The most dangerous number in a bond portfolio is a duration estimate that was accurate last month. In 1994, an entire market learned this at the same time, and the losses came less from the rate rise itself than from how the rate rise changed what investors actually owned.
The year mortgage bonds got longer as they fell
On February 4, 1994, the Federal Reserve raised the fed funds rate from 3% to 3.25%. It was the first hike in five years, and it would not be the last: by February 1995 the rate stood at 6%. The 10-year Treasury yield, which had sat near 5.2% in October 1993, climbed to roughly 8% by November 1994. Bond desks still call it the great bond massacre.
The damage concentrated in mortgage-backed securities, bonds whose cash flows come from pools of home loans. Holders had bought these securities believing they carried moderate interest-rate exposure. As rates rose, homeowners stopped refinancing, the expected life of each mortgage pool stretched out, and a bond that had behaved like a four-year instrument began behaving like a seven-year one. Its rate sensitivity grew while its price fell.
Askin Capital Management, which ran roughly $600 million in leveraged mortgage funds, collapsed that spring. Orange County, California lost about $1.6 billion on leveraged fixed-income positions and filed for bankruptcy in December 1994. Neither failure began with a wrong number on day one. The risk figures were reasonable when the positions were built. They were wrong by month three, because the bonds had changed shape underneath them.
That episode contains both risks named in the title. Duration explains why prices fell. Convexity explains why they fell faster than the models said they would.
Duration is a slope, not a size
Modified duration is the approximate percentage change in a bond's price for a one-percentage-point change in its yield. A bond with a modified duration of 8 loses about 8% of its value if yields rise from 4% to 5%, and gains about 8% if they fall to 3%. The relationship comes from discounting. A bond is a stream of future payments, and the further away a payment sits, the more its present value responds to a change in the discount rate.
Two features drive the number. Longer maturity raises duration because more of the cash arrives far in the future. Higher coupons lower duration because more of the cash arrives early. A zero-coupon 30-year bond is close to the purest duration exposure available; a high-coupon two-year note is close to the least.
The trap is the word "approximate." Duration is the slope of a curved line measured at a single point. It tells you how price responds to a small move from today's yield. It says nothing on its own about how that response changes once yields have moved.
The chart puts the slope in front of you. A long-Treasury fund and a mortgage fund respond to the same rate environment, but the long-Treasury fund's far greater duration produces much larger swings in both directions. For your own holdings, duration answers the first question, how much you lose on a modest move. It cannot answer the second question, which is what your exposure looks like after the move.
Convexity is the curvature the slope leaves out
Convexity measures how much duration itself changes as yields move. The standard approximation for a bond's price change adds a second term to the duration estimate:
%ΔP ≈ (−Duration × Δy) + (½ × Convexity × Δy²)
Here Δy is the yield change in decimal form. Take a 10-year Treasury with a 4% coupon priced at par. Its modified duration is about 8.18 and its convexity is about 79.
For a one-point rise in yields (Δy = 0.01): %ΔP ≈ (−8.18 × 0.01) + (½ × 79 × 0.0001) = −8.18% + 0.40% = −7.78%
For a one-point fall: %ΔP ≈ +8.18% + 0.40% = +8.58%
The convexity term carries a positive sign in both directions. The bond loses a little less than duration predicts when yields rise and gains a little more when they fall. On a one-point move the correction is small.
Push the move to three points, from 4% to 7%, and duration alone predicts a loss of 24.5%. Adding convexity gives roughly −21.0%. Discounting the bond's actual cash flows at 7% gives a price near 78.7, a loss of about 21.3%. The linear estimate overstated the damage by more than three points, and the gap widens with every additional point of movement.
For a plain government bond, this curvature works in the holder's favor. When you own positive convexity, your rate exposure shrinks as losses grow and expands as gains grow. The practical meaning is that a duration-only risk report on a portfolio of plain bonds is conservative on large moves. It overstates the pain.
Why some bonds bend the wrong way
Now reverse the sign. A bond has negative convexity when its duration lengthens as yields rise and shortens as yields fall. Your exposure grows exactly when the market is moving against you and shrinks exactly when it is moving your way.
The cause is an embedded option held by someone else. An American homeowner with a standard 30-year fixed mortgage can repay it at any time without penalty. When rates fall, homeowners refinance, and the mortgage investor receives principal back early, precisely when reinvesting it pays less. When rates rise, nobody refinances, and the investor is stuck holding a low-coupon loan for longer, precisely when its value is falling. Callable corporate bonds carry the same structure, with the issuer holding the option.
A stylized mortgage pool shows the asymmetry. Suppose its effective duration, a duration estimate that accounts for how cash flows change with rates, is 4 at today's yields. After a one-point rise, slower prepayments stretch it toward 6.5; after a one-point fall, faster prepayments compress it toward 2.5. Averaging the duration across each move gives a loss of roughly 5.25% on the way up and a gain of roughly 3.25% on the way down. A plain bond with the same starting duration would show about 4% in both directions, slightly better on each side.
These numbers are illustrative rather than measured from a specific pool, but the shape is the point. The negatively convex holder gets the worse outcome on both sides of the trade. For anyone owning mortgage funds or callable bonds, the starting duration on the fact sheet is the least informative number available. The useful figure is how far it moves in a stress scenario.
The actors who turn curvature into a market event
Why does the mortgage market get paid for accepting this? Because the homeowner's prepayment option has real value, and the investor is effectively short that option. The extra yield on a mortgage bond over a Treasury of similar duration is largely an option premium. It is income earned in calm markets as compensation for losses that arrive in volatile ones, which is the same economic position as selling insurance.
Positive convexity, by contrast, costs money. Investors who need protection against large moves, such as pension funds and insurers matching long-dated liabilities, accept lower yields on long, option-free bonds partly to own that curvature. Convexity is never free; someone pays for it and someone is paid to give it up.
The mechanism turns from a portfolio problem into a market event through hedging. Holders who manage interest-rate risk against a target, including mortgage servicers, banks, and dedicated mortgage portfolios, see their duration extend as rates rise. To restore the target, they sell Treasuries or pay fixed in interest-rate swaps. That selling pushes yields higher, which slows prepayments further, which extends duration again, which forces more selling. Bond traders call this convexity hedging, and in 1994 it helped turn a policy tightening into a rout.
The loop runs in reverse during rallies. Falling rates shorten mortgage duration, hedgers buy duration back, and yields fall further than fundamentals alone would justify. Practically, this means the size of the negatively convex market, and how actively it hedges, shapes how violent large rate moves become, independent of the economic news that started them.
Where the two-number model fails
Duration and convexity together form a far better risk picture than duration alone, but the framework rests on assumptions that break in exactly the episodes that matter most.
First, both measures assume the whole yield curve shifts in parallel. Real curves twist. A portfolio can show zero net duration while losing heavily on a steepening, because its long positions and short positions sit at different maturities. Key rate durations, which measure sensitivity to each point on the curve separately, exist to close this gap.
Second, effective duration for mortgages and callables is a model output, not a contractual fact. It depends on assumptions about how homeowners will behave at each rate level. In 1994 those assumptions proved too optimistic about how quickly prepayments would slow, so even the convexity-adjusted numbers understated the extension.
Third, leverage converts curvature into a liquidity problem. In September 2022, UK pension schemes running leveraged liability-driven strategies faced collateral calls as long gilt yields rose more than a full percentage point within days. Selling gilts to meet those calls pushed yields higher still, and the Bank of England stepped in on September 28 with a temporary purchase program of up to £65 billion. The bonds were plainly convex. The leverage on top of them created a forced-selling loop that behaved like negative convexity.
Fourth, accounting can hide duration without removing it. Silicon Valley Bank held a large book of long-dated mortgage securities in a held-to-maturity portfolio, where price declines did not run through reported earnings. When deposits fled in March 2023, the unrealized losses on those bonds became the story. The duration risk had been on the balance sheet all along.
The lesson across all four is consistent: a duration and convexity figure tells you how a bond responds to rates under normal liquidity. It does not tell you whether you will be allowed to hold the position while the move happens.
Reading a bond portfolio after 1994
The 1994 holders did not lack data. They lacked the habit of asking how their risk numbers would look after a move rather than before one. That habit is the practical inheritance of the episode.
When you evaluate a bond fund or portfolio, start with duration to size the first-order risk. Then ask what the duration becomes after a one-point rise and a one-point fall. If those two figures differ sharply, and the longer figure appears on the rising-rate side, you own negative convexity and are being paid a premium for absorbing losses in volatile markets. Decide whether that premium is large enough.
Check whether a fund reports modified or effective duration. For anything holding mortgages or callable bonds, only effective duration is meaningful, and it carries model risk. Treat any extra yield on such holdings as option income rather than free spread. And weigh leverage separately, because borrowed money can turn even a positively convex bond into a forced sale.
Duration is the slope of a bond's price curve, convexity is how quickly that slope changes, and the bonds that blow up are usually the ones whose slope steepens against their owners at the exact moment those owners can least afford it.
