FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation
An asset priced at 50 earns daily log returns of +2%, −1% and +3% on three consecutive days, with no income. What is the price at the end of day three?
The price is 52.04. Log returns are additive over time, so the three-day log return is 4%. Applying it as a continuously compounded rate gives 50 × e^0.04 = 52.04. Compounding the figures as simple returns or adding them as simple returns gives different, incorrect prices.
- A51.94
- B52.00
- C52.04Correct
- D52.50
Explanation
Log returns add across periods: 2% − 1% + 3% = 4%. Price = 50 × e^0.04 = 50 × 1.040811 = 52.04. Treating the returns as simple and compounding gives 51.94. Treating the 4% sum as a simple return gives 52.00.
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