This paper examines a 1991 pricing discrepancy in US Treasury bonds where callable bonds were trading above their synthetic non-callable equivalents—a market anomaly that should not occur under normal conditions. The analysis demonstrates how synthetic bonds combining traditional Treasury bonds and zero-coupon STRIPS can replicate cash flows and identify mispricings. By constructing two synthetic bonds that matched the potential cash flows of a callable bond under different redemption scenarios, the analysis reveals the magnitude of the pricing error and outlines two primary strategies for exploiting this arbitrage opportunity through bond substitution.
In 1991, major discrepancies in the prices of multiple long-maturity US Treasury bonds appeared in the market. An employee of Mercer and Associates developed a strategy to exploit this pricing opportunity by substituting superior bonds for existing holdings. The strategy centered on the 8ÂĽ May 00-05 callable bond, for which the analyst created two synthetic bonds that imitated its cash flows under different scenarios: one assuming the bond would be called in 2000 and one assuming it would be held to maturity in 2005.
Under normal market conditions, synthetic bonds that do not carry redemption rights should be worth more to investors than callable bonds. This is because callable bonds grant the issuer (in this case, the government) the right to redeem the bond early, which benefits the issuer but disadvantages the bondholder. Therefore, the callable bond should trade at a lower price than equivalent non-callable synthetic bonds. The analysis that follows demonstrates whether this theoretical relationship held in the 1991 market.
To construct the first synthetic bond, the analyst combined non-callable treasury bonds maturing in 2005 with zero-coupon treasuries (STRIPS) also maturing in 2005. This synthetic bond was designed to exactly replicate the cash flows of the 8ÂĽ May 00-05 callable bond if it were held to maturity, producing semiannual interest payments of $4.125 per $100 face value and a final payment of $100 at maturity.
The analyst calculated the required units of each component using straightforward algebra. For the 2005 Treasury bond, the number of units needed was determined by dividing the semiannual callable coupon rate by the semiannual 2005 Treasury bond coupon rate (4.125 Ă· 6). To find the number of units needed for the 2005 STRIP, the analyst used the final cash flows: the 00-05 callable bond paid $104.125 at maturity, the 2005 Treasury bond paid $106, and the STRIP paid $100 (since STRIPS have no coupon payments). Solving for the required STRIP units yielded 0.3125 units.
Using ask prices of $129.906 for the 2005 Treasury bond and $30.3125 for the 2005 STRIP, the synthetic price for the maturity scenario was calculated to be $98.78.
The second synthetic bond combined non-callable bonds maturing in 2000 with STRIPS maturing in 2000. This synthetic bond replicated the cash flows of the 8ÂĽ May 00-05 callable bond under the assumption that it would be called in 2000. It maintained the same semiannual interest payments of $4.125 per $100 face value and a final maturity payment of $100.
Using the same methodology as the first synthetic bond, the analyst determined that 0.0704 units of the 2000 STRIP were needed. The resulting price of this synthetic bond was $100.43.
The results revealed a significant market anomaly. Both synthetic bond prices—$98.78 for the maturity scenario and $100.43 for the call scenario—were substantially lower than the ask price of the 00-05 callable Treasury bond. In efficient markets, this pricing relationship should not occur. Since the synthetic bonds do not carry redemption rights and should therefore be worth more to investors, the callable bond should trade at a lower price, not higher.
This reversal indicated a clear misprice in the market: the callable bond was trading above its theoretical value when compared to its non-callable synthetic equivalents. This created an exploitable arbitrage opportunity, as the true value of the security became apparent through the synthetic replication method.
There are two ways that an investor could exploit this pricing anomaly. Investors who already held the 00-05 Treasury bond could immediately capitalize on the price discrepancy by selling the 00-05 Treasury bond and purchasing the underpriced synthetic bond combinations instead. Additionally, arbitrageurs could establish a short position in the overpriced callable bond while simultaneously taking long positions in the synthetic components, locking in the price difference as profit when the market corrected.
"Methods for capitalizing on the misprice"
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