What is one-sided convexity and which instruments exhibit it?

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AcadiFi · Accepted Answer

One-sided convexity describes a price-yield relationship where convexity is strongly positive on one side of the current yield but near-zero or even negative on the other side. The curvature is asymmetric.

Putable bonds exhibit positive one-sided convexity to the upside of yields. When rates rise sharply, the investor exercises the put, receiving par and sidestepping further losses. Downside is capped at (par minus current price). When rates fall, the bond behaves like a normal long bond and enjoys normal (positive) convexity.

Contrast:
- Plain bullet bond: symmetric positive convexity both directions
- Callable bond: one-sided negative convexity to downside (issuer call when rates fall)
- Putable bond: one-sided positive convexity to upside (investor put when rates rise)
- MBS: one-sided negative convexity to downside (prepayment)

Worked example — Birchwood Utilities 6% putable bond, puttable in 3 years at par, currently priced 98.20.

| Yield shock | Bond Price | Comment |
|---|---|---|
| -200 bp | 106.5 | Behaves like normal long bond |
| -100 bp | 102.3 | Normal convexity |
| 0 | 98.2 | Current |
| +100 bp | 96.8 | Put option starts gaining value |
| +200 bp | 97.1 | Put floor activates, loss capped |
| +300 bp | 97.8 | Put floor dominates |

Notice the loss at +200 bp is smaller than the loss at +100 bp — that's the put option kicking in. Effective convexity computed across the full ±200 bp window looks very positive (highly convex), but computed only on the downside of yields it is modestly negative.

Hedging implications: a trader cannot rely on a single effective convexity number. Scenario analysis at multiple yield shocks is required. Delta and gamma change sign across the yield spectrum, so hedges must be rebalanced when yields move through the strike region.

What is one-sided convexity and which instruments exhibit it?

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