Most people judge a bet by its average outcome. Professionals in fixed income learned long ago to look at something else: how the outcome changes as conditions move. Two positions with the same expected value can behave completely differently when the world shifts — and the difference has a name.
Duration is a straight-line guess
A bond's price falls when yields rise and rises when yields fall. Duration measures how sensitive that price is: a bond with a modified duration of 7 loses roughly 7% of its value if yields rise by one percentage point.
But duration is a tangent line. It assumes the relationship between price and yield is straight. It is not.
Convexity is the bend
Convexity measures the curvature. For an ordinary bond, the curve bows outward: when yields fall, price rises more than duration predicts; when yields rise, price falls less. Adding the second-order term fixes the estimate:
Take an illustrative bond with a modified duration of 7 and convexity of 80. For a one-point move in yields, the convexity term adds about 0.4%. A rise in yields costs roughly 6.6% rather than 7%; a fall gains roughly 7.4% rather than 7%. Same-size move, lopsided result — in your favour.
When convexity turns against you
Not every instrument bends the right way. Some have negative convexity, where gains are capped and losses are not:
- Callable bonds. When yields fall, the issuer is likely to call the bond and refinance, so its price stops rising just when it should.
- Mortgage-backed securities. Falling rates trigger prepayments, returning your money when reinvestment is least attractive.
- Short options. Selling insurance earns steady small premiums and occasionally pays out a large loss.
Negative convexity is usually paid for with extra yield. The question is whether that extra yield is enough compensation for giving away the upside.
The idea travels
Strip away the bond maths and convexity describes any payoff where the downside is bounded and the upside is open. A long option is convex. So is a small experiment that costs a week but could become a product, or a skill that keeps compounding after you learn it.
That is the asymmetric edge this site is about: arranging your decisions so that being wrong is cheap and being right is large.
What to take from it
- Averages hide shape. Ask how an outcome responds to change, not just where it lands.
- Duration is a first-order estimate; convexity corrects it, and matters most for large moves.
- Know which side of the curve you are on before you are paid to be there.
