Buying a range of bond maturities?

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mehujael
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Buying a range of bond maturities?

Post by mehujael »

What is the difference of buying a range of treasuries, short, intermediate, and long, with lets say, an average duration of 10 years, and just buying 10 year treasuries? Would there be a difference in behaviour as interest rates change, or a difference in yield?
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David Jay
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Re: Buying a range of bond maturities?

Post by David Jay »

In normal times, when future interest rates are unknown, holding a range of bond durations probably make sense. There is a widely-described “barbell” strategy of holding short term bonds and long term bonds to cover a wide range of outcomes.

In these near-zero interest times, I cannot bring myself to purchase long-term bonds because of the “hit” they will take as interest rates return to more reasonable levels. But of course I am in the decumulation phase and I don’t have 25 - 30 years for long term bonds to “catch up”.
Last edited by David Jay on Sun Apr 11, 2021 12:00 pm, edited 1 time in total.
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jimkinny
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Re: Buying a range of bond maturities?

Post by jimkinny »

Yes there will be a difference. Interest rates at various maturites do not go up by a fixed % or a fixed ratio at each maturity term. Sometimes the shorter stuff goes up a lot more than longer or just the reverserve.
Here is a link to Treasury yields which you can play around with
https://www.treasury.gov/resource-cente ... data=yield

Here is a link to the difference between 10 and 2 year Treasury bonds
https://fred.stlouisfed.org/series/T10Y2Y

Generally we think that if interest rates change that the longer term bonds will react more than the shorter term stuff. I guess this is generally true but a lot of times 30 year Treasury bonds don't change much. I suppose this is because of the market's perception of long term inflation prospects but I am only guessing.
dbr
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Re: Buying a range of bond maturities?

Post by dbr »

Yes, the key is the yield curve which does not maintain constant shape. That establishes that there is a difference. To determine what will be the difference requires forecasting the yield curve, which is not a practical possibility. You then have to convolute* the changing yield with the modified duration which is the log derivative of price with respect to yield. Convolute means to calculate that result for each duration held by the fund and add up the weighted results. The adding up of the weighted results is where the distribution of holdings over duration enters.

You can see the yield curve here and pull the red cursor to follow it over time: https://stockcharts.com/freecharts/yieldcurve.php

*Convolution: https://en.wikipedia.org/wiki/Convolution You could say this is a case of signal processing where the change in yield curve is the input, the duration is a signal detector, the weighting is a signal processor, and the change in fund NAV is an output. I think anyway, but sounds cool.
Robot Monster
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Re: Buying a range of bond maturities?

Post by Robot Monster »

jimkinny wrote: Sat Apr 10, 2021 10:04 am Yes there will be a difference. Interest rates at various maturites do not go up by a fixed % or a fixed ratio at each maturity term. Sometimes the shorter stuff goes up a lot more than longer or just the reverserve.
Could another way to think about this be that if the yield curve maintained a constant steepness, there would be no difference? But of course the slope of the yield curve significantly changes, it can be steep, flat, or even inverse (where long term yields are below short-term.)

Don't know if others find it helpful thinking in terms of the changes to the slope, but the Wall Street Journal does publish, on a daily basis, a graphic of how the yield curve has changed from a year ago.
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Re: Buying a range of bond maturities?

Post by Robot Monster »

As an experiment, let's compare the performance of two portfolios with matching durations. (Hope I did these calculations correctly.)

From Jan 2010 - Mar 2021:

Barbell -- 2.71% CAGR
84.95% VGSH
15.05% EDV

Intermediate -- 3.27% CAGR
100% VGIT

link

Average Duration
Vanguard Short-Term Treasury ETF (VGSH) -- 2.0 years
Vanguard Intermediate-Term Treasury ETF (VGIT) --5.4 years
Vanguard Extended Duration Treasury ETF (EDV) -- 24.6 years
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grabiner
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Re: Buying a range of bond maturities?

Post by grabiner »

Robot Monster wrote: Sun Apr 11, 2021 9:44 am
jimkinny wrote: Sat Apr 10, 2021 10:04 am Yes there will be a difference. Interest rates at various maturites do not go up by a fixed % or a fixed ratio at each maturity term. Sometimes the shorter stuff goes up a lot more than longer or just the reverserve.
Could another way to think about this be that if the yield curve maintained a constant steepness, there would be no difference? But of course the slope of the yield curve significantly changes, it can be steep, flat, or even inverse (where long term yields are below short-term.)
In particular, I would expect a portfolio of varying durations to have slightly less interest-rate risk than a portfolio of an equal fixed duration, because short-term rates are more volatile. If short-term, intermediate-term, and long-term yields all rise by 2%, then a portfolio of intermediate-term bonds will lose the same amount as a portfolio of the same duration with short-term and long-term bonds. But it is more likely that short-term yields will rise by 3% and long-term yields will rise by 1%, and thus the portfolio with varying durations will lose less. Similarly, if rates fall, the portfolio with varying durations will gain less/
Robot Monster wrote: Sun Apr 11, 2021 10:17 am As an experiment, let's compare the performance of two portfolios with matching durations. (Hope I did these calculations correctly.)

From Jan 2010 - Mar 2021:

Barbell -- 2.71% CAGR
84.95% VGSH
15.05% EDV

Intermediate -- 3.27% CAGR
100% VGIT
And this shows the effect. During the period in question, interest rates fell, and thus the barbell gained less than the all-intermediate portfolio.
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dbr
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Re: Buying a range of bond maturities?

Post by dbr »

grabiner wrote: Sun Apr 11, 2021 10:36 am
Robot Monster wrote: Sun Apr 11, 2021 9:44 am
jimkinny wrote: Sat Apr 10, 2021 10:04 am Yes there will be a difference. Interest rates at various maturites do not go up by a fixed % or a fixed ratio at each maturity term. Sometimes the shorter stuff goes up a lot more than longer or just the reverserve.
Could another way to think about this be that if the yield curve maintained a constant steepness, there would be no difference? But of course the slope of the yield curve significantly changes, it can be steep, flat, or even inverse (where long term yields are below short-term.)
In particular, I would expect a portfolio of varying durations to have slightly less interest-rate risk than a portfolio of an equal fixed duration, because short-term rates are more volatile. If short-term, intermediate-term, and long-term yields all rise by 2%, then a portfolio of intermediate-term bonds will lose the same amount as a portfolio of the same duration with short-term and long-term bonds. But it is more likely that short-term yields will rise by 3% and long-term yields will rise by 1%, and thus the portfolio with varying durations will lose less. Similarly, if rates fall, the portfolio with varying durations will gain less/
Robot Monster wrote: Sun Apr 11, 2021 10:17 am As an experiment, let's compare the performance of two portfolios with matching durations. (Hope I did these calculations correctly.)

From Jan 2010 - Mar 2021:

Barbell -- 2.71% CAGR
84.95% VGSH
15.05% EDV

Intermediate -- 3.27% CAGR
100% VGIT
And this shows the effect. During the period in question, interest rates fell, and thus the barbell gained less than the all-intermediate portfolio.
Thanks for that analysis. The thought issue here is that when it comes to interest rate risk duration is not a driver but a translator. To get the effect you still have to input the signal, which is changes in interest rate, and the fact, presumably at least, that those changes vary in nature across the spectrum. Good point.
jimkinny
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Re: Buying a range of bond maturities?

Post by jimkinny »

Robot Monster wrote: Sun Apr 11, 2021 9:44 am
jimkinny wrote: Sat Apr 10, 2021 10:04 am Yes there will be a difference. Interest rates at various maturites do not go up by a fixed % or a fixed ratio at each maturity term. Sometimes the shorter stuff goes up a lot more than longer or just the reverserve.
Could another way to think about this be that if the yield curve maintained a constant steepness, there would be no difference? But of course the slope of the yield curve significantly changes, it can be steep, flat, or even inverse (where long term yields are below short-term.)

Don't know if others find it helpful thinking in terms of the changes to the slope, but the Wall Street Journal does publish, on a daily basis, a graphic of how the yield curve has changed from a year ago.
As you wrote, the slope is not constant and it actually doesn't have one slope. It can be steeper at the long term end, flatter towards the middle and and flat at the short end or inverted as you wrote. The 10-2 year graph is interesting but still doesn't inform one about how much below or above the the expected inflation rate the yield is. Take a look at the Treasury daily yield curve and change it to the real yield curve rates (drop down selection).
This is the interest rate minus the expected inflation. Whether or not the expected inflation is what we end up getting is another question though to which no one has an answer.
jimkinny
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Re: Buying a range of bond maturities?

Post by jimkinny »

Robot Monster wrote: Sun Apr 11, 2021 9:44 am
jimkinny wrote: Sat Apr 10, 2021 10:04 am Yes there will be a difference. Interest rates at various maturites do not go up by a fixed % or a fixed ratio at each maturity term. Sometimes the shorter stuff goes up a lot more than longer or just the reverserve.
Could another way to think about this be that if the yield curve maintained a constant steepness, there would be no difference? But of course the slope of the yield curve significantly changes, it can be steep, flat, or even inverse (where long term yields are below short-term.)

Don't know if others find it helpful thinking in terms of the changes to the slope, but the Wall Street Journal does publish, on a daily basis, a graphic of how the yield curve has changed from a year ago.
As you wrote, the slope is not constant and it actually doesn't have one slope. It can be steeper at the long term end, flatter towards the middle and and flat at the short end or inverted as you wrote. The 10-2 year graph is interesting but still doesn't inform one about how much below or above the the expected inflation rate the yield is. Take a look at the Treasury daily yield curve and change it to the real yield curve rates (drop down selection).
This is the interest rate minus the expected inflation. Whether or not the expected inflation is what we end up getting is another question though to which no one has an answer.
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Re: Buying a range of bond maturities?

Post by watchnerd »

mehujael wrote: Fri Apr 09, 2021 11:58 pm What is the difference of buying a range of treasuries, short, intermediate, and long, with lets say, an average duration of 10 years, and just buying 10 year treasuries? Would there be a difference in behaviour as interest rates change, or a difference in yield?
The only individual bonds we buy are for our LMP ladder.

We buy 10 YR TIPS or STRIPS (alternating rungs) every July.

Because we hold them to maturity, and they're for LMP purposes, we don't care about fluctuations in price.
Global stocks, IG/HY bonds, gold & digital assets at market weights 75% / 19% / 6% || LMP: TIPS ladder
Northern Flicker
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Re: Buying a range of bond maturities?

Post by Northern Flicker »

mehujael wrote: Fri Apr 09, 2021 11:58 pm What is the difference of buying a range of treasuries, short, intermediate, and long, with lets say, an average duration of 10 years, and just buying 10 year treasuries? Would there be a difference in behaviour as interest rates change, or a difference in yield?
The range of maturities will provide more liquidity. Also, the duration if a 10-year treasury is less than 10 years because of coupon payments over the life of the bond.

A bond ladder is a popular way to hold a range of treasury maturities.

A bond ladder lets you ride the yield curve. If you hold say a 10-year ladder then when a bond matures, you buy a new 10-year bond. The 10-year bond you had a year ago is now a 9-year bond. Your 1-year bond is a 9-year-old 10-year bond. You thus are acquiring each bond at the 10-year rate. Your bond in the 1-year rung of the ladder was bought 9 years ago with the 10-year yield.
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