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
C
324.8
D
32.48
Explanation:
The portfolio variance can be calculated using the formula:
Portfolio Variance = w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov(A,B)
Where:
- w₁ = weight of fund A = 0.60
- w₂ = weight of fund B = 0.40
- σ₁² = variance of fund A = 700
- σ₂² = variance of fund B = 500
- Cov(A,B) = covariance between A and B = 200
Calculation:
Portfolio Variance = (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 approach using the covariance matrix directly: The portfolio variance can also be calculated as: [w₁ w₂] × Covariance Matrix × [w₁ w₂]ᵀ
= [0.60 0.40] × [[700, 200], [200, 500]] × [0.60, 0.40]ᵀ
= [0.60×700 + 0.40×200, 0.60×200 + 0.40×500] × [0.60, 0.40]ᵀ
= [420 + 80, 120 + 200] × [0.60, 0.40]ᵀ
= [500, 320] × [0.60, 0.40]ᵀ
= 500×0.60 + 320×0.40
= 300 + 128 = 428
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