FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation
A stock trades at USD 50 and pays a dividend of USD 1 at month-end, when the price is USD 54. A risk analyst computes the total simple return and the total log return for the month. Which pair is correct?
Including the dividend, the ending wealth is USD 55 against USD 50, so the simple return is 10.00% and the log return is ln(1.10), about 9.53%. Leaving out the dividend would understate returns, and the two measures differ for nonzero returns.
- ASimple 10.00%, log 9.53%Correct
- BSimple 8.00%, log 7.70%
- CSimple 10.00%, log 10.00%
- DSimple 9.53%, log 10.00%
Explanation
Total simple return = (54 + 1 - 50)/50 = 10.00%. Log return = ln(55/50) = ln(1.1) = 9.53%. Option B ignores the dividend (54/50 - 1 = 8%). Option D swaps the two measures, and option C wrongly equates them.
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