Bond Duration: How a 1% Rate Rise Moves Your Bond Price

Your bond fund statement drops 9% in a year when nothing defaulted, nobody missed a payment, and every issuer in the portfolio is still investment grade. Nothing broke. Rates went up, and the price of every existing bond had to fall until its yield matched what new bonds were paying.

Here is the number that explains it: multiply the bond’s modified duration by the change in yield, and that’s your percentage price move, with the sign flipped. Duration 6.2, rates up one percentage point, price down about 6.2%. Duration 17, same move, down about 17%. That single multiplication is the whole first-order answer, and it is why holdings people describe as safe can post double-digit losses.

Where that number comes from

Duration is the average time until you get your money, in years, with each payment weighted by its present value rather than its face amount. A payment of $20 arriving in six months counts for very little; the $1,000 principal arriving in year ten counts for a great deal.

Modified duration converts that average into price sensitivity. The conversion is modified duration = Macaulay duration ÷ (1 + y/k), where y is the annual yield and k is the number of coupon payments per year. On a bond yielding 4% with semiannual coupons the divisor is 1.02, so modified duration sits about 2% below Macaulay. Every figure below is modified duration, because that’s the one that maps onto price.

Current yields for every Treasury maturity are published each business day on the Treasury’s daily yield curve page. That’s the input if you want to price your own holdings rather than read a table.

One bond, followed all the way through

Say you hold $50,000 face of a 10-year Treasury-style bond. Coupon 4.00%, paid semiannually, so $1,000 lands in your account twice a year. Yield to maturity is also 4.00%, which means it prices at par: fifty bonds at $1,000 each.

Twenty payments, each discounted at 2.00% per period. Take each payment’s present value, multiply by the number of years until it arrives, add them up, divide by the price. The sum of the present values is $1,000 per bond, as it must be at par. The sum of present-value-times-years is $8,317.57.

Macaulay duration = 8,317.57 ÷ 1,000 = 8.318 years. Modified duration = 8.318 ÷ 1.02 = 8.155 years.

Now rates rise a full point and the bond’s yield goes to 5.00%. Duration predicts −8.155%: about $81.55 per bond, $4,078 on your position.

Reprice it properly and discount all twenty payments at 2.5% per period, and the bond comes to $922.05. Your fifty bonds are worth $46,102.50. The real loss is $3,897.50, or −7.80%.

Duration said you’d lose $4,078. You lost $3,898. It overstated the damage by $180, because the price-yield relationship is a curve and duration is the straight line tangent to it. That gap is convexity, and it always leans your way: losses arrive smaller than predicted, gains arrive larger.

What a one-point rise costs, by maturity

Same setup across the curve. Every bond priced at par with a 4% coupon paid semiannually. The estimate column is −modified duration × 1%; the actual column reprices the bond at a 5% yield. Per $1,000 face.

Duration is not maturity, and the two separate fast. At one year they’re nearly identical. At thirty years, duration is 17.00 — barely more than half the maturity.

The other thing worth reading off is how little extra risk the far end adds. Doubling maturity from 15 to 30 years raises duration from 11.12 to 17.00, an increase of 53%, not 100%. Coupons arriving in years one through fifteen anchor the weighted average, and each additional year of maturity you tack on past that point moves it less than the year before.

Coupon size does as much work as maturity

A large coupon returns cash sooner, which drags the weighted average time down. A small one leaves almost everything riding on the final principal payment. Here is modified duration across both axes, each bond priced at par with semiannual payments.

Zero-coupon is the ceiling. With no interim payments there is nothing to pull the average forward, so Macaulay duration equals maturity exactly. (The 0% column shows modified duration at a near-zero yield, the clean theoretical bound; at a positive yield it sits slightly below maturity.)

The practical read is in the bottom row. Thirty years to maturity with a 2% coupon gives you duration 20.66. Thirty years with a 6% coupon gives you 14.13. One point of rate rise costs the first holder roughly 20.7% and the second roughly 14.1% — six and a half percentage points of difference between two bonds that mature on comparable schedules. That is the mechanism behind long bonds issued in a low-rate stretch behaving so badly when rates normalise: a 2% coupon buys you almost 21 years of duration whether you wanted it or not.

Bigger moves, and where the straight line fails

Duration is a tangent. Small moves stay close to the curve; large ones don’t. Back to the 10-year bond with the 4% coupon, across a range of yield shocks.

The asymmetry is the interesting part. Three points down hands your $50,000 position roughly $14,270 in gains; three points up costs it roughly $10,660. Same size shock in each direction, and the outcomes are not mirror images. Convexity is what buys that.

For quarter-point moves the straight line is accurate to two hundredths of a percentage point. If you’re sketching what a single Fed decision does to a position, duration alone is plenty.

How much of a move erases a year’s income

Turn the question around. Rather than asking what a one-point move costs, ask how large a move it takes before the price loss swallows a full year of coupons.

Break-even yield rise ≈ coupon yield ÷ modified duration. Your $50,000 at a 4% coupon pays $2,000 a year.

Your 10-year position needs 49 basis points — half a standard Fed move — to wipe out the $2,000 you’ll collect over the next twelve months. At thirty years the threshold is 24 basis points, less than one move, on paper, in a session or two.

The reverse holds identically. A 24 basis point fall hands the 30-year holder a second year’s income in price appreciation, in a day. Long bonds are not low-volatility instruments with a bit of coupon attached. The coupon is a rounding error next to the price.

Six places the estimate breaks

Curves don’t shift in parallel. Duration assumes every maturity’s yield moves by the same amount. Real curves twist. Short rates can jump a full point while the 30-year barely flinches, or the long end can sell off while the front end rallies. Holding a range of maturities and applying one duration to one headline “rate change” hides which part of the curve actually moved — read it maturity by maturity on the Treasury’s daily rates page instead.

Callable bonds cap your upside. If the issuer can redeem early, falling rates trigger the call and your gain stops near the call price. Effective duration collapses toward the call date as rates fall and stretches back out as rates rise, which is exactly backwards from what a holder wants. Mortgage-backed securities behave the same way, since homeowners refinance when rates drop.

Credit spreads move on their own. Duration measures sensitivity to the risk-free rate. A corporate bond yields the Treasury rate plus a credit spread, and in a stress episode Treasury yields can fall while spreads widen further, so the corporate loses money while duration math promises a gain. Duration says nothing whatever about whether the issuer pays you back.

Floating rate notes barely have duration. A note whose coupon resets quarterly has an effective duration close to the time until the next reset, often under 0.25 years, no matter what the stated maturity says. Apply maturity-based duration to one and you’ll be off by a factor of forty.

Moves past a point need convexity. The shock table above shows a three-point move producing a 3.15 percentage point error on a 10-year bond. On a 30-year, larger still.

Fund duration is a moving snapshot. A fund’s number is a weighted average that shifts as the manager trades and as the holdings age. The figure on the fact sheet was computed on a date that may be weeks behind whatever you’re comparing it against.

Two claims worth correcting

“A bond fund can’t lose money if you hold long enough”

There’s a real mechanism underneath a misleading sentence. A single bond held to maturity returns your principal absent default, so the price dip is temporary by construction. A fund has no maturity date — but it does reinvest, at the new higher yields.

Run it on your position. The shock cost you 7.80%. From then on the portfolio earns roughly 5% instead of the 4% you’d expected, an extra one percentage point a year. Eight years of that extra income roughly offsets the price hit, assuming rates then sit still and ignoring compounding. Eight years is the honest horizon on a portfolio with this duration, and it is quite a lot of weight for the word “eventually” to carry.

“Duration is how long until I get my money back”

Close enough to sound right, wrong in a way that matters. Of the 8.32 years of Macaulay duration on your bond, the single principal payment at year ten contributes 6.86. Its present value is $686.43 — 68.6% of the bond’s price. All twenty coupons together contribute the remaining 1.45 years.

Two thirds of your rate risk sits in one payment at the very end. That’s also the reason a low coupon raises duration so sharply: fewer dollars arriving early means the final principal payment carries an even larger share of the weight.

What this does not tell you

Every figure here comes from a discounted cash flow model with tidy assumptions, and real portfolios leave that model behind in several directions.

The tables price every bond at par. Yours probably wasn’t bought at par. A bond held at a premium or a discount has a different duration than its par-priced twin, though for typical retail holdings the difference runs under half a year.

Taxes are absent throughout. Corporate coupon income is taxed as ordinary income, Treasury coupon income is exempt from state tax, and municipal income has its own treatment — enough to reorder some of these comparisons after tax.

So is inflation. A 4% nominal coupon against 3% inflation is a 1% real return, and none of the arithmetic above knows which one you’re being paid.

Trading costs aren’t modelled either. Individual bonds trade over the counter at wider spreads than exchange-listed instruments, and a retail-size lot routinely prices worse than an institutional one. When the cash actually settles changed with the SEC’s move to T+1 settlement, which affects timing rather than price.

And the limit that covers all of it: this is descriptive arithmetic. It tells you what a given rate move would do to a given bond. It has no opinion on whether that move happens.

FAQ

How much does a bond lose if interest rates rise 1%?

Roughly its modified duration expressed as a percentage. A bond with duration 5 loses about 5%; duration 10, about 10%. On the 10-year, 4% coupon bond used throughout this page, duration 8.16 predicts −8.16% and the exact repriced loss is 7.80%, or $78 per $1,000 of face value.

What is the duration of a 10-year Treasury?

About 8.2 years for one carrying a 4% coupon and yielding 4%. Not 10, because twenty coupon payments arrive before maturity and pull the weighted average time forward. Drop the coupon to 2% and duration rises to roughly 8.98; raise it to 6% and it falls to about 7.45.

Why did my bond fund lose money when bonds are supposed to be safe?

Because “safe” describes credit risk, not price risk. A Treasury fund has essentially no default risk and a great deal of rate risk. Duration 6.5 against a 1.5 point rise in yields is roughly −9.75% on price, partly offset by the coupons collected along the way. Both risks are real; duration only measures the second one.

Is a higher or lower duration better?

Neither on its own. Higher duration means bigger gains when rates fall and bigger losses when they rise — a 30-year bond with duration 17 moves roughly seventeen times as far per unit of rate change as a 1-year bond with duration 0.96. What matters is whether that swing fits your time horizon and your willingness to sit through a drawdown.

How do I calculate duration for my own bond?

Discount every remaining cash flow at the bond’s yield, multiply each present value by the years until it arrives, sum those products, and divide by the price. That’s Macaulay duration. Divide by (1 + yield ÷ payments per year) to get modified duration. The worked example above runs the full twenty-period version.

Does duration work the same way for bond ETFs?

Yes, with one caveat. A fund publishes a weighted average duration across its holdings, and multiplying it by a rate change gives the same first-order estimate. The caveat is drift: the fund’s duration changes as bonds age and the manager trades, while an individual bond’s duration declines predictably toward zero as maturity approaches.

What is convexity and do I need to care?

Convexity measures how much duration itself changes as yields change — practically, it’s the error term. Below one percentage point of rate movement, ignoring it costs under half a point of accuracy on most bonds. At a three point move on a 10-year bond, ignoring it overstates your loss by 3.15 points. Care above one point, ignore below.

What to look at next

Pull the current curve from the Treasury’s daily rates page and note the gap between the 2-year and the 10-year. Watching how that gap changes tells you whether a move was a parallel shift or a twist, and the parallel assumption is the one most likely to break everything above.

Then find the duration figure on whatever fixed income you hold — usually the fund fact sheet, or the trade confirmation for an individual bond. Divide your coupon yield by it. The answer is how many basis points of yield rise erase a year of income, and that number tells you more about the ride you’ve signed up for than any headline about rates.

This article is general information, not financial advice. See our disclaimer.

Also worth reading: TIPS Principal Adjustment: How Inflation Changes What You’re Paid at Maturity

More in Market Mechanics · all topics · calculators · how this was checked