Large portfolio risk management and optimal portfolio allocation with dynamic elliptical copulas

Abstract

Previous research has focused on the importance of modeling the multivariate distribution for optimal portfolio allocation and active risk management. However, existing dynamic models are not easily applied to high-dimensional problems due to the curse of dimensionality. In this paper, we extend the framework of the Dynamic Conditional Correlation/Equicorrelation and an extreme value approach into a series of Dynamic Conditional Elliptical Copulas. We investigate risk measures such as Value at Risk (VaR) and Expected Shortfall (ES) for passive portfolios and dynamic optimal portfolios using Mean-Variance and ES criteria for a sample of US stocks over a period of 10 years. Our results suggest that (1) Modeling the marginal distribution is important for dynamic high-dimensional multivariate models. (2) Neglecting the dynamic dependence in the copula causes over-aggressive risk management. (3) The DCC/DECO Gaussian copula and t-copula work very well for both VaR and ES. (4) Grouped t-copulas and t-copulas with dynamic degrees of freedom further match the fat tail. (5) Correctly modeling the dependence structure makes an improvement in portfolio optimization with respect to tail risk. (6) Models driven by multivariate t innovations with exogenously given degrees of freedom provide a exible and applicable alternative for optimal portfolio risk management.

Tail dependence in emerging ASEAN-6 equity markets: empirical evidence from quantitative approaches

“…For instance, correlation (or Pearson parameter) is usually used for linear dependence, but the estimation is criticized for being biased. Jin and Lehnert (2018) indicate that copulas would result in consistent results, robustness, and flexibility for these kinds of risk models.…”

Modeling the multivariate dynamic dependence structure of commodity futures portfolios

“…We further allow the degrees of freedom parameter to vary over time (Jin and Lehnert (2011)). The Student-t copula is therefore not only provided with the capability to adapt the level of dependence, but also the strength of tail dependence over time.…”

Risk Measures Estimation Under Wasserstein Barycenter

“…In particular, copulas method attains a robust structure for dependence in financial time series by producing joint distributions with known non gaussian marginal distributions. Modelling the marginal distributions via copulas allows VaR computations with a better performance than the classical methods; but it involves some untractable assumptions in the context of risk measures which are difficult to elucidate; a similar quotation for the multivariate extreme value theory are also addressed by [Jin and Lehnert (2018)] and [Barone et al(2015)].…”