Multi-period portfolio optimisation with alpha decay

Abstract

The traditional Markowitz MVO approach is based on a single-period model. Single period models do not utilise any data or decisions beyond the rebalancing time horizon with the result that their policies are myopic in nature. For long-term investors, multi-period optimisation offers the opportunity to make wait-and-see policy decisions by including approximate forecasts and long-term policy decisions beyond the rebalancing time horizon. We consider portfolio optimisation with a composite alpha signal that is composed of a short-term and a long-term alpha signal. The short-term alpha better predicts returns at the end of the rebalancing period but it decays quickly, i.e., it has less memory of its previous values. On the other hand, the long-term alpha has less predictive power than the short-term alpha but it decays slowly. We develop a simple two stage multi-period model that incorporates this alpha model to construct the optimal portfolio at the end of the rebalancing period. We compare this model with the traditional single-period MVO model on a simulated example from Israelov and Katz (2011) and also a large strategy with realistic constraints and show that the multi-period model tends to generate portfolios that are likely to have a better realised performance.