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FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation

A risk manager finds that monthly returns on a portfolio have first-order autocorrelation of +0.30, while the monthly standard deviation is 4%. Which statement best describes the effect on volatility estimation if she annualizes using 4% x sqrt(12) = 13.86%?

The true annual volatility is likely higher than 13.86%. Multiperiod variance includes autocovariance terms, and positive autocorrelation makes them positive, adding to variance. The square-root-of-time rule assumes no serial correlation, so it understates risk in this case.

  1. AThe true annual volatility is likely higher, because positive autocorrelation makes the square-root-of-time rule understate riskCorrect
  2. BThe true annual volatility is likely lower, because positive autocorrelation reduces the variance of multiperiod returns
  3. CThe square-root-of-time rule remains exact, because it only requires a constant mean
  4. DThe true annual volatility is unchanged, but the annual mean return is biased

Explanation

The multiperiod variance equals the sum of single-period variances plus twice the sum of autocovariances. Positive autocovariances add to variance, so the sqrt(T) rule understates volatility. The rule is exact only when returns are uncorrelated over time.

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