Financial Risk Manager Part 1

Explanation

The portfolio variance is calculated using the formula:

$\sigma_p^2 = w_A^2 \cdot \sigma_A^2 + w_B^2 \cdot \sigma_B^2 + 2 \cdot w_A \cdot w_B \cdot \text{Cov}(A,B)$

Where:

• $w_A = 0.6$ (weight of equities)
• $w_B = 0.4$ (weight of bonds)
• $\sigma_A^2 = 320$ (variance of equities)
• $\sigma_B^2 = 110$ (variance of bonds)
• $\text{Cov}(A,B) = 90$ (covariance between equities and bonds)

Substituting the values:

$\sigma_p^2 = (0.6)^2 \cdot 320 + (0.4)^2 \cdot 110 + 2 \cdot 0.6 \cdot 0.4 \cdot 90$

$\sigma_p^2 = 0.36 \cdot 320 + 0.16 \cdot 110 + 0.48 \cdot 90$

$\sigma_p^2 = 115.2 + 17.6 + 43.2 = 176$

Therefore, the portfolio variance is 176.

This calculation shows how portfolio diversification affects overall risk, where the covariance term captures the relationship between the two asset classes.