Point of indifference for a bond Fund/ETF, real life example

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InvestInPasta
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Point of indifference for a bond Fund/ETF, real life example

Post by InvestInPasta »

According to this BH wiki article
William Bernstein provides an insightful definition of duration as the "point of indifference" for the owner of a bond fund in dealing with interest rate changes. If interest rates rise after purchasing a bond fund, the NAV of the fund falls, which hurts the investor. However, the dividends that the bond fund throws off can now be reinvested at a higher rate. The duration is the length of time that an investor needs to hold the fund for the increased yields to compensate for the decrease in NAV. In that sense, duration represents the length of time it would take for the total value of the fund, with dividends reinvested, to be worth exactly what it would have been worth had interest rates not risen.
Let's say for instance that I bought this TLH bond ETF with the following characteristics at the date I bought it:
  • Average Yield to Maturity: 2.5%
  • Weighted Avg Coupon: 2.2%
  • Weighted Avg Maturity: 18 years
  • Effective Duration: 14 years
  • Let's pretend the ETF reinvest the dividends (I could not find a Treasury ETF on iShares website that reinvest the dividends on its own)
Can I say that if I bought $100K of it, and I'll sell it after 14 years I'll get back for sure at least:
$100K x (1+ 2.5%)^14 ?


I'm ignoring defaults on US Treasury or other ominous extreme events, of course. ;)
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by Dry-Drink »

InvestInPasta wrote: Sun Mar 20, 2022 11:15 am Can I say that if I bought $100K of it, and I'll sell it after 14 years I'll get back for sure at least:
$100K x (1+ 2.5%)^14 ?
No. But if you had bought the portfolio inside that ETFs and simply held (reinvesting all coupons into T-Bills), you would indeed get very close to that after 14 years. The ETF, however, reinvests dividends AND sells all bonds well before maturity into more long-term bonds, and so your results after 14 years will not be necessarily very similar to what you posted above.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by InvestInPasta »

Dry-Drink wrote: Sun Mar 20, 2022 11:28 am
InvestInPasta wrote: Sun Mar 20, 2022 11:15 am Can I say that if I bought $100K of it, and I'll sell it after 14 years I'll get back for sure at least:
$100K x (1+ 2.5%)^14 ?
No. But if you had bought the portfolio inside that ETFs and simply held (reinvesting all coupons into T-Bills), you would indeed get very close to that after 14 years. The ETF, however, reinvests dividends AND sells all bonds well before maturity into more long-term bonds, and so your results after 14 years will not be necessarily very similar to what you posted above.
I thought the BH wiki article was adressing exactly bond fund/ETF.
Duration
It's useful to focus on the duration of your bond fund, such as the Vanguard TIPS Fund, which currently has a duration of 7.6 years. William Bernstein provides an insightful definition of duration as the "point of indifference" for the owner of a bond fund in dealing with interest rate changes. If interest rates rise after purchasing a bond fund, the NAV of the fund falls, which hurts the investor. However, the dividends that the bond fund throws off can now be reinvested at a higher rate. The duration is the length of time that an investor needs to hold the fund for the increased yields to compensate for the decrease in NAV. In that sense, duration represents the length of time it would take for the total value of the fund, with dividends reinvested, to be worth exactly what it would have been worth had interest rates not risen. So, you should always hold bond funds with a duration equal to or shorter than the expected need for your money (note that holding the duration shorter than your need for the money leaves you exposed to the risk of lower returns if interest rates fall).
When you say:
Dry-Drink wrote: Sun Mar 20, 2022 11:28 am if you had bought the portfolio inside that ETFs and simply held (reinvesting all coupons into T-Bills), you would indeed get very close to that after 14 years.
are you basically talking about a non-rolling bond ladder?
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by Dry-Drink »

InvestInPasta wrote: Sun Mar 20, 2022 1:44 pm
Dry-Drink wrote: Sun Mar 20, 2022 11:28 am
InvestInPasta wrote: Sun Mar 20, 2022 11:15 am Can I say that if I bought $100K of it, and I'll sell it after 14 years I'll get back for sure at least:
$100K x (1+ 2.5%)^14 ?
No. But if you had bought the portfolio inside that ETFs and simply held (reinvesting all coupons into T-Bills), you would indeed get very close to that after 14 years. The ETF, however, reinvests dividends AND sells all bonds well before maturity into more long-term bonds, and so your results after 14 years will not be necessarily very similar to what you posted above.
I thought the BH wiki article I posted was adressing exactly bond fund/ETF.
Duration
It's useful to focus on the duration of your bond fund, such as the Vanguard TIPS Fund, which currently has a duration of 7.6 years. William Bernstein provides an insightful definition of duration as the "point of indifference" for the owner of a bond fund in dealing with interest rate changes. If interest rates rise after purchasing a bond fund, the NAV of the fund falls, which hurts the investor. However, the dividends that the bond fund throws off can now be reinvested at a higher rate. The duration is the length of time that an investor needs to hold the fund for the increased yields to compensate for the decrease in NAV. In that sense, duration represents the length of time it would take for the total value of the fund, with dividends reinvested, to be worth exactly what it would have been worth had interest rates not risen. So, you should always hold bond funds with a duration equal to or shorter than the expected need for your money (note that holding the duration shorter than your need for the money leaves you exposed to the risk of lower returns if interest rates fall).
It is true that if interest rates rise, say, X% today and then stay steady, then if you hold that bond fund for 14 years after that rise, you would obtain the current YTM of the bond fund (actually, more than that because of roll yield). That's what the quote says.

That doesn't, however, mean you will obtain that initial YTM of the bond fund after 14 years in all other interest rate scenarios (only in that specific one). A simple counterexample is that if in 2036 (the year when your 14 years are up), rates rise 1% (causing a 14% loss that year), then you will have obtained 2.5% yearly for the first 13 years and -14% on the final 14th year. So your return over those 14 years would obviously be lower than 2.5% yearly.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by Dry-Drink »

InvestInPasta wrote: Sun Mar 20, 2022 1:44 pm When you say:
Dry-Drink wrote: Sun Mar 20, 2022 11:28 am if you had bought the portfolio inside that ETFs and simply held (reinvesting all coupons into T-Bills), you would indeed get very close to that after 14 years.
are you basically talking about a non-rolling bond ladder?
Right, a non-rolling bond ladder will almost certainly deliver ~2.5% yearly after 14 years in this scenario, basically regardless of what interest rates do. The ladder's duration automatically decreases as time passes by so that at any given time, the duration is ~X years, but you also have ~X years until the 14 years are up so it is continuously "immunized" to a rate change.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by RubyTuesday »

You would need to continue to adjust your duration down to immunize your funds against interest rate changes.

Some do this by balancing across 2 (or more) funds of varying constant duration.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by InvestInPasta »

Dry-Drink wrote: Sun Mar 20, 2022 1:57 pm A simple counterexample is that if in 2036 (the year when your 14 years are up), rates rise 1% (causing a 14% loss that year), then you will have obtained 2.5% yearly for the first 13 years and -14% on the final 14th year. So your return over those 14 years would obviously be lower than 2.5% yearly.
yeah, it makes sense, thank you.
I did not understand the BH article.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by Dry-Drink »

InvestInPasta wrote: Sun Mar 20, 2022 7:58 pm
Dry-Drink wrote: Sun Mar 20, 2022 1:57 pm A simple counterexample is that if in 2036 (the year when your 14 years are up), rates rise 1% (causing a 14% loss that year), then you will have obtained 2.5% yearly for the first 13 years and -14% on the final 14th year. So your return over those 14 years would obviously be lower than 2.5% yearly.
yeah, it makes sense, thank you.
I did not understand the BH article.
Idk if it just got updated but I just took a look and they already address this actually:
Interest rates change continuously, not just at a single point in time. Therefore, as the time when you will need the money approaches, you must reduce your duration accordingly, to protect you against any further increases in prevailing rates. The ways in which this can be done are discussed below.
The two methods are buying a bond fund and reducing its duration over time (which is really similar to just holding a non-rolling bond ladder), or just buying zero-coupon bonds.

Good luck OP! :)
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by dbr »

There can hardly be a real life example because it never happens that the interest rates that apply jump up instantly by a certain amount and then remain unchanged for long enough to reach indifference. It is a characterization for the purpose of knowing some things about the concept. In the real world interest rates are constantly changing and different interest rates apply to different bonds in the fund anyway.

If the concern a person has is that there must be a holding period that immunizes the investor from losing money in his bond investment because interest rates might go up, then that is an exercise in futility. If this is important to you for some reason don't buy a bond fund.

I think a better approach to understanding what risk one is taking in a bond fund is to check on the usual standard deviation of annual returns to get a feel for how much worse or better the return might be one year or the other. Max drawdown is a statistic implied by return variability that might be useful to be aware of. As an example between 1987 and now the standard deviation of annual returns of VBMFX has been 3.8% and the max drawdown was -5.9% during a few months in 1987. If a person thinks something might be worse in 2022 and that doesn't suit then that person should not invest in a bond fund. If one does not like something that might happen then it is easy enough not to go there.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by InvestInPasta »

Apparently here they say the point of indifference in the worst case scenario is two times the ETF duration.

https://www.bankeronwheels.com/bond-etf ... vironment/

According to the article let's say I put 100$ in an safe bond ETF with a YTM of 1% and a duration of 7 years, in the worst case scenario I'll have to wait 14 years (two times the duration) and I'll get back my 100$+14$.

What do you think, is it correct?

I'm ignoring inflation, it's not the purpose of this thread.

He also provides a basic simulator: https://www.bankeronwheels.com/bond-etf-calculator/
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by dbr »

InvestInPasta wrote: Sun Apr 17, 2022 8:35 am Apparently here they say the point of indifference in the worst case scenario is two times the ETF duration.

https://www.bankeronwheels.com/bond-etf ... vironment/

According to the article let's say I put 100$ in an safe bond ETF with a YTM of 1% and a duration of 7 years, in the worst case scenario I'll have to wait 14 years (two times the duration) and I'll get back my 100$+14$.

What do you think, is it correct?

I'm ignoring inflation, it's not the purpose of this thread.

He also provides a basic simulator: https://www.bankeronwheels.com/bond-etf-calculator/
Holding the investment for any amount of time would not prevent the investment losing value against the 14 year accumulation in the case that interest rates increased shortly before the end of the 14 years.

I think the two data points are the one that after a single step change in interest rates one is whole after the duration and against a steady increase in interest rates one is whole after twice the duration. One is certainly not whole against a step change in interest rates less than the duration before the end point of your investment no longer how long you hold it and so on.

I think that people who have reason to be concerned that a bond investment not fall below some expectation at a point in time should buy single bonds with a certain date of maturity rather than bond funds.

A problem here is that people are looking at examples of how duration works and trying to find guarantees in their investment. What is not under control is forcing interest rates into some pattern or another.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by vineviz »

InvestInPasta wrote: Sun Apr 17, 2022 8:35 am Apparently here they say the point of indifference in the worst case scenario is two times the ETF duration.

https://www.bankeronwheels.com/bond-etf ... vironment/

According to the article let's say I put 100$ in an safe bond ETF with a YTM of 1% and a duration of 7 years, in the worst case scenario I'll have to wait 14 years (two times the duration) and I'll get back my 100$+14$.

What do you think, is it correct?

No, not correct. The same problem applies at 2x duration as at 1x duration or 0.5x duration: the yield curve can shift at any time in any direction and by any amount. These changes are uncertain and unknowable.

The only ways to avoid the uncertainty are to match your bond investments to your future consumption, either through cash-flow matching or duration matching.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by dbr »

vineviz wrote: Sun Apr 17, 2022 9:51 am
InvestInPasta wrote: Sun Apr 17, 2022 8:35 am Apparently here they say the point of indifference in the worst case scenario is two times the ETF duration.

https://www.bankeronwheels.com/bond-etf ... vironment/

According to the article let's say I put 100$ in an safe bond ETF with a YTM of 1% and a duration of 7 years, in the worst case scenario I'll have to wait 14 years (two times the duration) and I'll get back my 100$+14$.

What do you think, is it correct?

No, not correct. The same problem applies at 2x duration as at 1x duration or 0.5x duration: the yield curve can shift at any time in any direction and by any amount. These changes are uncertain and unknowable.

The only ways to avoid the uncertainty are to match your bond investments to your future consumption, either through cash-flow matching or duration matching.
Presumably these misconceptions that get posted are due to publishing the two examples of waiting the duration after a step change or of waiting twice the duration during a linear increase in interest rate over time. Neither of these ever happen in real life.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by Kevin M »

dbr wrote: Sun Apr 17, 2022 9:58 am Presumably these misconceptions that get posted are due to publishing the two examples of waiting the duration after a step change or of waiting twice the duration during a linear increase in interest rate over time. Neither of these ever happen in real life.
Let's look at both of these simplified scenarios, as well as the results for some real historical yields. This model uses a simple annual rolling ladder of 5-year zero-coupon bonds, so 5-year maturity/duration at the beginning of each year, and 4-year maturity/duration at the end of each year.

One-time increase in yield compared to no change in yield:

Image

As expected, point of indifference (where the lines cross) is 5 years from t=0 and 4 years from t=1 year.

Annually increasing yields:

Image

Point of indifference is 2 * D(0) - 1 = 2 * 5 - 1 = 9, as expected.

Finally, a 19-year period of generally rising 5-year constant maturity Treasury yields, where yield increased from 3.56% to 13.97%, but of course not in a straight line:

Image

Point of indifference somewhere between 7 and 8 years.

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Re: Point of indifference for a bond Fund/ETF, real life example

Post by dbr »

Thanks. That is an interesting picture.

I guess a person interested in knowing for sure when he won't lose money needs a copy of your calculation and knowledge of what interest rates will actually do.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by InvestInPasta »

dbr wrote: Sun Apr 17, 2022 9:39 am Holding the investment for any amount of time would not prevent the investment losing value against the 14 year accumulation in the case that interest rates increased shortly before the end of the 14 years.
vineviz wrote: Sun Apr 17, 2022 9:51 amNo, not correct. The same problem applies at 2x duration as at 1x duration or 0.5x duration: the yield curve can shift at any time in any direction and by any amount. These changes are uncertain and unknowable.
You don't have to hold the bond ETF for 14 years unless you end up in the worst case scenario.
Maybe a better way of saying it, is that a bond ETF with a duration of D has a point of indifference that is less equal D * 2

So if I need my money back in max 14 years, I can buy a 7 years duration ETF, and I'll have my money back in less than 14 years, or in 14 years in the worst case scenario.
dbr wrote: Sun Apr 17, 2022 9:39 amI think that people who have reason to be concerned that a bond investment not fall below some expectation at a point in time should buy single bonds with a certain date of maturity rather than bond funds
vineviz wrote: Sun Apr 17, 2022 9:51 amThe only ways to avoid the uncertainty are to match your bond investments to your future consumption, either through cash-flow matching or duration matching.
I agree that if someone needs is money back in 14 years he better buy a bond with maurity of 14 years and wait for its maturity. But for some type of bonds it's not so easy to buy a single bond, and buying an ETF would be an easier option.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by vineviz »

InvestInPasta wrote: Mon Apr 18, 2022 2:46 am
You don't have to hold the bond ETF for 14 years unless you end up in the worst case scenario.
Maybe a better way of saying it, is that a bond ETF with a duration of D has a point of indifference that is less equal D * 2
This is still not correct. This “ D * 2” number is just a made-up example by the author: it doesn’t represent any sort of actual limit.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by Admiral Fun »

This is all interesting but still theoretical.

In the historical record, what is the longest and the average time to recovery after a loss of X% in a Total Bond fund? X can be 5%, 10% or some other large loss.

Does anyone anyone know where to find this?
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by sycamore »

Admiral Fun wrote: Mon Apr 18, 2022 8:22 am This is all interesting but still theoretical.

In the historical record, what is the longest and the average time to recovery after a loss of X% in a Total Bond fund? X can be 5%, 10% or some other large loss.

Does anyone anyone know where to find this?
You can find some of the data using a portfoliovisualizer.com backtest of VBMFX (click on the Drawdowns tab). It shows the worst 10 drawdown and recovery information:

Image

The fund is still in its worst drawdown (both magnitude and length), so caution is warranted drawing conclusions based on prior drawdowns.

(As always, it would be worth reviewing portfoliovisualizer's methodology if you want to rely on them data for drawing conclusions.)
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by vineviz »

sycamore wrote: Mon Apr 18, 2022 8:48 am
Admiral Fun wrote: Mon Apr 18, 2022 8:22 am This is all interesting but still theoretical.

In the historical record, what is the longest and the average time to recovery after a loss of X% in a Total Bond fund? X can be 5%, 10% or some other large loss.

Does anyone anyone know where to find this?
You can find some of the data using a portfoliovisualizer.com backtest of VBMFX (click on the Drawdowns tab). It shows the worst 10 drawdown and recovery information:

The fund is still in its worst drawdown (both magnitude and length), so caution is warranted drawing conclusions based on prior drawdowns.

(As always, it would be worth reviewing portfoliovisualizer's methodology if you want to rely on them data for drawing conclusions.)
Because VBMFX is a relatively young fund, I looked at a similarly risky mix of indexes and found the longest period such a fund was underwater was about 25 months.

Two separate drawdowns in 1979-1981 were each worse than this one (so far) and in both cases full recovery only took 3 months from the bottom.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by dbr »

In my opinion attempts to explain what duration means by citing a theoretical point of indifference have resulted in very poor advice to prospective bond holders, especially those who are concerned to "not lose money."

It would be much better to cite the definition "Duration is a measure of the sensitivity of the price of a bond or other debt instrument to a change in interest rates." https://www.investopedia.com/terms/d/duration.asp and understand that the issue is not when one would "get one's money back" but rather what is the term risk in the investment measured in standard deviation of return. At the same time that allows one to understand the role of the bond as an asset in a portfolio.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by InvestInPasta »

vineviz wrote: Mon Apr 18, 2022 6:00 am
InvestInPasta wrote: Mon Apr 18, 2022 2:46 am
You don't have to hold the bond ETF for 14 years unless you end up in the worst case scenario.
Maybe a better way of saying it, is that a bond ETF with a duration of D has a point of indifference that is less equal D * 2
This is still not correct. This “ D * 2” number is just a made-up example by the author: it doesn’t represent any sort of actual limit.
Are you sure? :mrgreen:

I have just found this article
To maintain their average duration, bond funds employ what’s known as a bond ladder. With a ladder, the proceeds of any bond that matures are reinvested in another bond with a sufficiently long maturity and duration so that the ladder’s average remains more or less unchanged.

Notice what this means for how a bond ladder responds when interest rates rise. Though the prices of previously-held bonds will decline, new bonds will constantly be added to the portfolio with higher yields. It turns out that over time, those higher yields make up for those price declines.

How long must you hold for this happy result to occur? One year less than twice the bond ladder’s average duration. That’s according to a formula derived by Martin Leibowitz and Anthony Bova, managing director and executive director at Morgan Stanley, respectively, and Stanley Kogelman, a principal at New York-based investment-advisory firm Advanced Portfolio Management. They presented it in an article published in 2015 in the Financial Analysts Journal, entitled “Bond Ladders and Rolling Yield Convergence.”
- https://www.marketwatch.com/amp/story/y ... 1634742389
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by vineviz »

InvestInPasta wrote: Mon Apr 18, 2022 1:37 pm
vineviz wrote: Mon Apr 18, 2022 6:00 am
InvestInPasta wrote: Mon Apr 18, 2022 2:46 am
You don't have to hold the bond ETF for 14 years unless you end up in the worst case scenario.
Maybe a better way of saying it, is that a bond ETF with a duration of D has a point of indifference that is less equal D * 2
This is still not correct. This “ D * 2” number is just a made-up example by the author: it doesn’t represent any sort of actual limit.
Are you sure? :mrgreen:

I have just found this article
I’m sure. That article makes the same basic assumptions as the blog post cited earlier.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by InvestInPasta »

vineviz wrote: Mon Apr 18, 2022 1:53 pmI’m sure. That article makes the same basic assumptions as the blog post cited earlier.
Ok, to prove the article is wrong could you show me one interest rates path that does not satisfy the rule of thumb? In other words let's say I put $100 in an ETF with a duration of 5 years, and let's say an YTM of 1%. What's an interest rates path that does not let me have my money back in less than 10 years?
Thanks
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by Admiral Fun »

vineviz wrote: Mon Apr 18, 2022 9:33 am Because VBMFX is a relatively young fund, I looked at a similarly risky mix of indexes and found the longest period such a fund was underwater was about 25 months.

Two separate drawdowns in 1979-1981 were each worse than this one (so far) and in both cases full recovery only took 3 months from the bottom.
Very interesting. And in these cases, I wonder if declines in interest rates drove the recovery or something else.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by dbr »

InvestInPasta wrote: Mon Apr 18, 2022 2:29 pm
vineviz wrote: Mon Apr 18, 2022 1:53 pmI’m sure. That article makes the same basic assumptions as the blog post cited earlier.
Ok, to prove the article is wrong could you show me one interest rates path that does not satisfy the rule of thumb? In other words let's say I put $100 in an ETF with a duration of 5 years, and let's say an YTM of 1%. What's an interest rates path that does not let me have my money back in less than 10 years?
Thanks
Interest rate fixed at 1% for 9 years and then rising suddenly to 5% for the last year would do it. That doesn't mean such a path is likely.

I think that paper discusses some outcomes where the interest rate does not rise on a linear path but rather has some noise. In that case the time to indifference also becomes uncertain. The third example posted by Kevin shows how a noisy increase in interest rate might turn out. In that case the time to indifference actually went down, but then he threw in an interest rate decrease at just the right time. Note his interest rate curve is a historic example. In real life it is highly improbable that ten years would not be insurance enough for a five year duration fund but that is not because there is a mathematical demonstration of a 2D-1 result for any interest rate path but only for a linear increase.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by Kevin M »

dbr wrote: Mon Apr 18, 2022 4:24 pm
InvestInPasta wrote: Mon Apr 18, 2022 2:29 pm
vineviz wrote: Mon Apr 18, 2022 1:53 pmI’m sure. That article makes the same basic assumptions as the blog post cited earlier.
Ok, to prove the article is wrong could you show me one interest rates path that does not satisfy the rule of thumb? In other words let's say I put $100 in an ETF with a duration of 5 years, and let's say an YTM of 1%. What's an interest rates path that does not let me have my money back in less than 10 years?
Thanks
Interest rate fixed at 1% for 9 years and then rising suddenly to 5% for the last year would do it. That doesn't mean such a path is likely.
That would do it:

Image

In which case the POI is about 14 years.

Kevin
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by Charles Joseph »

My point of indifference is forever.

I view my bond fund holdings as I would owning an apartment building. I just keep collecting the rent, month in, month out. I wouldn't sell the apartment building due to fluctuating real estate prices. I'd just keep enjoying the positive cash flow. That's the way I mentally approach my bonds.

Of course, to do that, you have to plan on never selling.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by Charles Joseph »

My point of indifference is forever.

I view my bond fund holdings as I would owning an apartment building. I just keep collecting the rent, month in, month out. I wouldn't sell the apartment building due to fluctuating real estate prices. I'd just keep enjoying the positive cash flow. That's the way I mentally approach my bonds.

Of course, to do that, you have to plan on never selling.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by exodusNH »

Samuel Glover wrote: Mon Apr 18, 2022 5:09 pm My point of indifference is forever.

I view my bond fund holdings as I would owning an apartment building. I just keep collecting the rent, month in, month out. I wouldn't sell the apartment building due to fluctuating real estate prices. I'd just keep enjoying the positive cash flow. That's the way I mentally approach my bonds.

Of course, to do that, you have to plan on never selling.
And have a large enough balance that the dividend is a meaningful amount of money. $1M at 2% is only $20k per year before tax. $1M is more money than most Americans will have managed to save for retirement.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by Kevin M »

The chart for historical data I posted above was for 1962 (end of year or EOY) to 1981 (EOY). I thought it would be interesting to look at the steep runup from 1976 (6.13%) to 1981 (13.97%), and a few years after:

Image

Here the POI comes sometime before the end of year 6, aided by the drop in yield at the end of year 6.

Note that even with rising yields, the rolling bond never lost value, but actually increased in value during the period of increasing yields.

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Re: Point of indifference for a bond Fund/ETF, real life example

Post by hudson »

InvestInPasta,

Great discussion!
What would you buy?
$100K in TLH?
$100K in individual treasuries with comparable stats to TLH as possible?
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by InvestInPasta »

dbr wrote: Mon Apr 18, 2022 4:24 pm
InvestInPasta wrote: Mon Apr 18, 2022 2:29 pm Ok, to prove the article is wrong could you show me one interest rates path that does not satisfy the rule of thumb? In other words let's say I put $100 in an ETF with a duration of 5 years, and let's say an YTM of 1%. What's an interest rates path that does not let me have my money back in less than 10 years?
Thanks
Interest rate fixed at 1% for 9 years and then rising suddenly to 5% for the last year would do it. That doesn't mean such a path is likely.
If you do not move the interet rates for 9 years you are only shifting the question 9 years ahead, because in all those 9 years I could sell my ETF and get always my money back plus interst.
Kevin M wrote: Mon Apr 18, 2022 4:59 pm
dbr wrote: Mon Apr 18, 2022 4:24 pm
InvestInPasta wrote: Mon Apr 18, 2022 2:29 pm Ok, to prove the article is wrong could you show me one interest rates path that does not satisfy the rule of thumb? In other words let's say I put $100 in an ETF with a duration of 5 years, and let's say an YTM of 1%. What's an interest rates path that does not let me have my money back in less than 10 years?
Thanks
Interest rate fixed at 1% for 9 years and then rising suddenly to 5% for the last year would do it. That doesn't mean such a path is likely.
That would do it:

Image

In which case the POI is about 14 years.

Kevin
As said that would not do it.
It only proves that if investor has put his money in the 5Y duration (D) ETF on year 9, and all of a sudden the interest rates rise to 5%, the investor will still have his money back (plus interest) 5-6 years later that is less that 10 years (D*2)

I rephrase the question

Rule of thumb: if you buy a bond ETF with duration of D and an YTM, you will always get your money back (plus YTM interst) in less than 2*D years.

To prove the rule is wrong could someone show me one interest rates path that does not satisfy the rule of thumb?
Assumption, the interest rate path must start at the first interest rate movement, in other words if the interest rate movement happens at time T, the investor has put its money into the ETF at time T-1.
Last edited by InvestInPasta on Tue Apr 19, 2022 8:21 am, edited 3 times in total.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by InvestInPasta »

hudson wrote: Mon Apr 18, 2022 8:30 pm InvestInPasta,

Great discussion!
What would you buy?
$100K in TLH?
$100K in individual treasuries with comparable stats to TLH as possible?
TLH is rolling the treasuries inside to keep a duration of about 15 years.
In the worst case scenario, that is interest rates go on raising forever:
  • if you bought TLH (duration 14.4 years) you will still have your money back (plus interest, today is 3.05% gross) in less than 30 years (2 times the duration, unless someone proves the rule of thumb is wrong)
  • If you bought individual treasuries with a duration of 15 years, and you roll them, it's the same of TLH above
  • If you bought individual treasuries with a duration of 15 years, and you do not roll them, you will have your money back in less than 15 years.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by hudson »

InvestInPasta wrote: Tue Apr 19, 2022 4:50 am
hudson wrote: Mon Apr 18, 2022 8:30 pm InvestInPasta,

Great discussion!
What would you buy?
$100K in TLH?
$100K in individual treasuries with comparable stats to TLH as possible?
TLH is rolling the treasuries inside to keep a duration of about 15 years.
In the worst case scenario, that is interest rates go on raising forever:
  • if you bought TLH (duration 14.4 years) you will still have your money back (plus interest, today is 3.05% gross) in less than 30 years (2 times the duration, unless someone proves the rule of thumb is wrong)
  • If you bought individual treasuries with a duration of 15 years, and you roll them, it's the same of TLH above
  • If you bought individual treasuries with a duration of 15 years, and you do not roll them, you will have your money back in less than 15 years.
Thanks InvesInPasta!
What would I buy given the choice of TLH and individual treasuries.
Maybe TLH but 15 years of expenses would cost $2,250. (0.15% expense ratio X $100K X 15 years = $2,250)
Maybe individual treasuries (10, 20, and 30 year individual treasuries?)

Bottom Line: I have limited experience, but I would take a shot at individual treasuries.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by InvestInPasta »

hudson wrote: Tue Apr 19, 2022 5:16 am Thanks InvesInPasta!
What would I buy given the choice of TLH and individual treasuries.
Maybe TLH but 15 years of expenses would cost $2,250. (0.15% expense ratio X $100K X 15 years = $2,250)
Maybe individual treasuries (10, 20, and 30 year individual treasuries?)
I was trying to explain to you that they are two different beasts.
The single treasuries do not roll by their own.

To replicate TLH you would have to build something like a bond ladder, see here
https://www.bogleheads.org/wiki/Laddering_bonds_or_CDs

TLH does all this for you for an annual fee.

Holding TLH could be more than 15 years of expenses, if you want to be sure you'll have your money back you might have to wait 2 times its 15 years duration, hence you might have to hold it for more than 15 years.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by vineviz »

InvestInPasta wrote: Tue Apr 19, 2022 4:29 am
Rule of thumb: if you buy a bond ETF with duration of D and an YTM, you will always get your money back (plus YTM interst) in less than 2*D years.

To prove the rule is wrong could someone show me one interest rates path that does not satisfy the rule of thumb?
The rule of thumb was constructed using a particular set of assumptions named above, particularly yield curve that shifts linearly over time. Yields growing exponentially would violate that assumption, possibly pushing the breakeven past 2D+1.

For instance, the following sequence of yields would push the breakeven for the hypothetical 5 year zero coupon bond fund above to year 13+ (or 2D+3).

Code: Select all

Year	EOY Yield
0	1.00%
1	1.36%
2	1.72%
3	2.16%
4	2.73%
5	3.44%
6	4.34%
7	5.47%
8	6.90%
9	8.70%
10	10.98%
11	13.84%
12	17.46%
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by dbr »

vineviz wrote: Tue Apr 19, 2022 8:39 am
The rule of thumb was constructed using a particular set of assumptions named above, particularly yield curve that shifts linearly over time. Yields growing exponentially would violate that assumption, possibly pushing the breakeven past 2D+1.

For instance, the following sequence of yields would push the breakeven for the hypothetical 5 year zero coupon bond fund above to year 13+ (or 2D+3).

Good choice. The exponential has the property of "looking the same" after translation in time but serves the purpose in this case that an increasing rate of interest rate increase will extend the point of indifference to longer than 2d-1, apparently. It probably follows that a decreasing rate of interest rate increase shifts the point of indifference to shorter than 2d-1. The extreme examples are a step function at the beginning or a step function at the end.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by hudson »

InvestInPasta wrote: Tue Apr 19, 2022 8:19 am
hudson wrote: Tue Apr 19, 2022 5:16 am Thanks InvesInPasta!
What would I buy given the choice of TLH and individual treasuries.
Maybe TLH but 15 years of expenses would cost $2,250. (0.15% expense ratio X $100K X 15 years = $2,250)
Maybe individual treasuries (10, 20, and 30 year individual treasuries?)
I was trying to explain to you that they are two different beasts.
The single treasuries do not roll by their own.

To replicate TLH you would have to build something like a bond ladder, see here
https://www.bogleheads.org/wiki/Laddering_bonds_or_CDs

TLH does all this for you for an annual fee.

Holding TLH could be more than 15 years of expenses, if you want to be sure you'll have your money back you might have to wait 2 times its 15 years duration, hence you might have to hold it for more than 15 years.
Many thanks InvestInPasta!

I would likely not try to duplicate TLH. I'd likely just buy and hold individual treasuries that fit my situation.
I speculate that individual treasuries are the optimal choice; funds and ETFs are pretty good, but they come in second place mostly because of the expenses.

I'll likely do a non-rolling ladder probably with TIPS.

I've seen several recent posters that are doing half TIPS and half regular treasuries. I could warm up to that.
I have 22 months to figure all of this out: then I'll decide.
I've started buying individual treasuries to learn the ropes.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by Kevin M »

InvestInPasta wrote: Tue Apr 19, 2022 4:29 am
dbr wrote: Mon Apr 18, 2022 4:24 pm
InvestInPasta wrote: Mon Apr 18, 2022 2:29 pm Ok, to prove the article is wrong could you show me one interest rates path that does not satisfy the rule of thumb? In other words let's say I put $100 in an ETF with a duration of 5 years, and let's say an YTM of 1%. What's an interest rates path that does not let me have my money back in less than 10 years?
Thanks
Interest rate fixed at 1% for 9 years and then rising suddenly to 5% for the last year would do it. That doesn't mean such a path is likely.
If you do not move the interet rates for 9 years you are only shifting the question 9 years ahead, because in all those 9 years I could sell my ETF and get always my money back plus interst.

<snip>

To prove the rule is wrong could someone show me one interest rates path that does not satisfy the rule of thumb?
Assumption, the interest rate path must start at the first interest rate movement, in other words if the interest rate movement happens at time T, the investor has put its money into the ETF at time T-1.
Ah, but you are changing the rules used for the 2D-1 as POI, which posits a linearly increasing yield starting at t = 0, and the POI clock also starts at t = 0. The POI clock does not reset in year 8 (for 5-year duration). We are simply following the same rules for the linear 2D-1 case with other yield paths, which is what you asked for.

For the linear 2D-1 case, there is no single "interest rate movement happens at time T"--the interest rate changes at time - t1, t2, t3, etc., and yet the POI occurs at t = 2D - 1 with the investment at t = 0.

Your limitation is required for POI = D, which is the case for a one-time shift in the yield. This is explicitly not the case for a continuous linear increase in yields, so we are looking at other examples where it also is not the case.

Kevin
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by secondopinion »

hudson wrote: Tue Apr 19, 2022 10:47 am I would likely not try to duplicate TLH. I'd likely just buy and hold individual treasuries that fit my situation.
I speculate that individual treasuries are the optimal choice; funds and ETFs are pretty good, but they come in second place mostly because of the expenses.
Because you are meeting the expenses essentially risk-free at the guaranteed market price a prior, there is no source of speculative risk because there is no way to out- or under-perform; because there is no speculative risk, you are not speculating. Because you hedged out risk of meeting the expense, there is no pure risk either.
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Re: Point of indifference for a bond Fund/ETF, real life example

Post by hudson »

secondopinion wrote: Tue Apr 19, 2022 2:27 pm
hudson wrote: Tue Apr 19, 2022 10:47 am I would likely not try to duplicate TLH. I'd likely just buy and hold individual treasuries that fit my situation.
I speculate that individual treasuries are the optimal choice; funds and ETFs are pretty good, but they come in second place mostly because of the expenses.
Because you are meeting the expenses essentially risk-free at the guaranteed market price a prior, there is no source of speculative risk because there is no way to out- or under-perform; because there is no speculative risk, you are not speculating. Because you hedged out risk of meeting the expense, there is no pure risk either.
Many thanks secondopinion!
I like the advantages of individual treasuries and CDs.
I hope to earn my "merit badge" in individual treasuries.
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