Abstract

Capital allocation is a procedure for calculating the contribution of each source of risk to the aggregated risk. The gradient allocation rule, also known as the Euler principle, is a prevalent rule of capital allocation, under which the allocated capitals capture the diversification benefit of the marginal risks as components of the overall risk. This study concentrates on Expected Shortfall (ES) as a regulatory standard, which has replaced Value-at-Risk (VaR), and focuses on the gradient allocations of ES, known as ES contributions. Within the framework of the comparative backtest, we compare a variety of models for forecasting dynamic ES contributions. For robust forecast evaluation against the choice of scoring function, we develop a Murphy diagram for ES contributions, a graphical tool to check whether one forecast dominates another under a class of scoring functions. Leveraging the recent concept of elicitability, we also propose a novel semiparametric model for forecasting dynamic ES contributions based on a compositional regression model. We demonstrate the decent performance of the proposed model in an empirical analysis of stock returns. Moreover, our comparative backtest reveals distinct advantages of various models for forecasting ES contributions. This is a joint work with Cathy W.S. Chen in Feng Chia University and Edward M.H. Lin in Tunghai University.