Extensions of Constant Proportion Portfolio Insurance using the Geometric Ornstein-Uhlenbeck process and the Chan-Karolyi-Longstaff-Sanders process

Abstract

We investigate performance of the Constant Proportion Portfolio Insurance (CPPI) strategy and compare it with two of its extensions: Time Invariant Portfolio Protection (TIPP) and Exponential Proportion Portfolio Insurance (EPPI). In order to do this, we model a risky asset (a stock or an index) using a Geometric Ornstein-Uhlenbeck process, and estimate its parameters using the likelihood ratio method with historical price data. We model a non-risky asset (a zero-coupon bound) using a Chan-Karolyi-Longstaff-Sanders process and estimate its parameters using the maximum likelihood method where we approximate the transition probability density function using a Hermite expansion. We find that both extensions of the CPPI improve performance in different ways. The resulting distribution of simulated portfolio outcomes for the TIPP strategy has a lighter tail compared to the CPPI case, and the risk of loss is lower (this is also true compared to the EPPI strategy, but to a smaller degree). The EPPI strategy translates the distribution of simulated portfolio outcomes to the right, so that EPPI performs better than CPPI (and TIPP) in terms of both mean and median.