(The) effects of errors in means, variances, and correlations on all feasible portfolios

Abstract

In mean-variance framework, the mean and standard deviation of historical asset returns are used as the measure of asset return and risk. Even though Markowitz's mean-variance optimization is not used, the mean of the asset returns and the covariance matrix are still important factors in selecting components of a portfolio. It is therefore important to understand the sensitivity of portfolios to errors in mean and covariance matrix that occur in measuring. Many studies including the one of Chopra and Ziemba (1993) found the effect of errors in mean and covariance matrix but they only considered about the effect on single portfolio, mainly MV-optimal portfolio. This thesis examined the change in Sharpe-ratio distributions of all feasible portfolios due to the errors in means, variances, and correlations by adopting the concept of uniformly distributed random portfolio of Kim and Lee (2016). We found that the Sharpe-ratio distribution of all possible portfolios changed the most by errors in correlation.