An Improved Estimation to Make Markowitz's Portfolio Optimization Theory Users Friendly and Practically Useful

Abstract

Using the Markowitz mean-variance portfolio optimization theory, researchers have shown that the traditional estimated return greatly overestimates the theoretical optimal return, especially when the dimension to sample size ratio is large. Bai, Liu, and Wong (2006,2009a,b) propose bootstrap-corrected estimators to correct the overestimation, but there is no closed form for their estimator. To address this limitation, this paper derives explicit formulas for the estimator of the optimal portfolio return. We also prove that our proposed closed-form return estimator is consistent when sample size tends to infinite and when the sample size ratio tends to a constant. Our simulation results show that our proposed estimators dramatically outperform traditional estimators for both the optimal return and its corresponding allocation under different values of p/n ratios and different inter-asset correlations rho, especially when the sample size ratio is close to 1. We also find that our proposed estimators perform better than the bootstrap - corrected estimators for both the optimal return and its corresponding allocation. Another advantage of our improved estimation of returns is that we can also obtain an explicit formula for the standard deviation of the improved return estimate and it is smaller than that of the traditional estimate, especially when the sample size ratio is large.