Dynamic Correlation Hedging in Copula Models for Portfolio Selection

Abstract

In this paper we address the issue of modeling extreme asset co-movements and their implications for the hedging demands of a dynamic portfolio. We propose a model that is able to accommodate an extremal dependence structure through the stationary distribution of the state variables underlying the asset price process, as well as through a dynamic conditional correlation specification, driven by latent and observable factors. With this we aim at replicating the stylized fact of increased dependence during extreme market downturns, rising market-wide volatility, or worsening macroeconomic conditions. The model we propose accounts for stylized properties of asset returns in terms of univariate tail behavior as well as varying forms of dependence in the extremes , while keeping a continuous time complete market setup for a tractable portfolio solution. The paper further concentrates on the portfolio implications of those stylized facts. We isolate the intertemporal hedging demands, including those for correlation risk due to stochastic changes in the factors. Thus, we are able to analyze separately the impact of tail dependence through the unconditional distribution of the underlying state variables and that of conditional correlation on the portfolio holdings. We find that both correlation hedging demands and intertemporal hedges due to increased tail dependence have distinct portfolio implications and cannot act as substitutes to each other. As well, there are substantial economic costs for disregarding both the dynamics of conditional correlation and the dependence in the extremes.