Duration matching: should you match your bonds to your time horizon? [Members]
For MAVENS and MOGULS by The Accumulator
on August 15, 2023
The standard advice for passive investors is to match the duration of your bond holdings to your investment time horizon. Sensible enough – but, like many an oft-repeated heuristic, this duration matching strategy has been boiled down from a rich broth of nourishing guidance into a thin soup that amounts to empty calories for most people.
So let’s take a fresh look at duration matching’s nutrition label and find out:
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![Duration matching bond funds to your time horizon [Members]](https://monevator.com/wp-content/uploads/2022/11/duration-matching-with-a-present-value-calculator-1024x330.png "Duration matching bond funds to your time horizon [Members]")
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What a fantastic article. I look forward to the rest of this series. Whilst bonds currently make up 0% of my portfolio in 25-30 years time they surely will. Plus the articles are well written, clear and informative.
Cheers
AndyD4
Second that one @AndyD4. Super article @TA. Much obliged.
I’m in the accumulation phase but, like AndyD4, I need to begin to think about 30+ years hence (if I make it that far!), at which time I won’t be 100% in global equities, as now, but closer to 40% long and 15% short (perhaps index linked) gilt allocations in the UK version of Dalio’s All Weather portfolio, which @TA very usefully previewed in his recent excellent model portfolio piece. I’ll need to have wrapped my head around duration matching and bond maths well before then, and this excellent piece today from @TA will be very helpful indeed for that. Thank you @TA.
Another fantastic article. I’m grateful for the clarity that once in decumulation there is no point in trying to duration match. I have been confused ever since reading Lars Kroijer’s Investing Demystified, First Edition, and subsequent articles on Monevator. For the minimal risk asset he advocates short-duration government bonds or government bonds with duration matched to your time horizon without, in my opinion, ever really satisfactorily describing what this might be for a retiree. I’m glad to read here that it really is undefinable. Personally, apart from a disastrous dabble in INXG I’m sticking to cash and short-duration Gilt and TIPS ETFs for my non-equity investments.
Thanks all! I’ve come to realise that the best form of duration matching for me in retirement will almost certainly be an index-linked annuity later on in life. Happily they look much better value than they did.
The key thing about Macaulay Duration (MacD) is that it measures the average timing of cashflows. Compared to Modified Duration that measure the sensitivity to a yield change. They are related by a very simple formula but as metrics they have different purposes.
One way to visualize the Macaulay duration (MacD) of a bond is in terms of zero coupon bonds. A zero coupon bond delivers it’s entire future value (typically par or 100) on the maturity date. The duration-matched coupon bond may deliver nothing on that specific date. Yet if it is combined with it’s reinvested coupons it will (under certain circumstances, see below) deliver the same amount as the duration-matched zero with an identical yield.
Say you have a portfolio made up of 500 bonds in a fund, all with different maturities and yields. Yet I know the weighted yield of the portfolio and it’s weighted MacD. I can then visualize the entire portfolio as a single zero coupon bond with the same weighted yield. A big simplification in thought process.
The problem is this is only an approximation. It only works at that instant and only for (small) parallel shifts of the yield curve. As time moves on and yields change, the approximation will start to incur errors and will need to be recalced (hence requiring rebalancing if you are duration-matching).
This is useful little doc on duration and convexity that covers this sort of stuff. https://docdro.id/SbhyXqS. I read it when I started 25 years ago, so it’s very old (you can tell from the 10% coupon examples). It covers the basics though.
Thanks TA for the clear description.
To me, the choice to duration match (or not) is one of those issues that raises tricky questions about the line between active and passive investment approaches.
I can see why Kroijer and others argue that equity decisions should be fully passive. But I struggle to accept the same on bonds. Mainly because the bond decision feels so similar to fixed rate savings choices – obviously, when rates were low, people weren’t keen to lock-in those rates for 5 years. Little upside and plenty of possible opportunity cost. It seems strange not to approach bonds in the same way.
Though I’m glad to see Hale argue that most investors can omit duration risk (at least in his 3rd edition) and keep things simple.
For any (like me) who didn’t do maths beyond O-level/GCSE & who are working their way through the 1993 JPM Securities “Duration, Convexity, and Yield Curve” intro doc linked to above by @ZX #5; the following is an explanation of the use of Greek letter ∑, which appears severally in the doc (explanation taken off a maths tutor website, lightly edited for brevity).
∑ represents the sum. So 4 + 8 + 12 + 16 + 20 + 24 (sum 84) can be expressed as:
6
∑4n
n=1
Expression read as sum of 4n as n goes from 1 to 6. Variable n is the index of summation.
@ tetromino – I think it’s because most people are as bad at predicting the future path of interest rates as they are the stock market. People were talking about a bond apocalypse for well over a decade before it happened. Even then, it took a pandemic and war in Europe.
@ TLI – cheers! I’ve had to look that up a few times in the past too
I saw your email and thought I would pop by to put my oar in! You are absolutely right to be sceptical about duration matching. In the scenario you present, duration matching target date and a change in yield just after purchase, then everything works out just fine. If the change in yield happened later, then it may not be fine. Worse case scenario is a Truss moment just before the target date.
The problem is that the duration and target date do not stay in sync. Even with no change in yield the duration will drift forward of the target date, which is why this is a risky strategy. The risk can be reduced, but not eliminated, by going for a low coupon bond as that keeps the target date and duration closer together. For absolute safety, cash flow matching is required, with a bond maturing just short of the target date.
Worth remembering that if I hold bonds and interest rates rise, then over time I can going to be better off, albeit there will be a decline in the present valuation.
Rates fall, then I will have a capital gain now but I will be worse off over the long term.
Duration is the magic lever that amplifies or reduces that effect.
If I want to secure my future expenditure, then Inflation Protected bonds going from a real rate of negative 2% or 3% fairly recently, to a 2% positive real return is good news.
@Hariseldon #10: are there any ILGs of any duration which have 2% real rates? Or is this an inflation linked Corporate Bond?
@TLO.
Almost all TIPS are over 2%
https://www.wsj.com/market-data/bonds/tips
For ILGs I hold 0.125% 3/26 which is on 1.74% at present and quite a few are around 1.5%
Thanks @Hariseldon. Looks like TIPS and ILGs yields have, respectively, held up and continued to climb. US PCE way down (as for other inflation metrics), whilst picture over here is very murky (good news on headline measures, but perhaps some resurgent in service led core inflation). Interesting to see how this is playing out in real yields for linkers. 2% was my trigger to dip toe, but maybe no point my obsessing on it getting to exactly 2.00 or more.
“Before the duration point you’re up on the deal. After the duration point you’re down”
Before I read this article, I thought individual bonds should be held to their redemption date (cash flow matching). Why should we not do this, in fact? ie. why are we down on the deal if we hold longer than the duration point? This is the bit I would welcome some more explanation on if possible please.
Hi Chris,
That part of the article is describing an interest rate fall which boosted the bond’s return with a capital gain but also meant the investor would reinvest subsequent coupons at lower yields.
The duration point is the point of indifference to the capital gain (or loss if rates had risen). Reinvesting coupons at lower yields whittles away the benefit of the capital gain until – at the duration point – you earn the bond’s initial yield to maturity.
Before the duration point, the bond’s earlier capital gain meant it was delivering a yield-to-maturity over and above the initial YTM.
After the duration point, the lower yield on the remaining cashflows mean the bond earns less than the initial YTM.
At the duration point you earn precisely the YTM you originally bought in at.
The same is true in reverse i.e. an interest rate rise that inflicted a capital loss is wiped out by higher yielding reinvested coupons at the duration point, and you earn more than the initial YTM after the duration point – because of the return you earn reinvesting coupons in higher yielding bonds.
A zero coupon bond allows you to hold to maturity and receive precisely the YTM you bought into. There aren’t any coupons to throw off the calculation.
Coupon bearing bonds introduce reinvestment risk i.e. the chance of earning less than your expected return due to reinvesting in lower yielding bonds after an interest rate fall.
From what I’ve seen on cashflow matching, people deal with the risk by matching their future expenses to a given amount of bond principal. In this scenario, they’re not relying on reinvested coupons to do any of the work. They can guarantee their expenses are matched to a nominal amount and are effectively ‘over-insuring’ by ignoring the fate of coupons.
Thanks very much TA for your time in providing this helpful additional comment. Very useful. May I ask a follow up please?
Does Macaulay duration take account of the return on the reinvested coupons? If so does this imply the duration will increase when the YTM falls due to an interest rate fall? Ie because it will take longer to get back your principal.
You’re absolutely right that lower interest rates imply higher duration (and vice versa) because coupons are reinvested at lower yields and thus it takes longer to recover your principal. Similarly if two gilts matured on the same date but A paid a lower coupon than B then bond A would have a higher duration than B.
We’ve seen this play out in reverse over the last couple of years as durations of gilt tracker funds have fallen as yields rose.
That’s really helpful; thanks very much.