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FRM Part II · FRM Exam Part II · Validating Bank Holding Companies' Value-at-Risk Models for Market Risk

During validation, a bank holding company is found to scale its one-day 99% VaR to a ten-day horizon by multiplying by the square root of ten, for a portfolio whose daily returns show strong positive autocorrelation. What is the likely consequence?

Ten-day VaR is understated. The square-root-of-time rule assumes independent daily returns; with positive autocorrelation, multi-day variance is larger than scaling implies, so the scaled figure underestimates the true ten-day potential loss.

  1. ATen-day VaR is understated because the square-root-of-time rule assumes independent returnsCorrect
  2. BTen-day VaR is overstated because positive autocorrelation reduces multi-day variance
  3. CTen-day VaR is correct because the rule holds for any return process
  4. DTen-day VaR is unaffected because autocorrelation only impacts the mean

Explanation

The rule assumes serially independent returns. With positive autocorrelation, multi-day variance exceeds the sum of daily variances, so the scaled figure is too low. The overstated option reverses the sign of the effect.

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