Answer: USD 2.55 million

## Explanation ### Step 1: Calculate Initial Portfolio Variance For an equally weighted two-asset portfolio: \[\sigma_p^2 = w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2\sigma_1\sigma_2\rho_{12}\] Given: - w₁ = w₂ = 0.5 - σ₁ = σ₂ = 0.02 - ρ₁₂ = initial correlation \[\sigma_p^2 = 0.5^2(0.02)^2 + 0.5^2(0.02)^2 + 2\times0.5\times0.5\times0.02\times0.02\times\rho_{12}\] \[\sigma_p^2 = 0.0001 + 0.0001 + 0.0002\times\rho_{12}\] \[\sigma_p^2 = 0.0002\times(1 + \rho_{12})\] ### Step 2: Find Initial Correlation Given 10-day 99% VaR = USD 2.33 million 1-day VaR formula: \[\text{VaR}_{1-day} = z_{0.99} \times \sigma_p \times V_p\] 10-day VaR: \[\text{VaR}_{10-day} = \sqrt{10} \times z_{0.99} \times \sigma_p \times V_p\] Where: - z₀.₉₉ = 2.326 (for 99% confidence) - V_p = USD 20,000,000 \[2,330,000 = \sqrt{10} \times 2.326 \times 20,000,000 \times \sigma_p\] First calculate: \[\sqrt{10} \times 2.326 \times 20,000,000 = 2,080,123\] So: \[2,330,000 = 2,080,123 \times \sigma_p\] \[\sigma_p = \frac{2,330,000}{2,080,123} = 1.1201\] But this is incorrect - σ_p should be a volatility (0.01414), not 1.1201. Let's recalculate: \[\sigma_p = \sqrt{0.0002 \times (1 + \rho_{12})} = 0.01414 \times \sqrt{1 + \rho_{12}}\] \[2,330,000 = \sqrt{10} \times 2.326 \times 20,000,000 \times 0.01414 \times \sqrt{1 + \rho_{12}}\] \[2,330,000 = 2,080,123 \times \sqrt{1 + \rho_{12}}\] \[\sqrt{1 + \rho_{12}} = \frac{2,330,000}{2,080,123} = 1.1201\] \[1 + \rho_{12} = (1.1201)^2 = 1.2547\] \[\rho_{12} = 0.2547\] ### Step 3: Calculate New VaR with Doubled Correlation New correlation: ρ₁₂ = 2 × 0.2547 = 0.5094 New portfolio variance: \[\sigma_p^2 = 0.0002 \times (1 + 0.5094) = 0.0002 \times 1.5094 = 0.00030188\] \[\sigma_p = \sqrt{0.00030188} = 0.01737\] New 10-day VaR: \[\text{VaR}_{10-day} = \sqrt{10} \times 2.326 \times 20,000,000 \times 0.01737\] \[\text{VaR}_{10-day} = 2,080,123 \times 0.01737 = 2,549,000\] This is approximately USD 2.55 million, which matches option B. **Key Insight:** When correlation increases, portfolio diversification decreases, leading to higher portfolio volatility and higher VaR.

Author: LeetQuiz .