Financial Risk Manager Part 1

Explanation

The portfolio variance is calculated using the formula:

$\sigma_p^2 = w_X^2 \sigma_X^2 + w_Z^2 \sigma_Z^2 + 2w_Xw_Z\text{Cov}(X,Z)$

Where:

• $w_X = 0.35$ (weight of Asset X)
• $w_Z = 0.65$ (weight of Asset Z)
• $\sigma_X^2 = 0.1225$ (variance of Asset X)
• $\sigma_Z^2 = 0.4225$ (variance of Asset Z)
• $\text{Cov}(X,Z) = 0.19$ (covariance between X and Z)

Step-by-step calculation:

1. $w_X^2 \sigma_X^2 = (0.35)^2 \times 0.1225 = 0.1225 \times 0.1225 = 0.01500625$

2. $w_Z^2 \sigma_Z^2 = (0.65)^2 \times 0.4225 = 0.4225 \times 0.4225 = 0.17850625$

3. $2w_Xw_Z\text{Cov}(X,Z) = 2 \times 0.35 \times 0.65 \times 0.19 = 0.08645$

4. Total portfolio variance: $\sigma_p^2 = 0.01500625 + 0.17850625 + 0.08645 = 0.2799625 \approx 0.2800$

Therefore, the portfolio variance is 0.28, which corresponds to option A.