Answer-first summary for fast verification
Answer: 8.50%
The portfolio standard deviation is calculated using the formula: $$\sigma_p = \sqrt{w_A^2\sigma_A^2 + w_B^2\sigma_B^2 + 2w_Aw_B\rho_{AB}\sigma_A\sigma_B}$$ Where: - $w_A = 0.20$, $\sigma_A = 4\%$ - $w_B = 0.80$, $\sigma_B = 10\%$ - $\rho_{AB} = 0.60$ Plugging in the values: $$\sigma_p = \sqrt{(0.20)^2(4\%)^2 + (0.80)^2(10\%)^2 + 2(0.20)(0.80)(0.60)(4\%)(10\%)}$$ $$\sigma_p = \sqrt{(0.04)(0.0016) + (0.64)(0.01) + 2(0.20)(0.80)(0.60)(0.04)(0.10)}$$ $$\sigma_p = \sqrt{0.000064 + 0.0064 + 0.000768}$$ $$\sigma_p = \sqrt{0.007232}$$ $$\sigma_p = 0.0850 = 8.50\%$$ This matches the calculation shown in the provided solution.
Author: Nikitesh Somanthe
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Alan West, a portfolio manager, created the following portfolio:
| Security | Security Weight (%) | Expected Standard Deviation (%) |
|---|---|---|
| A | 20 | 4 |
| B | 80 | 10 |
If the correlation of returns between the two securities is 0.60, then what is the expected standard deviation of the portfolio?
A
9.50%
B
8.10%
C
9.15%
D
8.50%