Portfolio Insurance Strategies: OBPI Versus CPPI

We compare performances of the two standard portfolio insurance methods: the Option Based Portfolio Insurance (OBPI) and the Constant Proportion Portfolio Insurance (CPPI). First we examine basic properties of these two strategies and compare them by means of various criteria: comparison of their payoffs, possible property of stochastic dominance, expectations, variances, skewness and kurtosis of their returns, and some of the quantiles of their returns. We prove that the OBPI method can be analyzed as a kind of CPPI where the multiple is allowed to vary. We then study the properties of this varying multiple. In a second section, we analyze more deeply both method's dynamic properties. We turn our attention to the dynamics management involved by these two strategies. Although the pure OBPI do not require any management by the buyer (if the put or call option is available on the market), we can calculate the "greeks" of its call part. We derive the "greeks" of the CPPI and show the very different nature of the dynamic properties of the two strategies.