Portfolio Selection in a Noisy Environment Using Absolute Deviation as a Risk Measure

Summary Portfolio selection has a central role in finance theory and practical applications. The classical approach uses the standard deviation as risk measure, but a couple of alternatives also exist in the literature. Due to its computational advantages, portfolio optimization based on absolute deviation looks particularly interesting and it is widely used in practice. For the practical implementation of any variant, however, one needs to estimate the parameters from finite return series, which inevitably introduces measurement noise that, in turn, affects portfolio selection. Although much research has been devoted to investigating the noise in the classical model, hardly any attention has been paid to the problem in the case of absolute deviation. In this paper, we study the effect of estimation noise in the case of absolute-deviation-based portfolio optimization. We show that the key parameter determining the effect of noise is the ratio of the length of time series to portfolio size and that, other things being equal, the effect of noise is higher than in the classical, variance-based model. This finding points to the importance of checking whether theoretically „better“ portfolio selection models can indeed outperform the classical one in practice.