Stochastic Volatility in Underlyings and Downside Risk of Derivative Portfolios

We carry out a Monte-Carlo simulation of the downside risk of a standard derivative portfolio as a function of a change in stochastic volatility of the underlyings. We find that the reduction in downside risk for most loss levels becomes statistically significant only for very high volatility reversion levels. Those levels are hardly found in practice, and they lead to mild reductions of downside risk. The paper illustrates the counterintuitive property that the common selection of underlyings with low fluctuations in volatility does not significantly reduce the downside risk of derivative portfolios, whereas it severely narrows down the set of tradable assets.