A0238
Title: Forecasting and backtesting gradient allocations of expected shortfall
Authors: Takaaki Koike - Hitotsubashi University (Japan) [presenting]
Cathy W-S Chen - Feng Chia University (Taiwan)
Edward Meng-Hua Lin - Tunghai University (Taiwan)
Abstract: Capital allocation is a procedure for quantifying the contribution of each source of risk to aggregated risk. The gradient allocation rule, also known as the Euler principle, is a prevalent rule of capital allocation under which the allocated capital captures the diversification benefit of the marginal risk as a component of overall risk. This research concentrates on expected shortfall (ES) as a regulatory standard and focuses on the gradient allocations of ES, also called ES contributions. The comprehensive treatment of backtesting the tuple of ES contributions is achieved in the framework of the traditional and comparative backtests based on the concepts of joint identifiability and multi-objective elicitability. For robust forecast evaluation against the choice of scoring function, Murphy diagrams are further presented for ES contributions as graphical tools to check whether one forecast dominates another under a class of scoring functions. Finally, leveraging the recent concept of multi-objective elicitability, a novel semi-parametric model is proposed for forecasting dynamic ES contributions based on a compositional regression model. In an empirical analysis of stock returns, a variety of models are evaluated and compared for forecasting dynamic ES contributions, and the outstanding performance of the proposed model is demonstrated.
