Application of Robust Statistics to Asset Allocation Models

Abstract

Many strategies for asset allocation involve the computation of the expected value and the covariance matrix of the returns of financial instruments. How much of each instrument to own is determined by an attempt to minimize risk — the variance of linear combinations of investments in these financial assets — subject to various constraints such as a given level of return, concentration limits, etc. The covariance matrix contains many parameters to estimate and two main problems arise. First, the data will very likely have outliers that will seriously affect the covariance matrix. Second, with so many parameters to estimate, a large number of return observations are required and the nature of markets may change substantially over such a long period. In this paper we discuss using robust covariance procedures, FAST-MCD, Iterated Bivariate Winsorization and Fast 2-D Winsorization, to address the first problem and penalization methods for the second. When back-tested on market data, these methods are shown to be effective in improving portfolio performance. Robust asset allocation methods have great potential to improve risk-adjusted portfolio returns and therefore deserve further exploration in investment management research.