Beyond Value at Risk: Forecasting Portfolio Loss at Multiple Horizons

Abstract

We develop a portfolio risk model that uses high-frequency data to forecast the loss surface, which is the set of loss distributions at future time horizons. Our model uses a fully automated, semi-parametric fitting procedure that has its basis in extreme value statistics. We take account of distributional asymmetry, heavy tails, heteroscedasticity and serial correlation. Loss distributions are time aggregated by taking products of characteristic functions. We test loss-surface-implied forecasts of value at risk and expected shortfall out of sample on a diverse set of portfolios and we compare our forecasts to industry-standard risk forecasts that are based on asset and factor covariance matrices. The empirical results make a compelling case for the application and further development of our approach.

Keywords: value at risk, expected shortfall, loss surface, downside risk, tail risk, peaks over thresholds, semi-parametric distribution, Fourier transform, temporal dependence

JEL Classification: C14, C12, C22, C51, C52, C53, E37