Value at Risk and Expected Shortfall Forecasting : The use of Macro Factors in CAViaR Models

Sammanfattning

The ability to forecast risk is essential for all financial institutions, and indeed, all investors intending to manage their risk exposure. Two of the most common ways to do this, both in practice and in regulation, are Value at Risk (VaR) and Expected Shortfall (ES). Together they form vital measures to create an overview of an investor's potential losses across any number of investments, as well as a cornerstone to meet regulatory demands. It is therefore of great interest to build a comprehensive understanding of VaR-ES modeling to enable accurate VaR-ES forecasts, to ultimately improve the ability to adapt positions to available information. One area that has received limited attention in the literature is the use of macroeconomic information to improve VaR-ES estimations. To investigate this possibility, the VaR quantile is estimated directly using a CAViaR based framework, which is then combined with a macro variable input and a volatility measure through VIX. The macro-variables are introduced via the intercept term. Five macro variables are proposed, Geopolitical Risk Index (GPR), Industrial Production Change (IP) in the US, inflation for the USD, default yield spread (Dfy), and Term Spread (TS). By utilizing loss score functions to estimate the parametric CAViaR-VIX-macro model, the potential of this information is examined through evaluation of VaR-ES forecast accuracy using the same loss scoring function, and backtesting of VaR and ES. Furthermore, the VaR level is estimated for four different assets, the S\&P500, the FTSE100, Brent crude oil, and gold. It is found that macroeconomic variables have varied effects depending on asset coupled with. Generally, at least one macro-variable is found to improve backtesting results and to produce a more accurate forecast based on mean loss score in the out-of-sample. However, when using the Model Confidence Set test, it is found that there is no statistically significant difference in accuracy between the proposed CAViaR-VIX-macro model compared to a simpler CAViaR-VIX model based on loss scores. Furthermore, for the two commodities, it is also found that the CAViaR model, along with all of the proposed extensions, has only slightly more accurate forecasts compared to the benchmark model GARCH(1,1) at one of the tested quantile levels, implying a poor fit between these assets and the CAViaR framework. With that said, CAViaR does pass backtesting to a much larger extent than GARCH(1,1), signaling better statistical properties. Overall, it is found that CAViaR based models outperform GARCH(1,1), especially for stock indices when considering both forecast accuracy and statistical properties. Furthermore, macro-variables consistently rank as most accurate for all investigated assets and pass backtesting to a greater extent than the baseline CAViaR model.