Dynamic Semiparametric Models for Expected Shortfall (and Value-at-Risk)

About

Expected Shortfall (ES) is the average return on a risky asset conditional on the return being below some quantile of its distribution, namely its Value-at-Risk (VaR). The Basel III Accord, which will be implemented in the years leading up to 2019, places new attention on ES, but unlike VaR, there is little existing work on modeling ES. We use recent results from statistical decision theory to overcome the problem of "elicitability" for ES by jointly modelling ES and VaR, and propose new dynamic models for these risk measures. We provide estimation and inference methods for the proposed models, and confirm via simulation studies that the methods have good finite-sample properties. We apply these models to daily returns on four international equity indices, and find the proposed new ES-VaR models outperform forecasts based on GARCH or rolling window models.

Andrew J. Patton, Johanna F. Ziegel, Rui Chen · 2017

Related benchmarks

Task	Dataset	Result
Joint VaR-ES forecasting	US Equity (test)	DM Test Statistic1.04	78
Portfolio Performance Evaluation	Value-weighted decile portfolios (out-of-sample)	Return (P1)0.917	26
Expected Shortfall (ES) Validity Assessment	US Equity Data (test)	Pass Rate (alpha=0.01)88.84	13
Joint VaR-ES forecasting	US Equity Returns All stocks (out-of-sample)	Average Loss (Out-of-Sample)4.3461	13
Joint VaR-ES forecasting	US Equity Returns Mega stocks (out-of-sample)	Average Loss (OOS)2.9189	13
Joint VaR-ES forecasting	US Equity Returns Large stocks (out-of-sample)	Average Loss (ℓoos)3.1899	13
Joint VaR-ES forecasting	US Equity Returns Small stocks (out-of-sample)	Average Loss (Out-of-Sample)3.7713	13
Joint VaR-ES forecasting	US Equity Returns Micro stocks (out-of-sample)	Average Loss (OOS)5.5837	13
Joint VaR-ES forecasting	US Equity Returns Nano stocks (out-of-sample)	Average Loss (ℓoos)5.0057	13
Value at Risk (VaR) Validity Assessment	US Equity Data (test)	VaR Pass Rate (alpha=0.01)93.59	13