Assessment of the size of VaR backtests for small samples

• Authors: Kaszyński, Daniel , Kamiński, Bogumił , Pankratz, Bartosz

Abstracts

EN

The market risk management process includes the quantification of the risk connected with defined portfolios of assets and the diagnostics of the risk model. Value at Risk (VaR) is one of the most common market risk measures. Since the distributions of the daily P&L of financial instruments are unobservable, literature presents a broad range of backtests for VaR diagnostics. In this paper, we propose a new methodological approach to the assessment of the size of VaR backtests, and use it to evaluate the size of the most distinctive and popular backtests. The focus of the paper is directed towards the evaluation of the size of the backtests for small-sample cases – a typical situation faced during VaR backtesting in banking practice. The results indicate significant differences between tests in terms of the p-value distribution. In particular, frequency-based tests exhibit significantly greater discretisation effects than duration-based tests. This difference is especially apparent in the case of small samples. Our findings prove that from among the considered tests, the Kupiec TUFF and the Haas Discrete Weibull have the best properties. On the other hand, backtests which are very popular in banking practice, that is the Kupiec POF and Christoffersen’s Conditional Coverage, show significant discretisation, hence deviations from the theoretical size.

Keywords

EN

Value at Risk; market risk management; backtesting; empirical size assessment

• Publisher: Główny Urząd Statystyczny
• Journal: Przegląd Statystyczny
• Year: 2020
• Volume: 67
• Issue: 2
• Pages: 114-151

Dates

published

2020-12-10

Contributors

author

Kaszyński, Daniel

author

Kamiński, Bogumił

author

Pankratz, Bartosz

Identifiers

DOI

10.5604/01.3001.0014.5726