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?
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Explanation:
Portfolio Variance Calculation
The portfolio variance is calculated using the formula:
Portfolio Variance = (wₐ² × σₐ²) + (w_b² × σ_b²) + (2 × wₐ × w_b × Covₐ,b)
Where:
- wₐ = weight of Fund A = 0.6
- w_b = weight of Fund B = 0.4
- σₐ² = variance of Fund A = 700
- σ_b² = variance of Fund B = 500
- Covₐ,b = covariance between Fund A and B = 200
Calculation: = (0.6² × 700) + (0.4² × 500) + (2 × 0.6 × 0.4 × 200) = (0.36 × 700) + (0.16 × 500) + (0.48 × 200) = 252 + 80 + 96 = 428
The portfolio variance is 428._
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