Answer-first summary for fast verification
Answer: 6.36%
The portfolio standard deviation is calculated using the portfolio variance formula: $$\sigma_P^2 = w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2w_1w_2 \text{Cov}(R_1, R_2)$$ Given: - w₁ = 0.4, σ₁ = 7% = 0.07 - w₂ = 0.6, σ₂ = 12% = 0.12 - Cov(R₁, R₂) = -0.004 Calculation: $$\sigma_P^2 = (0.4)^2(0.07)^2 + (0.6)^2(0.12)^2 + 2(0.4)(0.6)(-0.004)$$ $$= (0.16)(0.0049) + (0.36)(0.0144) + (0.48)(-0.004)$$ $$= 0.000784 + 0.005184 - 0.00192$$ $$= 0.004048$$ $$\sigma_P = \sqrt{0.004048} = 0.063624 = 6.36\%$$ The negative covariance reduces the portfolio variance, resulting in a lower standard deviation than the weighted average of the individual standard deviations.
Author: Tanishq Prabhu
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Raul Perez, a portfolio manager, created the following portfolio:
| Security | Security Weight (%) | Expected Standard deviation(%) |
|---|---|---|
| A | 40 | 7 |
| B | 60 | 12 |
If the covariance of returns between the two securities is -0.004, then what is the expected standard deviation of the portfolio?
A
6.36%
B
6.56%
C
8.14%
D
6.10%
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