The analysis of Value at Risk for precious metal returns by applying extreme value theory, copula model and GARCH model

Abstract

This paper examines Value at Risk by applying GARCH-EVT-Copula model and finds the optimal portfolio for the precious metal. The 4,077 precious metal price observations are collected from 3rd January 2000 to 18th August 2015, traded in the London Metal Exchange, and all prices are traded in US dollars per troy ounce. First, we estimate the coefficients of the ARMA-GARCH equations based on the student t distribution. Second, we extract the filtered residuals from such estimation and then apply the extreme value distribution (EVT) for fitting the residual tails in order to model marginal residual distributions. Third, we use multivariate Student t-copula to construct the precious metal portfolio risk dependence structure. Finally, we simulate 10,000 portfolios and estimate value at risk (VaR) and Expected shortfall (ES). The empirical results displayed the VaR and ES values for an equally weighted portfolio of four precious metals. In addition, we found that the optimal investment focuses on the gold and silver investment due to high investment proportion, whereas palladium and platinum have little investment proportion.