Impact of error in parameter estimations on large scale portfolio optimization

Abstract

Portfolio selection is construction of portfolios that maximize level of the expected returns from investments, but at the same time have low involved risks. One fundamental approach for quantifying the risk–return trade-off of assets is mean–variance analysis. In this case, it is crucial to accurately estimate parameters of the model. We examine how estimation error for means and covariance matrix of stock returns may affect the results of selected portfolios. One of the main contributions of this research are different experiments conducted using both the real data from different stock markets and generated samples to compare the out-of-sample performance of the estimators and how estimation error may affect results of portfolio selection. A new surprising phenomenon is observed for large scale portfolio optimization: efficiency of obtained optimal portfolio is biased with respect to the true optimal portfolio. Different aspects of this phenomenon and possible ways to reduce its negative effect are discussed.