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# Arbitrage in the Government Market Essay

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.

2.
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. Once they do, she would buy the 00-05 bond for a lower price and give it back to the dealer, while pocketing about \$2 (given that she bought the 2005 synthetic bond). There’s plenty of risk when trying to take advantage of pricing arbitrage. For example, the prices may never converge and Thompson might end up waiting almost 15 years without anything happening. Another risk is that the dealer might call the bond back while the money is tied up in the synthetic bond. Because of these risks, it might be better if she doesn’t try and take advantage of the pricing arbitrage at all.

3.
Through close examination, a multitude of factors could have come into play resulting in the odd pricing of Thompson’s evaluated bonds. In studies conducted by Longstaff (1992) and Eldeson, Fehr, and Mason (1993) they found that negative option values were very common, ultimately implying that callable treasury bonds were significantly overpriced (35). Although it seems odd to have a negative option value, Thompson found herself in a rapidly changing bond market with the earlier introduction of derivative securities and STRIP bonds. With the introduction of STRIP bonds in 1985, problems arise in valuing callable treasury bonds using solely zero-coupon STRIP bonds being that they tend to undervalue the implied options (Jorden et al. 36). In addition, since negative option value bonds do not have implied volatilities, this raises the question whether callable bonds are priced rationally (Bliss and Ronn 2).

Furthermore into Longstaff’s (1992) research, they exercised the “striplets” approach to investigate implied call option values. The “striplets” approach uses a U.S. Treasury coupon STRIPS and a coupon bond to synthesize a noncallable bond with the desired coupon (Jordan et al. 37). Longstaff finds that “61.5% of the call values are negative when estimates are based on the midpoint of the bid and ask prices, whereas 50.7% of the negative call estimates are large enough to generate profits even after considering the bid-ask spread” (38). Ultimately, the odd pricing in Thompson’s current situation is most likely due to the mispricing of callable bonds at the time due to the method of callable bond valuation and the early introduction of new types of bond securities in the market.

4.
“Callable debt gives the treasury the right, but not the obligation, to redeem the callable treasuries at par (100) on any semiannual interest payment date within five years of maturity, provided that it gave investors four months’ notice” (Arbitrage in the Government Bond Market). There are multiple upsides for a company to issue callable debt. The main reason for this is to give the company (treasury) a sense of security in that they can redeem the bond in the event of an interest rate drop. For example, if the company issues bonds to investors at a 10% interest rate and then this rate goes down to 8%, the company may redeem the callable bonds they’ve issued and replace them with the lower interest rate (8%).

Callable debt is essential to have when there are long maturity dates. If you issue a non-callable bond for a fixed amount of years, there is a tremendous amount of risk for the treasury. For instance, if you issue a non-callable bond with a maturity of 25 years and the interest rate goes down over the years, this negatively affects the company. “Callability enables the treasury to respond to changing interest rates, refinance high-interest debts, and avoid paying more than the going rates for its long term debt” (Why Companies Issue Callable Bonds).

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. .

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