Normality, Solvency, and Portfolio Choice

This paper examines whether investors with power utility functions choose mean-variance-(MV) efficient portfolios when returns are approximately normally distributed and there is borrowing or lending at a riskless interest rate. The results show that the unlevered portfolios of power utility investors plot very closely to the MV-efficient frontier. However, there are marked differences in the mix of risky assets, regardless of whether the portfolios are highly concentrated or widely diversified. Such differences allow power investors to remain solvent even when they lever their optimal portfolios to a greater extent than “less risk-averse” MV investors who risk bankruptcy. It is concluded that the investment policies of power utility and MV investors with similar risk aversion measures are not as similar as is commonly believed. This is particularly true for high power investors, unless explicit solvency constraints are imposed on the MV problem, and for low power investors when quadratic utility approximations are made to the power utility functions. These differences in the investment policies of power utility and MV investors lead us to question the widely-accepted assertion that the assumptions of homogeneous beliefs, normality, a riskless asset, and risk-averse investors imply the simple MV CAPM where all investors, including power utility investors, hold combinations of the market portfolio and the riskless asset.