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FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods

A risk analyst scales a one-day 99% VaR of USD 2.0 million to a ten-day horizon for a portfolio with i.i.d. normal zero-mean returns. Later she learns that daily returns have positive first-order autocorrelation. Which statement is most accurate?

Scaling gives about USD 6.32 million (2.0 times the square root of 10). With positive autocorrelation, multi-day returns vary more than independent days imply, so the square-root-of-time rule likely understates the true ten-day VaR.

  1. AThe ten-day VaR under the square-root-of-time rule is about USD 6.32 million and is likely understated given positive autocorrelationCorrect
  2. BThe ten-day VaR is USD 20 million and is correct under autocorrelation
  3. CThe ten-day VaR under the square-root-of-time rule is about USD 6.32 million and is likely overstated given positive autocorrelation
  4. DThe ten-day VaR is about USD 4.47 million because the horizon factor is the square root of five

Explanation

Square-root-of-time gives 2.0 x sqrt(10) = USD 6.32m. Positive autocorrelation makes multi-day variance larger than the sum of daily variances, so the rule understates risk; the overstated option has the direction wrong.

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