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

Daily log returns of an equity index are assumed to be independent with mean 0.04% and standard deviation 1.10%. Using 25 trading days in the period, what are the mean and standard deviation of the 25-day log return?

The 25-day log return has mean 25 x 0.04% = 1.00% and standard deviation 1.10% x 5 = 5.50%. Means grow linearly with time, while volatility grows with the square root of time when returns are independent.

  1. AMean 1.00%, standard deviation 5.50%Correct
  2. BMean 1.00%, standard deviation 27.50%
  3. CMean 0.04%, standard deviation 5.50%
  4. DMean 0.04%, standard deviation 1.10%

Explanation

For independent log returns, the mean scales with time: 25 x 0.04% = 1.00%. The standard deviation scales with the square root of time: 1.10% x sqrt(25) = 5.50%. Option B scales volatility linearly, an error. Options C and D fail to scale the mean.

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