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Question 6 A company has a long position in a two-year bond and a three-year bond, as well as a short position in a five-year bond. Each bond has a principal of $100 million and pays a 5% coupon annually. Calculate the company's exposure to the one-year, two-year, three year, four-year and five-year rates. Use the data in Table 14.7 and 14.8 to calculate a 20-year 95% VaR on the assumption that rate changes are explained by (a) one factor, (b) two factors, and (c) three factors. Assume that the zero-coupon yield curve is flat at 5%. Table 1: 14.7: Factor loadings for swap data PC1 PC2 PC3 PC4 PCS PC6 PCZ PC8 1-year 0.216 -0.501 0.627 -0.487 0.122 0.237 0.011 -0.034 2-year 0.331 -0.429 0.129 0.354 -0.212 -0.674 -0.100 0.236 3-year 0.372 -0.267 -0.157 0.414 -0.096 0.311 0.413 -0.564 4-year 0.392 -0.110 -0.256 0.174 -0.019 0.551 -0.416 0.512 5-year 0.404 0.019 -0.355 -0.269 0.595 -0.278 -0.316 -0.327 7-year 0.394 0.194 -0.195 -0.336 0.007 -0.100 0.685 0.422 10-year 0.376 0.371 0.068 -0.305 -0.684 -0.039 -0.278 -0.279 30-year 0.305 0.554 0.575 0.398 0.331 0.022 0.007 0.032 Table 2: 14.8: Standard deviation of factor score PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 17.55 4.77 2.08 1.29 0.91 0.73 0.56 0.53 Question 6 A company has a long position in a two-year bond and a three-year bond, as well as a short position in a five-year bond. Each bond has a principal of $100 million and pays a 5% coupon annually. Calculate the company's exposure to the one-year, two-year, three year, four-year and five-year rates. Use the data in Table 14.7 and 14.8 to calculate a 20-year 95% VaR on the assumption that rate changes are explained by (a) one factor, (b) two factors, and (c) three factors. Assume that the zero-coupon yield curve is flat at 5%. Table 1: 14.7: Factor loadings for swap data PC1 PC2 PC3 PC4 PCS PC6 PCZ PC8 1-year 0.216 -0.501 0.627 -0.487 0.122 0.237 0.011 -0.034 2-year 0.331 -0.429 0.129 0.354 -0.212 -0.674 -0.100 0.236 3-year 0.372 -0.267 -0.157 0.414 -0.096 0.311 0.413 -0.564 4-year 0.392 -0.110 -0.256 0.174 -0.019 0.551 -0.416 0.512 5-year 0.404 0.019 -0.355 -0.269 0.595 -0.278 -0.316 -0.327 7-year 0.394 0.194 -0.195 -0.336 0.007 -0.100 0.685 0.422 10-year 0.376 0.371 0.068 -0.305 -0.684 -0.039 -0.278 -0.279 30-year 0.305 0.554 0.575 0.398 0.331 0.022 0.007 0.032 Table 2: 14.8: Standard deviation of factor score PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 17.55 4.77 2.08 1.29 0.91 0.73 0.56 0.53

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