M. Senneret, Y. Malevergne, P. Abry, G. Perrin, L. Jaffrès
We conduct an empirical analysis of the relative performance of several estimation methods for the covariance and the precision matrix of a large set of European stock returns with application to portfolio selection in the mean-variance framework. We develop several precision matrix estimators and compare their performance to their covariance matrix estimators counterpart. We account for the presence of short-sale restrictions, or the lack thereof, on the optimization process and study their impact on the stability of the optimal portfolios. We show that the best performing estimation strategy, on the basis of the ex-post Sharpe ratio, does not actually depend on the fact that we choose to estimate the covariance or the precision matrix. Nonetheless, the optimal portfolios derived from the estimated precision matrix enjoy a much lower turnover rate and concentration level even in the absence of constraints on the investment process.
