Sensitivity of cautious-relaxed investment policies to target variation

Abstract

This study builds on recent findings that target-based utility measures, used in the dynamic portfolio optimisation, deliver investment policies that can generate leftskewed payoff distributions. These policies can lead to small probabilities of low payoffs. This is in contrast to the classical portfolio optimisation strategies that commonly deliver right-skewed payoff distributions, which imply a high probability of losses. The left-skewed payoff distributions can be obtained when a “cautious-relaxed” investment policy is applied in portfolio management. Such a policy will be adopted by investors who are both cautious in seeking a payoff meeting a certain target, but relaxed toward the possibility of exceeding it. We use computational methods to analyse the effects of varying the target on the payoff distribution and also examine how the fund manager’s explicit preferences, when they differ from the investor’s, can impact the distribution. We found that increasing the target causes the distribution to become less left skewed. Lowering the target slightly, keeps the left-skewed payoff distribution albeit the mode diminishes. Decreasing the target substantially so it is below the safe investment payoff, changes the skew. Investor’s payoff will not suffer even if the actual fund manager allows for their own utility in the optimisation problem.