MGT 409 Case 1: Arbitrage in the Government Market
In 1991, major discrepancies in the prices of multiple long maturity US Treasury bonds seemed to appear in the market. An employee of the firm Mercer and Associates, Samantha Thompson, thought of a way to exploit this opportunity in order to take advantage of a positive pricing difference by substituting superior bonds for existing holdings. Thompson created two synthetic bonds that imitated the cash flows of the 8¼ May 00-05 bond; one for if the bond had been called at the year 2000, and one for if it hadn’t been called and was held to its maturity at year 2005. The first synthetic bond combined noncallable treasury bonds that matured in 2005 with zero coupon treasuries (STRIPS) that matured in 2005. The synthetic bond had semiannual interest payments of $4.125 per $100 face value and a final payment of $100 at maturity in order to exactly match the cash flows of the 8¼ May 00-05 callable bond if it had been held to maturity. Thompson found the price of this synthetic bond by using this formula:
The ask price of the two bonds were given as $129.906 and $30.3125, respectively. She calculated the number of units needed of the 2005 treasury bond by dividing the semi-annual callable 00-05 coupon rate by the semi-annual 2005 treasury bond (4.125/6). The only part of the equation that she did not have was the number of units needed of the 2005 STRIP. She had to calculate the correct amount in order to imitate the cash flows of the 00-05 callable bond. Thompson did this by using this equation. 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 as there are no coupon payments in STRIPs. She found that the number of units needed of the 2005 STRIP bond was 0.3125, and then found that the synthetic price of this bond was $98.78. The second synthetic bond combined the noncallable bonds maturing in 2000 with STRIPS maturing in 2000. This synthetic bond also had semiannual interest payments of $4.125 per $100 face value and a final payment of $100 at maturity in order to exactly match the cash flows of the 8¼ May 00-05 callable bond if it had been called in 2000. Through similar calculations of the first synthetic bond, she found that she needed 0.0704 units of the 2000 STRIP, and the price of this synthetic bond was $100.43. What Thompson found was surprising because both of these synthetic prices were less than the ask price of the 00-05 treasury bond. In normal markets this shouldn’t be the case because the synthetic bond would be worth more to investors since it does not have a redemption right to the government. In other words, the callable bond should have a lower price than the synthetic noncallable bond.
There are two ways that Thompson could exploit this pricing anomaly that she found. If she already held the 00-05 treasury bond, then she could immediately capitalize on the price discrepancy by selling the 00-05 treasury bond for the bid price of $101.125 and buying one of these synthetic bonds. Whether to buy the 2000 synthetic bond or 2005 synthetic bond is up for debate and opinion but it might be suggested to go with the 2005 one since the price of $98.78 is even smaller than the price of $100.43 and there would be larger price impact. By selling the 00-05 bond and buying the 2005 treasury bond, she would be getting the same cash flows for an immediate lower price. The second way that Thompson could exploit this pricing anomaly would be if she does not currently hold any bonds at all. A profit could be earned by establishing short positions in the relatively overpriced security and long positions in the relatively underpriced security. Thompson would borrow the 00-05 treasury bond from a dealer and then sell it. With that money, she would buy a synthetic bond and wait for the 00-05 treasury bond to decrease in price as prices converge....
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