Sharp Target Range Strategies with Application to Dynamic Portfolio Selection

A family of sharp target range strategies is presented for portfolio selection problems. Our proposed strategy maximizes the expected portfolio value within a target range, composed of a conservative lower target representing capital guarantee and a desired upper target representing investment goal. This strategy favorably shapes the entire probability distribution of return, as it simultaneously seeks a high expected return, cuts off downside risk, and implicitly caps volatility, skewness and other higher moments of the return distribution. To illustrate the effectiveness of our new investment strategies, we study a multi-period portfolio selection problem with transaction cost, where the results are generated by the Least-Squares Monte-Carlo algorithm. Our numerical tests show that the presented strategy produces a better efficient frontier, a better trade-off between return and downside risk, and a wider range of possible risk profiles than classical constant relative risk aversion utility. Finally, straightforward extensions of the sharp target range are presented, such as purely maximizing the probability of achieving the target range, adding an explicit target range for realized volatility, and defining the range bounds as excess return over a stochastic benchmark, for example, stock index or inflation rate. These practical extensions make the approach applicable to a wide array of investment funds, including pension funds, controlled-volatility funds, and index-tracking funds.