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Answer: 23.6%.
## Explanation The continuously compounded return is calculated using the formula: $$r = \ln\left(\frac{P_t}{P_0}\right)$$ Where: - $P_0$ = initial price = $30 - $P_t$ = ending price = $38 - $\ln$ = natural logarithm **Calculation:** 1. First calculate the price ratio: $\frac{38}{30} = 1.2667$ 2. Take the natural logarithm: $\ln(1.2667) = 0.2364$ 3. Convert to percentage: $0.2364 \times 100 = 23.64\%$ **Why not the other options:** - **Option A (7.0%)**: This is the simple return calculation: $(38-30)/30 = 8/30 = 0.2667 = 26.67\%$, not 7.0%. - **Option C (26.7%)**: This is the simple return, not the continuously compounded return. **Key Concept:** Continuously compounded returns use natural logarithms of price ratios, which gives slightly different results than simple returns, especially for larger price changes. For small changes, the two measures are approximately equal, but for a 26.7% simple return, the continuously compounded return is 23.6%.
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An analyst gathers the following closing prices of a stock:
| Date | Closing Price($) |
|---|---|
| 1 January | 30 |
| 15 January | 38 |
The continuously compounded return for the period 1 January to 15 January is closest to:
A
7.0%.
B
23.6%.
C
26.7%.
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