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P2.T5.713. Backtesting in the Basel rules (Jorion Ch.6)

Nicole Seaman

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Learning objectives: Define and identify type I and type II errors. Explain the need to consider conditional coverage in the backtesting framework. Describe the Basel rules for backtesting.

Questions:

713.1. In comparison to Basel III, which itself essentially incorporated the previous quantitative requirements for backtesting under the internal models approach (IMA) to market risk, which of the following BEST summarizes the change(s), if any, to the backtesting requirements under the fundamental review of the trading book (FRTB; aka, Basel IV)?

a. The backtest methodology is unchanged in the FRTB
b. One-day value at risk (VaR) is backtested at both 97.5% and 99.0% confidence levels
c. There are two tests: 10-day 99.0% expected shortfall and 10-day 99.0% stressed value at risk (sVaR)
d. The 10-day horizon and 99.0% confidence level are unchanged but these parameters are applied to expected shortfall (ES) rather than VaR


713.2. Barbara is a Risk Analyst at a financial services firm and she is simulating the backtest of proposed value at risk (VaR) model for her firm. She is revising the simulation because the previous version was submitted to the Risk Committee of the Board and the following feedback came back: they asked to reduce the probability of a Type II error in the backtest. The previous version assumed a 97.5% value at risk (VaR) model and the backtest assumed a two-tailed confidence level of 95.0%. The sample size was two years of daily profit and loss (P/L); i.e., 500 trading days. Which of the following adjustments is the MOST EFFECTIVE way to REDUCE the Type II error rate, per the Board's preference?

a. Decrease the sample size form 500 days to 250 days
b. Increase the cutoff (the number of acceptable exceptions)
c. Increase the VaR confidence level from 97.5% to 99.0%
d. Decrease the two-tailed backtest confidence level from 95.0% to 90.0%


713.3. Peter is a happily employed Risk Analyst who recently passed the Financial Risk Manager (FRM) exam, an impressive accomplishment that duly impressed his managers and contributed to his promotion. He is evaluating the latest backtest results of his firm's value at risk (VaR) model. He concludes that his firm should shift to a VaR model that employs filtered historical simulation with GARCH volatility, and his PRIMARY reason for this view is that he has determined that a framework for conditional coverage is necessary based on his statistical test. Which of the following is the MOST LIKELY to be the proximate justification for a shift to a conditional coverage model?

a. Extreme losses are bunching (i.e., not independent) in the sample
b. His test provides evidence of the existence of a long-run (aka, unconditional) volatility in the series
c. The historical sample size is not large enough to generate sufficiently low Type I and Type II error rates
d. His Kupiec test implies a confidence region that extends to zero exceptions such that he cannot evaluate outcomes will low exceptions

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