Answer: VaR(20-day) = USD 537M

## Explanation In Value at Risk (VaR) calculations, when scaling VaR over time periods, the relationship follows the square root of time rule: \[ VaR(T) = VaR(1) \times \sqrt{T} \] This means that VaR should scale proportionally with the square root of the time period. Let's verify the consistency: - **VaR(10-day) = USD 316M** - **VaR(15-day) = USD 465M** - **VaR(20-day) = USD 537M** - **VaR(25-day) = USD 600M** **Checking the ratios:** - From 10-day to 15-day: √(15/10) = √1.5 ≈ 1.2247 Expected: 316 × 1.2247 ≈ 387M (but actual is 465M) - From 10-day to 20-day: √(20/10) = √2 ≈ 1.4142 Expected: 316 × 1.4142 ≈ 447M (but actual is 537M) - From 10-day to 25-day: √(25/10) = √2.5 ≈ 1.5811 Expected: 316 × 1.5811 ≈ 500M (but actual is 600M) **Alternative check - calculate implied 1-day VaR:** - From 10-day: 316/√10 ≈ 316/3.1623 ≈ 99.9M - From 15-day: 465/√15 ≈ 465/3.873 ≈ 120.0M - From 20-day: 537/√20 ≈ 537/4.472 ≈ 120.0M - From 25-day: 600/√25 ≈ 600/5 = 120.0M The 10-day VaR implies a 1-day VaR of approximately 99.9M, while the 15-day, 20-day, and 25-day VaRs all imply a 1-day VaR of approximately 120.0M. Therefore, **VaR(10-day) = USD 316M** is inconsistent with the others as it suggests a different underlying 1-day VaR. **Correction:** Actually, upon re-examination, the 10-day VaR appears to be the outlier. However, let me check more carefully: If we assume the 15-day, 20-day, and 25-day VaRs are consistent: - 15-day to 20-day: 465 × √(20/15) = 465 × √1.333 ≈ 465 × 1.155 = 537M ✓ - 15-day to 25-day: 465 × √(25/15) = 465 × √1.667 ≈ 465 × 1.291 = 600M ✓ But 10-day to 15-day: 316 × √(15/10) = 316 × √1.5 ≈ 316 × 1.225 = 387M (but actual is 465M) Therefore, **VaR(10-day) = USD 316M** is the inconsistent one.

Author: LeetQuiz .