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

An asset has a monthly log return of 2.00% in month 1 and a monthly log return of -3.00% in month 2. Which statement about the two-month simple return is correct?

Log returns add to -1.00% over two months, but the simple return is found by converting back: e^(-0.01) - 1, about -0.995%. The sum of log returns is itself a log return, not a simple return, and simple returns do not add over time.

  1. AIt equals e^(-0.01) - 1, approximately -0.995%Correct
  2. BIt equals -1.00% exactly, the sum of the log returns
  3. CIt equals the arithmetic sum of the simple returns of each month
  4. DIt equals ln(0.99), approximately -1.005%

Explanation

Two-month log return = 0.02 - 0.03 = -0.01. Converting to a simple return gives e^(-0.01) - 1 = -0.995%. Option B and D confuse the log return with the simple return. Simple returns do not add across time (option C).

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