Financial Risk Manager Part 1

Explanation

To find the covariance between securities A and B, we use the portfolio variance formula:

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

Given:

• Weight of A (w_A) = 10% = 0.10
• Weight of B (w_B) = 90% = 0.90
• Standard deviation of A (σ_A) = 6% = 0.06
• Standard deviation of B (σ_B) = 15% = 0.15
• Portfolio standard deviation (σ_p) = 14.1% = 0.141

Step 1: Calculate portfolio variance $\sigma_p^2 = (0.141)^2 = 0.019881$

Step 2: Calculate individual variance components $w_A^2 \sigma_A^2 = (0.10)^2 \times (0.06)^2 = 0.01 \times 0.0036 = 0.000036$ $w_B^2 \sigma_B^2 = (0.90)^2 \times (0.15)^2 = 0.81 \times 0.0225 = 0.018225$

Step 3: Set up the equation $0.019881 = 0.000036 + 0.018225 + 2 \times 0.10 \times 0.90 \times \text{Cov}(A,B)$ $0.019881 = 0.018261 + 0.18 \times \text{Cov}(A,B)$

Step 4: Solve for covariance $0.019881 - 0.018261 = 0.18 \times \text{Cov}(A,B)$ $0.00162 = 0.18 \times \text{Cov}(A,B)$ $\text{Cov}(A,B) = \frac{0.00162}{0.18} = 0.009$

Therefore, the covariance between the two securities is 0.009.