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Arbitrage in the Government Bond Market Case Solution
| Solution Id | Length | Case Author | Case Publisher |
|---|---|---|---|
| 2552 | 1414 Words (7 Pages) | Michael E. Edleson, Peter Tufano | Harvard Business School : 293093 |
A Word File
In 1991, the market saw significant price discrepancies in a range of long-term US Treasury bonds. Thompson replied by producing two synthetic bonds; both simulated 814 May ‘005 bond’s cash flows. One of these bonds was held till maturity till year 2005 and one of those was called in year 2000. Combining noncallable treasury bonds from 2005 with zero coupon treasuries (STRIPS) from the same year yielded the first synthetic bond. In the second synthetic bond, the noncallable bonds that were due to mature were combined. Because STRIPs have no coupon payments, the final cash flow of the 00-05 bond was $104.125, the final cash flow of the 2005 Treasury bond was $106, and the final cash flow of the 2005 STRIP bond was $100. She realized that she needed 0.3125 units of the 2005 STRIP bond, which had a synthetic price of $98.78.
Following questions are answered in this case study solution
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Create the two synthetic bonds described in the case. How should the price of these synthetics relate to callable bonds? Why? On January 7, 1991, how much would it cost to create the synthetic using the ‘05s? The ‘00s?
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On January 7, 1991, how could Thompson exploit this apparent anomaly for investors who own the 8.25 May ’00-’05? What can investors not owning the callable bond do to profit?
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What might underlie the odd relative prices of the bonds Thompson is considering?
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Why should the treasury issue callable debt? When should they exercise their right to call or redeem the bonds? Why would corporations issue callable debt? Why should investors want to buy callable debt?
Case Analysis for Arbitrage in the Government Bond Market
1. Create the two synthetic bonds described in the case. How should the price of these synthetics relate to callable bonds? Why? On January 7, 1991, how much would it cost to create the synthetic using the ‘05s? The ‘00s?
Create the two synthetic bonds described in the case:
o c/r = 8.25/12 = 0.6875 Synthetic Bond 05
0.3125 c/r = 1-c/r
Bonds that are not callable (68.75 percent):
Ask Price (Bid): $129.71875 Purchase Price (Ask): $129.90625
14 years to maturity, a 12% coupon rate, and a fair value of $100
STRIP FROM THE TREASURY (31.25%):
$30.3125 Purchase Price (Ask)
$29.90625 Ask Price (Bid)
FV = $100, 14 years until maturity, zero coupon payment
Synthetic Bond:
68.75 percent *129.90625+31.25 percent *30.3125 = $98.78 Purchase Price (Ask): 68.75 percent *129.90625+31.25 percent *30.3125 = $98.78
*129.71875+31.25 percent *29.90625 = $98.53 Ask Price (Bid): 68.75 percent *129.71875+31.25 percent *29.90625 = $98.53
Term to maturity is 14 years, with an 8.25 percent coupon rate and a fair value of $100.
Synthetic Bond 00:
c/r = 8.25/8.875 = 0.9296 c/r = 8.25/8.875 c/r = 8.25/8.875 c/r
c/r = 0.0704 c/r = 0.0704 c/r = 0.0704 c/
Bonds that are not callable (92.96 percent):
$104.50 Purchase Price (Ask)
$104.375 Asking Price (Bid)
9.875 percent coupon rate, FV = $100, 9 years until maturity
Purchase Price (Ask): $46.65625 Treasury STRIP (7.04 percent)
$46.25 Ask Price (Bid)
9 years to maturity, no coupon payments, and an FV of $100
Synthetic Bond:
*104.5+7.04 percent *$46.65625 = $100.43 Purchase Price (Ask): 92.96 percent *104.5+7.04 percent *$46.65625 = $100.43
92.96 percent *104.375+7.04 percent *46.25 = $100.28 Ask Price (Bid)
9.25 percent coupon rate, FV = $100, 9 years to maturity
Because these synthetic bonds do not give the government a redemption right, they should be more expensive than callable bonds with higher yields and the same maturity.
A synthetic bond using the '05s would cost $98.78 in purchasing price on January 7, 1991, whereas a synthetic bond using the '00s would cost $100.43.
2. On January 7, 1991, how could Thompson exploit this apparent anomaly for investors who own the 8.25 May ’00-’05? What can investors not owning the callable bond do to profit?
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