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Answer: CAD1,203
The correct answer to the question is D, CAD 1,203. The calculation for the standard deviation of the daily change in portfolio value is based on the variance formula, which accounts for the individual variances of the key rate durations (KR01s) for the 2-year and 10-year spot rates, as well as the covariance between these rates due to their correlation. The equation provided in the file content is: \[ \sigma^2 = (P_{2Y} \cdot \sigma_{2Y} \cdot \sigma_{2Y} \cdot KR_{01_{2Y}} \cdot KR_{01_{2Y}}) + (P_{10Y} \cdot \sigma_{2Y} \cdot \sigma_{10Y} \cdot KR_{01_{2Y}} \cdot KR_{01_{10Y}}) + (P_{10Y} \cdot \sigma_{10Y} \cdot \sigma_{2Y} \cdot KR_{01_{10Y}} \cdot KR_{01_{2Y}}) + (P_{10Y} \cdot \sigma_{10Y} \cdot \sigma_{10Y} \cdot KR_{01_{10Y}} \cdot KR_{01_{10Y}}) \] This equation is broken down into four components: 1. The first component represents the variance of the 2-year rate's impact on the portfolio. 2. The second and third components represent the covariance between the 2-year and 10-year rates' impacts on the portfolio. 3. The fourth component represents the variance of the 10-year rate's impact on the portfolio. Plugging in the given values: - \( P_{2Y} = 52 \) million CAD - \( P_{10Y} = 97 \) million CAD - \( \sigma_{2Y} = 4 \) basis points - \( \sigma_{10Y} = 11 \) basis points - \( KR_{01_{2Y}} = 52 \) million CAD - \( KR_{01_{10Y}} = 97 \) million CAD - Correlation between 2-year and 10-year rates \( \rho = 0.6 \) The calculation results in a variance of 1,448,076, and taking the square root of this number gives the standard deviation of 1,203.36, which is rounded to CAD 1,203. This is why option D is the correct answer.
Author: LeetQuiz Editorial Team
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The Chief Risk Officer (CRO) of a small financial institution aims to evaluate the volatility of the institution's asset portfolio by leveraging its key rate durations. This is to aid in determining the required capital to mitigate market risk. The institution's portfolio is solely influenced by the 2-year and 10-year spot rates. The relevant data regarding market rates and the portfolio is summarized in the table below:
| Maturity | Standard Deviation of Daily Spot Rate Changes (bps) | Correlation of Spot Rates | Portfolio Key Rate Durations (CAD) |
|---|---|---|---|
| 2-year | 4 | 0.6 | 52 |
| 10-year | 11 | 0.6 | 97 |
Considering the given data, what is the standard deviation of the daily change in the value of the portfolio?
A
CAD 516
B
CAD988
C
CAD 1,026
D
CAD1,203