ROBUST ASSET ALLOCATION FOR LONG-TERM TARGET-BASED INVESTING

Abstract

This paper explores dynamic mean-variance (MV) asset allocation over long horizons. This is equivalent to target-based investing with a quadratic loss penalty for deviations from the target level of terminal wealth. We provide a number of illustrative examples in a setting with a risky stock index and a risk-free asset. Our underlying model is very simple: the value of the risky index is assumed to follow a geometric Brownian motion diffusion process and the risk-free interest rate is specified to be constant. We impose realistic constraints on the leverage ratio and trading frequency. In many of our examples, the MV optimal strategy has a standard deviation of terminal wealth less than half that of a constant proportion strategy which has the same expected value of terminal wealth, while the probability of shortfall is reduced by a factor of two to three. We investigate the robustness of the model through resampling experiments using historical data dating back to 1926. These experiments also show much lower standard deviation and shortfall probability for the MV optimal strategy relative to a constant proportion strategy with approximately the same expected terminal wealth.