Elicitability and backtesting: Perspectives for banking regulation

TL;DR

This paper explores how comparative backtests, which require elicitable risk measures, can improve the assessment and selection of risk forecasting methods in banking regulation, especially for measures like VaR, ES, and expectiles.

Contribution

It advocates for supplementing traditional backtests with comparative backtests to better compare risk estimation procedures based on forecasting accuracy.

Findings

Comparative backtests are better suited for method comparison.

Elicitability is essential for effective backtesting of risk measures.

Simulation and data analysis support the proposed framework.

Abstract

Conditional forecasts of risk measures play an important role in internal risk management of financial institutions as well as in regulatory capital calculations. In order to assess forecasting performance of a risk measurement procedure, risk measure forecasts are compared to the realized financial losses over a period of time and a statistical test of correctness of the procedure is conducted. This process is known as backtesting. Such traditional backtests are concerned with assessing some optimality property of a set of risk measure estimates. However, they are not suited to compare different risk estimation procedures. We investigate the proposal of comparative backtests, which are better suited for method comparisons on the basis of forecasting accuracy, but necessitate an elicitable risk measure. We argue that supplementing traditional backtests with comparative backtests will enhance the existing trading book regulatory framework for banks by providing the correct incentive for accuracy of risk measure forecasts. In addition, the comparative backtesting framework could be used by banks internally as well as by researchers to guide selection of forecasting methods. The discussion focuses on three risk measures, Value-at-Risk, expected shortfall and expectiles, and is supported by a simulation study and data analysis.