Forecasting Expected Shortfall: Should We Use a Multivariate Model for Stock Market Factors?

Abstract

Is univariate or multivariate modelling more effective when forecasting the market risk of
stock portfolios? We examine this question in the context of forecasting the one-week-ahead
Expected Shortfall of a stock portfolio based on its exposures to the Fama-French and momentum
factors. Applying extensive tests and comparisons, we find that in most cases there are no
statistically significant differences between the forecasting accuracy of the two approaches. This
result suggests that univariate models, which are more parsimonious and simpler to implement
than multivariate factor based models, can be used to forecast the downside risk of equity
portfolios without losses in precision.

Keywords: Fama-French and momentum factors, Value-at-Risk, Expected Shortfall, Condi- tional Value-at-Risk, Elicitability, Model comparison, Backtesting, Comparative predictive ac- curacy, Model confidence set

JEL Classification: C22, C32, C52, C53, G17