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Duration matching: an introduction

Much of what I remember from my investment exams is now occluded by the mists of time. Just like all other exams, you remember the bits you use in your day job, and almost instantly forget the other 90%.

Included in that hazy 90% is a concept known as asset-liability matching.

The idea behind asset-liability matching involves an institution (say, a pension fund or an endowment) matching their investment’s cashflows to the value and timing of their expected costs. As a simple example, if a university endowment had a liability of £10,000 in 5 years time (say, they needed to pay for a student’s financial aid), they could buy £9,000 of zero-coupon bonds which mature for £10,000 in 5 years’ time. They’ve bought an asset to match their liability.

And, in very simple terms, that’s how it works for institutions. But I’d never thought about applying this liability matching idea to my own portfolio before.

Then, during my daily perusal of the Bogleheads forum a few months ago (an incredible resource for DIY investors), I came across a trove of posts by the user ‘Vineviz’. His personal expertise seems to be in bond portfolio management, and he’s been providing convincing arguments for the merits of duration matching bond portfolios on the forum for years. This guy knows his stuff.

So I’m shamelessly plagiarising his ideas, and synthesising it all here. I take zero credit for coming up with any of this. Any revelatory insights are his, and any howling errors are my own.

Writing this series of posts was a learning experience for me, too. And that’s one of the reasons I love writing about investing. There’s always more to learn, and no better way to learn than through writing.

What’s interesting about the idea of duration matching in particular is that it’s an alternative to the conventional wisdom. The traditional approach to passive investing in bonds is to put all your bond allocation into intermediate term bonds. But this duration matching approach forced me to up my game on how to think about bond allocations, and I thought it was a strong enough idea to be worth considering.

To be honest, it took me a while to grasp the concept – it’s not the most intuitive (well, it wasn’t for me anyway). I’ll do my best to explain it clearly.

So this is the first in a series of posts on duration matching. I’m not sure exactly how many parts it’ll be yet, but it’s looking like it’s shaping up to be a 5-parter.

We’ll start with this introductory post, followed by a post on the benefits of long-term bonds, followed by how to put the theory into practice, followed by the drawbacks of duration-matching, followed by a conclusion.

But first, let’s start with the basics.

 

What is duration?

 

Time to start with a quick refresher on duration.

It’s worth getting a strong handle on this concept first, because if you don’t understand duration, the idea of duration matching will make absolutely no sense, and the next few posts are going to sound like gibberish.

In short, duration is a measure of how sensitive a bond is to interest rate moves. The higher the number, the more the bond or bond fund will fall when rates rise, and vice versa. For example, if rates were to rise 1%, a bond with a five-year average duration would lose approximately 5% of its value.

It’s also a measure of how long it takes, in years, for an investor to be repaid the bond’s price by the bond’s total cash flows.

And that’s the important bit.

The way I was taught duration was to think of it like a see-saw. If you lined up all the cashflows from a bond on a see-saw – all the coupon payments followed by the final principal repayment – the duration of the bond would be where the fulcrum would have to be placed to balance the see-saw – i.e. the point at which the cashflows are balanced.

Here’s how it’d look for a regular bond with a few smaller coupon payments, and the large principal repayment at maturity:

Duration matching 1

Source: The Financial Engineer

Because it has no coupons, a zero-coupon bond has a duration equal to its maturity:

Duration matching 2

Source: The Financial Engineer

This means there are two things which affect a bond’s duration: its time to maturity, and its coupon rate. The longer the maturity, the higher the duration. The higher the coupon rate, the lower the duration.  

 

What is duration matching?

 

Once you understand duration, the concept of duration matching is pretty simple. All you do is try and match the duration of your bond portfolio to your investment horizon.

If you think you’ll be investing for 20 more years, then you try and fiddle around with your bond (or bond fund) weightings until you average a duration of 20 years. If you have the option of buying a 20-year duration bond, then great – you buy that bond and you’ve just matched your duration. If you only have the option of buying a bond with a 10-year duration and a bond with a 30-year duration, then it still works. You simply own 50% in each of them to arrive at your average 20-year duration.

If your investment horizon is 10 years, you aim for a 10-year duration. A 30-year horizon, 30 year duration.

So that’s the concept. But why would we want to do it?

 

Why use duration matching?

 

Because it can completely eliminate one of the most important risks facing fixed income investors – interest rate risk.

But before we get to how exactly it does this, we’ll first need to get to grips with interest rate risk itself.

Interest rate risk (aka “duration risk” or “term risk”) is made up of two components.

  1. Price risk is the risk that interest rates go up and the bond price goes down.
  2. Reinvestment risk is the risk that interest rates go down, and coupon payments from the bond are reinvested at lower rates than when you bought it.

These two risks tend to move in opposite directions – a high price risk (i.e. bonds falling due to higher interest rates), leads to a lower reinvestment risk (the higher interest rates means you’re reinvesting at higher rates).

Conversely, a low price risk (due to interest rates falling), leads to a high reinvestment risk (you’re reinvesting at a lower rate).  

For an investor with a short-term investment goal, the price risk of owning a long-term bond is by far the dominant risk. If you have a time horizon of one year and interest rates rise between now and then, the price of your long-term bond will fall and there isn’t enough time for reinvestment at the higher rates to kick in.

Similarly, for an investor with a long-term investment goal, the reinvestment risk is dominant. If you have a time horizon of 40 years and interest rates fall between now and then, your bond price will rise but the cumulative impact of reinvesting at lower rates over the 40 years will reduce returns.

The duration of your bond (or bond fund) is the time where the price risk and reinvestment risk are equal. If you can match the duration of your bond portfolio to your investment horizon, you’ve eliminated interest rate risk. It doesn’t matter what interest rates do between now and then – as long as your duration matches your time horizon, your price risk and reinvestment risk cancel each other out, and you have zero interest rate risk.

One of the key concepts in duration matching is that you’ll need to make sure your duration is periodically monitored and adjusted to make sure it stays in line with your investment horizon. And obviously this works slightly differently for a bond than for a bond fund.

A direct bond’s duration naturally declines to zero at it gets closer to maturity, but most bond funds are managed to a specified maturity and don’t change duration much. There will be a whole post on how to implement duration matching later, but in short, when using bond funds (as most of us will be) the idea is that you manually adjust your bond fund allocations once a year to reduce the average duration of your bond portfolio by one. This is to keep duration in line with your investment horizon, which is now one year closer. In doing this, you replicate the natural declining maturity of a direct bond.

And that’s duration matching, in a nutshell.

If you successfully match your duration to your investment horizon, you completely eliminate all interest rate risk. It’s a mathematical certainty, and is true regardless of interest rate movements, shifts in the yield curve, or any other macro factors. It’s the equivalent of buying a 5 year zero-coupon bond for an expense you know you’re going to pay in 5 years. Once you buy the bond, your cashflows from the bond are certain. And as long as your future liability is also certain (more on that later), then the cashflows from the bond will exactly meet the future liability, regardless of what interest rates do in the interim.

One of the great things about bonds is how predictable their cashflows are. It’s the contractual nature of the cashflows from bonds which makes duration matching possible. Because we know both the size and the timing of each cashflow before ever buying the bond (or bond fund), we can use this information to match its cashflows to our own spending.  

It does, of course, assume the bonds don’t default. But readers by now should be aware that I’ve always preferred high-quality government bonds over corporates.

Despite the common practice of referring to bonds as having interest rate risk, it’s important to acknowledge that interest rate risk is something investors have. And the amount of interest rate risk they face depends on the difference between the investor’s investment time horizon and the duration of the bonds they hold.

A long-term investor is more exposed to interest rate risk if they own short-term bonds than if they own long-term bonds.

A short-term investor is more exposed to interest rate risk if they own long-term bonds than if they own short-term bonds.

 

Long-term bonds vs short-term bonds

 

Duration matching naturally lends itself to the use of long-term bonds for long-term investors.

The argument is that if you hold a bond with a duration of 40 years and hold it for exactly 40 years, you have zero interest rate risk. Rates can go up 50%, they can go down 50%, it doesn’t matter. Because your investment horizon matches your bond’s duration, you have zero interest rate risk and you’ll earn your bond’s starting yield.  

It’s true, long-term bonds do have more short-term price volatility than short-term bonds.

It’s possible you purchase a long-term bond fund, interest rates rise, and your bond fund falls 20%. That sounds super risky to me!

And yes, your bond fund might’ve lost 20%. But its yield has just gone up 20%!

Your bond fund will now grow at a faster pace, recovering those losses. And the amount of time it’ll take to recover those losses is equal to the fund’s duration. If your bond fund has a 20-year duration, it’ll take 20 years for that recovery. But that’s OK for you, because you (in this example) have a 20-year time horizon – that’s why you picked a fund with a 20 year duration, because it matched your time horizon. 

Short-term price volatility isn’t a financial risk for a long-term investor.

(although it might be behavioural one – more on that later)

This can lead to a weird situation where owning a short-term bond fund with low duration actually increases the interest rate risk of your portfolio.

For long-term investors, by reducing the price risk of your portfolio through owning a short-term bond fund, you increase reinvestment risk.

The risk for you is that if yields fall, you’ll be forced to reinvest the interest in lower yielding short-term bonds for the rest of your long-term investment horizon, reducing your total return compared to what you could’ve earned had you matched your duration to your investment horizon and owned longer-term bonds.

By owning a short-term bond fund with a long-term time horizon, you’re betting that short-term rates will go up enough soon enough – and stay that way – that rolling over short-term bonds will have you better off than accepting the higher long-term rate which matched your time horizon.

If you’re an investor with a time horizon longer than the bond fund’s duration, then you’re now taking on more interest rate risk. So unless your time horizon is very short, shifting to short term bonds actually increases interest rate risk.

If you have a long investment horizon, but a short bond duration, you’re taking on more reinvestment risk and less price risk.

If you have a short investment horizon, but a long bond duration, you’re taking on less reinvestment risk and more price risk.

Matching the investment horizon to the bond duration (i.e. both are short or both are long) means you’re allowing those risks to cancel each other out – you’re taking no interest rate risk.

And that’s duration matching.

You can eliminate your interest rate risk by matching the duration of your bond portfolio to your investment horizon. Now, there are obviously limitations to this approach, which I’ll be going through in a future post. But that’s how it all works in theory. And as I mentioned, there are a few more posts coming on this topic, one of which will be how to implement duration matching in practice.

It’s a fascinating idea once you’ve wrapped your head around it, and it raises all sorts of interesting ideas about bond portfolio construction.

As an example of one such idea is that for those investors with time horizons longer than the duration of a standard intermediate-term bond fund, by holding longer-term bonds over intermediate-term bonds, you can reduce (or perhaps even eliminate) your interest rate risk while also increasing diversification and increasing returns.

But that’s for next week’s post.

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Charles
May 16, 2022 8:52 pm

Very interesting read! Never heard about duration matching until now so really enjoying this post. Quite a head scratcher – although I had to reread this a few times to fully understand it. With UK inflation at +7%, i think it’s an interesting time to learn more about bonds and its suitability within your long term portfolio. 31 yr old reader here with no kids so haven’t give much thought to bonds yet to put within my portfolio. But I imagine that will change though over the next 10 years or so, and it never hurts to learn more. Thanks.

far_wide
February 26, 2022 10:50 pm

I’ll be watching with interest too as I was also scratching my head over that series of posts on bogleheads.
My conclusion was that whilst it was reassuring to understand the recovery aspect better, it still didn’t negate the point that you obviously have to hold on to claim the benefit. So when YTM’s have been so low, it seems almost akin to having to have a decade long fixed account, and only at similar rates to those accounts. It would previously have had the ability to be negatively correlated with stocks, but that’s somewhat weakened at the moment.
So for the moment I’m just using 1 year and 2 year fixed cash savings, but with yields rising VAGP is looking more tempting.
Above said, I’m not sure I grasped all of that thread, so yes look forward to reading your posts, cheers!

far_wide
February 26, 2022 10:59 pm
Reply to  far_wide

Reading MrBatch’s comment, I suppose my corresponding/similar challenge for me is – when does a bond fund like VAGP become a good idea?

I’m FIRE’d, late 30’s, but need some diversifiers to dampen volatility/give optionality.

The average duration of VAGP is currently is 7.6 years and the YTM is 1.7%, so if I’ve understood the logic, then I should be prepared to hold on for 14 years to ensure I earn that 1.7% a year.

Meanwhile, though I find it difficult to quantify, let’s say there’s a limited scope for a bounce higher due to stocks falling at the moment.

So overall……It’s not quite yet appealing I think. I can earn similar %’s on a 2 year cash fix, and it seems likely that that will improve further soon too. Set against a 14 year wait potentially for the same return, that feels a bit lopsided in risk/return.

If it was, say 2.5-3% YTM and with some moderate expectation of inverse correlation with stocks, now we’re talking!

Again apologies if I’ve misunderstood anything in my half-arsed attempt at understanding that bogleheads thread.

MrBatch
February 25, 2022 2:15 pm

Looking forward to this series. Bonds are generally discouraged at present but if rates rise and prices drop / yield up there must be a time where they become buyable again. I hold small amount of IBTL us t bonds 20 years duration. They are very volatile !
Interesting with bonds is “investment horizon” – bit hard to define in drawdown as you constantly want income hence duration hard to define. Thoughts on drawdown bond usage would be helpful

MrBatch
February 25, 2022 7:47 pm
Reply to  MrBatch

A couple more thoughts on reflection

Focus on bond funds as most will hold these, so any rates changes calcs examples should assume funds where not held to maturity

You mention duration is time to get money back from bond cash flows but in another article mention the same return as durationx2 minus 1. Can you clarify

Stupid question. £100 bond 3%. Rates up now bond worth £90. Is the 3% coupon £3 pa (3% of original value ie 3.33% yield against current price) or £2.70 (3% of 90). If yield does go up how does this help bond holder. ( your article mentioned yield up 20% on 20 year duration down 20% on 1% rate rise)

MrBatch
February 26, 2022 11:16 am
Reply to  Occam

Thanks Occam – good answers.

That raises the question on etf bonds or funds if you can buy 10 then 9 then 8 then 7 etc duration bond funds coming down from a 10 year horizon say fir correct matching. Most bond funds seem to be to run on keeping a fixed duration of either 20, 10, 7, 3 or 1 – not seen 8 years or 14 etc.

Perhaps a real life example with actual etfs used on a yearly basis could be given as a guide. DYOR of course noted.

Seems to me duration matching is like a bond ladder which is easier to get correct results by buying real bonds not funds??

Also your point on reinvesting when bond matures into new bond is important particularly if yield is up – which is what we expect 2022/23 to get duration matching benefits.

Last thing – horizon time in decumulation phase to set matching time frame is Hard to define. For me at 56 maybe 11 years to State Pension at 67 – after that unknown. Maybe just go 20-30 years to benefit LT bonds or go shorter say review every 5 years. Sure i read somewhere short term bonds on a long horizon increases risks.

Look forward to next blog. Bit like Netflix want them all online in 1 go! We are so greedy and impatient in life now….. 👍

Thanks again for all your research. Best uk based commentary i have seen. Most other US centric.