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Q 06. 11: Theoretical Price of Treasury Bond Futures Contract |
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7/30/2005 |
2/4/2005 |
2/4/2005 |
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Cheapest to deliver (CTD) will be 12% coupon, CF = 1.5 |
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9/30/2005 |
7/30/2005 |
8/4/2005 |
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62 |
176 |
181 |
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Face |
$100.00 |
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Coupon |
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Current Quoted Price |
$110.00 |
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Coupon |
13.0% |
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177 |
days |
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Interest rate |
11.65% |
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F=(Spot - Lump Sum Income)*EXP[rT] |
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Conversion Factor |
1.50 |
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Current |
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1. Use COC to calculate "dirty" Forward |
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Delivery (days) |
62 |
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Spot = |
$116.32 |
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Last Coupon (-days) |
177 |
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5 |
days |
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Lump Income = |
$6.490 |
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Next Coupon (+ days) |
5 |
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Forward Price = |
$112.028 |
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Coupon |
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(implied cash futures price if 12% bond) |
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Accrued Interest |
$6.321 |
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Cash (Dirty Price) |
$116.321 |
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57 |
days |
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2. Tranlate dirty > clean, standard bond |
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PV of coupon |
$6.490 |
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Quoted Price, 12% bond = |
$110.003 |
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Cash Futures Price |
$112.028 |
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Maturity |
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(add AI) |
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Days Accrue, @ delivery |
57 |
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Days Remain, @ delivery |
126 |
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days |
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Quoted Futures price |
$73.34 |
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Quoted FP, 12% bond |
$110.003 |
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(divide CF) |
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Coupon |
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Quoted FP, CTD |
$73.335 |
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