Portfolio Selection with Contrarian Strategy

Compared with the extensive empirical literature on contrarian strategy, we develop a dynamic mean-variance model with geometric value-reversion asset prices, which implies a contrarian strategy. The model is solved (semi) explicitly under three asset price evaluations: constant valuation, exponential-varying valuation, and geometric average valuation. From a mathematical perspective, it is nontrivial to solve the extended HJB equations under stochastic opportunities. We demonstrate that our strategy exhibits the same monotonicity as that of the traditional constant relative risk-averse utility, and the welfare loss of using the dynamic mean-variance criterion is rather small, supporting that our model is a good approximation to the constant relative risk-averse utility. Empirical tests show that our strategies can help an investor achieve a less volatile wealth trajectory.