Asset Pair-Copula Selection with Downside Risk Minimization

Copulae provide investors with tools to model the dependency structure among financial products. The choice of copulae plays an important role in successful copula applications. However, selecting copulae usually relies on general goodness-of-fit (GoF) tests which are independent of the particular financial problem. This paper ¯rst proposes a pair-copula-GARCH model to construct the dependency structure and simulate the joint returns of five U.S. equites. It then discusses copula selection problem from the perspective of downside risk management with the so-called D-vine structure, which considers the Joe-Clayton copula and the Student t copula as building blocks for the vine pair-copula decomposition. Value at risk, expected shortfall, and Omega function are considered as downside risk measures in this study. As an alternative to the traditional bootstrap approaches, the proposed pair-copula-GARCH model provides simulated asset returns for generating future scenarios of portfolio value. It is found that, although the Student t pair-copula system performs better than the Joe-Clayton system in a GoF test, the latter is able to provide the loss distributions which are more consistent with the empirically examined loss distributions while optimizing the Omega ratio. Furthermore, the economic benefit of using the pair-copula-GARCH model is revealed by comparing the loss distributions from the proposed model and the conventional exponentially weighted moving average model of RiskMetrics in this case.