Arbitrage in the Government Bond Market?

Arbitrage in the Government Bond Market?

Samantha Thompson, an analyst at Mercer and Associates found major anomalies regarding the prices of long term US Treasury bonds on January 7, 1991. Thompson noticed that the pricing of the callable 8.25 May 00-05 Treasury bond was out of bounds relative to other bonds in the market. Although this situation was unusual because it occurred in the U.S Treasury bond market: the largest fixed-income securities market which is closely observed, it created an opportunity for arbitrage.

Ms. Thompson came up with two synthetic bond constructions in order for her firm and its clients to potentially benefit from. The first was to create a synthetic bond through the combination of non-callable bonds which were maturing in 2005 with zero coupon Treasuries (STRIPS) with the same maturity, semi-annual coupon payments and $100 face value at maturity (if the bond was not called) as the non-callable bonds. In this case, because the government does not hold any redemption rights to the synthetic bonds, it will be valued more to investors than the STRIPS with the same maturity. An alternative solution was to combine non-callable bonds maturing in 2000 with STRIPS with the same maturity to create a synthetic non-callable Treasury bonds. This synthetic bond corresponded to the callable bond if it were called at the first possible date and was worth more than the callable bond.

Calculations

Assume;

• Callable bond coupon rate = c
• Non-callable coupon rate = n

Synthetic bond 00

• Portion of the non-callable = [pic 1]
• Portion of the STRIPS = [pic 2]

Bid price; [pic 3]

Ask price; [pic 4]

Synthetic bond 05

• Portion of the non-callable = [pic 5]
• Portion of the STRIPS = [pic 6]

Bid price; [pic 7]

Ask price; [pic 8]

[pic 9]

On January 7, 1991, an investor who already owns the 8.25 May 00-05 callable bond should sell it at $101.125 and buy the synthetic bond at $98.78 in order to profit. Also, an investor who does not own the callable bond can short sell the relatively overpriced callable bond and buy the underpriced synthetic bond.

The price of the callable bond should be lower than the synthetic bonds. Clearly, this is not the case. When interest rates fall, a callable 00-05 bond can be called by the government so they can refinance at a lower rate. Again, the callable 00-05 should be lower than the 00 bond because in the event that interest rates rises, the government will not call the bond and benefit from lower financing charges.