Financial Risk Manager Part 1
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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?
Other
Community
NNikitesh
A
6.36%
B
6.56%
C
8.14%
D
6.10%
Explanation:
The portfolio standard deviation is calculated using the formula:
σ²ₚ = w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov(R₁,R₂)
Where:
- w₁ = 0.4 (40%)
- σ₁ = 0.07 (7%)
- w₂ = 0.6 (60%)
- σ₂ = 0.12 (12%)
- Cov(R₁,R₂) = -0.004
Step-by-step calculation:
- w₁²σ₁² = (0.4)² × (0.07)² = 0.16 × 0.0049 = 0.000784
- w₂²σ₂² = (0.6)² × (0.12)² = 0.36 × 0.0144 = 0.005184
- 2w₁w₂Cov(R₁,R₂) = 2 × 0.4 × 0.6 × (-0.004) = 0.48 × (-0.004) = -0.00192
- σ²ₚ = 0.000784 + 0.005184 + (-0.00192) = 0.004048
- σₚ = √0.004048 = 0.063624 = 6.36%
The negative covariance reduces the portfolio risk through diversification benefits, resulting in a portfolio standard deviation (6.36%) that is lower than the weighted average of the individual standard deviations.
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