FRM Part I · FRM Exam Part I · Measuring and Monitoring Volatility
A stock rises from 80 to 88 over one day. What is its continuously compounded (log) return for the day, rounded to two decimals?
The continuously compounded return is the natural log of the price ratio, ln(88/80) = ln(1.1), which is about 9.53%. The 10% figure is the simple return, and dividing the gain by the ending price gives 9.09%, which uses the wrong base.
- A10.00%
- B9.53%Correct
- C9.09%
- D8.00%
Explanation
The log return is ln(88/80) = ln(1.10) = 0.09531, or 9.53%. The 10.00% option is the simple return, which understates nothing but is not the log return. The 9.09% option divides the gain by the ending price, which is the wrong base.
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