Duration & Convexity: Measuring Rate Sensitivity
The previous lesson established that bond prices fall when rates rise. Duration answers the question that actually matters next: by how much? It turns a direction into a number you can size a portfolio with.
One number for 'how much will this hurt'
Modified duration is the percentage a bond's price moves for each percentage point change in yields. Duration 6 means roughly a 6% price move per point — down when rates rise, up when they fall. That's the working definition, and it's most of what you need.
The SEC's bulletin explains what drives it: maturity and coupon. Longer maturity means more distant payments to reprice. Lower coupon means more of the value sits in the final repayment rather than in cash arriving along the way. A 30-year zero-coupon bond maximises both at once, which makes it the most rate-sensitive bond there is.
Keep two names straight, because they get used interchangeably and shouldn't be. Macaulay duration is the weighted average time until cash flows arrive, in years. Modified duration is the price sensitivity you multiply by — related, not equal, and it's the one this lesson uses.
Price change ≈ −(modified duration) × (change in yield). Duration 8, rates up 1 point, price down about 8%.
The estimate is a straight line through a curve
Duration draws a tangent to the price/yield relationship, and that relationship is curved rather than straight. So the estimate is accurate for small moves and drifts as moves get larger.
It drifts in a direction that happens to favour the bondholder. For a conventional bond, duration overstates the loss when rates rise and understates the gain when they fall — the real curve sits above the straight line in both directions. Convexity is the name for that curvature.
So a duration-10 bond facing a 1.5-point rise loses somewhat less than the 15% the formula predicts, and the same bond facing a 1.5-point fall gains somewhat more than 15%. That asymmetry is genuinely valuable and it's why convexity gets quoted alongside duration rather than instead of it. It is also why the straight-line estimate is a first approximation, not an answer — treat a large predicted move as an indication of scale.
Duration averages, which is what makes it usable
A portfolio's duration is the weighted average of its holdings' durations. That property is what turns duration from a description into a control: you can build a portfolio to a target sensitivity by choosing the mix.
Shortening duration reduces how much rate moves affect you, in both directions. That is the honest framing — you're not avoiding a loss, you're reducing exposure to an outcome you can't predict, and giving up the gain if rates fall instead.
Which matters, because the tempting version of this is to shorten duration when you expect rates to rise. Nobody reliably knows. The defensible reason to hold short duration is that you need the money soon and can't absorb a price swing; the indefensible one is a forecast.
Modified duration estimates the percentage price change for a one-point move in yields — duration 8 means roughly 8% per point. It's a straight-line estimate of a curved relationship, and convexity is the name for what it misses.
Sources
- Investor Bulletin: Fixed Income Investments — When Interest Rates Go Up, Prices of Fixed-Rate Bonds Fall — U.S. Securities and Exchange Commission (2026)
- Brush Up on Bonds: Interest Rate Changes and Duration — FINRA (2026)