Optimal policy for a time consistent mean-variance model with regime switching

This paper investigates a time consistent multiperiod mean-variance (MV) portfolio selection problem under the Markov regime-switching framework. We use a vector auto-regression model to forecast the values of market factors and then predict the returns of risky assets by using a regime-dependent linear multifactor model. By introducing the notion of separable expected conditional mapping, we construct a time consistent multiperiod MV model with regime switching. Under the self-financing constraint, we derive an analytical optimal investment policy satisfying time consistency and the corresponding MV efficient frontier by using dynamic programming. Empirical results are provided to illustrate the reasonability and practicality of the proposed new model and the derived explicit investment strategy. Especially, we find that the investor invests more in risky assets under a bull market than that under a consolidation market or a bear market; the MV efficient frontier under a bull market is much superior to those determined under a consolidation market and a bear market.