Portfolio Performance Maximization with Generalized Kappa Ratio

We examine the maximization problem of performance measure of financial structured products. For this purpose, we introduce the Kappa ratios, based on downside risk measures which take account of the asymmetry of the return probability distribution. First, we deal with the optimization of some standard structured portfolios. We examine in particular the optimal combination of risk free, stock and call/put instruments with respect to Kappa performance measures and in particular to the SharpeOmega ratio. Then, we provide the general solution of the optimal positioning problem with respect to Kappa ratios. We analyze its properties and compare it to the portfolio profile that is optimal with respect to the standard expected utility criterion