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

The weekly log-return volatility of a fund is 2.50%. Returns are i.i.d. and a year has 52 weeks. What is the volatility over a 13-week quarter?

The quarterly volatility is about 9.01%. Because returns are independent and identically distributed, 13 weeks of variance add up, so weekly volatility of 2.50% is scaled by the square root of 13, about 3.606, giving roughly 9.01%.

  1. A9.01%Correct
  2. B18.03%
  3. C32.50%
  4. D6.25%

Explanation

Variance scales with the number of periods. Quarterly volatility = 2.50% x sqrt(13) = 2.50% x 3.6056 = 9.01%. Using 13 x 2.5% = 32.5% is the linear-scaling error; 18.03% is the annual figure (2.5 x sqrt(52)), which is the wrong horizon.

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