Performance analysis and optimal selection of large mean-variance portfolios under estimation risk

We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of assets remains comparable in magnitude to the sample size, we provide a characterization of the estimation risk by providing deterministic equivalents of the portfolio out-of-sample performance in terms of the underlying investment scenario. The previous estimates represent a means of quantifying the amount of risk underestimation and return overestimation of improved portfolio constructions beyond standard ones. Well-known for the latter, if not corrected, these deviations lead to inaccurate and overly optimistic Sharpe-based investment decisions. Our results are based on recent contributions in the field of random matrix theory. Along with the asymptotic analysis, the analytical framework allows us to find bias corrections improving on the achieved out-of-sample performance of typical portfolio constructions. Some numerical simulations validate our theoretical findings

Coherent Asset Allocation and Diversification in the Presence of Stress Events

We propose a method to integrate frequentist and subjective probabilities in order to obtain a coherent asset allocation in the presence of stress events. Our working assumption is that in normal market asset returns are sufficiently regular for frequentist statistical techniques to identify their joint distribution, once the outliers have been removed from the data set. We also argue, however, that the exceptional events facing the portfolio manager at any point in time are specific to the each individual crisis, and that past regularities cannot be relied upon. We therefore deal with exceptional returns by eliciting subjective probabilities, and by employing the Bayesian net technology to ensure logical consistency. The portfolio allocation is then obtained by utility maximization over the combined (normal plus exceptional) distribution of returns. We show the procedure in detail in a stylized case.Stress tests, asset allocation, Bayesian Networks