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Module 3 · Duration: How Far a Bond Can Fall Core

In 2022, many investors were shocked to see their “safe” bond funds lose more than 10%. The number that warned them was printed on every fact sheet: duration. This module shows you how to read it and use it, so you know how far a bond or bond fund can fall before it happens.

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By the end of this module you'll be able to

  • Define duration as a bond’s sensitivity to changes in interest rates.
  • Estimate a price change from a bond’s duration and a change in rates.
  • Explain why a longer maturity and a lower coupon both mean a higher duration.
  • Explain 2022 using duration, and match duration to when you need the money.

What duration measures

Module 2 showed that bond prices fall when rates rise. The next question is: by how much? The answer is duration. It is measured in years, but the easiest way to read it is as a multiplier: roughly, the percentage a bond’s price changes for each one-point move in interest rates.

% price change ≈ − duration × change in yield (in percentage points)

Example. A bond fund has a duration of 7. If interest rates rise by 1 percentage point, for example from 3% to 4%, its price falls by about 7 × 1 = 7%. If rates rise by 2 points, it falls about 14%. If rates fall by half a point, it rises about 3.5%.

The minus sign is the seesaw from Module 2: rates and prices move in opposite directions. Duration tells you how long the seesaw’s arm is.

Where to find itEvery bond ETF and bond fund fact sheet lists duration, often as “effective duration” or “modified duration”. For a single bond, your broker’s bond screen shows it. You will almost never need to calculate it yourself, only to use it.

What makes duration bigger

Three things push duration up. The longer you have to wait for your money, the more a change in rates affects what that money is worth today.

Bond funds are grouped by how long their bonds are, and their durations differ a lot. The ranges below are typical for Canadian bond index funds. Always check the current figure on the fund’s fact sheet.

Type of bond fundBonds maturing inTypical durationEstimated move if rates rise 1 point
Short-term1 to 5 yearsabout 2.5 to 3about −3%
Broad (“universe” or aggregate)All maturitiesabout 7about −7%
Long-term10 years or moreabout 14 or moreabout −14%
Estimated price change when rates rise one point Three horizontal bars. A short-term bond fund with a duration of about 3 falls about 3 percent. A broad bond fund with a duration of about 7 falls about 7 percent. A long-term bond fund with a duration of about 14 falls about 14 percent. If interest rates rise by 1 percentage point… Short-term (duration ~3) about −3% Broad (duration ~7) about −7% Long-term (duration ~14) about −14% Same rate move, three very different results. Duration is the only thing that changed.
Estimates from duration alone, before interest income. Typical durations for Canadian bond index funds; check the fact sheet of any fund you hold.

Convexity, briefly

Duration is an estimate, and it works best for small moves. Go back to the five-year, 4% bond from Module 2. Its duration is about 4.45. Here is what duration predicts, and what actually happens:

Rates moveDuration estimateActual price change
Up 1 point, to 5%−4.45%−4.33% (about $956.71)
Down 1 point, to 3%+4.45%+4.58% (about $1,045.80)

The real losses are a little smaller than the estimate, and the real gains a little bigger. This curve in the price–yield relationship is called convexity, and for ordinary bonds it works in your favour. For everyday decisions, duration alone is close enough. Just remember that for big rate moves it slightly overstates the loss.

Case study: 2022

For most of 2020 and 2021, interest rates were close to the lowest levels in history. The Bank of Canada’s policy rate was 0.25%, and government bonds paid very little. Then inflation surged, and in 2022 central banks raised rates faster than they had in decades. The Bank of Canada took its rate from 0.25% to 4.25% in under a year, and the US Federal Reserve moved just as fast.

Longer-term bond yields followed. Over the year, yields on Canadian government bonds rose by roughly two percentage points or more. Now apply duration:

StepRough figure
Duration of a broad Canadian bond indexabout 7 to 7.5
Rise in yields over the yearabout 2 points
Price change from duration (7.5 × 2)about −15%
Interest earned during the yearabout +2% to +3%
Total returnabout −12%

That is roughly what happened. The broad Canadian bond market lost about 12% in 2022, and the broad US bond market about 13%, the worst calendar years for bonds in decades. Long-term bond funds, with durations of 14 or more, lost far more.

Three things made 2022 so painful: yields started extremely low, so there was little income to cushion the fall; durations were high, partly because yields were so low; and rates rose very fast. Nothing about it was hidden. The duration on the fact sheet said how sensitive these funds were.

“Safe” described the borrower, not the price. Government of Canada bonds did not default in 2022, and every one of them was repaid in full at maturity. What fell was their market price, because rates rose. Credit risk and interest rate risk are two different risks, and duration measures the second one.

The silver lining: higher yields

There is a reason duration losses are not the whole story. When rates rise, the bond fund’s price falls, but from then on it earns the new, higher yield, because it reinvests its coupons and maturing bonds at higher rates.

Example. You have $10,000 in a bond fund with a duration of 7, yielding 2%. Rates rise by one point overnight. Compare that with a world where rates stayed put.

YearRates stay at 2%Rates jump to 3% (−7% first, then 3% a year)
Start$10,000$9,300
3$10,612$10,162
5$11,041$10,781
8$11,717$11,781

In this simple example, the investor who suffered the rate shock catches up after about seven and a half years, close to the fund’s duration, and is ahead after that. In real life rates rarely jump once and then sit still, so treat this as a rule of thumb: if you can hold for about the duration, a rate rise mostly hurts now and pays you back later.

value after n years = starting value × (1 + yield)^n

Match duration to when you need the money

Put the last two sections together and you get the most useful rule in this course: the duration of the bonds you hold should not be much longer than the time until you need the money.

The duration ruleDuration ≈ the percentage you lose for each one-point rise in rates. Don’t hold money you need in N years in bonds with a duration much longer than N.

Put it into practice

Your mission
  1. Open the fact sheet of a bond ETF or bond fund you own. If you don’t own one, use a broad Canadian bond index ETF.
  2. Write down its duration and its yield to maturity.
  3. Estimate its price change if rates rise by 1 point, and by 2 points.
  4. Open Portfolio & Net Worth, find how many dollars you hold in that fund, and turn both estimates into dollars.
  5. In your notes, write when you expect to need that money, and whether the fund’s duration fits that timeline.

Open Portfolio & Net Worth →

💡 Turn a duration estimate into dollars for your own holdings in Portfolio & Net Worth.

Educational purposes only; not financial advice. Any bonds, funds, tickers, rates and figures are illustrative examples, not recommendations. Interest rates, deposit-insurance limits and tax rules change, so confirm current details with the issuer, CDIC and your tax authority. Worked examples are not forecasts. Written by Elizabeta Dimoska. Always do your own research and consult a licensed advisor.