Treasury Bond Arbitrage: Synthetic Replication and Market Pricing
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.
- Introduction and Market Anomaly: 1991 Treasury bond pricing discrepancy discovered
- Synthetic Bond Construction: Maturity Scenario: Creating synthetic bond for hold-to-maturity scenario
- Synthetic Bond Construction: Call Scenario: Creating synthetic bond for early call scenario
- Pricing Analysis and Findings: Comparison reveals market pricing anomaly
- Arbitrage Exploitation Strategies: Methods for capitalizing on the misprice
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What makes this paper effective
- Clear problem identification: Opens with a concrete 1991 market anomaly that motivates the entire analysis.
- Systematic construction: Walks through two separate synthetic bond scenarios with explicit calculations, showing the reader exactly how cash flows are matched.
- Quantitative precision: Provides actual bond prices, coupon rates, and formula-based unit calculations, grounding the analysis in real numbers.
- Logical framework: Establishes the theoretical principle (callable bonds should trade lower than non-callable equivalents) before demonstrating its violation.
Key academic technique demonstrated
The paper employs financial replication—a core arbitrage technique where complex securities are deconstructed into constituent building blocks. By combining Treasury bonds and zero-coupon STRIPS in precise quantities, the author creates synthetic bonds that perfectly replicate the target bond's cash flows under different scenarios. This technique isolates the pricing error and makes the arbitrage opportunity quantifiable and actionable.
Structure breakdown
The paper follows a natural progression: (1) problem statement establishing the anomaly, (2) detailed construction of the maturity scenario synthetic bond with formulas and calculations, (3) construction of the call scenario synthetic bond using parallel methodology, (4) comparative pricing analysis revealing the discrepancy, and (5) transition to exploitation strategies. The repetition of structure across both synthetic scenarios reinforces the analytical method while permitting direct comparison of results.
Introduction and Market Anomaly
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 8¼ 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.
Synthetic Bond Construction: Maturity Scenario
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 8¼ 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 ÷ 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.
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