Dynamic Mean-variance Portfolio Optimization With Correlated Returns

In 1952,Markowitz published the paper ”portfolio selection” in 1952, and in the same year he published the homonymic monograph,in his work,he proposed the meanvariance portfolio selection model which tells the investor not only to focus the expected return but also the risk of the investment.Markowitz's model has laid the foundation of modern finance and portfolio selection theory. Number of risk measures and decisionmaking frameworks have been developed in the past 50 years.However,the study in dynamic mean-variance portfolio selection was stagnated beacause the variance term is non separable in sense of dynamic programming.In 2000,Li and Ng successfully extended the mean-variance portfolio selection formulation to the dynamic setting with embedding method.Lots study in dynamic mean-variance portfolio selection were published base on Li and Ng's work and majority of the literature assumed that the returns of asset in different stages are independent.On the basis of former works, this paper is devoted to dynamic portfolio selection with correlated returns.We extend Li and Ng's model from situations with independent returns to situations with return vectors correlated among different time periods.Then we extend the model from situations with return vectors correlated to situations with one more risk-free asset and situations with no-shorting constraint.In fact,the situations with one more risk-free asset is a special case of the base model which one of the assets has 0 volatility.The optimal strategy of the situations with no-shorting constraint get different value with different size of the state variables.At last we conduct simulated analysis and empirical analysis.We introduce the two-stage Monte Carlo method to calculate a more accurate numerical solution.The results show that the strategy in this paper is more effective to the situations with correlated returns.The results also prove that risk-free asset can reduce the portfolio's volatility.In the empirical analysis,we use Cointegration techniques to calculate the example with no-shorting constraint.The result shows that the strategy in this paper is better that the static policy strategy.