Journal of Risk

A dynamic asset allocation model with downside risk control

Yonggan Zhao, William T. Ziemba


This paper presents a new stochastic control model for investment. The investors' objective is to maximize the expected terminal wealth while controlling for downside risk. Assuming lognormally distributed prices, the strategy that determines the optimal dynamic portfolio weights by changing the risk-neutral excess rate (RNER) is determined by a stochastic differential equation. This strategy has a payoff structure similar to that of portfolio insurance. The maximum loss can be limited almost surely. A constrained optimization model is developed, given investors' preferences on the minimum subsistence reward among all possible scenarios. Taking VaR as the risk measure, the efficient portfolio can be identified by solving an optimization model. A comparison with typical asset allocation strategies, such as buy and hold, fixed mix, and constant proportional portfolio insurance, shows that an RNER strategy has superior return/risk performance.

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