Generalizing the Allan Roth TIPS ladder results

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McQ
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Generalizing the Allan Roth TIPS ladder results

Post by McQ »

[If you haven’t been following that thread, it’s a rare case where multiple participants spend time complimenting the quality of the debate, rather than just continuing to debate. Check it out: viewtopic.php?t=388845&sid=c3896690e969 ... 9354165f18 and see how the discussion continues here: viewtopic.php?t=391371&sid=c3896690e969 ... 9354165f18]

As of the December 2nd close, TIPS yields are down substantially from when Allan set up the ladder. You could not get a 4.31% withdrawal rate for a 30-year TIPS ladder set up today.

What withdrawal rate could you get? Here is a simple rubric for approximating the withdrawal rate, now or for any level of TIPS yields in the future.

1. Calculate the average real yield across the curve. Take only one TIPS per year if there are multiple ones, and double or triple the weight placed on the yields on either side of any gap (2032 and 2040 issues, currently).
2. That average came to about 1.75% for Allan at the time, maybe 1.25% to 1.40% currently (based on TIPS prices at the close on December 2nd).
3. Divide the yield by 25 bp

Retain the results of that division.

4. Next, if the TIPS real yield across the curve is exactly zero, then we know that the 30-year withdrawal rate must be about 3.33% (1 of 30 TIPS bonds per year).
5. Take the result of step 3, multiply by 0.14, and add that to 3.33% to estimate the SWR at the current TIPS yield if this differs from zero (see this thread for the math behind the 0.14 delta: viewtopic.php?t=388277 )

Numerical examples

Allan got 4.31% because the average yield across the curve at the time was about 1.75%, seven increments of 25 bp above zero; 7 * .14 = .98, 3.33% plus 98 bp = 4.31%.

If today’s average yield is 1.25%, then a withdrawal rate of 4.03% should be obtainable (5 * .14 = .70, .70 + 3.33 = 4.03).

If TIPS yields are negative, averaging about minus 50 bp across the curve, as earlier this year, then 2 * minus .14 = minus .28, and a withdrawal rate of 3.33% - .28 = 3.05% can be achieved from a TIPS ladder.

Still way more than some of the scary SWR numbers floating around out there.

Caveat: this is back of the envelope stuff. Actual SWR could be 5 or 10 bp more or less, once you went to a broker website as Allan did and began to buy TIPS in some amount at some ask yield, which might have changed in the seconds since you started to type the order; likewise, if the yield curve doesn’t have the normal shape, making the arithmetic average yield less informative.

Disclaimer: if I have made an error here I expect #Cruncher, Kevin M or both to catch it.
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Looking4Answers
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Re: Generalizing the Allan Roth TIPS ladder results

Post by Looking4Answers »

I hope this does not get merged back into the previous thread. I was following the other thread with interest, but it diverged into the subject of annuities to the point that it was hard to extract and follow the basic info on the TIPS ladder.
dbr
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Re: Generalizing the Allan Roth TIPS ladder results

Post by dbr »

Yes, it is very important for a person setting up a TIPS ladder to look at what yield he is buying today. The range of effective payout rate is significantly affected by the yields you buy. From 3.0% to 3.3% to 4.0% to 4.3% is not trivial.
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Re: Generalizing the Allan Roth TIPS ladder results

Post by #Cruncher »

McQ wrote: Sun Dec 04, 2022 10:07 pmHere is a simple rubric for approximating the withdrawal rate, now or for any level of TIPS yields in the future.
  1. Calculate the average real yield across the curve. ...
  2. That average came to about 1.75% for Allan at the time, maybe 1.25% to 1.40% currently (based on TIPS prices at the close on December 2nd).
  3. Divide the yield by 25 bp ... Retain the results of that division.
  4. Next, if the TIPS real yield across the curve is exactly zero, then we know that the 30-year withdrawal rate must be about 3.33% (1 of 30 TIPS bonds per year).
  5. Take the result of step 3, multiply by 0.14, and add that to 3.33% to estimate the SWR at the current TIPS yield if this differs from zero (see this thread for the math behind the 0.14 delta: viewtopic.php?t=388277 )
Doesn't seem "simple" to me. I was curious how and why someone came up with this "Rube Goldberg" solution. But I wasn't curious enough to wade through over 60 posts in the thread you linked -- not when there's a much simpler calculation: use either the annuity payment formula shown here or the Excel PMT function with a present value (PV) of $1. Here are the results for four yields referred to in your post: -0.5%, 0%, +1.25%, and +1.75%:

Code: Select all

Row   Col A     Col B
  2   Years        30
  
  3   Yield  Withdraw      Using Annuity Payment Formula        Using PMT function
     ------  --------   -----------------------------------   ----------------------
  4  -0.50%     3.08%  =IF(A4=0, 1/B$2, A4/(1-(1+A4)^-B$2))  =PMT(A4, B$2, -1, 0, 0)
  5   0.00%     3.33%  =IF(A5=0, 1/B$2, A5/(1-(1+A5)^-B$2))  =PMT(A5, B$2, -1, 0, 0)
  6   1.25%     4.02%  =IF(A6=0, 1/B$2, A6/(1-(1+A6)^-B$2))  =PMT(A6, B$2, -1, 0, 0)
  7   1.75%     4.31%  =IF(A7=0, 1/B$2, A7/(1-(1+A7)^-B$2))  =PMT(A7, B$2, -1, 0, 0)
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McQ
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Re: Generalizing the Allan Roth TIPS ladder results

Post by McQ »

#Cruncher wrote: Mon Dec 05, 2022 1:08 pm
McQ wrote: Sun Dec 04, 2022 10:07 pmHere is a simple rubric for approximating the withdrawal rate, now or for any level of TIPS yields in the future.
  1. Calculate the average real yield across the curve. ...
  2. That average came to about 1.75% for Allan at the time, maybe 1.25% to 1.40% currently (based on TIPS prices at the close on December 2nd).
  3. Divide the yield by 25 bp ... Retain the results of that division.
  4. Next, if the TIPS real yield across the curve is exactly zero, then we know that the 30-year withdrawal rate must be about 3.33% (1 of 30 TIPS bonds per year).
  5. Take the result of step 3, multiply by 0.14, and add that to 3.33% to estimate the SWR at the current TIPS yield if this differs from zero (see this thread for the math behind the 0.14 delta: viewtopic.php?t=388277 )
Doesn't seem "simple" to me. I was curious how and why someone came up with this "Rube Goldberg" solution. But I wasn't curious enough to wade through over 60 posts in the thread you linked -- not when there's a much simpler calculation: use either the annuity payment formula shown here or the Excel PMT function with a present value (PV) of $1. Here are the results for four yields referred to in your post: -0.5%, 0%, +1.25%, and +1.75%:

Code: Select all

Row   Col A     Col B
  2   Years        30
  
  3   Yield  Withdraw      Using Annuity Payment Formula        Using PMT function
     ------  --------   -----------------------------------   ----------------------
  4  -0.50%     3.08%  =IF(A4=0, 1/B$2, A4/(1-(1+A4)^-B$2))  =PMT(A4, B$2, -1, 0, 0)
  5   0.00%     3.33%  =IF(A5=0, 1/B$2, A5/(1-(1+A5)^-B$2))  =PMT(A5, B$2, -1, 0, 0)
  6   1.25%     4.02%  =IF(A6=0, 1/B$2, A6/(1-(1+A6)^-B$2))  =PMT(A6, B$2, -1, 0, 0)
  7   1.75%     4.31%  =IF(A7=0, 1/B$2, A7/(1-(1+A7)^-B$2))  =PMT(A7, B$2, -1, 0, 0)
I take your point about the Rube Goldberg construction, #Cruncher. It is possible that I have been spending too much time reading IRS instructions, which blindly lead the reader through such computations.

I will have to let the forum decide whether the Excel code you displayed is more simple than my shorthand: “for each 25 bp in average TIPS yield above 0%, add 14 basis points to the base SWR of 3.33%.”

Much more important to me personally: thank the Lord, my results checked out in your more rigorous setup!

For those who did get more value from the #Cruncher setup, let me expand it a bit.

Q: What is the present value of a 30-year stream of $1 payments?
A: Tell me the discount rate and I will answer your question.
Q: Okay, let the discount rate be 0%
A: The present value is $30. In Excel, =PV (0, 30, 1)
Q: So each year’s withdrawal represents a 3.33% rate?
A: Ah, I see where you are going. Yes, the annual withdrawal rate is 1/PV
Q: Let’s check. What is the present value of thirty years of $1 per year discounted now at 0.25%?
A: Okay, I’ll play: it is $28.87.
Q: Corresponding to a withdrawal rate of …
A: About 3.464%, just under 14 basis points more than what you could sustain from TIPS with a 0% yield.
Q: One last check: when Allan bought TIPS with an average yield of 1.75%, he had reason to expect what SWR?
A: PV = $23.19, so his SWR would be … 4.313%.

Concluding note: with TIPS, you can get a stream of real dollars, so that thirty payments of exactly one dollar can be plugged directly into the PV formula. With a nominal bond ladder, the real value of the future stream is unknown.
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2pedals
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Re: Generalizing the Allan Roth TIPS ladder results

Post by 2pedals »

Why when creating a TIPS ladder is it referred to as a SWR? I think a SWR is typically used for when a portfolio someone has an asset allocation, say 60/40 stocks bonds. It's okay to compare it to a SWR though. Someone using a TIPS ladder is already spending down 100% after the ladder period is complete. Not likely to happen when someone is using a SWR as benchmark for spending.
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Re: Generalizing the Allan Roth TIPS ladder results

Post by dbr »

2pedals wrote: Mon Dec 05, 2022 4:03 pm Why when creating a TIPS ladder is it referred to as a SWR? I think a SWR is typically used for when a portfolio someone has an asset allocation, say 60/40 stocks bonds. It's okay to compare it to a SWR though. Someone using a TIPS ladder is already spending down 100% after the ladder period is complete. Not likely to happen when someone is using a SWR as benchmark for spending.
This should not be taken as a safe withdrawal rate. In fact it is conversion of a set of assets into an exactly known income stream that is as safe as the security of owning any Treasury bonds. The more common term is liability matching portfolio. While technically a stash of TIPS is a portfolio the reason for it existing, the use of it, and the properties it has are those of an income stream and it has nothing to do with being an investment portfolio except that if necessary a person could disrupt the investment and take the money prematurely. It is also true that the remaining assets would be inherited by heirs, which does not happen with Social Security payments or pensions or with an SPIA unless the SPIA is bought with riders that provide such benefits.

The comparison to an SWR is to compare the prospects of two completely different ways of spending one's assets. A significant difference is that the TIPS ladder is explicitly designed to be exhausted at the end while a person spending at the rate of an SWR from a portfolio will have a 95% chance or more of not running out at the end of 30, or whatever, years and also has a good chance of dying with a lot of money even after 30 years.

The two approaches are so different in so many ways it is difficult to keep a straight head regarding what is actually being accomplished. That is one reason the two should not be viewed as an either/or but rather possibly as a both/and, the same as any other combination of portfolios, Social Security, pensions, annuities, and any other assets including even use of a paid off house as a resource under some circumnstances.
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Re: Generalizing the Allan Roth TIPS ladder results

Post by vineviz »

dbr wrote: Mon Dec 05, 2022 4:19 pm
2pedals wrote: Mon Dec 05, 2022 4:03 pm Why when creating a TIPS ladder is it referred to as a SWR? I think a SWR is typically used for when a portfolio someone has an asset allocation, say 60/40 stocks bonds. It's okay to compare it to a SWR though. Someone using a TIPS ladder is already spending down 100% after the ladder period is complete. Not likely to happen when someone is using a SWR as benchmark for spending.
This should not be taken as a safe withdrawal rate. In fact it is conversion of a set of assets into an exactly known income stream that is as safe as the security of owning any Treasury bonds. The more common term is liability matching portfolio.
Agreed.

For better or worse, a SWR analysis presupposes certain conditions which include a fixed asset allocation with periodic rebalancing.
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2pedals
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Re: Generalizing the Allan Roth TIPS ladder results

Post by 2pedals »

^ +1
dbr, thanks for the summary. I think many folks like the "belt and suspenders" approach. If your suspenders fail you have a belt also.
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Re: Generalizing the Allan Roth TIPS ladder results

Post by squirrel1963 »

vineviz wrote: Mon Dec 05, 2022 4:49 pm
dbr wrote: Mon Dec 05, 2022 4:19 pm
2pedals wrote: Mon Dec 05, 2022 4:03 pm Why when creating a TIPS ladder is it referred to as a SWR? I think a SWR is typically used for when a portfolio someone has an asset allocation, say 60/40 stocks bonds. It's okay to compare it to a SWR though. Someone using a TIPS ladder is already spending down 100% after the ladder period is complete. Not likely to happen when someone is using a SWR as benchmark for spending.
This should not be taken as a safe withdrawal rate. In fact it is conversion of a set of assets into an exactly known income stream that is as safe as the security of owning any Treasury bonds. The more common term is liability matching portfolio.
Agreed.

For better or worse, a SWR analysis presupposes certain conditions which include a fixed asset allocation with periodic rebalancing.
Agree 100% with both of you.
LMP | Liability Matching Portfolio | safe portfolio: TIPS ladder + I-bonds + Treasuries | risky portfolio: US stocks / US REIT / International stocks
GAAP
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Re: Generalizing the Allan Roth TIPS ladder results

Post by GAAP »

McQ wrote: Mon Dec 05, 2022 3:34 pm Q: So each year’s withdrawal represents a 3.33% rate?
A: Ah, I see where you are going. Yes, the annual withdrawal rate is 1/PV
Minor note: You can get the rate directly using the PMT function like #Cruncher did by formatting the result as percent instead of currency)
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