On Path–dependency of Constant Proportion Portfolio Insurance Strategies

Abstract

This paper evaluates the path-dependency/independency of most widespread Portfolio Insurance strategies. In particular, we look at Constant Proportion Portfolio Insurance(CPPI) structures and compare them to both the classical Option Based Portfolio Insurance(OBPI) and naive strategies such as Stop-loss Portfolio Insurance (SLPI) or a CPPI with a multiplier of one.

The paper is based upon conditional Monte Carlo simulations and we show that CPPI strategies with a multiplier higher than 1 are extremely path-dependent and that they can easily get cash-locked, even in scenarios when the underlying at maturity can be worth much more than initially. The likelihood of being cash-locked increases with the size of the multiplier and the maturity of the CPPI, as well as with properties of the risky underlying’s dynamics.

To emphasize the path-dependency of CPPIs, we show that even in scenarios where the investor correctly“guesses” a higher future value for the underlying, CPPIs can get cash-locked, losing the linkage to the risky asset. Thiscash-lock problem is specific of CPPIs, it goes against its European style nature of traded CPPIs, and it introduces into the strategy risks not related to the underlying risky asset – a design risk. Design risk does not occur for path-independent portfolio insurance strategies, like the classical case of OBPI strategies, nor in naive strategies.This study contributes to reinforce the idea that CPPI strategies suffer from a serious design problem.

Keywords: Portfolio Insurance, CPPI, OBPI, SLPI, path-dependencies, cash-lock, Conditioned GBM Simulations

JEL Classification: G11