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

An investment gains 30% in year 1 and loses 20% in year 2, both stated as simple returns. What is the average per-year log return over the two years?

The average per-year log return is 1.96%. The log returns are ln(1.30) = 0.2624 and ln(0.80) = −0.2231. They sum to 0.0392 over two years, which is 1.96% per year. The 5% arithmetic mean of the simple returns overstates the compound growth.

  1. A1.96%Correct
  2. B1.98%
  3. C3.92%
  4. D5.00%

Explanation

Log returns: ln(1.30) = 0.26236 and ln(0.80) = −0.22314, which sum to 0.03922. The average is 0.03922/2 = 1.96%. The 5% figure is the arithmetic mean of the simple returns. The 1.98% figure is the geometric simple return, √1.04 − 1, and 3.92% is the two-year total, not the average.

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