Optimal VPPI strategy under Omega ratio with stochastic benchmark

Abstract

This paper studies a variable proportion portfolio insurance (VPPI) strategy. The objective is to determine the risk multiplier by maximizing the extended Omega ratio of the investor's cushion, using a binary stochastic benchmark. When the stock index declines, investors aim to maintain the minimum guarantee. Conversely, when the stock index rises, investors seek to track some excess returns. The optimization problem involves the combination of a non-concave objective function with a stochastic benchmark, which is effectively solved based on the stochastic version of concavification technique. We derive semi-analytical solutions for the optimal risk multiplier, and the value functions are categorized into three distinct cases. Intriguingly, the classification criteria are determined by the relationship between the optimal risky multiplier in Zieling et al. (2014 and the value of 1. Simulation results confirm the effectiveness of the VPPI strategy when applied to real market data calibrations.