Forecast combinations for value at risk and expected shortfall

Combining provides a pragmatic way of synthesising the information provided by individual forecasting methods. In the context of forecasting the mean, numerous studies have shown that combining often leads to improvements in accuracy. Despite the importance of the value at risk (VaR), though, few papers have considered quantile forecast combinations. One risk measure that is receiving an increasing amount of attention is the expected shortfall (ES), which is the expectation of the exceedances beyond the VaR. There have been no previous studies on combining ES predictions, presumably due to there being no suitable loss function for ES. However, it has been shown recently that a set of scoring functions exist for the joint estimation or backtesting of VaR and ES forecasts. We use such scoring functions to estimate combining weights for VaR and ES prediction. The results from five stock indices show that combining outperforms the individual methods for the 1% and 5% probability levels.     

Forecasting value at risk and expected shortfall with mixed data sampling

I propose applying the Mixed Data Sampling (MIDAS) framework to forecast Value at Risk (VaR) and Expected shortfall (ES). The new methods exploit the serial dependence on short-horizon returns to directly forecast the tail dynamics of the desired horizon. I perform a comprehensive comparison of out-of-sample VaR and ES forecasts with established models for a wide range of financial assets and backtests. The MIDAS-based models significantly outperform traditional GARCH-based forecasts and alternative conditional quantile specifications, especially in terms of multi-day forecast horizons. My analysis advocates models that feature asymmetric conditional quantiles and the use of the Asymmetric Laplace density to jointly estimate VaR and ES.     

An approximate long-memory range-based approach for value at risk estimation

This paper proposes new approximate long-memory VaR models that incorporate intra-day price ranges. These models use lagged intra-day range with the feature of considering different range components calculated over different time horizons. We also investigate the impact of the market overnight return on the VaR forecasts, which has not yet been considered with the range in VaR estimation. Model estimation is performed using linear quantile regression. An empirical analysis is conducted on 18 market indices. In spite of the simplicity of the proposed methods, the empirical results show that they successfully capture the main features of the financial returns and are competitive with established benchmark methods. The empirical results also show that several of the proposed range-based VaR models, utilizing both the intra-day range and the overnight returns, are able to outperform GARCH-based methods and CAViaR models.     

Forecasting risk measures using intraday data in a generalized autoregressive score framework

A new framework for the joint estimation and forecasting of dynamic value at risk (VaR) and expected shortfall (ES) is proposed by our incorporating intraday information into a generalized autoregressive score (GAS) model introduced by Patton et al., 2019 to estimate risk measures in a quantile regression set-up. We consider four intraday measures: the realized volatility at 5-min and 10-min sampling frequencies, and the overnight return incorporated into these two realized volatilities. In a forecasting study, the set of newly proposed semiparametric models are applied to four international stock market indices (S&P 500, Dow Jones Industrial Average, Nikkei 225 and FTSE 100) and are compared with a range of parametric, nonparametric and semiparametric models, including historical simulations, generalized autoregressive conditional heteroscedasticity (GARCH) models and the original GAS models. VaR and ES forecasts are backtested individually, and the joint loss function is used for comparisons. Our results show that GAS models, enhanced with the realized volatility measures, outperform the benchmark models consistently across all indices and various probability levels.     

Incorporating correlation regimes in an integrated stressed risk modeling process

The practice of using stress tests to complement Value at Risk (VaR) estimates suffers from some limitations such as the lack of coherence between a statistical risk measure and a subjective one. On the other hand there is a wide consensus that using the same correlation matrix to design various stress tests is not likely to provide an accurate representation of relationship amongst risk factors in periods of market stress. In this paper we introduce a solution to these problems by explicitly considering different correlation regimes and incorporating the result of the stress test to the traditional market risk measurement models.

Forecasting expected shortfall: Should we use a multivariate model for stock market factors?

Is univariate or multivariate modeling 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 exposure 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.