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# fm23 10 - The value of each futures contract will be...

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Mini Case: 23 - 11 T-bond futures contracts are priced off of a hypothetical 20-year, 6 percent coupon, semiannual payment bond, and the 111-25 futures price translates to a \$1,117.81 for each \$1000 face value bond. The implied yield can be caluclated with a financial calculator to be (N = 40; Pmt = 30; FV = 1000; PV = -1117.81; calculate I/Y = 2.5284% semi-annually, which is an annual rate of about 5.057%. If interest rates increase by 1 percent, then the new yield on this underlying bond will be 6.057%. The six month rate is 6.057%/2 = 3.0285%. The corresponding price at this yield is found by inputting N = 40, I/YR = 3.0285, PMT = -30, FV = -1000 and solving for PV = 993.44.
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Unformatted text preview: The value of each futures contract will be \$99,344 at this higher interest rate. This represents a decrease of \$111,781 \$99,344 = \$12,437 for each contract. Since TS has sold futures contracts, this represents a profit to TS. The total profit from the futures contracts is 45(\$12,437) = \$559,665. TS will lose \$494,819 on the bonds it issues but gain \$559,665 on its futures contracts. The net hedging gain is \$559,665 - \$494,819 = \$64,846. Thus TS will end up just a little bit better off if interest rates increase by 1%. Note that if interest rates were to decrease instead, then TS would gain on the bonds it issues but lose on its futures contracts....
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