Duration and Interest-Rate Risk

What it measures

Macaulay duration is the weighted average time, in years, until a bond's cash flows arrive, with each payment weighted by its present value. A bond paying most of its value back at maturity has most of the weight sitting far out on the timeline; a bond returning cash sooner through large coupons pulls that average inward. Modified duration takes that time-based figure and converts it into a price sensitivity, and it is the version almost everyone means when they say duration in ordinary conversation.

The rule of thumb that matters: percentage price change is approximately minus modified duration multiplied by the change in yield, in percentage points. A duration of seven means that when yields rise one percentage point, price falls about 7%, and when yields fall one point, price rises about 7%.

Duration rises with maturity, since more of the cash flow sits further out. It falls as the coupon rises, because more money arrives sooner and pulls the weighted average inward. It falls as the yield itself rises, because higher discount rates shrink the present value of the distant payments relative to the near ones.

A zero-coupon bond's Macaulay duration equals its maturity exactly, since there is only one cash flow and all the weight sits at that single date — the maximum duration available at a given maturity. Duration is therefore not maturity: a thirty-year bond with a large coupon has a duration well under thirty, while a thirty-year zero has a duration of thirty.

How it is calculated

Macaulay duration is the sum, across every payment, of the time in years to that payment multiplied by its present value, divided by the bond's current price. Modified duration divides that figure by one plus the yield per period; at low yields the two numbers sit close together, and at high yields modified duration is noticeably the smaller of the two.

Dollar duration, quoted as DV01 or the price value of a basis point, equals modified duration multiplied by price multiplied by 0.0001. It expresses the same sensitivity in dollars per one-basis-point yield move rather than in percentage terms, and it is the figure a trading desk actually hedges against.

A portfolio's duration is the market-value-weighted average of its holdings' durations, which is how a bond fund reduces hundreds of individual bonds to a single reported number. For anything with an embedded option — a callable bond, a mortgage pool — that formula does not apply, because the cash flows themselves shift when yields move. The fix is effective duration, computed by repricing the security under a small upward and a small downward yield shift and dividing the difference in price by twice the current price times the size of the shift.

Convexity is the second-order correction to all of this. Duration draws a straight line through what is actually a curved price-yield relationship; positive convexity means price falls a little less than duration predicts when yields rise, and rises a little more than predicted when yields fall.

How to read it

The honest way to read duration is percent of price at risk per percentage point of yield change. The unit of years is an artefact of how the number is derived from cash-flow timing, not a holding period or a warning label about time.

The estimate is local and linear: accurate for small yield moves, increasingly wrong for large ones, which is exactly the gap convexity is built to correct. It also only measures sensitivity to the bond's own yield. If credit spreads widen while the underlying Treasury yield falls, a corporate bond can still lose value even though the rate move alone predicted a gain; spread duration is the parallel measure for that separate risk.

A fund reporting a duration of six will show roughly a 6% decline in net asset value for a one-point rise in yields across its curve, an effect that is gradually offset in subsequent years as maturing bonds get reinvested at the new, higher yield. Holding an individual bond to maturity removes the realized price loss but not the opportunity cost — the below-market coupon is still what arrives every period until maturity. Duration is roughly the horizon at which price loss and reinvestment gain offset each other, which is the logic behind matching a portfolio's duration to a spending horizon.

Where it misleads

The whole calculation assumes the yield curve moves in a parallel shift — every maturity up or down by the same amount. Real curves steepen, flatten, and twist instead, so a portfolio duration figure can be correct in aggregate while being wrong about what happens at any individual maturity along the curve.

Callable bonds show negative convexity: as yields fall, the issuer's call becomes more likely, effective duration shortens, and the price stops rising as it nears the call price. Standard modified duration misses this shape entirely. Mortgage-backed securities do something similar in reverse — they extend when rates rise and shorten when rates fall, the opposite of what a holder would want, which is why their duration is unstable and is always quoted as effective duration rather than the standard formula.

For very large yield moves the straight-line estimate breaks down in both directions, so a long-duration portfolio can lose somewhat less than a naive estimate implies over part of a selloff and more over another part. And duration says nothing whatsoever about default: a short-dated bond from a failing issuer carries almost no duration risk and can still be worth a fraction of par.

Perpetual securities, including most fixed-rate preferred stocks, have very long effective durations because their cash flows never mature. That is why they trade like long bonds and reprice like long bonds despite sitting in an equity wrapper.

Where you will meet it on this site

On Treasury and corporate bond pages, where maturity is the main determinant of how far a price moves when yields change. On bond ETF and mutual fund pages, where the reported average duration is the single most useful figure for judging a fund's rate sensitivity at a glance.

On preferred stock pages, where a fixed-rate perpetual behaves like a very long bond and reprices accordingly when yields move. In the discussion of mortgage-backed securities and callable agency notes, where effective duration and negative convexity are the whole point rather than a footnote.

More generally, whenever this site states that a price fell because yields rose, duration is the number behind that sentence — it is the size of the move, not just the direction.