Why do mortgage-backed securities have negative convexity, and how does it affect effective duration?

Question

AcadiFi · Accepted Answer

This is one of the trickiest Fixed Income concepts at CFA Level II, but once you understand the prepayment mechanism, it clicks. Let me walk through it.

**Normal Bonds: Positive Convexity**
For a standard bullet bond, when interest rates fall, duration increases (because distant cash flows become more valuable relative to total price). The bond's price–yield curve is convex — price gains accelerate as rates drop.

**MBS: The Prepayment Problem**
Mortgage-backed securities are pools of home loans. When interest rates fall, homeowners refinance their mortgages, returning principal early. This prepayment effectively shortens the life of the MBS.

```mermaid
flowchart TD
    A["Interest Rates Fall"] --> B["Homeowners Refinance"]
    B --> C["Prepayments Accelerate"]
    C --> D["MBS Cash Flows Received Earlier"]
    D --> E["Effective Duration Shortens"]
    E --> F["Price Appreciation Capped
= Negative Convexity"]
    
    G["Interest Rates Rise"] --> H["Homeowners Hold Mortgages"]
    H --> I["Prepayments Slow"]
    I --> J["MBS Cash Flows Extend"]
    J --> K["Effective Duration Lengthens"]
    K --> L["Price Declines Amplified"]
```

**The Worst-of-Both-Worlds Effect**
- Rates fall → Duration shortens → You participate less in the rally
- Rates rise → Duration extends → You suffer more in the selloff

This is negative convexity in a nutshell: the MBS adjusts its duration in the direction that hurts the investor.

**Numerical Example:**
Pacific Mortgage Trust holds an MBS pass-through currently priced at $102.50. An analyst shocks the yield curve:

| Rate Change | Price | Implied Duration |
|---|---|---|
| −100bp | $105.80 | 3.2 years |
| No change | $102.50 | 4.8 years |
| +100bp | $97.10 | 5.3 years |

Notice: The price gain for a 100bp drop ($3.30) is smaller than the price loss for a 100bp rise ($5.40). This asymmetry is negative convexity.

**Calculating Effective Duration for MBS**
Because cash flows change with rates (due to prepayments), you can't use modified duration. You must use the effective duration formula:

**EffDur = (P₋ − P₊) / (2 × P₀ × Δy)**
= (105.80 − 97.10) / (2 × 102.50 × 0.01)
= 8.70 / 2.05 = **4.24 years**

**Exam Tip:** An MBS question will often present price changes for up/down rate shifts. If the price gain is smaller than the price loss, the security exhibits negative convexity.

Explore more MBS concepts in our CFA Level II Fixed Income course.

Why do mortgage-backed securities have negative convexity, and how does it affect effective duration?

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Practice Questions

Rate Change	Price	Implied Duration
−100bp	$105.80	3.2 years
No change	$102.50	4.8 years
+100bp	$97.10	5.3 years