Portfolio Optimization Under a Stressed-Beta Model
نویسندگان
چکیده
This paper presents a closed-form solution to the portfolio optimization problem where an agent wishes to maximize expected terminal wealth, trading continuously between a risk-free bond and a risky stock following Stressed-Beta dynamics specified in Fouque and Tashman (2010). The agent has a finite horizon and a utility of the Constant Relative Risk Aversion type. The model for stock dynamics is an extension of the Capital Asset Pricing Model (CAPM); it is expressed in continuous-time, and the slope relating excess stock returns to excess market returns switches between two values. This mechanism reflects the fact that the slope may steepen during periods of stress, a feature which has been demonstrated to better model stock dynamics than CAPM. An asymptotic expansion technique is used to write an explicit expression for the agent’s optimal strategy. Lastly, the optimization approach is illustrated with market data, and its outperformance versus the Merton approach is demonstrated.
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