less risk averse investors underdiversify more, and a less diversified portfolio (inclusive of the risk-free investment) is less risky than a more diversified one. These main results still hold in equilibrium. Moreover, our equilibrium model shows that a less diversified stock portfolio has a higher expected return, a higher volatility, and maybe also a higher skewness and a lower Sharpe ratio, all consistent with existing empirical findings. Finally, underdiversification in equilibrium implies that idiosyncratic risks can be priced. Journal of Economic Literature Classification Numbers: D11, D91, G11, C61.