Answer: CAD 1,203

The correct answer to the question is D, CAD 1,203. The explanation for this is based on the calculation of the standard deviation of the daily change in portfolio value, which involves understanding the volatility of the bank's asset portfolio in relation to its exposure to 2-year and 10-year spot rates. The calculation uses the key rate durations (KRO1s) for both the 2-year and 10-year rates, the standard deviation of daily changes in the spot rates, and the correlation between these rates. The formula for the variance of the change in portfolio value is given by: \[ \sigma^2 = \left( \omega_{2y} \sigma_{2y}^2 KRO1_{2y}^2 \right) + \left( \omega_{10y,2y} \sigma_{2y} \sigma_{10y} KRO1_{2y} KRO1_{10y} \right) + \left( \omega_{2y,10y} \sigma_{2y} \sigma_{10y} KRO1_{2y} KRO1_{10y} \right) + \left( \omega_{10y} \sigma_{10y}^2 KRO1_{10y}^2 \right) \] Where: - \( \omega_{2y} \) and \( \omega_{10y} \) are the weights of the 2-year and 10-year rates in the portfolio. - \( \sigma_{2y} \) and \( \sigma_{10y} \) are the standard deviations of the daily changes in the 2-year and 10-year spot rates, respectively. - \( KRO1_{2y} \) and \( KRO1_{10y} \) are the key rate durations for the 2-year and 10-year rates. - \( \omega_{10y,2y} \) and \( \omega_{2y,10y} \) are the cross-weights between the 2-year and 10-year rates, which take into account the correlation between the rates. Plugging in the values from the question: - \( \sigma_{2y} = 11 \) bps - \( \sigma_{10y} = 11 \) bps - \( KRO1_{2y} = 52 \) CAD - \( KRO1_{10y} = 97 \) CAD - \( \omega_{2y} = \omega_{10y} = 1 \) (since the portfolio is only exposed to these two rates, each has a weight of 1) - \( \omega_{10y,2y} = \omega_{2y,10y} = 0.6 \) (the correlation between the rates) The calculation then proceeds as follows: \[ \sigma^2 = (1 \cdot 11^2 \cdot 52^2) + (2 \cdot 0.6 \cdot 11 \cdot 11 \cdot 52 \cdot 97) + (0.6 \cdot 11 \cdot 4 \cdot 97 \cdot 52) + (1 \cdot 11^2 \cdot 97^2) \] \[ \sigma^2 = 1,448,076 \] The standard deviation is the square root of the variance: \[ \sigma = \sqrt{1,448,076} \approx 1,203.36 \] Thus, the standard deviation of the daily change in portfolio value is approximately CAD 1,203, which corresponds to option D.

Author: LeetQuiz Editorial Team