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Answer: The realized return is 26.7%, and the annual volatility is 9.6%.
## Explanation Given: - T = 6 months = 6/12 = 0.5 years - S₀ = 280 - S_T = 320 - Monthly volatility = 2.76% = 0.0276 **Realized Return Calculation (Continuous Compounding):** \[\text{Realized return} = \frac{1}{T} \times \ln\left(\frac{S_T}{S_0}\right)\] \[\text{Realized return} = \frac{1}{0.5} \times \ln\left(\frac{320}{280}\right) = 2 \times \ln(1.142857)\] \[\text{Realized return} = 2 \times 0.1335 = 0.2670 = 26.70\%\] **Annual Volatility Calculation:** \[\text{Annual volatility} = \sigma_{\text{monthly}} \times \sqrt{12}\] \[\text{Annual volatility} = 0.0276 \times \sqrt{12} = 0.0276 \times 3.4641 = 0.0956 = 9.56\%\] Therefore: - Realized return = 26.7% - Annual volatility = 9.6% This matches option C.
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A portfolio manager is calculating the realized return and the historical volatility of returns for the stock of company VMG. The stock ended the month of June 2021 at a price per share of INR 280, and ended the month of December 2021 at INR 320. The manager reports that the monthly volatility of the stock returns over the 6-month period was 2.76%. Assuming continuous compounding, and that the stock's returns are independent over time, what are the realized return over the 6-month period and the volatility of the stock returns per year?
A
The realized return is 12.5%, and the annual volatility is 9.6%.
B
The realized return is 12.5%, and the annual volatility is 33.1%.
C
The realized return is 26.7%, and the annual volatility is 9.6%.
D
The realized return is 26.7%, and the annual volatility is 33.1%.