Mortgage Bond Prepayment Convexity
Mortgage Bond Prepayment Convexity
Mortgage-backed securities are like bonds where thousands of homeowners collectively decide when to repay you—and they always repay when it hurts you the most.
Key takeaways
- Mortgage-backed securities (MBS) are bundles of home mortgages; when homeowners refinance or move, the MBS is prepaid and the investor receives principal early.
- Prepayment is economically rational for homeowners but disastrous for MBS investors: falling rates trigger refinancing waves that cap gains and force reinvestment at lower rates.
- MBS have strong negative convexity because prepayment is correlated with falling rates.
- Effective duration (not stated maturity) is the correct measure for MBS; effective duration shrinks as rates fall and extends as rates rise.
- Despite negative convexity, MBS have offered attractive yields, making them popular with yield-hungry investors.
What is a mortgage-backed security?
A mortgage-backed security is a bond backed by a pool of home mortgages. A bank originates £100 million in 30-year mortgages to homeowners at, say, 4% interest. The bank then bundles these mortgages and sells them to investors as an MBS. The MBS investor receives pass-through principal and interest payments as homeowners pay their mortgages.
If all homeowners paid mortgages for 30 years without prepaying, the MBS would be a straightforward 30-year bond with a 4% coupon. But homeowners do not always hold mortgages for 30 years. They refinance, move, or pay off early. This creates prepayment risk.
Prepayment behavior and the S-curve
Homeowners refinance mortgages when it is economically rational. If a homeowner has a 4% mortgage and rates fall to 2%, refinancing saves them 200 basis points annually in interest. The incentive is strong.
Prepayment behavior follows an "S-curve" pattern:
- At high rates (5%+ coupon rate on the MBS, current market rates 3%+): Prepayment is low. Homeowners are happy with their mortgages; refinancing makes little sense.
- At moderate in-the-money rates (4% coupon, 3% market rates): Prepayment increases. Some homeowners refinance, especially those with strong credit.
- At very low rates (4% coupon, 1% market rates): Prepayment is high. Nearly all homeowners refinance.
The S-curve creates a natural cap on MBS price appreciation. As rates fall and the MBS price rises, prepayment accelerates. The rising prepayment rate shortens the effective maturity, capping price appreciation.
Negative convexity from prepayment
Consider an MBS with a 4% coupon, initially yielding 4% at par value £100. It has a stated maturity of 30 years but an expected life of 10 years (based on historical prepayment rates).
Scenario 1: Rates fall to 2%
- A non-prepayable 30-year bond with 4% coupon would rise significantly to, say, £125 (a 25% gain). Duration is roughly 15 years, so a 2% fall would give a ~30% gain, dampened by convexity.
- The MBS rises to, say, £112 (a 12% gain). Here is why: as rates fall, prepayment accelerates. Homeowners rush to refinance, paying off the MBS early. The investor receives principal back at a 2% rate environment and must reinvest the proceeds. The MBS' effective duration shrinks from 10 years (the initial assumption) to perhaps 6–7 years. The price cap limits the gain.
- The investor's expected cash flow changes. Instead of 30 years of payments, the investor now expects to be paid off in 6 years (as rapid prepayment accelerates).
The bondholder loses the upside they expected from long-duration bonds.
Scenario 2: Rates rise to 6%
- A non-prepayable 30-year bond would fall significantly to, say, £75 (a 25% loss).
- The MBS falls to, say, £68 (a 32% loss). Here is why: as rates rise, prepayment slows dramatically. Homeowners keep their 4% mortgages; refinancing to 6% makes no sense. The MBS' effective duration extends from 10 years to perhaps 18–20 years (much closer to the 30-year stated maturity). With extended duration, the MBS falls more than the non-prepayable bond.
The bondholder suffers amplified losses because effective duration expanded.
This is negative convexity in its most punishing form: falling rates cap gains; rising rates amplify losses.
Why prepayment is so costly
The economic cost of prepayment is asymmetrical. Consider the MBS investor's perspective:
- Wanted outcome: I buy MBS at 4% yield. I collect coupons for 30 years and earn 4% annualized.
- Falling-rates outcome: Rates fall to 2%. My MBS price rises to £112. I collect some coupons and then receive principal back. I can reinvest at 2%, not 4%. My effective annual return is not the 4% I expected; it is dragged down to 2.5% or 3% by the reinvestment of returned principal.
- Rising-rates outcome: Rates rise to 6%. My MBS price falls to £68. I collect coupons at 4% while I could earn 6% elsewhere. I am stuck holding a low-yield bond, and I cannot call it (it is not my option). My effective return is dragged down to 2% or 3% instead of 4%.
In both scenarios, actual returns fall short of expected returns because of asymmetrical prepayment behavior.
Historical prepayment waves
Significant falling-rate environments trigger massive prepayment waves. When the Federal Reserve cut rates sharply:
2008–2009 financial crisis: Rates fell from 5%+ to near 0%. MBS that investors bought for high yield prepaid within a few months. Investors who expected 30-year cash flows received principal back in 2–3 years and had to reinvest at 0% near-zero rates. Many endowments and pension funds suffered unexpected losses from MBS underperformance.
2019–2020 pandemic: Rates fell sharply in March 2020. MBS prepaid faster than models predicted. Investors who thought they had long-duration bonds found themselves with short-duration, low-yield investments.
2023–2024 pivot: When the Federal Reserve signaled potential rate cuts in late 2023, analysts anticipated a prepayment wave. MBS did not rally as much as Treasuries. The expected prepayment (and resulting reinvestment risk) suppressed MBS valuations, even as rates fell.
Effective duration and the moving target
Stated maturity of an MBS is usually 30 years (the life of a typical mortgage). But effective duration is much shorter and varies with rates:
- At high rates (5%+): Effective duration might be 8–10 years (prepayment is slow).
- At moderate rates (3–4%): Effective duration might be 6–8 years.
- At very low rates (1–2%): Effective duration might be 3–5 years (rapid prepayment).
This moving-target nature of duration makes MBS tricky to manage. A portfolio manager thinks "I have 10-year duration MBS," and then rates fall and effective duration shrinks to 5 years. The portfolio becomes shorter-duration than intended, reducing returns.
Conversely, if rates rise sharply (as in 2022), effective duration extends. A manager who thought they had 8-year MBS suddenly finds themselves with 12-year duration MBS, amplifying losses when rates are rising.
MBS valuations and the prepayment option value
The value of an MBS is its cash flows discounted at the appropriate yield, but the cash flows are uncertain due to prepayment. Pricing models (like the OAS—Option-Adjusted Spread model) try to estimate the value of the prepayment option and build it into the yield calculation.
In practice, the market quotes MBS yields with a built-in compensation for prepayment risk. When the prepayment option is very valuable (rates are low and refinancing is likely), the MBS yield is higher than a comparable non-prepayable bond. When the prepayment option is less valuable (rates are high and refinancing is unlikely), the MBS yield is closer to comparable bonds.
In 2024, MBS might yield 4.0% while a 10-year non-prepayable Treasury yields 3.5%. The 50-basis-point spread is partly credit compensation (mortgages have modest credit risk) and partly prepayment compensation.
Managing MBS in a portfolio
Institutional investors use several strategies to manage MBS prepayment risk:
- Diversify: Hold MBS alongside non-prepayable bonds. When rates fall and MBS prepay, the non-prepayable bonds rally, offsetting reinvestment risk.
- Hedge: Use interest rate futures or swaptions to hedge prepayment risk. A manager might short Treasury futures to hedge the duration extension risk if rates rise.
- Active trading: Managers who believe rates will fall sell MBS before rates decline, avoiding the prepayment wave. Managers who believe rates will rise hold MBS to capture the extended-duration losses (a contrarian bet that MBS will outperform due to extended duration).
- Targeted duration: Hold MBS with specific effective duration targets (e.g., "I want 6-year effective duration"), actively rebalancing as prepayment assumptions change.
For retail investors in MBS funds (like ETFs holding agency MBS), the fund manager handles these decisions. The fund's duration is maintained by trading and rebalancing. The investor simply owns the fund and collects the yield.
Agency MBS versus non-agency MBS
Most MBS trading in the US market are agency MBS—backed by the Government National Mortgage Association (Ginnie Mae), Federal National Mortgage Association (Fannie Mae), or Federal Home Loan Mortgage Corporation (Freddie Mac). These have implicit or explicit US government backing, meaning the principal is guaranteed.
Non-agency MBS (private-label MBS) do not have government backing. They have higher yield to compensate for credit risk and prepayment risk. Non-agency MBS became popular before the 2008 financial crisis and nearly disappeared afterward. They are returning to favor as investors seek higher yields.
The negative convexity of non-agency MBS is greater because both credit risk and prepayment risk contribute to losses when rates rise (borrowers default more in economic downturns that cause rate declines).
Flowchart: MBS prepayment dynamics
Next
Both callable bonds and mortgage-backed securities exhibit negative convexity because of embedded options. The next article bridges these concepts: it introduces the convexity adjustment formula, which quantifies the curvature effect and explains how convexity modifies the simple duration-based price approximation. Understanding this formula is essential for precisely predicting bond prices in changing rate environments.