The impact of the time-varying dependence structure on the Value at Risk of a portfolio of exchange rates during the Covid-19 pandemic

Purpose – The purpose of this paper is to introduce a generalization of the time-varying correlation elliptical copula models and to analyse its impact on the tail risk of a portfolio of foreign currencies during the Covid-19 pandemic. Design/methodology/approach – The authors consider a multivariate time series model where marginal dynamics are driven by an autoregressive moving average (ARMA) – Glosten-Jagannathan-Runkle – generalized autoregressive conditional heteroscedastic (GARCH) model, and the dependence structure among the residuals is given by an elliptical copula function. The correlation coef fi cient follows an autoregressive equation where the autoregressive coef fi cient is a function of the past values of the correlation. The model is applied to a portfolio of a couple of exchange rates, speci fi cally US dollar – Japanese Yen and US dollar – Euro and compared with two alternative speci fi cations of the correlation coef fi cient: constant and with autoregressive dynamics. Findings – The use of the new model results in a more conservative evaluation of the tail risk of the portfolio measured by the value-at-risk and the expected shortfall suggesting a more prudential capital allocation policy. Originality/value – The main contribution of the paper consists in the introduction of a time-varying correlation model where the past values of the correlation coef fi cient impact on the autoregressive structure.