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Duration matching in practice

This is the third post in a series on duration matching. The first post covered an introduction to duration, what duration matching is, and why we might want to use it.

The second post looked at why we shouldn’t be afraid of using long-duration bonds, especially if we also have a long-term investment horizon.  

Now we get to the practical bit. How do we actually go about implementation a duration matching approach for our own portfolios?

 

Duration matching using bond funds

 

As we saw in this post on predicting bond fund returns, there’s not much of a difference between a bond and a bond fund. After all, a bond fund is made up entirely of individual bonds.

The practical difference, though, is the bond fund managers are usually working to keep the average duration of the fund relatively constant over time. This means you’ll need to take some action if you want to keep your duration matched to your investment horizon.

Since your investment horizon naturally grows shorter over time, you want the average duration of your bonds to grow shorter over time as well. Individual bonds automatically do this as they move closer to maturity, but you’ll have to do it yourself if you’re using bond funds (which I’m guessing almost all of us are).

This means you’ll need to periodically reduce the duration of your bond funds by exchanging a small amount of long-term bonds for shorter-term bonds/cash (e.g. as part of your rebalancing strategy).

Buying a single individual bond and letting it “age” by a year produces the exact same result as rebalancing between two bond funds of fixed duration to reduce the average duration by a year.

For example, moving from holding 50% in a 5-year bond fund and 50% in a 15-year bond fund (an average duration of 10-years) to 60% in the 5-year fund and 40% in the 15-year bond fund (now an average duration of 9-years) over the course of a year will produce the same result as letting a 10-year bond reduce naturally to a 9-year bond.

The former approach requires a little more effort, but otherwise the approaches are interchangeable.

Matching bond duration to the investment horizon eliminates interest rate undertaken by the investor, and that’s true regardless of the manner in which the matching is done.

If you want to manage interest rate risk using bond funds you simply use two or more bond funds to keep the average duration on a continuously declining path, mimicking the natural behaviour of an individual bond.

Using a fund doesn’t perfectly replicate the cash flow characteristics of building a ladder of direct bonds, but as long as the duration of the fund matches the duration of the ladder, the two approaches will support the same cash flows with the same amount of risk.

 

Coming up with your investment horizon

 

In order to figure out what duration we should be targeting, we first need to know what our investment horizon is.

And your investment horizon is the average time it takes you to distribute all your cash flows, weighted by the present value of each of the cash flows.

It isn’t actually necessary to have perfect knowledge about your future cash flows to benefit from this exercise. Any financial plan will require making a certain number of estimates and assumptions, and estimating your investment horizon is just one of them. Uncertainty is easily accommodated when making these kinds of estimates, and there are no problems updating your estimates and assumptions when new information comes to light.

The following examples are taken from this excellent Bogleheads thread.

Investment horizon – some examples

The simplest case has just one single cash flow in the future.

In this case, the investment time horizon is simply the amount of time until that cash flow. For instance, if you borrow £100 from a friend and promise to pay them back in full in 15 years, the time horizon of that promise is 15 years since 100% of the cash flows are in year 15:

Duration matching example 1

Only slightly more complicated is a case involving a series of equal cash flows evenly spaced across a period of time. For instance, imagine you’re planning for a series of nine annual expenses starting 11 years from now and ending 19 years from now. These nine cash flows also produce an average time, and thus investment horizon, of 15 years:

Duration matching example 2

When the timing or amount of cash flows is uncertain, you can apply a probability weighting to each possible outcome.

For instance, let’s say there’s a household appliance or car that you’ll need to replace at some point in the future. You establish that there is a 40% chance you’ll need to do that in 14 years, a 30% chance you’ll need to do it in year 15, a 20% chance you’ll need to do it in year 16, and a 10% chance you’ll need to do it in year 17. This also produces an investment horizon of 15 years since 15 = (40% x 14) + (30% x 15) + (20% x 16) + (10% x 17):

Duration matching example 3

And that’s all there is to it.

Yes, it requires a bit of guesswork, as nobody can know for sure when/how much they’re going be spending in the future. But it doesn’t need to be perfectly accurate, and can always be updated with new information. The important idea is that by owning bonds whose durations are roughly equivalent to your investment horizon, you can significantly reduce your interest rate risk.

 

A practical example

 

Now let’s take a fully worked example using some numbers.

Let’s say you know you spend £30k a year and you’ll be spending that amount for another 30 years.

Your investment horizon will be 15 years (30/2), assuming your spending remains at £30k over the whole 30 years. This is the same as in the second scenario above.

To match the duration of your bond portfolio to your investment horizon, you’d find two bond funds with durations either side of your investment horizon – i.e. one with a duration longer than 15 years, and one with a duration shorter than 15 years.

You could use the Vanguard U.K. Long Duration Gilt Index Fund, which has a duration of 29 years, and the iShares UK Gilts 0-5yr UCITS ETF, which has a duration of 2 years.

Now you’ll need to work out how much of each fund you’d need to buy for your average duration to equal 15. Dusting off some primary-school maths, we can solve for ‘x’, which is the percentage you’ll want to allocate to your long-duration fund:

x * 29 years + (1-x) * 2 years = 15 years

29x + 2 – 2x = 15

27x = 13

x = 48%

So you’d put 48% of your bond exposure into the 29-year duration fund, and 52% into the 2-year duration fund to give you a weighted duration of 15 years. So roughly 50/50 – which makes sense, as 15 years is roughly halfway between 2 years and 29 years.

Now you know which funds to own, and in what proportions. But how much do you need in those bond funds to cover that £30k per year spending?

Here comes a bit more basic maths.

First, you figure out the weighted average yield of the two funds you’re buying.

Let’s say our Vanguard long-duration fund has a yield of 2%, and our iShares short-duration fund has a yield of 1% (in reality they have very similar yields, so I’ve had to change them slightly to make the example clear):

48% * 2% + 52% * 1% = 1.48%

Let’s call it 1.5% – this is the yield of our bond portfolio.

Now this becomes what’s known as a ‘time value of money’ problem.

You can stick the numbers into a financial calculator and it’ll work out how much money you’ll need today to fund your cashflows given an interest rate. Here we’ll need to use a ‘present value of an annuity’ calculator, like this one.

Number of periods = 30

Interest rate = 1.5%

Payment amounts = £30,000

Stick those three inputs into the calculator and…

Your ‘present value of the annuity’ is = £720,475.

This is the portfolio size you’d need today to cover your £30k per year spending.

Here’s the link where you can see how to do it yourself with the values we’ve used here.

So in order to fund your spending of £30k per year over the next 30 years, you’d need a portfolio of roughly £702k, split between 48% in the Vanguard 29-year duration bond fund, and 52% in the iShares 2-year duration bond fund.

This portfolio is guaranteed to provide an income stream of £30k per year, which perfectly matches your spending. It’s duration-matched, so is safe from both interest-rate risk and shortfall risk (i.e. you won’t run out of money).

Congratulations, you’ve just created a duration-matched bond portfolio!

 

The moving parts

 

Now obviously there’s a few moving parts here.

As we saw in the previous section, you’ll need to adjust the weightings in each of the bond funds as your investment horizon changes. Assuming no changes in spending, you’ll likely be reducing your investment horizon by one year at the end of each year, which means re-adjusting how much you hold in each fund.

Changes in the funds’ yields will also change how large your portfolio would need to be to create this safe income stream.

Any changes in the level of anticipated spending, the timing of the spending, or the probabilities of each cash outflow, will need to be considered and adjusted for.

I’m aware this all sounds a bit complicated, but remember it doesn’t need to be perfect.

Nobody can be expected to perfectly forecast the timing and amount of their future cashflows. But this approach doesn’t require precision, it only requires some sensible guesswork (which is all investing is anyway).

By at least taking our investment horizon into consideration when considering the structure of our bond portfolio, we have a high chance of meaningfully reducing interest rate risk – and in a much more substantial way than we could when simply ignoring the risk by allocating to only intermediate-term bonds.

As part of your annual portfolio review, it shouldn’t take long to take a stab at how much you’re spending from your portfolio, and roughly how long you think it’ll need to last.

We’ll never be able to totally eliminate interest rate risk from our bond portfolios because we’ll never be 100% sure of what we’re going to be spending and when. But by making some educated guesses, we’ll at least take some meaningful steps towards mitigating it.

So now we’ve seen what duration matching is, why it’s an attractive option, and how to implement it.

But what are the downsides to duration matching? Are there any other strategies for constructing a bond portfolio which might be equally good, or better?

That’s for the next post.

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MrBatch
March 14, 2022 8:29 am

Thanks Occam – good post to get to the facts – what to buy / invest.

For me with state pension starting in 10 years I could say a 10 year investment horizon hence 5 year durartion etc.

But this does raise the question “Why are you holding bonds?” Obviously we would like safety AND growth. This series of posts looks at investing to get a known return over time – fine. But are you happy to hold bonds to simply dampen & reduce loss risks even if you know return is sub inflation. ie on the basis that even positively correlated to equitiy drops, they will fall less and either reduce losses or generate cash to buy cheaper equities.

At present unless you are building duration matched fund to allow spending bonds vs cash holding is a tricky choice. I sold some IBLT 20year treasury recently at small gain and expect to buy some back and probably index linked tips or IL global bonds after the expected interest rate rises in USA over coming weeks. Holdings will unlikely be duration matched, but held as offset to volatility in world affecting share prices ready to be sold to buy on share price slide flightpath.

You … ?????