The effects of errors in means, variances, and correlations on the mean-variance framework

Abstract

The mean-variance (MV) framework has been a fundamental tenet of investment management, yet it has been criticized for being too sensitive to parameter estimation errors. Hence, it is important to understand how the errors in parameters affect the MV framework. Although a number of researchers have studied how errors in parameters affect MV optimal portfolios, these studies do not show the complete picture. The MV framework is a tool for systematic evaluation of investment alternatives based on the risk-return trade-off, and MV optimal portfolios are its outputs. In this study, we investigate the effect of errors in parameters on the entire MV framework. We analyze the Sharpe ratio distribution of all possible portfolios, which represents how investments are evaluated under the risk-return trade-off. While means have been widely considered as the most important parameter in the MV optimization, our full-distributional analyses reveal that correlations mostly dominate other parameters.