Fixed Income Case: Arbitrage in the Government Bond Market

FIXED INCOME CASE: ARBITRAGE IN THE GOVERNMENT BOND MARKET

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Case study analysis

Samantha Thompson who is an analysis at Mercer and Associates realized that there were increased anomalies surrounding the prices of the long term US Treasury bonds on January 7, 1991. With reference to callable 8.25 May 00-05 Treasury bond, Thompson realized that its pricing was out of bounds in contrast to the other bonds in the market by then. This hence created an arbitrage opportunity with regard to the U.S Treasury bond market that is widely recognized as the largest fixed-income securities and bonds market. Thompson hence found a way to construct two synthetic bonds to increase the prospective benefits that the firm and clients would enjoy. The first main construction was the creation of a synthetic bond through combining the non-callable bonds that would mature in 2005 with the zero coupon Treasuries that had the same maturity (STRIPS), the semi-annual coupon payments as well as the $100 face value at bond maturity in the event of not being called off. As such, the synthetic bond created would be valuable to the investors than the STRIPS with the same maturity because the government would not enjoy any redemption rights to it. This would hence create, non-callable bonds.

The second synthetic bond creation option was the combination of non-callable bonds that would mature in 2000 with STRIPS that had the same maturity. This alternative would lead to the creation of non-callable Treasury bonds. The synthetic bond would be similar to the callable bond in the event that they would be called at the first possible data and was worth more than the callable bond itself.

Let’s assume that the non-callable bond coupon rate is “a” and the callable bond coupon rate is “b”. NB? Non-taxable. Thus, the synthetic bond, the proportion of the non-callable bond is c/s and the proportion of STRIPS is 1-c/s.

This means that: B-callable= B-non-callable – embedded option to call the bond back

YTM call= YTM non-callable + risk premium

In that case, the synthetic bond 00:

c/s = 8.25/8.875

= 0.9296

The portion of the STRIPS= 1-c/s

= 1/0.9296= 0.0704

Price of synthetic bond (using the ask price) = (104.5 x 0.9296) + (46.66 x 0.0704) = $100.43