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Solution 6 - Fin 448 Fixed-Income Securities Homework...

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Fin 448: Fixed-Income Securities Homework Solution 6 Wei Yang 1 Interest rate swap (1.1) Since it is immediately after an exchange, the FRN will trade at par. The value of the floating rate side is thus $100M. (1.2) The fixed rate side is a 3.5-year bond paying semi-annual coupons at a coupon rate c =4.5%, while the yield curve is flat at y = 4.2%. P = Z c y " 1 - 1 ( 1 + y 2 ) 2 n # + Z 1 ( 1 + y 2 ) 2 n The price is $100.967M. (1.3) As a buyer you have a long position in FRN and a short position in the fixed rate bond, so you have realized a loss of $0.967M. 2 Hedging bond position with swaps (2.1) A long position in swaps implies that you have bought an FRN and sold a fixed rate bond. To hedge a long position in bonds, you need to long a swap. The swap rate is just 5%, the same as the par yield of the Libor quality bonds. (2.2) The DV 01 of a $1M face value par bond is $779.458. For the FRN, which is priced at par P = 10 6 DV 01 = 1 2 1 + l 2 × P × 1 10 4 = 49 . 0196 (2.3) Our swap position implies buying floating and paying fixed, and thus a total DV 01 of 49 . 0196 - 779 . 458. The DV 01 of the bond holdings cancel with 1
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the DV 01 of the fixed side of the swap. We are left with a positive
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