Backtesting AVaR and VaR with a simulated copula

Abstract

The aim of this study is to verify whether the average value at risk (AVaR) can be a good alternative to the value at risk (VaR) for estimating portfolio losses, especially regarding tail events. To achieve this aim, we use a copula framework to estimate the dependence between the stock returns of a portfolio composed of 94 components of the S&P100 index to compute the AVaR and VaR and compare the results with respect to the Gaussian exponentially weighted moving average (EWMA). To compute the simulated returns, we employ the algorithm used by Biglova et al. (2014) in portfolio selection problems and then backtest the model with Kupiec’s and Christoffersen’s tests. The results are coherent with the literature; in particular, the VaR computed both via the copula and via the EWMA seems to fail to provide an accurate risk measurement while the AVaR with the copula and EWMA appears to be more reliable.