Answer: CAD 1,203

## Explanation The standard deviation of the daily change in portfolio value is calculated using the variance formula for a portfolio with correlated risk factors: $$\sigma_P^2 = \sum_{i=1}^{n} \sum_{j=1}^{n} \rho_{ij} \sigma_i \sigma_j KR01_i * KR01_j$$ For two risk factors (2-year and 10-year rates), this expands to: $$\sigma_P^2 = \sigma_{2Y}^2 * KR01_{2Y}^2 + 2 * (\rho_{2Y,10Y} * \sigma_{2Y} * \sigma_{10Y} * KR01_{2Y} * KR01_{10Y}) + \sigma_{10Y}^2 * KR01_{10Y}^2$$ **Step-by-step calculation:** 1. **First term:** $\sigma_{2Y}^2 * KR01_{2Y}^2 = (4)^2 * (52)^2 = 16 * 2,704 = 43,264$ 2. **Second term:** $2 * (\rho_{2Y,10Y} * \sigma_{2Y} * \sigma_{10Y} * KR01_{2Y} * KR01_{10Y}) = 2 * (0.6 * 4 * 11 * 52 * 97) = 2 * (0.6 * 4 * 11 * 5,044) = 2 * (0.6 * 221,936) = 2 * 133,161.6 = 266,323.2$ 3. **Third term:** $\sigma_{10Y}^2 * KR01_{10Y}^2 = (11)^2 * (97)^2 = 121 * 9,409 = 1,138,489$ 4. **Total variance:** $43,264 + 266,323.2 + 1,138,489 = 1,448,076.2$ 5. **Standard deviation:** $\sqrt{1,448,076.2} = 1,203.36$ Therefore, the standard deviation of the daily change in portfolio value is approximately **CAD 1,203**. This calculation accounts for the correlation between the 2-year and 10-year rate movements, which significantly impacts the portfolio's overall volatility. The positive correlation (0.6) increases the portfolio variance compared to uncorrelated rates.

Author: LeetQuiz .