Why do mortgage-backed securities exhibit negative convexity and what does that mean for investors?
In my FRM Part I studies, I've learned that MBS have 'negative convexity' while most bonds have positive convexity. I know it's related to prepayment risk, but I'm struggling to understand the price-yield relationship visually and why this matters for portfolio risk management.
Negative convexity means that as interest rates fall, the MBS price rises less than you'd expect from a comparable non-callable bond. Conversely, when rates rise, the MBS price falls about as much as expected. The result is an asymmetric return profile that's unfavorable for investors.
The Prepayment Mechanism
Mortgage borrowers have the right to prepay their loans at any time (essentially a call option). When rates drop:
- Homeowners refinance at lower rates.
- The MBS investor receives principal back early — at par, not at the higher market value.
- The investor must reinvest at the new lower rates.
This caps the price upside. When rates rise, homeowners hold onto their low-rate mortgages longer (extension risk), so the MBS behaves like a longer-duration bond on the downside.
Visual Comparison
For a non-callable bond, the price-yield curve bows upward (positive convexity): the bond gains more from a rate decrease than it loses from an equal rate increase. For an MBS:
Numerical Illustration
Consider a $10 million position in Pinewood Capital MBS Trust (coupon 5.5%) vs. a comparable Treasury bond:
| Rate Change | Treasury Price Change | MBS Price Change | Difference |
|---|---|---|---|
| −100 bps | +$620,000 | +$340,000 | MBS gains $280K less |
| +100 bps | −$580,000 | −$560,000 | Nearly the same |
The MBS investor captures only 55% of the upside but nearly 97% of the downside.
Why This Matters for Risk Management:
- Duration is unstable. MBS effective duration shortens when rates fall (prepayments accelerate) and extends when rates rise (prepayments slow). This is called 'negative convexity' or 'extension/contraction risk.'
- Hedging is harder. A static duration hedge will under-hedge in rising-rate environments and over-hedge in falling-rate environments. MBS portfolio managers must dynamically rebalance their hedges.
- OAS compensates for this. The option-adjusted spread on MBS is wider than on comparable corporate bonds partly because investors demand compensation for bearing the prepayment option risk.
- Servicer incentives matter. Faster prepayment speeds (higher CPR) increase negative convexity. Factors like loan size, credit score, and geographic concentration affect prepayment behavior.
Exam Tip: If asked about convexity adjustments, remember: convexity adjustment = 0.5 x Convexity x (Delta_y)^2. For negative convexity instruments, this term is negative, meaning actual price change is less favorable than the duration-only estimate.
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