UK government bonds have given investors a painful kick in the portfolio recently. Many of us found out bond funds are riskier than we realised. But with one simple(-ish) metric you can assess the riskiness of your bond assets ahead of any market crash. That metric is bond duration.
Quick note – Duration applies to bond funds [1], individual bonds, and portfolios of individual bonds. I’ll mostly just refer to ‘bonds’ throughout the article because it’s snappier. I’ll specifically call out bond funds when duration applies differently to them. Please check out our bond jargon buster [2] for a brief refresher on confusing bond terminology.
What is bond duration?
Bond duration expresses a bond’s vulnerability to interest rate risk. The larger the bond duration number, the more reactive a bond’s price is to interest rate changes, as the bond’s yield adjusts to reflect those changes.
For example, if a bond’s duration number is 11, then it:
- Loses approximately 11% of its market value for every 1% rise in its yield1 [3]
- Gains approximately 11% for every 1% fall in its yield
Whatever your bond’s duration number2 [4], that’s how big a gain or loss you can expect for every 1% move in its yield.
A duration three bond will rise or fall in value by approximately 3% if its yield moves by 1%.
In a rising interest rate environment? Shorter duration bonds will be less risky than longer duration equivalents. But they won’t do much for you when rates fall.
Conversely, long duration bonds are more comforting than your favourite teddy bear when interest rates fall. They go up in price!
But that would-be teddy bear is about as welcome as a grizzly at a picnic when interest rates rise.
What affects bond duration?
A bond’s time to maturity, yield, and coupon rate determine its duration:
Remaining time to maturity
The more coupon payments a bond has yet to make until it matures, the more price-sensitive it is to interest rate changes.
That’s because a long-dated bond is stuck with its fixed interest advantage or disadvantage for many years in the future. A short-dated bond has only a few more payments due.
- A distant maturity date implies a higher duration.
- A near-term maturity date implies a lower duration.
[5]Yield and / or coupon payment
Bonds with lower yields / coupon payments are more price-sensitive than similar types with higher yields / coupons.
- A higher yield implies a shorter duration – because the bond returns your money at a faster rate.
- A lower yield implies a longer duration.
The diagram below shows the tug-of-war that resolves a bond’s duration:
[6]- Higher durations are primarily a function of longer bond maturities. Low bond yields / coupons also contribute.
- Lower durations are primarily a function of shorter bond maturities. High bond yields / coupons also contribute.
Higher durations equate to a more volatile bond price (up or down) when interest rates change.
Lower durations mean smaller price swings.
All this helps explain why long duration bonds took horrible losses in 2022. As interest rates escalated, bonds trading in the market became less valuable.
Though it’s little comfort right now, duration also sheds light on why long bonds stepped up in value when interest rates plunged during the Global Financial Crisis [7].
The ups and downs of being a bond
Bear in mind that duration is an approximate measure. It makes various simplifying assumptions about the relationship between interest rates, bond prices, and yields.
But it helps to remember these opposing bond dynamics:
- When interest rates rise, bond prices fall.
- When interest rates fall, bond prices rise.
- When bond prices fall, yields rise.
- When bond prices rise, yields fall.
[8]Long bonds react more violently to these forces, for good or for ill.
When interest rates rise, investors demand more compensation for tying up their money in bonds.
New bonds entering the market must have higher coupon payments to match the rate increase.
But longer bonds are saddled with their old, lower, coupon payments for years – even decades. So their price falls to reflect their less competitive fixed rates.
That price cut pushes the old bond’s yield up. It rises to the point where it’s just as attractive to a buyer as a new bond (of the same type) that waltzes in flashing its higher coupon payment.
An analogy with cash savings accounts might help.
Let’s say you’re in the market for a fixed-rate savings account. Now suppose that interest rates had just risen from 3% to 4%. There’s no way you’d pick the same 3% account you might have gone for yesterday. At least not without a hefty bribe cashback offer.
Bonds on sale
The discounted price of a less competitive bond is a bit like cashback given to new buyers to make it just as profitable as the new bonds they’d otherwise choose.
In the savings business, banks withdraw old, fixed-interest accounts from the market. Existing savers, however, are stuck with their outmoded choice. Curses.
With government bonds, debt obligations are seldom taken off the market. Instead they’re priced at a discount or premium to reflect their altered competitiveness, as interest rates yo-yo.
Naturally, the process works in reverse, too. You earn a premium on bonds boasting a yield higher than prevailing interest rates.
Bond duration captures the short-term capital gain (price premium) or loss (price discount) part of these moves in one simple number.
(Although even this this isn’t the end of the story. Counterintuitively, bond funds have higher expected returns [9] after a price drop. That’s due to the impact of rising bond yields [10].)
How far do bond yields move?
It’s all very well saying duration measures the price change sparked by a 1% yield move. But how far – and how fast – can bond yields bounce in the real world?
It’s the size and speed of your bond’s yield change that determines the scale of your capital loss or gain.
Below is a snapshot of UK gilt yields, with changes in yield over the course of a day, month, and year:
[11]Source: Trading Economics. [12]12 October 2022.
The daily, monthly, and annual shifts in yield shows you the impact of recent changes in market interest rates for each UK government bond in the table.
You can see, for instance, that the yield (note: not the price) on the UK’s benchmark ten-year gilt rose 1.4% in the last month. In the last year the yield is up 3.5%.
Indeed, every gilt with a maturity of three years or more saw its yield increase at least 1.35% in the last month, up to 3.8% over the past year.
If you multiply shifts of that size by duration then that’s going to hurt. As every bond fund owner knows all too well in 2022!
Moving too fast
The duration calculation assumes instantaneous moves. But the longer the change actually takes to unfold, the less violent the price swing. Reinvested cashflows mitigate the impact.
So it’s not quite right to multiply duration by real world movements that evolve over a year.
All the same, the size of the yield rises in the table above show us that just multiplying your bond’s duration by 1% doesn’t nearly capture the scale of the drama that can engulf us.
Which bond is my bond fund like? – Compare your bond fund to individual bonds of the same type. Look up your fund’s weighted average maturity. It’ll behave similarly to an equivalent individual bond with approximately the same maturity. The yield-to-maturity of the fund and the bond should be pretty close. Do check the dates though. Published bond fund yields can be quite stale.
Bond duration: making your money back
There’s another aspect of bond duration which is much more debatable.
This assertion is that your bond’s duration number tells you how many years it takes to recover from a capital loss after a yield rise – your breakeven point.
Or, to put it another way: how long it will take to make the annualised returns you expected before rising yields put a dent in your portfolio.
Let’s say you own a duration 11 bond fund, with a yield-to-maturity of 4%.
Interest rates go up, prices go down, and your bond’s value takes a hit.
However, your bond fund fully makes up that lost ground by the 11 year mark. At that point, you’ve now earned a 4% annualised return over the entire period going back 11 years. The scar of the price drop has healed. It’s as if the interest rate rise never happened.
Beyond 11 years, you’re up on the deal. That’s because your higher-yielding bonds pay you a better return than you would have received without the rate rise, when the yield would have remained lower.
All this assumes that your coupon payments and maturing bonds are reinvested.
The maths work the other way round, too.
If yields fall, then your bond return immediately jacks up (capital gain). But ultimately your returns soften like a tyre with a slow puncture. Beyond your duration number (expressed in years), you’re worse off over the whole period, because your cashflows are reinvested into lower-yielding bonds.
The downgrade in return happens to a duration 3 bond after three years. A duration 11 bond has more staying power. It wouldn’t show a worse annualised return until 11 years passed.
Here for the duration
All this is rule-of-thumb stuff. It works just fine for an individual bond that’s held until maturity, declining in duration as its coupons pay out.
However ‘holding for the duration’ is less applicable to bond funds operating in the real world.
In reality, bond funds turn over their holdings to keep the fund’s average maturity and duration relatively stable. The same goes for rolling portfolios of individual bonds.
Moreover, interest rates don’t change course only once, and then remain static. They weave around like a drunk at a wedding reception.
The traditional advice is to match your bond duration to your time horizon to ensure you get your money back.
But that is based on assumptions that are about as realistic as diesel emissions tests.
Indeed, there’s evidence to suggest you may have to wait for up to twice your bond fund’s initial duration in years to earn your initially expected yield-to-maturity.
The twice duration rule-of-thumb
This rule of thumb says that twice your bond fund’s initial duration is a better guide to your breakeven point.
Of course, you could earn your initially expected return faster if interest rates trend down and you enjoy a series of capital gain boosts.
But when your holding period is dominated by rising rates then twice duration is a more pragmatic time horizon.
This bracing finding comes from a research paper [13]: Constant-Duration Bond Portfolios’ Initial (Rolling) Yield Forecasts Return Best at Twice Duration. The author is Gabriel A. Lozada, associate professor of economics at the University of Utah.
A hat tip to Occam Investing [14]. Occam pointed to Lozada’s research as part of a very good piece on bond returns.
The ‘twice duration’ paper specifically investigates the returns of bond portfolios held at constant durations. It employs a more realistic model for fluctuating interest rates than allowed for above.
The author also empirically tested his model versus 60-years worth of historical returns.
Lozada’s conclusion is you’re more likely to earn your initial yield-to-maturity over a twice duration timespan in a world where interest rates can go for a random walk, or trend upward for decades.
A better, not perfect, guide
Here’s the key finding for ordinary investors:
In summary, almost all the time, initial yield was within a percent or two of average annual realized return with a horizon of twice initial duration.
Are you a fellow glass-half-empty type? Then know this rule-of-thumb looks more rigorous than the happy-clappy ‘just hold for the duration’ advice of old.
But the message isn’t that it will definitely take 22 years to earn say a 4% annualised return from a duration 11 bond fund. We’re not trapped by some boa constrictor of fate.
If interest rates stayed relatively flat for the next eleven years, your bond’s yield would be about what you could expect.
And if rates go down then you may earn more for a while. Though longer-term you’ll likely earn less.
But given that interest rates are inherently unpredictable – and could relentlessly trend up – estimating that it could take somewhere between your bond fund’s duration and twice its duration to earn its yield is the hardheaded approach.
Even then, this doesn’t tell you much about real returns.3 [15]
Other complicating factors
If inflation is higher than expected, nominal bonds do poorly. If inflation is lower than expected, nominal bonds do relatively well.
It’s true too that if you pound-cost average into your bond fund then you’ll:
- Shorten your path to higher overall returns in a rising rate environment
- Shorten your path to worse overall returns in a falling rate environment
Lozada says his findings apply to default-free bonds that aren’t callable [16] (i.e. high-grade government bonds), but notes they aren’t a good fit for long bond portfolios.
Sometimes the best fit was 1.25 times duration or 1.75 times. Much depended on the type of bonds and the time period Lozada put under examination.
Lozada also didn’t look at what happens if you periodically rebalance, withdraw cash, or spend interest. Or any other of the common investor behaviours that influence your particular outcome.
Twice duration then is no more than a rule-of-thumb for short and intermediate government bond fund risk. Albeit a more steely-eyed (steely-thumbed?) one.
If that doesn’t sound especially reassuring then check out the Banker On Wheels bond ETF calculator [17].
This suggests the twice duration rule should be reserved for gloomy scenarios [18] when rates rise constantly during your time horizon.
Duration and convexity
Duration simplifies the real world complexity of bond maths to broad strokes. Convexity fills in more of the detail.
Convexity provides more accurate insights into bond price sensitivity because it accounts for the fact that yield changes also alter a bond’s duration.
Picture the difference in price outcomes between the two measures like this:
[19]The relationship between bond prices and yields is curved, whereas duration assumes it’s linear.
The practical outcome is:
- Duration (white line) tends to underestimate the bond price rise (green line) when yields fall. (Left-hand side of pic).
- Duration typically overestimates price drops when yields rise. (Right-hand side).
The difference between the green line and the white line reveals convexity at work. The convex curve of the bond price shows how it differs from the duration estimate as yields change.
When bonds exhibit positive convexity (as pictured above):
- Yield falls, price spikes, duration lengthens (duration underestimates actual price rise)
- Yields rise, price drops, duration shortens (duration overestimates actual price fall)
Essentially, the lower yields go, the faster bond prices accelerate versus duration’s estimate.
Meanwhile, the higher yields float, the slower bond prices decline vs duration’s readout.
Convexity amounts to a welcome tailwind. One that enhances your portfolio protection in a falling rate environment. And moderates expected bond damage in rising rate conditions.
The effect is barely noticeable for short bonds. But is pronounced at extreme ends of the yield curve, as bond maturities head over 15 years until maturity.
Portfolio Charts has produced some fantastic graphs [20] that give you a proper feel for convexity.
And we demonstrate convexity’s effects in our bond prices [21] post.
Incidentally, watch out for negative convexity. This occurs when bonds become less price sensitive as yields fall. (And vice versa). It’s the exact opposite of what you’d want to happen.
Negative convexity is not a concern for default-free, non-callable government bonds. It is a worry if you stray into corporate / municipal bond territory where call options rear their heads.
If convexity is more accurate then why does everyone use duration? Mainly because it’s simpler, but also because duration is good enough in most circumstances.
Where to find bond duration numbers
A bond fund’s home page should tell you its duration number.
Though as usual, providers love to shower us with a confusion of different terms.
Average duration – A bond fund’s duration is the weighted average of the individual bond durations that it contains. So no cause for alarm if you see this label.
You can flip Vanguard’s site to the financial advisor view (wee dropdown menu, top-right, on desktop) to see its duration figures. For some unearthly reason you can’t see them on the consumer site.
Modified duration – Strictly-speaking the correct term for the type of duration that measures price sensitivity to interest rate changes. Use this number where you see it.
Effective duration – Modified duration diluted by the effect of any bonds with call options in the portfolio. Effective duration trumps modified duration if a fund gives you the choice.
Use Trade Web [22] to find out the modified duration for individual gilts.
If you’d like to calculate bond duration then check out this calculator [23].
Beware that duration doesn’t capture every dimension of bond risk [24]. Credit quality is another major factor – and duration does not address this at all.
Bond risk: higher or lower?
As a Brucie Bonus, bond funds actually become less risky after the yield rises and the price falls.
I appreciate that’s in complete contrast to our instincts after big capital gains and losses. But the eagle-eyed might have noticed their own bond fund’s duration shorten following the recent falls.
For instance, here’s how the key numbers have moved for the SPDR’s intermediate gilt ETF (ticker: GLTY):
On 30 April 2020:
- Duration: 13.85
- Yield-to-maturity: 0.35%
On 30 September 2022:
- Duration: 10
- Yield-to-maturity: 4.09%
The fund’s yield is vastly improved while its lower duration number shows its price sensitivity is less volatile than a couple of years ago.
The fund is now a better investment prospect than it was in 2020! But as ever after a big investment shock, some people will be too bruised to go back for more.
Investing often defies our human intuitions. And bond investing perhaps most of all.
Take it steady,
The Accumulator
PS – When we mention ‘interest rates’ in this post we’re referring to bond market interest rates, not central bank interest rates. References to ‘yield’ mean yield-to-maturity. Please see our bond jargon buster [2] for more.
- Yield to maturity. You can think of it like the interest rate you’ll get if you hold the bond to maturity. [↩ [29]]
- Technically, it’s called ‘modified duration’. [↩ [30]]
- Real returns subtract inflation from your investment results. In other words, they’re a more accurate portrayal of your capital growth in relation to purchasing power than standard nominal returns. [↩ [31]]