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FRM Part II · FRM Exam Part II · Beyond Exceedance-Based Backtesting of Value-at-Risk Models

Two models A and B are compared over 250 days using average quantile scores at 99%. Model A averages 0.052 and Model B averages 0.047. The daily score differences have a standard deviation of 0.040. A Diebold-Mariano style test uses the mean difference divided by (sd / sqrt(n)), with scores assumed uncorrelated. What is the test statistic for A minus B, and the conclusion at the 5% two-sided level (critical value 1.96)?

The statistic is about 1.98, calculated as 0.005 divided by a standard error of 0.040 over the square root of 250. It exceeds 1.96, so equal predictive ability is rejected, and because lower scores are better, Model B is superior.

  1. AAbout 1.98; reject equal predictive ability, B is betterCorrect
  2. BAbout 0.13; fail to reject equal ability
  3. CAbout 1.98; reject, A is better
  4. DAbout 0.03; fail to reject equal ability

Explanation

Mean difference = 0.052 - 0.047 = 0.005. Standard error = 0.040 / sqrt(250) = 0.040 / 15.811 = 0.00253. Statistic = 0.005 / 0.00253 = 1.976, above 1.96. Lower score means better, and A's score is higher, so B is better. Forgetting sqrt(n) gives about 0.125.

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