Normality, Solvency, and Portfolio Choice
研究幂效用投资者在正态分布回报下是否选择均值方差有效组合，发现其与均值方差投资者的投资政策存在显著差异，尤其在高杠杆或低幂效用时，挑战了经典CAPM的普适性。
This paper examines whether investors with power utility functions choose mean-vari? ance- (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. How? ever, 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 ex? tent than less 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 inves? tors, 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 func? tions. 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 ofthe market portfolio and the riskless asset.