Negative convexity is a bond characteristic where the price gains you receive when interest rates fall are smaller than the price losses you suffer when rates rise by the same amount. In a normal bond, the opposite is true: price gains from falling rates exceed price losses from rising rates, which works in the investor’s favor. Negative convexity flips that advantage, and it shows up most commonly in callable bonds and mortgage-backed securities.
How Bond Prices Normally Behave
To understand negative convexity, you first need the baseline. A standard bond with no special features has a curved relationship between its price and prevailing interest rates. As rates drop, the bond’s price rises. As rates climb, its price falls. But the curve bows upward, meaning price increases are slightly larger than price decreases for the same size rate move. This upward bowing is called positive convexity, and it’s a free benefit for bondholders.
Think of it this way: if rates drop by 1%, a positively convex bond might gain $8 in price. If rates rise by 1%, that same bond might lose only $7. The asymmetry favors you as the investor. Duration, which measures how sensitive a bond’s price is to rate changes, naturally increases as rates fall and decreases as rates rise. That shifting sensitivity is what creates the favorable curvature.
What Makes Convexity Turn Negative
Negative convexity appears when something caps the bond’s price from rising freely as rates decline. The price-yield curve bends the wrong way, curving downward instead of upward. The actual price of the bond ends up lower than what simple duration math would predict. In this zone, the asymmetry works against you: your upside is capped, but your downside stays fully intact.
The key mechanism is an embedded option that benefits the borrower, not the lender. When rates fall far enough, the borrower can effectively escape the old, higher-rate loan. For the investor holding that bond, this means the duration of the investment shrinks right when you’d want it to grow. Instead of your bond becoming more sensitive to favorable rate drops (letting you ride the wave higher), it becomes less sensitive. The price appreciation stalls out.
There’s a critical yield threshold, often labeled y* in textbook diagrams. When market yields sit above this level, the bond behaves normally with positive convexity. Once yields drop below y*, the curve flattens and bends, entering negative convexity territory.
Callable Bonds: The Classic Example
A callable bond gives the issuing company the right to buy the bond back from investors at a predetermined price, usually a small premium over par value. If a company issued bonds paying 6% and rates later fall to 4%, the company can call those bonds back, repay investors the call price, and issue new bonds at the lower rate. The company saves money on interest. The investor gets their principal back but loses a stream of above-market income.
This call feature puts an effective ceiling on the bond’s price. No matter how far rates fall, the bond’s market price won’t rise much above the call price because everyone knows the issuer will likely redeem it. NYU Stern research illustrates this with a callable bond whose value maxes out at $112.94 regardless of further rate declines, while an equivalent non-callable bond would keep climbing.
The result is a lopsided deal for the investor. You participate fully in price declines when rates rise, but your gains are capped when rates fall. That’s negative convexity in practice: the bond “goes up less than it goes down.”
Mortgage-Backed Securities and Prepayment
Mortgage-backed securities (MBS) are the largest real-world source of negative convexity in financial markets. These are pools of home mortgages packaged into bonds. When homeowners refinance their mortgages because rates have dropped, they’re effectively “calling” their loans early. Investors in MBS get their principal back sooner than expected, at exactly the worst time, when reinvestment options offer only lower yields.
A Wall Street saying captures the problem neatly: a mortgage-backed security “goes up like a two-year bond” when rates fall and “goes down like a six-year bond” when rates rise. When rates drop, prepayments accelerate and the effective duration of MBS shrinks, limiting price gains. When rates rise, nobody refinances, the duration extends, and the security’s price becomes more sensitive to further rate increases.
Refinancing behavior doesn’t happen smoothly. Homeowners typically follow a trigger rule, refinancing only when the rate difference is large enough to justify closing costs and paperwork. This creates waves of activity. Depending on the historical path of mortgage rates, there are periods when millions of households move from being far from refinancing to being right on the edge simultaneously. These waves create large, sudden shifts in the effective duration of outstanding mortgage securities.
Extension Risk and Contraction Risk
Negative convexity creates two specific problems that go by their own names. Contraction risk is the danger that borrowers repay early when rates fall. You expected years of interest payments, but the loan gets paid off ahead of schedule. You receive your principal back in a low-rate environment where you can’t reinvest it at the same return. Contraction risk increases as interest rates decline because borrowers have more incentive to refinance.
Extension risk is the opposite scenario. When rates rise, borrowers hold onto their existing low-rate loans as long as possible. Nobody refinances, and the average life of the security stretches out. Your investment is now stuck in a longer-duration position while rates are climbing, amplifying your losses. Fixed-rate borrowers have zero incentive to prepay when rates are higher than their current loan rate.
Together, these two risks are what give negatively convex securities their characteristic behavior: shorter when you want longer, longer when you want shorter.
Why It Matters for Investors
Negatively convex bonds typically offer higher yields than comparable bonds without this feature. That extra yield is compensation for accepting the lopsided risk profile. The question for any investor is whether the additional income is enough to justify the downside.
For individual investors, negative convexity is most relevant if you hold bond funds that include callable corporate bonds or mortgage-backed securities. In a falling-rate environment, these funds won’t appreciate as much as you might expect based on their stated duration. In a rising-rate environment, they can lose more than expected because extension risk kicks in and the portfolio’s effective duration grows.
Large institutional investors, particularly those managing MBS portfolios, actively hedge negative convexity using interest rate derivatives. During periods of sharp rate movements, the hedging activity itself can amplify market swings. When rates rise quickly, MBS holders need to sell other bonds or use swaps to offset the extending duration of their mortgage holdings, which can push rates even higher. The Federal Reserve has flagged this dynamic as a source of volatility in Treasury markets.
How to Spot Negative Convexity
Any bond with an embedded call option held by the borrower can exhibit negative convexity. This includes callable corporate bonds, callable municipal bonds, and mortgage-backed securities. Non-callable government bonds, by contrast, always have positive convexity.
You can identify the risk by looking at a bond’s convexity measure, which is reported alongside duration in most bond analytics. A negative number signals the unfavorable curvature. You can also look at the bond’s option-adjusted spread, which accounts for the embedded option, compared to its nominal spread. A large difference between the two suggests the embedded option is significant and convexity risk is meaningful. If you’re evaluating a bond fund, the fund’s effective convexity will tell you whether the portfolio as a whole leans positive or negative.