A scenario-based description of optimal American capital guaranteed strategies

The aim of the paper is to describe portfolio strategies with partial guarantee of the initial capital. We consider the option-based (OBPI) and the constant proportion portfolio insurance (CPPI) strategies with both European and American features. First, we provide explicit formulae for all strategies and contribute to the literature by providing the value of the American CPPI. Second, relying on both historical data and path simulations, we show that strategies perform differently in a bear market. We focus on liquidation values when the market recovers after a sharp drop. We find that the American CPPI strategy usually outperforms the American OBPI one due to the Asian component of the former and despite the lookback feature of the latter. To complete our analysis, we investigate both deltas and gammas of our strategies.