Solvency Constraint, Underdiversification, and Idiosyncratic Risks

Contrary to the prediction of the standard portfolio diversification theory, many investors place a large fraction of their stock investment in a small number of stocks. I show that underdiversification may be caused by solvency requirements. My model predicts that for quite general preferences and return distributions: (1) underdiversification decreases in discretionary wealth; and (2) expected return and covariance determine which stocks to invest in, but variance, higher moments, and Sharpe ratio do not matter for this choice. In addition, a less-diversified stock portfolio has a higher expected return, a higher volatility, and a higher skewness, and idiosyncratic risks are priced.