On Path–dependency of Constant Proportion Portfolio Insurance Strategies

This paper evaluates the path-dependency/independency of the most widespread Portfolio Insurance strategies. In particular, we look into various Constant Proportion Portfolio Insurance (CPPI) structures and compare them to the classical Option Based Portfolio Insurance (OBPI) and with naive strategies such as Stop-loss Portfolio Insurance (SLPI).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. This likelihood of being cash-locked increases with maturity of the CPPI as well as with properties of the underlying's dynamics and is a major drawback to investors.To emphasise 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 and lead to losses. This path-dependency problem is specific of CPPIs, it goes against theEuropean-style nature of most traded CPPIs, and it does not occur in the classical case of OBPI strategies.We expect that this study will contribute to reinforce the idea that CPPI strategies suffer from a serious design problem. To clearly show the path dependency and the problems of CPPI strategies, the simulation exercise preformed in this paper takes a point of view that is not the one of the previous literature. Although we use a standard geometric Brownian motion to model the underlying, our Monte Carlo simulated paths are all conditioned to fixed final value, using the methodology proposed by Sousa, Esquivel and Gaspar (2015). The financial intuition is to consider the point of view of an investor who has some expectation about the future value of an underlying asset at maturity, but uses portfolio insurance hedge against the possibility of being wrong. In our simulations we consider the investor is right, and show that, despite this, CPPI strategies with multipliers higher than one, can still lead to losses. This occurs due to the ``cash-lock'' property of CPPI strategies, which makes the risk of the strategy to become unrelated to the evolution of the underlying. Term sheets of most real life CPPIs simply ignore this important path-dependency risk. The existence of this path dependency make it hard to understand which investor risk profile is this product meant to satisfy. In fact, the traditional alternatives always stochastically dominate CPPIs with multipliers higher than 1 are. We expect this study contributes to the debate on design risk of structured products and reinforce the idea that CPPI products are ill conceived.