What it means
Plain bonds have a kindly bend, as their prices rise faster when yields fall than they drop when yields rise, a shape called positive convexity that quietly rewards the holder. Negative convexity bends the wrong way, with price appreciating less as rates fall and losing more as rates rise, an asymmetry working against the investor.
The cause is an embedded option. A callable bond's issuer can redeem early when rates fall, capping your upside, while a mortgage borrower's right to prepay does the same to mortgage-backed securities.
Mortgages make it concrete: when rates fall, homeowners refinance and your high-yielding mortgages return principal at par just as reinvestment rates collapse, and when rates rise, prepayments stop and you are stuck in low coupons longer. Duration stops being a stable guide, because a negatively convex security's effective duration shortens as rates fall and lengthens as they rise, so hedges built on yesterday's duration drift wrong exactly when needed.
Measurement has its own vocabulary, with effective duration and effective convexity, computed from models of prepayment behaviour, replacing the textbook measures that assume cash flows are fixed. The Federal Reserve studies the phenomenon closely, and New York Fed research on mortgage-backed securities models how prepayment behaviour creates the negative convexity that shapes these markets.
The option is not free to the borrower, as lenders price prepayment and call rights into higher initial yields, so the negatively convex security starts life paying more than its option-free cousin. For the bond's buyer, the shape is visible in pricing, since a negatively convex bond trades cheap to its cash flows precisely because the market charges for the option the holder has sold.
Portfolio effects compound at scale. When huge mortgage portfolios hedge together, their rebalancing flows can amplify rate moves, a feedback loop researchers call convexity hedging.
For a business owner holding mortgage funds or callable bonds, the takeaway is price behaviour, as such holdings can underperform in both directions of a rate move, and their higher yield is the fee for carrying that risk.
In practice
Real-world examples.
Example
A callable corporate bond trades to a ceiling near its call price, refusing to rise further even as comparable non-callable bonds rally. The call price acts as a gravitational ceiling.
Example
A mortgage fund's duration jumps as rates rise and refinancing stops, surprising investors who thought they held short-duration assets. Extension risk, the mirror of prepayment risk, arrives uninvited.
Example
A hedged mortgage portfolio loses on both legs when rates whip, as the hedge ratio goes stale within weeks. Model-driven rebalancing is now calendar work, not crisis work.
Formula
Calculation
Price-yield curvature flips sign: for a normal bond, price change accelerates as yields fall; for a callable one it decelerates. A mortgage pool yielding 5% may gain only 2 points when rates drop 1%, but lose 6 when rates rise 1%.
Compare it with an option-free bond that gains 8 points when yields fall 1% and loses 7 when they rise 1%. Over the two scenarios the normal bond nets +8 - 7 = +1 point, while the mortgage pool nets +2 - 6 = -4 points. On a $1,000,000 position, the pool gains $20,000 in the good scenario and loses $60,000 in the bad one.Case study
Seen in the real world.
In this illustrative fictional case, Halvor, investment head at an insurer, holds a large mortgage-backed portfolio for its yield. Rates fall sharply and prepayments flood in, forcing reinvestment at far lower rates while his duration hedges, sized for the old profile, overshoot. He rebuilds the hedge using effective duration from prepayment models and accepts a lower, honest yield.
His quarterly report now shows convexity alongside duration, and the board asks better questions. On an illustrative $100,000,000 portfolio, a 1% fall in rates lifted its value by only 2%, or $2,000,000, when an option-free bond of similar yield would have gained 8%, or $8,000,000. The $6,000,000 difference was the price of the prepayment option the borrowers held, which is exactly what his higher starting yield had been paying him to carry.
Watch out
Common mistakes.
- Using stated duration as fixed, when negative convexity makes duration a moving target that shifts against the holder as rates move.
- Chasing the higher yield of callable and mortgage securities without pricing the option, when the extra income is payment for the capped upside. The borrower's option is your liability.
- Assuming all bonds gain from falling rates equally, when callable and prepayable bonds stall while option-free bonds rally. Read the call schedule before the yield.
Questions
People also ask.
What is negative convexity?
A bond price pattern where gains shrink as yields fall but losses grow as yields rise. Embedded options, like call rights and mortgage prepayment, cause it. Positive convexity is the friendly mirror image. The holder has effectively sold an option.
Which securities show negative convexity?
Callable bonds and mortgage-backed securities most prominently. The borrower's right to repay early caps price gains and extends losses, as Federal Reserve research on mortgage securities documents. Some structured notes show the same shape.
Why do investors hold such bonds?
For higher yield. The market pays extra income to compensate for the unfavourable price behaviour, and skilled managers hedge the option risk with effective duration measures. The compensation is measurable as option-adjusted spread.
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