Asset allocation with different covariance/correlation estimators

Abstract

The subject of the study is to test whether the use of different covariance – correlation estimators than the historical covariance matrix that is widely used, would help in portfolio optimization through the mean-variance analysis. In other words, if an investor would like to use the mean-variance analysis in order to invest in assets like stocks or indices, would it be of some help to use more sophisticated estimators for the covariance matrix of the returns of his portfolio? The procedure that it follows to answer this question is the following. First, it defines seven different universes of data. Second, for each universe, it uses fifteen years of data to estimate the parameters of each covariance matrix estimator and next it computes the covariance matrix of each estimator. Third, it estimates the mean-variance efficient frontiers of the seven universes. The expected returns are estimated by the sample historical average, because they are not a subject to our study and although their estimation might not be the best, it is sufficient for our purposes. Next, according to the created mean-variance efficient frontiers, it defines three portfolios for each universe with different expected returns: the conservative, the average and the aggressive portfolio. It computes the realized returns and the forecasted standard deviations for each portfolio of each universe for all the four estimators of covariance matrices and finally, it compares the performance according to the estimators used. The metrics of performance are the Informational ratio, the Conditional Sharpe Ratio and the Certainty Equivalent.