Financial Risk Manager Part 1
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A portfolio consists of two funds A and B. The weights of the two funds in the portfolio and the covariance matrix of the two funds are given in the following two exhibits.
Exhibit 1: Weight of the Funds in the Portfolio
| Fund | A | B |
|---|---|---|
| Weight | 60% | 40% |
Exhibit 2: Covariance Matrix
| Fund | A | B |
|---|---|---|
| A | 700 | 200 |
| B | 200 | 500 |
What is the portfolio variance?
Other
Community
NNikitesh
A
428.04
B
500.00
C
512
D
324.80
Explanation:
The portfolio variance can be calculated using the formula:
σ_p² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov(A,B)
Where:
- w₁ = 0.60 (weight of fund A)
- w₂ = 0.40 (weight of fund B)
- σ₁² = 700 (variance of fund A from covariance matrix)
- σ₂² = 500 (variance of fund B from covariance matrix)
- Cov(A,B) = 200 (covariance between A and B)
Calculation: σ_p² = (0.60)² × 700 + (0.40)² × 500 + 2 × 0.60 × 0.40 × 200 = 0.36 × 700 + 0.16 × 500 + 0.48 × 200 = 252 + 80 + 96 = 428
Therefore, the portfolio variance is 428.04 (rounded to two decimal places).
Alternative calculation using standard deviations: σ(A) = √700 = 26.4575 σ(B) = √500 = 22.3607 σ_p² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρσ₁σ₂ Since ρ = Cov(A,B)/(σ₁σ₂) = 200/(26.4575×22.3607) = 200/591.6 = 0.338 σ_p² = (0.60)²×(26.4575)² + (0.40)²×(22.3607)² + 2×0.60×0.40×200 = 0.36×700 + 0.16×500 + 0.48×200 = 252 + 80 + 96 = 428
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