A company has a long position in a 2-year bond and a 3-year bond, as well as a short position in a 5-year bond. Each bond has a principal of $100 and pays a 5% coupon annually. Calculate the companys exposure to the 1-year, 2-year, 3-year, 4-year, and 5-year rates. Use the data in Tables 22.7 and 22.8 to calculate a 20-day 95% VaR on the assumption that rate changes are explained by

(a) one factor,

(b) two factors,

(c) three factors.

Assume that the zero-coupon yield curve is flat at 5%

Table 22.7 Factor loadings for swap data

PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8

1y 0.216 -0.501 0.627 -0.487 0.122 0.237 0.011 -0.034

2y 0.331 -0.429 0.129 0.354 -0.212 -0.674 -0.100 0.236

3y 0.372 -0.267 -0.157 0.414 -0.096 0.311 0.413 -0.564

4y 0.392 -0.110 -0.256 0.174 -0.019 0.551 -0.416 0.512

5y 0.404 0.019 -0.355 -0.269 0.595 -0.278 -0.316 -0.327

7y 0.394 0.194 -0.195 -0.336 0.007 -0.100 0.685 0.422

10y 0.376 0.371 0.068 -0.305 -0.684 -0.039 -0.278 -0.279

30y 0.305 0.554 0.575 0.398 0.331 0.022 0.007 0.032

Table 22.8 Standard deviation of factor scores (basis points).

PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8

17.55 4.77 2.08 1.29 0.91 0.73 0.56 0.53