arbitrage in the government bond market
MGT 409 Case 1: Arbitrage in the Government Market
1.
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
1.
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
Bibliography: 1. "Bonds 200." Why Companies Issue Callable Bonds. N.p., 24 Sept. 2014. Web. 30 Sept. 2014. 2. Jordan, Bradford D., Susan D. Jordan, and David R. Kuipers. "The Mispricing of Callable U.S. Treasury Bonds: A Closer Look." Journal of Futures Markets 18.1 (1998): 35-51. Web. 3. Bliss, Robert R., and Ehud I. Ronn. "Callable U.S. Treasury Bonds: Optimal Calls, Anomalies, and Implied Volatilities." The Journal of Business 71.2 (1998): 211-52. Web. 4. "Bonds 200." Why Companies Issue Callable Bonds. N.p., 24 Sept. 2014. Web. 30 Sept. 2014. 4. 5. "Harvard Business School." Arbitrage in The Government Bond Market. N.p., 20 Sept. 2014. Web. 28 June 1995. .