Optimal Strategies with Tail Correlation Constraints

Abstract

Optimal strategies under worst-case scenarios have been studied in Bernard et al. [2013a]. Bernard et al. utilize copulas to construct cost-efficient strategies with a predefined dependence structure in the tail between the payoff and the market. In their study they show that such strategies with state-dependent copula constraints dominate traditional diversification strategies in terms of the provided protection in the states of market downturns. We derive similar strategies, however using correlation constraints instead of copula constraints in the tail. We found that for an investor seeking negative dependence with the market, it is cheaper to construct a strategy with conditional correlation constraint in the tail. However, the constructed strategies with conditional correlation constraints do not provide sufficient protection in bad states of the economy. Therefore, when analyzing a strategy, negative correlation with the market in the tail is not a sufficient indicator for the protection level in the event of a market crisis.