Market Timing Strategy in Dynamic Portfolio Selection: A Mean-Variance Formulation

Abstract

Investment could be costly for several reasons. The most significant contributor, undoubtedly, goes to bad market timing. Investors thus have to consider market timing strategies, i.e., to strategically shift the funds completely between risky and risk free assets after analyzing market conditions and carrying out predictions. Market friction, such as management fees charged by fund managers, makes market timing more necessary as cost and benefit of investment may change the dominance relationship during the investment process. Thus, smart investors do not always invest their wealth in the market and they do so only in these time periods with sufficiently good investment opportunities (market condition). Motivated by such common phenomena, this paper investigates market timing strategies for a market with correlated returns and management fees under a dynamic mean-variance framework. More specifically, for a finite time horizon with correlated returns and a form of management fee which is a concave increasing function of both the investment time periods and the initial wealth, we offer an analytical solution to help investors to decide best time cardinality (the total number of time periods to invest), to identify market timing (when to stay in the market) and to decide the optimal investment policy when investing. Our results reveal that the optimal market timing strategy (whether investing in risky assets or not in a given time period) depends entirely on the realization of an adaptive process, which is dictated by the modified first and second order conditional moments of the excess returns of the risky assets.

Keywords: Market timing, Multi-period portfolio selection, Multi-period mean-variance formulation, Time cardinality