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The naive hedge for relative duration and relative

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the naive hedge for relative duration and relative yield volatility, we obtain the adjusted hedge position: 300 0 . 1 0 . 8 6 . 7 806 . 315 = × × contracts Situation B . Here, the treasurer seeks to hedge the purchase price of the bonds; this requires a long hedge. The market value of the bonds to be purchased is: $20 million × 0.93 = $18.6 million The duration ratio is 7.2/8.0, and the relative yield volatility is 1.25. Therefore, the hedge requires the treasurer to take a long position in: 330 25 . 1 0 . 8 2 . 7 330 , 63 000 , 600 , 18 = × × contracts 23-10
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28. a. % change in T-bond price = modified duration × change in YTM = 7.0 × 0.50% = 3.5% b. When the YTM of the T-bond changes by 50 basis points, the predicted change in the yield on the KC bond is 1.22 × 50 = 61 basis points. Therefore: % change in KC price = modified duration × change in YTM = 6.93 × 0.61% = 4.23% 29. If the exchange of currencies were structured as three separate forward contracts, the forward prices would be determined as follows: Forward exchange rate × $1 million euros = dollars to be delivered Year 1: 1.20 × (1.05/1.04) × $1 million euros = $1.2115 million Year 2: 1.20 × (1.05/1.04) 2 × $1 million euros = $1.2232 million Year 3: 1.20 × (1.05/1.04) 3 × $1 million euros = $1.2349 million Instead, we deliver the same number of dollars (F*) each year. The value of F* is determined by first computing the present value of this obligation: 3300 . 3 05 . 1 2349 . 1 05 . 1 2232 . 1 05 . 1 2115 . 1 1.05 * F 1.05 * F 1.05 * F 3 2 1 3 2 1 = + + = + + F* equals $1.2228 million per year. 30. a. The swap rate moved in favor of firm ABC. ABC should have received 1% more per year than it could receive in the current swap market. Based on notional principal of $10 million, the loss is: 0.01 × $10 million = $100,000 per year. b. The market value of the fixed annual loss is obtained by discounting at the current 7% rate on 3-year swaps. The loss is: $100,000 × Annuity factor (7%, 3) = $262,432 c. If ABC had become insolvent, XYZ would not be harmed. XYZ would be happy to see the swap agreement cancelled. However, the swap agreement ought to be treated as an asset of ABC when the firm is reorganized. 31. The firm receives a fixed rate that is 2% higher than the market rate. The extra payment of (0.02 × $10 million) has present value equal to: $200,000 × Annuity factor (8%, 5) = $799,542 23-11
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