A Dynamic Asset Allocation Model with Downside Risk Control

Abstract

This paper presents a new stochastic model for investment. The investor's objective is to maximize the expected growth rate while controlling for downside risk. Assuming lognormally distributed prices, the strategy that determines the o optimal dynamic portfolio weights by changing risk neutral excess rate is determined by a stochastic differential equation. The maximum loss can be limited almost surely. A constrained optimization model is developed given investors' preference on the minimum subsistence reward among all possible scenarios. The relative changes in the expected terminal wealth, minimum subsistence and the risk aversion are studied. Taking VaR as the risk measure, the return/risk tradeoff efficient frontier is constructed. A comparison of the downside risk control model for a typical example to Buy and Hold (BH) and Fixed Mix (FM) strategic asset allocation models shows that the downside risk control model has superior performance in the return/VaR framework.