D is correct. The equation for the variance of the change in portfolio value is:

$\sigma_P^2 = \sum_{i=1}^n \sum_{j=1}^n \rho_{ij} \sigma_i \sigma_j \times KR01_i \times KR01_j$

$= (1 \times \sigma_{2Y} \times \sigma_{2Y} \times KR01_{2Y} \times KR01_{2Y}) + (\rho_{2Y,10Y} \times \sigma_{2Y} \times \sigma_{10Y} \times KR01_{2Y} \times KR01_{10Y})$

$+ (\rho_{10Y,2Y} \times \sigma_{10Y} \times \sigma_{2Y} \times KR01_{10Y} \times KR01_{2Y})$

$+ (1 \times \sigma_{10Y} \times \sigma_{10Y} \times KR01_{10Y} \times KR01_{10Y})$

$= \sigma_{2Y}^2 \times KR01_{2Y}^2 + 2 \times (\rho_{2Y,10Y} \times \sigma_{2Y} \times \sigma_{10Y} \times KR01_{2Y} \times KR01_{10Y}) + \sigma_{10Y}^2 \times KR01_{10Y}^2$

$= [(4)^2 \times (52)^2] + [0.6 \times 4 \times 11 \times 52 \times 97] + [0.6 \times 11 \times 4 \times 97 \times 52] + [(11)^2 \times (97)^2]$

$= 1,448,076$

The standard deviation is therefore: $\sqrt{1,448,076} = 1,203.36$.

Analysis of Incorrect Options

• A is incorrect. This calculates the variance as: $= [0.6 \times 4 \times 11 \times 52 \times 97] + [0.6 \times 11 \times 4 \times 97 \times 52]$.
• B is incorrect. This calculates the variance as: $= [0.6 \times (4)^2 \times (52)^2] + [0.6 \times (11)^2 \times (97)^2]$.
• C is incorrect. This calculates the variance without the KR01 terms, and then multiplies the result by the average of the KR01s.