FRM Part I · FRM Exam Part I · Measuring Return, Volatility, and Correlation
A stock is bought at 40 and, one year later, trades at 42 after paying a dividend of 1 during the year. Ignoring reinvestment of the dividend, what is the continuously compounded total return for the year?
The continuously compounded total return is 7.23%. Including the dividend, the gross total return is (42 + 1)/40 = 1.075. Its natural log is 0.0723. Ignoring the dividend gives 4.88%, and 7.50% is the simple total return rather than the log return.
- A4.88%
- B5.00%
- C7.23%Correct
- D7.50%
Explanation
The total simple return = (42 + 1)/40 − 1 = 7.5%. The log return = ln(1.075) = 0.0723, or 7.23%. The 4.88% figure is ln(42/40), which omits the dividend. The 7.50% figure is the simple return, not the log return.
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