Why do callable bonds and mortgage-backed securities exhibit negative convexity?

Question

AcadiFi · Accepted Answer

Negative convexity arises when a bond's price gains less in a rally than it loses in a sell-off of equal magnitude. The price-yield relationship is concave rather than convex. Two products famously exhibit this: callable bonds and mortgage-backed securities. Callable bond intuition — when yields fall below the call trigger, the issuer refinances at the lower rate, capping the bond's upside at the call price. When yields rise, the bondholder still takes full mark-to-market pain. Upside is truncated; downside is intact. MBS intuition — when yields fall, homeowners prepay (refinance into lower-rate mortgages). The MBS holder receives principal back early exactly when they'd prefer to keep the high-yielding asset. When yields rise, prepayment slows and the holder is stuck holding the low-rate asset longer (extension risk). The holder is on the wrong side of both moves. Numeric example — Kalispell MBS Agency pool pricing at various yield shocks: | Yield shock | Price MBS | Price Treasury | |---|---|---| | -100 bp | +3.8% | +8.4% | | -50 bp | +2.4% | +4.1% | | 0 | 100.0 | 100.0 | | +50 bp | -4.3% | -4.0% | | +100 bp | -8.7% | -7.9% | The MBS gains 3.8% on a 100 bp rally but loses 8.7% on a 100 bp sell-off. The asymmetry is the negative convexity 'tax.' ```mermaid flowchart LR A[Yields Fall] --> B[Homeowners
Prepay] B --> C[Early Principal
Return at Par] C --> D[Reinvest at
Lower Rates] D --> E[Capped Upside] ``` Practical implications: MBS investors demand option-adjusted spread (OAS) compensation for bearing negative convexity. Portfolio hedges need dynamic adjustment — a static duration hedge fails because effective duration shortens in rallies and lengthens in sell-offs.

Why do callable bonds and mortgage-backed securities exhibit negative convexity?

Master Level II with our CFA Course

Related Questions

Practice Questions