How do I calculate the return from riding the yield curve?

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AcadiFi · Accepted Answer

Riding the yield curve means buying a bond at its current yield and expecting to sell it before maturity at a lower yield (higher price) because it has rolled down an upward-sloping curve. **Return formula**: Total return = coupon income + price appreciation from yield change + pull-to-par. **Worked example**: Assume a flat spot curve: | Maturity | Yield | |---|---| | 1-year | 3.40% | | 2-year | 3.85% | | 3-year | 4.20% | | 5-year | 4.75% | Settleford Debt Advisors considers buying a zero-coupon 5-year bond at 4.75% and holding for 2 years, then selling as a 3-year bond. **Step 1**: Price now (5-year zero, $1,000 face): P₀ = $1,000 / (1.0475)⁵ = $793.66. **Step 2**: Expected price in 2 years (now a 3-year bond), ASSUMING curve unchanged, it will trade at the 3-year yield 4.20%: P₂ = $1,000 / (1.0420)³ = $883.94. **Step 3**: 2-year holding period return: (883.94 / 793.66) − 1 = 11.38% total over 2 years, ≈ 5.54% annualized. **Step 4**: Compare to simply buying the 2-year zero at 3.85% → 3.85% annualized. Ride-the-curve gives ~170bps extra annual return. **Source of extra return**: The 5-year was bought at 4.75% yield. After 2 years (now 3-year remaining), market prices 3-year bonds at only 4.20%. The 55bps yield decline on a ~3-year duration gives ~1.65% price gain per year on top of the 4.75% yield — getting to ~5.54%. **Key risk**: If curve steepens (yields rise), roll-down gain is erased or reversed. Strategy bets on curve stability. ```mermaid graph LR A[Buy 5Y
at 4.75%] -->|2 years pass
curve unchanged| B[Now 3Y
at 4.20%] B --> C[Yield drop
55bps] C --> D[Price gain +
coupon yield] ```

How do I calculate the return from riding the yield curve?

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