Time cardinality constrained mean-variance dynamic portfolio selection and market timing: A stochastic control approach

An investor does not always invest in risky assets in all the time periods, often due to a market timing consideration and various forms of market friction, including the management fee. Motivated by this observed common phenomenon, this paper considers the time cardinality constrained mean-variance dynamic portfolio selection problem (TCCMV) in markets with correlated returns and in which the number of time periods to invest in risky assets is limited. Both the analytical optimal portfolio policy and the analytical expression of the efficient mean-variance (MV) frontier are derived for TCCMV. It is interesting to note whether investing in risky assets or not in a given time period depends entirely on the realization of the two adaptive processes which are closely related to the local optimizer of the conditional Sharpe ratio. By implementing such a solution procedure for different cardinalities, the MV dynamic portfolio selection problem with management fees can be efficiently solved for a purpose of developing the best market timing strategy. The final product of our solution framework is to provide investors advice on the best market timing strategy including the best time cardinality and its distribution, as well as the corresponding investment policy, when balancing the consideration of market opportunity and market frictions.