Portfolio Construction and Uncertainty

Abstract

Traditional mean variance optimization assumes that future returns and covariances of all the assets in the universe are known exactly. In practice, these input parameters are subject to estimation errors that may render the output of the optimization algorithm essentially useless. Here we present three alternative ways to deal with parameter uncertainty when constructing optimal portfolio allocations. The portfolio resampling is a heuristic method to achieve less concentrated portfolios that deliver stable results out-of-sample. Bayesian estimators provide a mathematical framework to update prior beliefs with estimation uncertainty to derive more stable portfolios. The naïve equal weighted portfolio assumes that there is no knowledge about the future. We show that these portfolios outperform the traditional mean variance efficient portfolios and recommend using such techniques or a combination of these techniques to construct passive investment benchmarks. Furthermore we recommend using a more active approach to portfolio investing in order to profit from the generally smaller estimation errors of near term forecasts than long term forecasts. This approach results in allocating more than half the total portfolio risk to tactical asset allocation. At the same time the freedom of the active manager needs to be controlled by an asymmetric tracking error resulting in asymmetric payoff structures through active management.

Keywords: portfolio construction, Bayesian efficient frontier, resampled efficient frontier, equal weighted portfolios

JEL Classification: C11, C13, C15