INDUSTRY STANDARD AND ECONOMETRIC STANDARD: THE SEARCH FOR POWERFUL APPROACH TO EVALUATE VaR MODELS

Marta Małecka

Under the Basel III and Basel IV accords, risk model validation remains based on the VaR
measure. According to the industry practice, VaR backtesting procedures rely on two likelihood
ratio tests, which, in light of the academic research, have been criticized for their unsatisfactory
power. This paper aims to show the differences between VaR model evaluation based on the
standard likelihood ratio approach and backtesting by means of other econometric methods
applicable to the binary VaR failure process. The author decomposed the model evaluation into
testing the unconditional coverage, replaced the likelihood ratio with a normal statistic, and in
the next stage in order to verify the conditional coverage, employed the Ljung-Box statistic.
The study experimentally confirmed the superiority of the proposed procedures over the
industry standards. The main contribution, however, is the empirical study designed to
demonstrate the practical differences in risk analysis attributable to the choice of the backtesting
method. Using data on leading stock market indexes, from various periods, the author showed
that the practical conclusions from backtesting diverge markedly due to the test choice. The
proposed, more powerful tests, contrary to the standard procedures, allowed for distinguishing
distinct models of index behaviour connected with undergoing the financial crises.

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Keywords: Value-at-Risk, backtesting VaR, Kupiec test, Markov test, test size, test power
JEL Classification: C22, C52, D53, G11
DOI: 10.15611/aoe.2021.1.01