Risk management of time varying floors for dynamic portfolio insurance

Abstract

We propose several important extensions of the standard Constant Proportion Portfolio Insurance (CPPI), which are based on the introduction of various conditional floors. In this framework, we examine in particular both the margin and the ratchet based strategies. The first method prevents the portfolio from being monetized, known as the cash-lock risk; the second one allows to keep part of the past gains whatever the future significant drawdowns of the financial market, which corresponds to ratchet effects. However, as for the standard CPPI method, the investor can benefit from potential market rises. To control the risk of such strategies, we introduce risk measures based both on quantile conditions and on the Expected Shortfall (ES). For each of these criteria, we prove that the conditional floor must be higher than a lower bound. We illustrate the advantages provided by such strategies, using a quite general ARCH type model. Our empirical analysis is mainly conducted on S&P 500 and Euro Stoxx 50. Using parameter estimation, we provide portfolio simulations and measure their respective performances using both the Sharpe and the Omega ratios. We also backtest the strategies, using a sliding window method to dynamically estimate the parameters of the models based on the last two years of weekly returns. Our results emphazise the advantages of introducing time varying floors from both the theoretical and operational points of view.