Conference Agenda

This paper examines the properties of the loss functions used for forecasting Value-at-Risk (VaR) and

Expected Shortfall (ES). We show that the weighted arithmetic average commonly used to construct a

forecast combination utilises the convexity property of the loss function only in case of Value-at-Risk. This

paper introduces a novel forecasting combination approach for Expected Shortfall, which is constructed using

weighted harmonic means. We show that only in this case the insurance against model risk is guaranteed.

To construct combination weights consistent with this aggregation result, we propose a novel forecast

combination for tail risk measures based on the Bagged Pretested Forecast Combination (BPFC) algorithm.

The combination weights assigned to candidate models are determined by their predictive performance

using the Model Confidence Set (MCS) test. Unlike many traditional combination methods, BPFC adapts

to changing market conditions while simultaneously facilitating model selection and improving forecast

stability. We evaluate the performance of forecasting combinations for VaR and ES within the framework of

consistent loss functions, highlighting the role of convexity in performance improvements. Our results show

that the advantages of combining forecasts are especially evident when there is substantial disagreement

among candidate models, a situation that commonly arises during turbulent financial periods.

To empirically validate our approach, we apply it to a dataset of 90 stocks spanning various market

capitalizations and covering periods of severe financial stress, including the Global Financial Crisis and the

COVID-19 pandemic. The results illustrate the ability of BPFC to dynamically select and combine the

most effective models from a pool of over 60 candidates, continuously adjusting weights based on model’s

forecasting performance and evolving market conditions.