On the optimality of path-dependent structured funds: The cost of standardization

This paper examines the suitability of an important class of standard financial structured products, namely those whose performances are based on smoothing the return of a given risky underlying asset while providing a guarantee at maturity. Using various assumptions about the customers attitudes towards risk, we show that such standardized products are not optimal, even if the financial market volatility is constant. As a by-product, we provide in particular the optimal portfolio value in the regret/rejoice framework to go further with the notion of aversion of getting a return smaller than the risk-free one. Using the notion of compensating variation, we determine for the first time, the monetary losses of providing these standardized products instead of the optimal ones to the customers. We show that these monetary losses can be very significant when the volatility of the risky asset is stochastic. From the operational point of view, such results highly suggest to trade on the Volatility Index (VIX) and/or to introduce derivatives written on it, when selling standardized funds in order to better meet investors needs and preferences.