Backtesting Portfolio Value-at-Risk with Estimated Portfolio Weights

Abstract

This paper theoretically and empirically analyzes backtesting portfolio VaR with estimation risk in an intrinsically multivariate framework. For the first time in the literature, it takes into account the estimation of portfolio weights in forecasting portfolio VaR and its impact on backtesting. It shows that the estimation risk from estimating the portfolio weights as well as that from estimating the multivariate dynamic model of asset returns make the existing methods in a univariate framework inapplicable. And it proposes a general theory to quantify estimation risk applicable to the present problem and suggests practitioners a simple but effective way to carry out valid inference to overcome the effect of estimation risk in backtesting portfolio VaR. A simulation exercise illustrates our theoretical findings. In application, a portfolio of three stocks is considered.