## How risky is interest rate risk in TIPS ladders longer than 30 years?

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StillGoing
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### How risky is interest rate risk in TIPS ladders longer than 30 years?

The upper limit of a non-rolling TIPS ladder is usually considered to be 30 years since that is longest maturity of TIPS currently available. If an inflation protected income floor of longer than 30 years is required (e.g., for retirees aged 65, there is a non-negligible chance of living to longer than 95, so a 35 year ladder might be more appropriate).

Consider an example, where the retirees want to construct a ladder to 35 years that will provide inflation adjusted income of 4% of the initial portfolio, the TIPS yield is 2.135% which, not entirely coincidentally, will exactly meet that condition (as entering rate(35,4,-100,0,1) in a spreadsheet package will show). A flat yield curve has been assumed and taxes and fees ignored.

However, at the start of retirement there are no TIPS available to cover the 31st to 35th 'withdrawals', so the retirees construct a ladder to 30 years with just under 90% of the portfolio (the payout rate on a 30 year ladder with 2.135% yield is pmt(2.135%,30,-100,0,1)=4.45% and therefore the 'premium' is required income 4.0/4.45=89.82%). The remaining part of the portfolio (10.18% of the initial portfolio) is invested in a 30 years TIPS, which when it matures 30 years later has grown, in real terms, to 19.18% (i.e., 10.18*power(1.02135,30) ) of the initial portfolio value. If the TIPS yield in 30 years time is equal to or exceeds 2.135%, then the retirees can construct the final 5 year portion of their ladder since the number of periods supported will be lat least 5 years (e.g., nper(2.135%,4,-19.18,0,1) ).

The question then becomes how many periods (i.e. years) can the maturing 30 year TIPS support if the reinvestment yield is less than 2.135%? In the following table, the number of periods (NPER) supported is given as a function of (reinvestment yield, Y2)-(original yield, Y1) where Y1 is 2.135%.

Code: Select all

``````Y2-Y1	NPER
0	5.00
-1	4.90
-2	4.81
-5	4.55
-10	4.19
-13	4.00
-20	3.63
``````
For reinvestment rates higher than -10.8%, i.e. Y2-Y1=-13, income of 4% is supplied for withdrawals 31-34, and the 35th withdrawal covers part of the required income (this is smaller at lower yields). For reinvestment yields lower than -10.8%, income of 4% is only supplied for withdrawals 31-33, partially for the 34th withdrawal, and not at all for the 35th withdrawal (which is zero).

In other words, in this example, interest rate risk is minimal unless TIPS yields fall to well below those seen historically (and even lower than the equivalent UK inflation linked gilts were a few years ago). It is relatively easy to calculate what happens at other yields or required income rates (I note that the '-13' is a fairly constant threshold though). However, for a longer ladder (e.g., 40 years covering the retirees to 105yo), the interest rate risk is higher (e.g., with Y2-Y1=-5, only 8 rungs out of 10 are filled).

However, there are other risks with this approach (none of which are really quantifiable)
1) The retirees will need to construct the follow up TIPS ladder when they are 95 (which, they may or may not be able to). Doing this earlier, introduces more interest rate risk (of course, doing the reinvestment over a number of years is an alternative to doing it all in one go).
2) TIPS of the relevant maturities may not be available after 30 years.
3) TIPS may not be available at all.

cheers
StillGoing
RyeBourbon
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

You don't have to hold those extra TIPS to maturity. You can sell them and buy the appropriate rung TIPS as soon as they become available and get the YTM at that time.
Retired June 2023. LMP (TIPS Ladder/SS Bridge) 25%/Risk Portfolio 75%, AA = 60/30/10
dbr
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

The not often recognized huge risk in a TIPS ladder is what the available yield is at the time one is ready and able to invest in the ladder. In the last few years that has flipped from -2% real to +2% real, probably the biggest single change in bond investing over this recent time. A change of 4% in real yield is tremendous. It certainly dwarfs the I bond feeding frenzy for one thing.
Stormbringer
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

If you get to the end of a 30-year TIPS ladder, you have a big worry: longevity. If you are 85 when the ladder runs out, extending it by 5 years isn't sufficient if you live to be 97.

What I would do is use the lump sum from year 30 to purchase a simple income annuity to provide longevity protection. The mortality credits from an annuity purchased at that age will be significant, and the impact of inflation will be less because of a shorter time horizon.
“The greatest shortcoming of the human race is our inability to understand the exponential function.” - Albert Allen Bartlett
dbr
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

Stormbringer wrote: Wed Jun 26, 2024 7:14 am If you get to the end of a 30-year TIPS ladder, you have a big worry: longevity. If you are 85 when the ladder runs out, extending it by 5 years isn't sufficient if you live to be 97.

What I would do is use the lump sum from year 30 to purchase a simple income annuity to provide longevity protection. The mortality credits from an annuity purchased at that age will be significant, and the impact of inflation will be less because of a shorter time horizon.
I am not sure what is the upper age at which one can buy an annuity. I think one sometimes hears that option goes away at age 85. Maybe someone knows for sure.
ResearchMed
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

dbr wrote: Wed Jun 26, 2024 7:17 am
Stormbringer wrote: Wed Jun 26, 2024 7:14 am If you get to the end of a 30-year TIPS ladder, you have a big worry: longevity. If you are 85 when the ladder runs out, extending it by 5 years isn't sufficient if you live to be 97.

What I would do is use the lump sum from year 30 to purchase a simple income annuity to provide longevity protection. The mortality credits from an annuity purchased at that age will be significant, and the impact of inflation will be less because of a shorter time horizon.
I am not sure what is the upper age at which one can buy an annuity. I think one sometimes hears that option goes away at age 85. Maybe someone knows for sure.

As of very recently, TIAA allows life annuitization up to age 90.
I sort of guessed that at least some others would be similar.

RM
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StillGoing
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

RyeBourbon wrote: Wed Jun 26, 2024 6:37 am You don't have to hold those extra TIPS to maturity. You can sell them and buy the appropriate rung TIPS as soon as they become available and get the YTM at that time.
Of course, but the effect is potentially much larger. For example, if the yield started at 2.135% when building the initial 30 year ladder, let's say that the yield drops by 1 percentage point and stays there for the next 5 years (since we need to add 5 years to get to our desired 35 year ladder). In order to provide the 4% income 30 years later will cost 2.85% of the portfolio for the first extra rung (i.e., 4/power(1+1.0135,30) ), 2.82% of the portfolio the year after (i.e., 4/power(1.0135,31) ) and so on. Only three complete rungs can be added and one partial. However, If the yield drops by 2 percentage points, then only two complete rungs can be completed and one partial. Smaller changes in yield have much larger consequences for the later rungs.

cheers
StillGoing
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StillGoing
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

ResearchMed wrote: Wed Jun 26, 2024 7:46 am
dbr wrote: Wed Jun 26, 2024 7:17 am
Stormbringer wrote: Wed Jun 26, 2024 7:14 am If you get to the end of a 30-year TIPS ladder, you have a big worry: longevity. If you are 85 when the ladder runs out, extending it by 5 years isn't sufficient if you live to be 97.

What I would do is use the lump sum from year 30 to purchase a simple income annuity to provide longevity protection. The mortality credits from an annuity purchased at that age will be significant, and the impact of inflation will be less because of a shorter time horizon.
I am not sure what is the upper age at which one can buy an annuity. I think one sometimes hears that option goes away at age 85. Maybe someone knows for sure.

As of very recently, TIAA allows life annuitization up to age 90.
I sort of guessed that at least some others would be similar.

RM
Yes, the upper age is generally seems to be 90 but there appear to be fewer companies offering annuities at that age.

I recently modelled two approaches to purchasing an annuity in combination with a TIPS ladder in viewtopic.php?t=433101 in order to assess how well longevity protection would actually work.

a) Purchase of a deferred income annuity at the beginning of retirement to start at the end of the TIPS ladder
b) Purchase of an SPIA after a delay, corresponding to the length of the TIPS ladder.

While a a detailed description of the method and some example results can be found in that thread, for those not wanting to read further, the modelling found that for an initial TIPS yield of 2%, income after 35 years using the delayed SPIA approach met the 4% requirement provided that annualised inflation over the 35 year period was less than about 7% (historically, the highest inflation over 30-40 year rolling periods for the US was about 5%) and that the duration of TIPS used to purchase the annuity was well matched with that of the annuity.

cheers
StillGoing
RyeBourbon
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

StillGoing wrote: Wed Jun 26, 2024 11:12 am
RyeBourbon wrote: Wed Jun 26, 2024 6:37 am You don't have to hold those extra TIPS to maturity. You can sell them and buy the appropriate rung TIPS as soon as they become available and get the YTM at that time.
Of course, but the effect is potentially much larger. For example, if the yield started at 2.135% when building the initial 30 year ladder, let's say that the yield drops by 1 percentage point and stays there for the next 5 years (since we need to add 5 years to get to our desired 35 year ladder). In order to provide the 4% income 30 years later will cost 2.85% of the portfolio for the first extra rung (i.e., 4/power(1+1.0135,30) ), 2.82% of the portfolio the year after (i.e., 4/power(1.0135,31) ) and so on. Only three complete rungs can be added and one partial. However, If the yield drops by 2 percentage points, then only two complete rungs can be completed and one partial. Smaller changes in yield have much larger consequences for the later rungs.

cheers
StillGoing
I'm not really following your math here.

My point is after 1 year, the next rung of the ladder (year 31) will be available. You sell enough of the year 30 TIPS to buy the year 31 rung. The following year, you buy the year 32 rung. Can you model that?

I'm not sure how yields are going to affect it, because if yields fall, the value of your year 30 TIPS will increase, but you also need to buy more TIPS for your year 31 rung. I kinda feel it's going to cancel out. Whereas if you wait until year 30, you don't know what yields will be.
Retired June 2023. LMP (TIPS Ladder/SS Bridge) 25%/Risk Portfolio 75%, AA = 60/30/10
JackoC
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

This is a useful discussion IMO in terms of being aware of the 'break even math' of various situations. 30 yr TIPS to cover 40 yr out liability, roll out after 30 yrs or after TIPS to that original 40 yr point get issued, what inflation rate kills TIPS+ later SPIA, etc. But it leaves out what would be to me a now non-negligible concern: US federal credit risk in 30 yrs. I would (I do) now limit my exposure to the 'credit riskless' assumption even at ~20 yrs. I'm willing to take more reinvestment risk in return, no free lunch. Moreover I well realize a US federal debt crisis would be ugly for almost every other fundamental asset class too (by 'fundamental' I'm excluding eg. rolling below money puts on the S&P, that's a different discussion). And the ones for which it *probably* wouldn't be ugly, eg. gold, have questionable past risk/return relationship when things muddle along, which they usually do, which I'm not predicting they won't for the next 30 yrs. I don't know.
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

RyeBourbon wrote: Wed Jun 26, 2024 11:35 am
StillGoing wrote: Wed Jun 26, 2024 11:12 am
RyeBourbon wrote: Wed Jun 26, 2024 6:37 am You don't have to hold those extra TIPS to maturity. You can sell them and buy the appropriate rung TIPS as soon as they become available and get the YTM at that time.
Of course, but the effect is potentially much larger. For example, if the yield started at 2.135% when building the initial 30 year ladder, let's say that the yield drops by 1 percentage point and stays there for the next 5 years (since we need to add 5 years to get to our desired 35 year ladder). In order to provide the 4% income 30 years later will cost 2.85% of the portfolio for the first extra rung (i.e., 4/power(1+1.0135,30) ), 2.82% of the portfolio the year after (i.e., 4/power(1.0135,31) ) and so on. Only three complete rungs can be added and one partial. However, If the yield drops by 2 percentage points, then only two complete rungs can be completed and one partial. Smaller changes in yield have much larger consequences for the later rungs.

cheers
StillGoing
I'm not really following your math here.

My point is after 1 year, the next rung of the ladder (year 31) will be available. You sell enough of the year 30 TIPS to buy the year 31 rung. The following year, you buy the year 32 rung. Can you model that?

I'm not sure how yields are going to affect it, because if yields fall, the value of your year 30 TIPS will increase, but you also need to buy more TIPS for your year 31 rung. I kinda feel it's going to cancel out. Whereas if you wait until year 30, you don't know what yields will be.
If the goal was to minimize interest rate risk, you could roll the whole thing (now the 29 year TIPS) into the new 30 year TIPS after the first year. Then each subsequent year, leave enough for one rung and roll the rest to the new 30 year and so on. This will incur higher transactions costs, but I believe will minimize interest risk.
rockstar
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

For 30 years out, I’d rather buy I Bonds. If I need to redeem early I can without interest rate risk. And I’m good for 30 years. Even with a \$10k yearly buy limit per person, you can build up a years of expenses.
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

Stormbringer wrote: Wed Jun 26, 2024 7:14 am If you get to the end of a 30-year TIPS ladder, you have a big worry: longevity. If you are 85 when the ladder runs out, extending it by 5 years isn't sufficient if you live to be 97.

What I would do is use the lump sum from year 30 to purchase a simple income annuity to provide longevity protection. The mortality credits from an annuity purchased at that age will be significant, and the impact of inflation will be less because of a shorter time horizon.
In my original example I had in mind retirees around 65yo, so a 30 year ladder would take them to 95yo, while a 35 year one would take them to 100 (there is still a non-negligible chance of them living past that age). The same method can be used to extend the ladder by 10 years to 40 years total, but a) (obviously) the payout rate is lower and b) the effect of changes in yield when reinvesting the maturing TIPS is much larger. The example I gave for a 40 year ladder was a decrease in yield of 5 percentage points (large enough) would reduce the number of fully funded extra rungs from 10 to 8 (in other words, for our 65 year couple, the ladder would run out at 103 instead of 105.

Given much earlier retirement (e.g., at 50), where a 50 year ladder might reasonably be required, then assuming a target income of 3.2% (and TIPS yield of 2.13%), a reduction in yield of 1 percentage point would see the purchase of 18 additional rungs (i.e., a 48 year ladder in total), while a drop of 2 percentage points would see an extra 16 complete rungs (46 year ladder), 3 percentage points 15 complete rungs, and so on. Again, the sensitivity to yield is much greater than for a shorter ladder.

cheers
StillGoing

ps As an aside, in the UK the longest dated inflation linked gilt (the equivalent of TIPS) matures in 2073!
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

RyeBourbon wrote: Wed Jun 26, 2024 11:35 am
StillGoing wrote: Wed Jun 26, 2024 11:12 am
RyeBourbon wrote: Wed Jun 26, 2024 6:37 am You don't have to hold those extra TIPS to maturity. You can sell them and buy the appropriate rung TIPS as soon as they become available and get the YTM at that time.
Of course, but the effect is potentially much larger. For example, if the yield started at 2.135% when building the initial 30 year ladder, let's say that the yield drops by 1 percentage point and stays there for the next 5 years (since we need to add 5 years to get to our desired 35 year ladder). In order to provide the 4% income 30 years later will cost 2.85% of the portfolio for the first extra rung (i.e., 4/power(1+1.0135,30) ), 2.82% of the portfolio the year after (i.e., 4/power(1.0135,31) ) and so on. Only three complete rungs can be added and one partial. However, If the yield drops by 2 percentage points, then only two complete rungs can be completed and one partial. Smaller changes in yield have much larger consequences for the later rungs.

cheers
StillGoing
I'm not really following your math here.

My point is after 1 year, the next rung of the ladder (year 31) will be available. You sell enough of the year 30 TIPS to buy the year 31 rung. The following year, you buy the year 32 rung. Can you model that?

I'm not sure how yields are going to affect it, because if yields fall, the value of your year 30 TIPS will increase, but you also need to buy more TIPS for your year 31 rung. I kinda feel it's going to cancel out. Whereas if you wait until year 30, you don't know what yields will be.
I think I misunderstood your approach - I assumed the 'premium' for the extra rungs would be placed in short term TIPS (1 to 5 years) while waiting to be used to purchase a new 30 year TIPS. What you are proposing is that you purchase a 30 year TIPS and sell an amount each year to construct the next rung. Assuming any change in yield is exactly the same at all maturities, my first thought is that, in the first year the price change of the 30 year TIPS to be purchased will almost match that of the 29 year TIPS to be sold, but I would need to model it properly.

The outcome my modelling is that if you do wait to year 30, any changes in yields that can reasonably be expected have a relatively small effect on the ladder that can then be constructed.

cheers
StillGoing
Last edited by StillGoing on Wed Jun 26, 2024 12:06 pm, edited 1 time in total.
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

JackoC wrote: Wed Jun 26, 2024 11:40 am This is a useful discussion IMO in terms of being aware of the 'break even math' of various situations. 30 yr TIPS to cover 40 yr out liability, roll out after 30 yrs or after TIPS to that original 40 yr point get issued, what inflation rate kills TIPS+ later SPIA, etc. But it leaves out what would be to me a now non-negligible concern: US federal credit risk in 30 yrs. I would (I do) now limit my exposure to the 'credit riskless' assumption even at ~20 yrs. I'm willing to take more reinvestment risk in return, no free lunch. Moreover I well realize a US federal debt crisis would be ugly for almost every other fundamental asset class too (by 'fundamental' I'm excluding eg. rolling below money puts on the S&P, that's a different discussion). And the ones for which it *probably* wouldn't be ugly, eg. gold, have questionable past risk/return relationship when things muddle along, which they usually do, which I'm not predicting they won't for the next 30 yrs. I don't know.
I think this is an area that is probably not fully discussable here, but it is a risk. However, recent Canadian experience shows that new issues of inflation linked bonds (Real Return Bonds) can be stopped.

cheers
StillGoing
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

GoWithTheCashFlow wrote: Wed Jun 26, 2024 11:42 am
RyeBourbon wrote: Wed Jun 26, 2024 11:35 am
StillGoing wrote: Wed Jun 26, 2024 11:12 am
RyeBourbon wrote: Wed Jun 26, 2024 6:37 am You don't have to hold those extra TIPS to maturity. You can sell them and buy the appropriate rung TIPS as soon as they become available and get the YTM at that time.
Of course, but the effect is potentially much larger. For example, if the yield started at 2.135% when building the initial 30 year ladder, let's say that the yield drops by 1 percentage point and stays there for the next 5 years (since we need to add 5 years to get to our desired 35 year ladder). In order to provide the 4% income 30 years later will cost 2.85% of the portfolio for the first extra rung (i.e., 4/power(1+1.0135,30) ), 2.82% of the portfolio the year after (i.e., 4/power(1.0135,31) ) and so on. Only three complete rungs can be added and one partial. However, If the yield drops by 2 percentage points, then only two complete rungs can be completed and one partial. Smaller changes in yield have much larger consequences for the later rungs.

cheers
StillGoing
I'm not really following your math here.

My point is after 1 year, the next rung of the ladder (year 31) will be available. You sell enough of the year 30 TIPS to buy the year 31 rung. The following year, you buy the year 32 rung. Can you model that?

I'm not sure how yields are going to affect it, because if yields fall, the value of your year 30 TIPS will increase, but you also need to buy more TIPS for your year 31 rung. I kinda feel it's going to cancel out. Whereas if you wait until year 30, you don't know what yields will be.
If the goal was to minimize interest rate risk, you could roll the whole thing (now the 29 year TIPS) into the new 30 year TIPS after the first year. Then each subsequent year, leave enough for one rung and roll the rest to the new 30 year and so on. This will incur higher transactions costs, but I believe will minimize interest risk.
Yes, that's what I said (not clearly). Or meant to say.
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JackoC
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

StillGoing wrote: Wed Jun 26, 2024 12:05 pm
JackoC wrote: Wed Jun 26, 2024 11:40 am This is a useful discussion IMO in terms of being aware of the 'break even math' of various situations. 30 yr TIPS to cover 40 yr out liability, roll out after 30 yrs or after TIPS to that original 40 yr point get issued, what inflation rate kills TIPS+ later SPIA, etc. But it leaves out what would be to me a now non-negligible concern: US federal credit risk in 30 yrs. I would (I do) now limit my exposure to the 'credit riskless' assumption even at ~20 yrs. I'm willing to take more reinvestment risk in return, no free lunch. Moreover I well realize a US federal debt crisis would be ugly for almost every other fundamental asset class too (by 'fundamental' I'm excluding eg. rolling below money puts on the S&P, that's a different discussion). And the ones for which it *probably* wouldn't be ugly, eg. gold, have questionable past risk/return relationship when things muddle along, which they usually do, which I'm not predicting they won't for the next 30 yrs. I don't know.
I think this is an area that is probably not fully discussable here, but it is a risk. However, recent Canadian experience shows that new issues of inflation linked bonds (Real Return Bonds) can be stopped.
You're right, a possible risk in limiting exposure to long TIPS is ones you later need for those dates don't get issued at all, besides the everyday risk they get issued at lower yields. I'm not a 'stay the course' absolutist: long TIPS now are more attractive IMO than when they yielded negative. I've built up my significant term TIPS inventory from nothing in last year+ (as I did in 2008-9 TIPS yield rise), but I'm cautious about very long maturities for credit reasons. This part of my portfolio is for when things are *really* bad. If I knew things would never be really bad, I wouldn't have bonds at all. But, besides limits on discussion, IME people who haven't come to their own conclusion that US credit risk is now real tend to be quite resistant to the idea anyway. I'm glad you acknowledge it's a risk.
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

dbr wrote: Wed Jun 26, 2024 7:17 am
Stormbringer wrote: Wed Jun 26, 2024 7:14 am If you get to the end of a 30-year TIPS ladder, you have a big worry: longevity. If you are 85 when the ladder runs out, extending it by 5 years isn't sufficient if you live to be 97.

What I would do is use the lump sum from year 30 to purchase a simple income annuity to provide longevity protection. The mortality credits from an annuity purchased at that age will be significant, and the impact of inflation will be less because of a shorter time horizon.
I am not sure what is the upper age at which one can buy an annuity. I think one sometimes hears that option goes away at age 85. Maybe someone knows for sure.
On blueprintincome.com I just got eight quotes from A to A++ insurance companies for a 90-year-old single woman. At age 95 I got just one quote.
Wrench
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

dbr wrote: Wed Jun 26, 2024 7:17 am
Stormbringer wrote: Wed Jun 26, 2024 7:14 am If you get to the end of a 30-year TIPS ladder, you have a big worry: longevity. If you are 85 when the ladder runs out, extending it by 5 years isn't sufficient if you live to be 97.

What I would do is use the lump sum from year 30 to purchase a simple income annuity to provide longevity protection. The mortality credits from an annuity purchased at that age will be significant, and the impact of inflation will be less because of a shorter time horizon.
I am not sure what is the upper age at which one can buy an annuity. I think one sometimes hears that option goes away at age 85. Maybe someone knows for sure.
Every company is different. Some are 85, some are 90. A few years ago, my MIL purchased an SPIA from an A+ rated company at age 89 so I know that is possible. At that time, I did not see any SPIAs that allowed purchase age greater than 90, but they may exist now or in the future.

Wrench
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

GoWithTheCashFlow wrote: Wed Jun 26, 2024 11:42 am
RyeBourbon wrote: Wed Jun 26, 2024 11:35 am
StillGoing wrote: Wed Jun 26, 2024 11:12 am
RyeBourbon wrote: Wed Jun 26, 2024 6:37 am You don't have to hold those extra TIPS to maturity. You can sell them and buy the appropriate rung TIPS as soon as they become available and get the YTM at that time.
Of course, but the effect is potentially much larger. For example, if the yield started at 2.135% when building the initial 30 year ladder, let's say that the yield drops by 1 percentage point and stays there for the next 5 years (since we need to add 5 years to get to our desired 35 year ladder). In order to provide the 4% income 30 years later will cost 2.85% of the portfolio for the first extra rung (i.e., 4/power(1+1.0135,30) ), 2.82% of the portfolio the year after (i.e., 4/power(1.0135,31) ) and so on. Only three complete rungs can be added and one partial. However, If the yield drops by 2 percentage points, then only two complete rungs can be completed and one partial. Smaller changes in yield have much larger consequences for the later rungs.

cheers
StillGoing
I'm not really following your math here.

My point is after 1 year, the next rung of the ladder (year 31) will be available. You sell enough of the year 30 TIPS to buy the year 31 rung. The following year, you buy the year 32 rung. Can you model that?

I'm not sure how yields are going to affect it, because if yields fall, the value of your year 30 TIPS will increase, but you also need to buy more TIPS for your year 31 rung. I kinda feel it's going to cancel out. Whereas if you wait until year 30, you don't know what yields will be.
If the goal was to minimize interest rate risk, you could roll the whole thing (now the 29 year TIPS) into the new 30 year TIPS after the first year. Then each subsequent year, leave enough for one rung and roll the rest to the new 30 year and so on. This will incur higher transactions costs, but I believe will minimize interest risk.
Here is an attempt to model this approach. Scenario as before, a 35 year ladder, required income of 4%, TIPS yields of 2.135% (which just enables the ladder to be constructed).

At the start, a 30 year TIPS is bought with the amount left over from constructing the initial 30 year ladder. In this example, the amount left over is 10.18% of the original portfolio.

In the calculation I have assumed zero coupon TIPS since this makes the maths easier - I can't think of a reason why including coupons would significantly change the result. I have also assumed a flat yield curve and that any changes in yield are the same across maturities of 30 and 29 years (i.e. the yield curve starts flat and remains so).

The following table shows the situation if the yields stay at 2.135% for the five years required to add the extra 5 rungs.

Code: Select all

``````Year	InitVal	Yield	P(30)	P(29)	RungC	EndVal
0	10.18	2.135%	53.06	54.19	0.00	10.39
1	10.39	2.135%	53.06	54.19	2.17	8.40
2	8.40	2.135%	53.06	54.19	2.17	6.37
3	6.37	2.135%	53.06	54.19	2.17	4.29
4	4.29	2.135%	53.06	54.19	2.17	2.17
5	2.17	2.135%	53.06	54.19	2.17	0.00
``````
Year is the year since retirement (i.e. zero is the instant of retirement). InitVal is the initial amount (expressed in real terms as a percentage of the initial portfolio) invested in the 30 year TIPS that will be used to purchase the additional rungs. Yield is the yield at the start of the year, P(30) and P(29) are the price of the 30 and 29 year TIPS, respectively (100 is the maturing value). RungC is the cost of purchasing the rung that will mature 30 years later and endval is the amount remaining in the portfolio after purchase (which happens at the beginning of the year) multiplied by the return (which is P(29)/P(30) ).

In this example, we can see that the end value after 5 years is zero, i.e., each rung has been successfully purchased and the retiree now has a functioning 30 year ladder (i.e. taking them to 35 years after their original retirement age).

Now lets do another example, where the yield drops by 1 percentage point to 1.135% at the start of year 1 and then stays at that level.

Code: Select all

``````Year	InitVal	Yield	P(30)	P(29)	RungC	EndVal	RungVal
0	10.18	2.135%	53.06	54.19	0.00	10.39
1	13.83	1.135%	71.28	72.09	2.88	11.07	4.00
2	11.07	1.135%	71.28	72.09	2.88	8.28	4.00
3	8.28	1.135%	71.28	72.09	2.88	5.46	4.00
4	5.46	1.135%	71.28	72.09	2.88	2.60	4.00
5	2.60	1.135%	71.28	72.09	2.88	-0.29	3.61
``````
The extra column, RungVal, indicates how much income the rung will generate on maturity.

Year zero is as before, however, the drop in yield leads to an increase in the prices, an increase in the amount necessary to construct each rung, and an increase in the amount available to purchase the extra rungs.

The outcome is that 4 rungs are completed while the final one delivers 3.61% which is the similar to the 3.6% delivered by waiting for the 30 year TIPS to mature before purchasing the extra rungs in the ladder (i.e., my original method). Having checked for various other values of drops in yield, the results are virtually identical for all of them.

It would appear that the method in this post (i.e., each year rolling the 29 year TIPS into a 30 year one) is preferable since the purchases occur soon after retirement (rather than very late) negating at least some potential risks. It is useful that the results are the same, since it is easier to calculate the outcomes for the other method (i.e., allowing the 30 year TIPS to mature before constructing the extra ladder).

cheers
StillGoing
BlenBlenBlue
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

StillGoing wrote: Thu Jun 27, 2024 2:13 am In the calculation I have assumed zero coupon TIPS since this makes the maths easier - I can't think of a reason why including coupons would significantly change the result.
Changing coupon rate could impact the early part of the ladder. For example, if you initially had a 2% coupon then a lot of the early part of the ladder might be covered by the coupons. If the coupon drops close to zero then you need to purchase more shorter terms bonds? Or maybe you need to ignore the coupons for the 30s and use them to reinvest each year as the new 30s come out?
Last edited by BlenBlenBlue on Thu Jun 27, 2024 4:41 am, edited 1 time in total.
GoWithTheCashFlow
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

StillGoing wrote: Thu Jun 27, 2024 2:13 am It would appear that the method in this post (i.e., each year rolling the 29 year TIPS into a 30 year one) is preferable since the purchases occur soon after retirement (rather than very late) negating at least some potential risks. It is useful that the results are the same, since it is easier to calculate the outcomes for the other method (i.e., allowing the 30 year TIPS to mature before constructing the extra ladder).
It looks like in both scenarios you get 30 years of 2.135% interest followed by 1.135% interest. This is surprising to me. Thank you for bringing the results to my attention. I will have to think about it some more.

I suppose then, that biggest advantage (outside of there being less time for the yields to change) of rolling the 30 year TIPS over (relative to waiting until maturity) is as a hedge against non-parallel shifts in the yield curve, rather than parallel shifts.
Last edited by GoWithTheCashFlow on Thu Jun 27, 2024 9:06 am, edited 1 time in total.
AlmstRtrd
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

dbr wrote: Wed Jun 26, 2024 7:01 am The not often recognized huge risk in a TIPS ladder is what the available yield is at the time one is ready and able to invest in the ladder. In the last few years that has flipped from -2% real to +2% real, probably the biggest single change in bond investing over this recent time. A change of 4% in real yield is tremendous. It certainly dwarfs the I bond feeding frenzy for one thing.
Could not agree more.

Another thing I wonder about - and this is related to what dbr wrote - is how many on here with long TIPS ladders don't feel so great having most or all of their positions in the red... depending on what the real YTM was when they purchased. I know most say that they don't care because they are planning to hold to maturity. But it's just human nature to feel at least a little bit upset if all your positions are down.

All five of my positions from 2025 to 2029 are in the red but I only have a five-year ladder (and I did buy when real rates were at least positive). Those who bought long-dated TIPS when real yields were low or even negative have to be looking at large paper "losses". I guess the question I am really addressing is "How risky is interest-rate risk for a long TIPS ladder?"
watchnerd
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

RyeBourbon wrote: Wed Jun 26, 2024 6:37 am You don't have to hold those extra TIPS to maturity. You can sell them and buy the appropriate rung TIPS as soon as they become available and get the YTM at that time.
Yep.

Obvious solution.

Global stocks, IG/HY bonds, gold & digital assets at market weights 75% / 19% / 6% || LMP: TIPS ladder
GoWithTheCashFlow
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

watchnerd wrote: Thu Jun 27, 2024 9:01 am
RyeBourbon wrote: Wed Jun 26, 2024 6:37 am You don't have to hold those extra TIPS to maturity. You can sell them and buy the appropriate rung TIPS as soon as they become available and get the YTM at that time.
Yep.

Obvious solution.

Except StillGoing modeled this and showed that for a permanent 1% point drop across (Edit: a flat) (thanks BlenBlenBlue) yield curve occurring the day after constructing the ladder, the results are essentially identical to the strategy of holding until maturity.

Obviously rolling the 30 year TIPS over is superior since it allows less time for yields to change and protects against non-parallel shifts. But, as StillGoing stated, holding to maturity is easier to model and thus still useful in analyzing the risk.

That is my interpretation anyway.
Last edited by GoWithTheCashFlow on Thu Jun 27, 2024 11:01 am, edited 1 time in total.
firebirdparts
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

dbr wrote: Wed Jun 26, 2024 7:01 am The not often recognized huge risk in a TIPS ladder is what the available yield is at the time one is ready and able to invest in the ladder. In the last few years that has flipped from -2% real to +2% real, probably the biggest single change in bond investing over this recent time. A change of 4% in real yield is tremendous. It certainly dwarfs the I bond feeding frenzy for one thing.
I think so too. Nominal interest rates can go to 1000%, but the real rate doesn't.

If I was concerned about "risk" then I would knock the door off the hinges trying to go somewhere and buy the whole ladder today. I am thinking the risk is that you didn't do it today.
This time is the same
JackoC
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

firebirdparts wrote: Thu Jun 27, 2024 9:50 am
dbr wrote: Wed Jun 26, 2024 7:01 am The not often recognized huge risk in a TIPS ladder is what the available yield is at the time one is ready and able to invest in the ladder. In the last few years that has flipped from -2% real to +2% real, probably the biggest single change in bond investing over this recent time. A change of 4% in real yield is tremendous. It certainly dwarfs the I bond feeding frenzy for one thing.
I think so too. Nominal interest rates can go to 1000%, but the real rate doesn't.

If I was concerned about "risk" then I would knock the door off the hinges trying to go somewhere and buy the whole ladder today. I am thinking the risk is that you didn't do it today.
With the caveat I mentioned before, I generally agree. Nominal rates could change to a new regime significantly higher or lower than now's, depending on respectively an eventual adoption of a higher central bank inflation target or reemergence of deflationary forces which made 2% inflation target (on PCE) hard to get up to for a long time. The real rate *could* go to any level on the principal of 'anything is possible' but I believe has less potential to settle for a long time much higher than now. It relates to my caveat: a sustained govt cost of funds of 3 or 4% real wouldn't be affordable at 100%+ debt to GDP ratio, with no realistic near/medium prospect of reducing that ratio (slowing its rapid growth would I think be the outer limit of likely tolerance for fiscal tightening, I believe this to be a politics-free statement, unless there *is* a big federal debt crisis). But either reemergence of deflationary forces or a higher inflation target (IOW easy money) would tend to reduce the real yield. Unless there's a loss of confidence in the credit...
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

GoWithTheCashFlow wrote: Thu Jun 27, 2024 9:22 am
watchnerd wrote: Thu Jun 27, 2024 9:01 am
RyeBourbon wrote: Wed Jun 26, 2024 6:37 am You don't have to hold those extra TIPS to maturity. You can sell them and buy the appropriate rung TIPS as soon as they become available and get the YTM at that time.
Yep.

Obvious solution.

Except StillGoing modeled this and showed that for a permanent 1% point drop across yield curve occurring the day after constructing the ladder, the results are essentially identical to the strategy of holding until maturity.

Obviously rolling the 30 year TIPS over is superior since it allows less time for yields to change and protects against non-parallel shifts. But, as StillGoing stated, holding to maturity is easier to model and thus still useful in analyzing the risk.

That is my interpretation anyway.
It seems that this might be heavily influenced by the flat yield curved assumption and/or only having to fund 5 additional years (so purchasing relatively short duration after the initial 30 years).

In my case, I have close to a 30 year ladder going out to 70 (thinking of early retirement soon) and am considering funding 70 to 85. Buying the 30s now, to later purchase a 15 year ladder in 30 years would have more risk of since yield curve may not be that flat.
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

BlenBlenBlue wrote: Thu Jun 27, 2024 10:49 am
GoWithTheCashFlow wrote: Thu Jun 27, 2024 9:22 am
watchnerd wrote: Thu Jun 27, 2024 9:01 am
RyeBourbon wrote: Wed Jun 26, 2024 6:37 am You don't have to hold those extra TIPS to maturity. You can sell them and buy the appropriate rung TIPS as soon as they become available and get the YTM at that time.
Yep.

Obvious solution.

Except StillGoing modeled this and showed that for a permanent 1% point drop across yield curve occurring the day after constructing the ladder, the results are essentially identical to the strategy of holding until maturity.

Obviously rolling the 30 year TIPS over is superior since it allows less time for yields to change and protects against non-parallel shifts. But, as StillGoing stated, holding to maturity is easier to model and thus still useful in analyzing the risk.

That is my interpretation anyway.
It seems that this might be heavily influenced by the flat yield curved assumption and/or only having to fund 5 additional years (so purchasing relatively short duration after the initial 30 years).

In my case, I have close to a 30 year ladder going out to 70 (thinking of early retirement soon) and am considering funding 70 to 85. Buying the 30s now, to later purchase a 15 year ladder in 30 years would have more risk of since yield curve may not be that flat.
I guess there are two things here:

1) The flat yield curve. While it is unlikely(?) that there would be a strong gradient in the yield between 29 years and 30 years, an upward yield curve would lower the price of the 30 year TIPS compared to what I had in the tables above and this would mean that you'd get slightly more ladder for your money (an example of 'rolling down the yield curve'), while an inverted yield curve would have the opposite effect. I suspect (without having calculated it) that unless the difference in yields between the 29 and 30 year TIPS is large, then the effect will be small compared to a large change in overall yields.

2) For a longer ladder extension the effect of changes in yield is larger. Taking your example of a 45 year ladder - with a yield of 2.123%, you could purchase that to provide an income of 3.4% of 'premium'. Having built the 30 year part (with 76.46% of the available portfolio), if the yields dropped by 1 percentage point after the first year, then you could build just under 14 rungs, if it dropped by 2 percentage points 13 rungs, 5 percentage points 11 rungs, etc. In this case, the answer is the same whether you hold the 30 year TIPS until maturity and build the extension all in one go (aged 70 in your example) or you purchase a 30 year TIPS, sell it after 1 year and purchase a 30 year TIPS, and so on. In the first approach, only the yield at maturity is important (in other words, the path between year 0 and year 30 is unimportant), while for the one rung at a time approach, yields will vary from one year to the next and change the outcome (I have yet to model that).

cheers
StillGoing
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

AlmstRtrd wrote: Thu Jun 27, 2024 8:19 am
dbr wrote: Wed Jun 26, 2024 7:01 am The not often recognized huge risk in a TIPS ladder is what the available yield is at the time one is ready and able to invest in the ladder. In the last few years that has flipped from -2% real to +2% real, probably the biggest single change in bond investing over this recent time. A change of 4% in real yield is tremendous. It certainly dwarfs the I bond feeding frenzy for one thing.
Could not agree more.

Another thing I wonder about - and this is related to what dbr wrote - is how many on here with long TIPS ladders don't feel so great having most or all of their positions in the red... depending on what the real YTM was when they purchased. I know most say that they don't care because they are planning to hold to maturity. But it's just human nature to feel at least a little bit upset if all your positions are down.

All five of my positions from 2025 to 2029 are in the red but I only have a five-year ladder (and I did buy when real rates were at least positive). Those who bought long-dated TIPS when real yields were low or even negative have to be looking at large paper "losses". I guess the question I am really addressing is "How risky is interest-rate risk for a long TIPS ladder?"
The fact that positions are in the red is only of any importance if they are sold. Once purchased, provided a rung of a non-rolling ladder is held to maturity there is no interest rate risk.

cheers
StillGoing
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

watchnerd wrote: Thu Jun 27, 2024 9:01 am
RyeBourbon wrote: Wed Jun 26, 2024 6:37 am You don't have to hold those extra TIPS to maturity. You can sell them and buy the appropriate rung TIPS as soon as they become available and get the YTM at that time.
Yep.

Obvious solution.

However, interestingly the results (given the assumptions made) are identical whether the appropriate rungs are bought one at a time when available or whether the extra rungs are bought all in one go after 30 years. Of course, there are limitations to the simple model I have described here, for example, a more sophisticated one would allow for more changes in yield than just one.

The second point, is how much does the change in YTM affect how much of the ladder can be constructed? The answer, for an extension of 5 years is not much (a reduction in YTM of 13 percentage points is required before there is nothing available for the 5th rung), while for an extension of 15 years, each 1 percentage point drop in YTM removes funding for one of the rungs. Again, this behaviour is fairly obvious, but it is nice to quantify the effect.

cheers
StillGoing
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

GoWithTheCashFlow wrote: Thu Jun 27, 2024 9:22 am
watchnerd wrote: Thu Jun 27, 2024 9:01 am
RyeBourbon wrote: Wed Jun 26, 2024 6:37 am You don't have to hold those extra TIPS to maturity. You can sell them and buy the appropriate rung TIPS as soon as they become available and get the YTM at that time.
Yep.

Obvious solution.

Except StillGoing modeled this and showed that for a permanent 1% point drop across (Edit: a flat) (thanks BlenBlenBlue) yield curve occurring the day after constructing the ladder, the results are essentially identical to the strategy of holding until maturity.

Obviously rolling the 30 year TIPS over is superior since it allows less time for yields to change and protects against non-parallel shifts. But, as StillGoing stated, holding to maturity is easier to model and thus still useful in analyzing the risk.

That is my interpretation anyway.
That's not what I'm talking about.

You hold TIPS to maturity.

If you have more than you need to consume in a non-rolling ladder, you take the excess and buy the newly auctioned TIPS that extend the ladder into the future.

Example:

It's 2027, and I have TIPS maturing that year.

I have X% dedicated to consumption for living expenses.

I have Y% dedicated to buying the new 2057 TIPS to extend my ladder.
Global stocks, IG/HY bonds, gold & digital assets at market weights 75% / 19% / 6% || LMP: TIPS ladder
GoWithTheCashFlow
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

watchnerd wrote: Thu Jun 27, 2024 1:12 pm
GoWithTheCashFlow wrote: Thu Jun 27, 2024 9:22 am
watchnerd wrote: Thu Jun 27, 2024 9:01 am
RyeBourbon wrote: Wed Jun 26, 2024 6:37 am You don't have to hold those extra TIPS to maturity. You can sell them and buy the appropriate rung TIPS as soon as they become available and get the YTM at that time.
Yep.

Obvious solution.

Except StillGoing modeled this and showed that for a permanent 1% point drop across (Edit: a flat) (thanks BlenBlenBlue) yield curve occurring the day after constructing the ladder, the results are essentially identical to the strategy of holding until maturity.

Obviously rolling the 30 year TIPS over is superior since it allows less time for yields to change and protects against non-parallel shifts. But, as StillGoing stated, holding to maturity is easier to model and thus still useful in analyzing the risk.

That is my interpretation anyway.
That's not what I'm talking about.

You hold TIPS to maturity.

If you have more than you need to consume in a non-rolling ladder, you take the excess and buy the newly auctioned TIPS that extend the ladder into the future.

Example:

It's 2027, and I have TIPS maturing that year.

I have X% dedicated to consumption for living expenses.

I have Y% dedicated to buying the new 2057 TIPS to extend my ladder.
The strategy you describe trades price risk for reinvestment risk (as compared to the strategy described by RyeBourbon and myself), but I don't see how it minimizes the interest rate risk in funding spending over 30 years away via TIPS. I could be wrong. Perhaps minimizing interest rate risk is not even your goal.
watchnerd
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

GoWithTheCashFlow wrote: Thu Jun 27, 2024 1:42 pm
watchnerd wrote: Thu Jun 27, 2024 1:12 pm
GoWithTheCashFlow wrote: Thu Jun 27, 2024 9:22 am
watchnerd wrote: Thu Jun 27, 2024 9:01 am
RyeBourbon wrote: Wed Jun 26, 2024 6:37 am You don't have to hold those extra TIPS to maturity. You can sell them and buy the appropriate rung TIPS as soon as they become available and get the YTM at that time.
Yep.

Obvious solution.

Except StillGoing modeled this and showed that for a permanent 1% point drop across (Edit: a flat) (thanks BlenBlenBlue) yield curve occurring the day after constructing the ladder, the results are essentially identical to the strategy of holding until maturity.

Obviously rolling the 30 year TIPS over is superior since it allows less time for yields to change and protects against non-parallel shifts. But, as StillGoing stated, holding to maturity is easier to model and thus still useful in analyzing the risk.

That is my interpretation anyway.
That's not what I'm talking about.

You hold TIPS to maturity.

If you have more than you need to consume in a non-rolling ladder, you take the excess and buy the newly auctioned TIPS that extend the ladder into the future.

Example:

It's 2027, and I have TIPS maturing that year.

I have X% dedicated to consumption for living expenses.

I have Y% dedicated to buying the new 2057 TIPS to extend my ladder.
The strategy you describe trades price risk for reinvestment risk (as compared to the strategy described by RyeBourbon and myself), but I don't see how it minimizes the interest rate risk in funding spending over 30 years away via TIPS. I could be wrong. Perhaps minimizing interest rate risk is not even your goal.
You can't do anything to minimize the interest rate risk for bonds that don't exist yet and have to be purchased.

If you have to purchase them, there will be interest rate risk.

The interest rate could be anything at the time of purchase.

The best you can do is try to plan for the spending.
Global stocks, IG/HY bonds, gold & digital assets at market weights 75% / 19% / 6% || LMP: TIPS ladder
Wrench
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

AlmstRtrd wrote: Thu Jun 27, 2024 8:19 am
dbr wrote: Wed Jun 26, 2024 7:01 am The not often recognized huge risk in a TIPS ladder is what the available yield is at the time one is ready and able to invest in the ladder. In the last few years that has flipped from -2% real to +2% real, probably the biggest single change in bond investing over this recent time. A change of 4% in real yield is tremendous. It certainly dwarfs the I bond feeding frenzy for one thing.
Could not agree more.

Another thing I wonder about - and this is related to what dbr wrote - is how many on here with long TIPS ladders don't feel so great having most or all of their positions in the red... depending on what the real YTM was when they purchased. I know most say that they don't care because they are planning to hold to maturity. But it's just human nature to feel at least a little bit upset if all your positions are down.

All five of my positions from 2025 to 2029 are in the red but I only have a five-year ladder (and I did buy when real rates were at least positive). Those who bought long-dated TIPS when real yields were low or even negative have to be looking at large paper "losses". I guess the question I am really addressing is "How risky is interest-rate risk for a long TIPS ladder?"
I'll bite. My TIPS ladder goes from 2027-2054 with the gap years filled by iBonds. I started it in 2019 and have been filling in years if YTM is attractive. I don't track the mark-to-market values, though I am sure it is down by quite a lot, probably 10% or more. I only look at the principal value since that is what I will cash out at maturity. That is going up nicely. This is no different than nominal bonds. In that case, if rates go up after purchase the mark-to-market value goes down, but you are still guaranteed the face value at maturity. You should not own individual bonds if you can't live with the volatility before maturity as interest rates change. Just like stocks, one has to learn to "stay the course" and not panic-sell. It also cuts both ways - rates can (and likely will) go down some day and the mark-to-market bond values will go up. Doesn't matter. Stay the course.

Wrench
GoWithTheCashFlow
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

watchnerd wrote: Thu Jun 27, 2024 2:23 pm You can't do anything to minimize the interest rate risk for bonds that don't exist yet and have to be purchased.

If you have to purchase them, there will be interest rate risk.

The interest rate could be anything at the time of purchase.

The best you can do is try to plan for the spending.
Minimize, not eliminate. Yes, the 30 year TIPS rate could be anything at the time of purchase. But, it seems likely that the 30 year TIPS rate is highly correlated with the 29 year TIPS rate. Similarly, the 30 year TIPS rate today probably has a higher correlation to the 30 year TIPS rate 1 year from now than to the 30 year TIPS rate 10 years from now.
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StillGoing
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

GoWithTheCashFlow wrote: Thu Jun 27, 2024 2:40 pm
watchnerd wrote: Thu Jun 27, 2024 2:23 pm You can't do anything to minimize the interest rate risk for bonds that don't exist yet and have to be purchased.

If you have to purchase them, there will be interest rate risk.

The interest rate could be anything at the time of purchase.

The best you can do is try to plan for the spending.
Minimize, not eliminate. Yes, the 30 year TIPS rate could be anything at the time of purchase. But, it seems likely that the 30 year TIPS rate is highly correlated with the 29 year TIPS rate. Similarly, the 30 year TIPS rate today probably has a higher correlation to the 30 year TIPS rate 1 year from now than to the 30 year TIPS rate 10 years from now.
In the following graphs I've plotted the yields for 20 year, Y(20) and 30 years, Y(30) TIPS (upper panel) and the difference between them Y(30)-Y(20) (lower panel). Data were obtained from https://fred.stlouisfed.org/tags/series?t=tips . I note that 30 year TIPS were issued at the end of the 20th century but had been discontinued sometime between then and 2003 (judging by yield curves available in the link from https://home.treasury.gov/policy-issues ... statistics) before being reissued (replacing 20 year TIPS) in February 2010. While no changes in the issuance (i.e., 5 years, 10 years, and 30 years) have been made since then, this will not necessarily be the case in the future.

Two points to make:
1) The yields at 20 and 30 years were fairly well correlated
2) The difference in yields ranged from 0 to just over 0.4 percentage points. If the gradient was constant over the 10 years between 20 year and 30 year maturities, then dividing by 10 would provide an estimate of Y(30)-Y(29). Of course, the entire value Y(30)-Y(20) might have occurred in the final year, i.e. Y(30)-Y(29)=Y(30)-Y(20), although this seems unlikely. In either case, the Y(30)-Y(29) (between 4.5 and 45 basis points) was small compared to the change in Y(30) with time (approx 300 basis points)

The usual caveats about, what is a relatively short period of historical data, should be taken on board.

cheers
StillGoing
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

watchnerd wrote: Thu Jun 27, 2024 2:23 pm
GoWithTheCashFlow wrote: Thu Jun 27, 2024 1:42 pm
watchnerd wrote: Thu Jun 27, 2024 1:12 pm
GoWithTheCashFlow wrote: Thu Jun 27, 2024 9:22 am
watchnerd wrote: Thu Jun 27, 2024 9:01 am

Yep.

Obvious solution.

Except StillGoing modeled this and showed that for a permanent 1% point drop across (Edit: a flat) (thanks BlenBlenBlue) yield curve occurring the day after constructing the ladder, the results are essentially identical to the strategy of holding until maturity.

Obviously rolling the 30 year TIPS over is superior since it allows less time for yields to change and protects against non-parallel shifts. But, as StillGoing stated, holding to maturity is easier to model and thus still useful in analyzing the risk.

That is my interpretation anyway.
That's not what I'm talking about.

You hold TIPS to maturity.

If you have more than you need to consume in a non-rolling ladder, you take the excess and buy the newly auctioned TIPS that extend the ladder into the future.

Example:

It's 2027, and I have TIPS maturing that year.

I have X% dedicated to consumption for living expenses.

I have Y% dedicated to buying the new 2057 TIPS to extend my ladder.
The strategy you describe trades price risk for reinvestment risk (as compared to the strategy described by RyeBourbon and myself), but I don't see how it minimizes the interest rate risk in funding spending over 30 years away via TIPS. I could be wrong. Perhaps minimizing interest rate risk is not even your goal.
You can't do anything to minimize the interest rate risk for bonds that don't exist yet and have to be purchased.

If you have to purchase them, there will be interest rate risk.

The interest rate could be anything at the time of purchase.

The best you can do is try to plan for the spending.
I think the approach you have described from "It's 2027, and I have TIPS maturing that year" is the similar to that I've modelled at viewtopic.php?p=7929841#p7929841 except (I think) that while I've assumed a target ladder length (35 years in the example I've used) you have excess (which you've named as Y%) in each of your rungs rather than a single rolling TIPS a portion of which is used to construct a new rung each year.

For me the purpose of this thread (which arose out of asking the question - how big is interest rate risk when trying to construct ladder longer than 30 years?) was to try to quantify the risk given a change in yield. I think the answers are instructive - if a short extension is required (5 years in the example I've been using), it takes a 13 percentage point drop in yields over the first 5 years of retirement before it is impossible to construct the final (35th rung). I think a drop of that magnitude is unlikely, but not impossible. However, if trying to build a 45 year ladder, it only takes a drop of 1 percentage point over the first 15 years of retirement before the final (i.e., 45th rung) cannot be constructed. That interest rate risk is more pronounced for a longer extension is probably not surprising, but the magnitude of the risk, to me at least, was.

cheers
StillGoing
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

dbr wrote: Wed Jun 26, 2024 7:01 am The not often recognized huge risk in a TIPS ladder is what the available yield is at the time one is ready and able to invest in the ladder. In the last few years that has flipped from -2% real to +2% real, probably the biggest single change in bond investing over this recent time. A change of 4% in real yield is tremendous. It certainly dwarfs the I bond feeding frenzy for one thing.
I thought it would be interesting to look at the best data we have to evaluate this statement:

The blue line is for the Apr 2028 TIPS that was issued in Apr 1998, and FRED provides history for it since then. The red line is the inflation indexed CMT, which I added just so we could see that the Apr 2028 provides a pretty good TIPS yield history even though it's not constant maturity. The green line is for the 30y inflation indexed CMT, which I added since it's most relevant to the thread topic, although it has the shortest history.
If I make a calculation error, #Cruncher probably will let me know.
dbr
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

Kevin M wrote: Fri Jun 28, 2024 10:23 am
dbr wrote: Wed Jun 26, 2024 7:01 am The not often recognized huge risk in a TIPS ladder is what the available yield is at the time one is ready and able to invest in the ladder. In the last few years that has flipped from -2% real to +2% real, probably the biggest single change in bond investing over this recent time. A change of 4% in real yield is tremendous. It certainly dwarfs the I bond feeding frenzy for one thing.
I thought it would be interesting to look at the best data we have to evaluate this statement:

The blue line is for the Apr 2028 TIPS that was issued in Apr 1998, and FRED provides history for it since then. The red line is the inflation indexed CMT, which I added just so we could see that the Apr 2028 provides a pretty good TIPS yield history even though it's not constant maturity. The green line is for the 30y inflation indexed CMT, which I added since it's most relevant to the thread topic, although it has the shortest history.
Thanks. That is really helpful as it should give some perspective on the general prospect. How does the data in the chart compare to the data at this site: https://home.treasury.gov/resource-cent ... nth=202406
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

RyeBourbon wrote: Wed Jun 26, 2024 11:35 am
StillGoing wrote: Wed Jun 26, 2024 11:12 am
RyeBourbon wrote: Wed Jun 26, 2024 6:37 am You don't have to hold those extra TIPS to maturity. You can sell them and buy the appropriate rung TIPS as soon as they become available and get the YTM at that time.
Of course, but the effect is potentially much larger. For example, if the yield started at 2.135% when building the initial 30 year ladder, let's say that the yield drops by 1 percentage point and stays there for the next 5 years (since we need to add 5 years to get to our desired 35 year ladder). In order to provide the 4% income 30 years later will cost 2.85% of the portfolio for the first extra rung (i.e., 4/power(1+1.0135,30) ), 2.82% of the portfolio the year after (i.e., 4/power(1.0135,31) ) and so on. Only three complete rungs can be added and one partial. However, If the yield drops by 2 percentage points, then only two complete rungs can be completed and one partial. Smaller changes in yield have much larger consequences for the later rungs.

cheers
StillGoing
I'm not really following your math here.

My point is after 1 year, the next rung of the ladder (year 31) will be available. You sell enough of the year 30 TIPS to buy the year 31 rung. The following year, you buy the year 32 rung. Can you model that?

I'm not sure how yields are going to affect it, because if yields fall, the value of your year 30 TIPS will increase, but you also need to buy more TIPS for your year 31 rung. I kinda feel it's going to cancel out. Whereas if you wait until year 30, you don't know what yields will be.
I've been doing some modeling of gap year coverage methods, and based on that, I've learned that the value of the portion of the 30 year you're holding to to buy the next 30y when it's issued a year later will increase more than the cost of the new issue if yields decrease. Here's why.

The 30y you hold trades on the secondary market, and therefore price changes with respect to yield changes based on duration. However, the price of new issues is relatively constant at 100 unless yields are negative, so the only thing that affects how much you need to buy to get a given desired annual real amount (DARA) is the interest from that bond and later bonds in the ladder. So if 30y yields decrease enough, the coupon also will decrease, providing less interest for that rung than you would have got from the higher coupon 30y you were holding (and there are no later bonds in this case). The coupon effect is much less than than the duration effect.

If yields increase enough though, the value of the coverage holding will decrease more than the new issue costs decreases for the same reason--duration has a bigger impact on the coverage holding than the higher coupon does on the new issue.
If I make a calculation error, #Cruncher probably will let me know.
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

StillGoing wrote: Thu Jun 27, 2024 2:13 am
GoWithTheCashFlow wrote: Wed Jun 26, 2024 11:42 am
RyeBourbon wrote: Wed Jun 26, 2024 11:35 am
StillGoing wrote: Wed Jun 26, 2024 11:12 am
RyeBourbon wrote: Wed Jun 26, 2024 6:37 am You don't have to hold those extra TIPS to maturity. You can sell them and buy the appropriate rung TIPS as soon as they become available and get the YTM at that time.
Of course, but the effect is potentially much larger. For example, if the yield started at 2.135% when building the initial 30 year ladder, let's say that the yield drops by 1 percentage point and stays there for the next 5 years (since we need to add 5 years to get to our desired 35 year ladder). In order to provide the 4% income 30 years later will cost 2.85% of the portfolio for the first extra rung (i.e., 4/power(1+1.0135,30) ), 2.82% of the portfolio the year after (i.e., 4/power(1.0135,31) ) and so on. Only three complete rungs can be added and one partial. However, If the yield drops by 2 percentage points, then only two complete rungs can be completed and one partial. Smaller changes in yield have much larger consequences for the later rungs.

cheers
StillGoing
I'm not really following your math here.

My point is after 1 year, the next rung of the ladder (year 31) will be available. You sell enough of the year 30 TIPS to buy the year 31 rung. The following year, you buy the year 32 rung. Can you model that?

I'm not sure how yields are going to affect it, because if yields fall, the value of your year 30 TIPS will increase, but you also need to buy more TIPS for your year 31 rung. I kinda feel it's going to cancel out. Whereas if you wait until year 30, you don't know what yields will be.
If the goal was to minimize interest rate risk, you could roll the whole thing (now the 29 year TIPS) into the new 30 year TIPS after the first year. Then each subsequent year, leave enough for one rung and roll the rest to the new 30 year and so on. This will incur higher transactions costs, but I believe will minimize interest risk.
Here is an attempt to model this approach. Scenario as before, a 35 year ladder, required income of 4%, TIPS yields of 2.135% (which just enables the ladder to be constructed).

At the start, a 30 year TIPS is bought with the amount left over from constructing the initial 30 year ladder. In this example, the amount left over is 10.18% of the original portfolio.

In the calculation I have assumed zero coupon TIPS since this makes the maths easier - I can't think of a reason why including coupons would significantly change the result. I have also assumed a flat yield curve and that any changes in yield are the same across maturities of 30 and 29 years (i.e. the yield curve starts flat and remains so).

The following table shows the situation if the yields stay at 2.135% for the five years required to add the extra 5 rungs.

Code: Select all

``````Year	InitVal	Yield	P(30)	P(29)	RungC	EndVal
0	10.18	2.135%	53.06	54.19	0.00	10.39
1	10.39	2.135%	53.06	54.19	2.17	8.40
2	8.40	2.135%	53.06	54.19	2.17	6.37
3	6.37	2.135%	53.06	54.19	2.17	4.29
4	4.29	2.135%	53.06	54.19	2.17	2.17
5	2.17	2.135%	53.06	54.19	2.17	0.00
``````
Year is the year since retirement (i.e. zero is the instant of retirement). InitVal is the initial amount (expressed in real terms as a percentage of the initial portfolio) invested in the 30 year TIPS that will be used to purchase the additional rungs. Yield is the yield at the start of the year, P(30) and P(29) are the price of the 30 and 29 year TIPS, respectively (100 is the maturing value). RungC is the cost of purchasing the rung that will mature 30 years later and endval is the amount remaining in the portfolio after purchase (which happens at the beginning of the year) multiplied by the return (which is P(29)/P(30) ).

In this example, we can see that the end value after 5 years is zero, i.e., each rung has been successfully purchased and the retiree now has a functioning 30 year ladder (i.e. taking them to 35 years after their original retirement age).

Now lets do another example, where the yield drops by 1 percentage point to 1.135% at the start of year 1 and then stays at that level.

Code: Select all

``````Year	InitVal	Yield	P(30)	P(29)	RungC	EndVal	RungVal
0	10.18	2.135%	53.06	54.19	0.00	10.39
1	13.83	1.135%	71.28	72.09	2.88	11.07	4.00
2	11.07	1.135%	71.28	72.09	2.88	8.28	4.00
3	8.28	1.135%	71.28	72.09	2.88	5.46	4.00
4	5.46	1.135%	71.28	72.09	2.88	2.60	4.00
5	2.60	1.135%	71.28	72.09	2.88	-0.29	3.61
``````
The extra column, RungVal, indicates how much income the rung will generate on maturity.

Year zero is as before, however, the drop in yield leads to an increase in the prices, an increase in the amount necessary to construct each rung, and an increase in the amount available to purchase the extra rungs.

The outcome is that 4 rungs are completed while the final one delivers 3.61% which is the similar to the 3.6% delivered by waiting for the 30 year TIPS to mature before purchasing the extra rungs in the ladder (i.e., my original method). Having checked for various other values of drops in yield, the results are virtually identical for all of them.

It would appear that the method in this post (i.e., each year rolling the 29 year TIPS into a 30 year one) is preferable since the purchases occur soon after retirement (rather than very late) negating at least some potential risks. It is useful that the results are the same, since it is easier to calculate the outcomes for the other method (i.e., allowing the 30 year TIPS to mature before constructing the extra ladder).

cheers
StillGoing
If I understand your analysis correctly, the problem with it is that coupons do matter, and the price of new issues is relatively constant at 100. The latter is because coupon is not constant for new issues--it is determined by the yield, and is set such that price is close to 100 unless yields are negative.

I started out with similar assumptions in my gap coverage analysis, and then an astute participant in the thread asked the question about the coupons changing for the auctioned TIPS, and from that I realized that using a model assuming fixed coupons (in your case 0%) was flawed. I've since modified my modeling to rectify this.

Here's a chart of 10y auction prices vs. yield that I put together to show that this is indeed the case:

If I make a calculation error, #Cruncher probably will let me know.
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

AlmstRtrd wrote: Thu Jun 27, 2024 8:19 am
dbr wrote: Wed Jun 26, 2024 7:01 am The not often recognized huge risk in a TIPS ladder is what the available yield is at the time one is ready and able to invest in the ladder. In the last few years that has flipped from -2% real to +2% real, probably the biggest single change in bond investing over this recent time. A change of 4% in real yield is tremendous. It certainly dwarfs the I bond feeding frenzy for one thing.
Could not agree more.

Another thing I wonder about - and this is related to what dbr wrote - is how many on here with long TIPS ladders don't feel so great having most or all of their positions in the red... depending on what the real YTM was when they purchased. I know most say that they don't care because they are planning to hold to maturity. But it's just human nature to feel at least a little bit upset if all your positions are down.

All five of my positions from 2025 to 2029 are in the red but I only have a five-year ladder (and I did buy when real rates were at least positive). Those who bought long-dated TIPS when real yields were low or even negative have to be looking at large paper "losses". I guess the question I am really addressing is "How risky is interest-rate risk for a long TIPS ladder?"
I never even look at that, but since I have way too many TIPS maturing in 2025-2027, and I'd like to sell much of that excess to add to the longer rungs, I'm rooting for yield increases, which would put my ladder more into the red--the darker red the better. I can think of nothing more satisfying than selling a 2025, purchased at say 2%, at a loss to buy a 2045 at 3% or more.

As long as you use the ladder as intended, there is no relevant interest rate risk. Each rung of your ladder delivers the desired annual real amount at maturity regardless of yield changes along the way. Of course one can still experience regret that they could have paid less for the ladder if yields are higher than they were when the ladder was constructed.
If I make a calculation error, #Cruncher probably will let me know.
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

dbr wrote: Fri Jun 28, 2024 10:34 am
Kevin M wrote: Fri Jun 28, 2024 10:23 am
dbr wrote: Wed Jun 26, 2024 7:01 am The not often recognized huge risk in a TIPS ladder is what the available yield is at the time one is ready and able to invest in the ladder. In the last few years that has flipped from -2% real to +2% real, probably the biggest single change in bond investing over this recent time. A change of 4% in real yield is tremendous. It certainly dwarfs the I bond feeding frenzy for one thing.
I thought it would be interesting to look at the best data we have to evaluate this statement:

The blue line is for the Apr 2028 TIPS that was issued in Apr 1998, and FRED provides history for it since then. The red line is the inflation indexed CMT, which I added just so we could see that the Apr 2028 provides a pretty good TIPS yield history even though it's not constant maturity. The green line is for the 30y inflation indexed CMT, which I added since it's most relevant to the thread topic, although it has the shortest history.
Thanks. That is really helpful as it should give some perspective on the general prospect. How does the data in the chart compare to the data at this site: https://home.treasury.gov/resource-cent ... nth=202406
Those are the inflation indexed CMT yields, so you could construct the same chart for the 10y and 30y from the corresponding columns in that table, but it's much easier to just use FRED.
If I make a calculation error, #Cruncher probably will let me know.
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StillGoing
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

Kevin M wrote: Fri Jun 28, 2024 10:52 am
[large snip]

If I understand your analysis correctly, the problem with it is that coupons do matter, and the price of new issues is relatively constant at 100. The latter is because coupon is not constant for new issues--it is determined by the yield, and is set such that price is close to 100 unless yields are negative.

I started out with similar assumptions in my gap coverage analysis, and then an astute participant in the thread asked the question about the coupons changing for the auctioned TIPS, and from that I realized that using a model assuming fixed coupons (in your case 0%) was flawed. I've since modified my modeling to rectify this.

Here's a chart of 10y auction prices vs. yield that I put together to show that this is indeed the case:

I will do the analysis with coupons at some stage.

However, in the meantime I note that I agree that new issues of a coupon bearing TIPS will have an issue price of close to 100, but a stripped TIPS (i.e., a zero coupon bond) will not have a price of 100. Since zero coupon bonds exist and are purchasable then using those in a model is a valid approach and the results also valid.

Since for a given YTM, bonds with coupons have lower modified durations than the equivalent zero coupon bond, then prices change by less after a change in yield which I think is the point you were making in you other post (correct me if I'm wrong). I also note that I've been using yield and return interchangeably (which is acceptable for zero coupon bonds), but that the zero coupon yield is not the same as par yield and one needs to be converted to the other.

cheers
StillGoing
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

StillGoing wrote: Fri Jun 28, 2024 12:43 pm ...a stripped TIPS (i.e., a zero coupon bond) will not have a price of 100. Since zero coupon bonds exist and are purchasable...
Stripped TIPS are not available anywhere that I have seen. Stripped treasuries, yes. But not TIPS. If they are, please point me in the right direction - I would love to buy some!

Wrench
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

StillGoing wrote: Wed Jun 26, 2024 6:26 amConsider an example, where the retirees want to construct a ladder to 35 years ... However, at the start of retirement there are no TIPS available to cover the 31st to 35th 'withdrawals', so the retirees construct a ladder to 30 years with just under 90% of the portfolio (the payout rate on a 30 year ladder with 2.135% yield is pmt(2.135%,30,-100,0,1)=4.45% and therefore the 'premium' is required income 4.0/4.45=89.82%). The remaining part of the portfolio (10.18% of the initial portfolio) is invested in a 30 years TIPS, which when it matures 30 years later has grown, in real terms, to 19.18% (i.e., 10.18*power(1.02135,30) ) of the initial portfolio value. (underline added)
This would work if the TIPS maturing in 30 years had a zero coupon. But it fails badly for the real case where the TIPS maturing February 2054 has a 2-1/8% coupon. This TIPS value at maturity would not grow from 10.18% to 19.18% of the initial portfolio value. Since its yield is about the same as its coupon, it sells close to par and hardly grows at all in 30 years. If we started with the 30-year ladder and then used 10% of its cost to buy additional 2054 maturity, we'd end up collecting too much each year 2025-2053 and not enough in 2054.

The best way to proceed would be to build a ladder to cover 35 years by buying about six times the amount in 2054 as one would for a 30-year ladder. [1] The coupon interest thrown off every year by the additional purchase of the 2054 substantially reduces the amount needed of TIPS maturing in 2025-2053.

For example, using my TIPS Ladder Builder Excel workbook we can see that a 30-year ladder running 2025-2054 with 40,000 of constant dollars collected each year 2025-2054 would cost \$879K. If we then modify the ladder to have six times the amount of the 2054 maturity, the cost becomes \$983K, an increase of \$104K. But this is the net result of the cost of the 2025-2053 maturities falling \$92K while the cost of the 2054 maturity rose \$196K. [2]

Code: Select all

``````           30-yr   35-yr  Change
2025-2053    840     748     -92
2054     39     235    +196
Total    879     983    +104``````
We get similar figures from the easy-to-use tipsladder.com tool: [3]

Code: Select all

``````           30-yr   35-yr  Change
2025-2053    856     765     -91
2054     39     236    +197
Total    895    1001    +106``````
1. This would be enough to extend the ladder five more years in 2054. The extra \$200K of TIPS maturing in 2054 would be enough to buy \$40K of TIPS maturing each year 2055-2059 if their real yield at that time is 0%. (Since these would be short-term purchases, yields differing from 0% wouldn't have much effect on how much could be bought.)
2. These figures are from the "ToPaste" sheet of my TIPS Ladder Builder Excel workbook. The 30-year column reflects increasing the "Desired Annual Real Amount" in cell B2 on the "Ladder" sheet from "30000" to "40000". The 35-year column reflects then changing the "Multiplier" for the 2054 TIPS in cell N59 from "1" to "6".
• Change the "Last year to be funded" to 2054.
• Change the "Desired annual real income" to "40000".
• Change the "Income requirement kind" to "Specified for each year".
To then create a 35-year ladder:
• Press the browser back button to return to the entry page.
• Change the "Desired annual real income" in 2054 from "40000" to "240000".
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

StillGoing wrote: Fri Jun 28, 2024 12:43 pm
Kevin M wrote: Fri Jun 28, 2024 10:52 am
[large snip]

If I understand your analysis correctly, the problem with it is that coupons do matter, and the price of new issues is relatively constant at 100. The latter is because coupon is not constant for new issues--it is determined by the yield, and is set such that price is close to 100 unless yields are negative.

I started out with similar assumptions in my gap coverage analysis, and then an astute participant in the thread asked the question about the coupons changing for the auctioned TIPS, and from that I realized that using a model assuming fixed coupons (in your case 0%) was flawed. I've since modified my modeling to rectify this.

Here's a chart of 10y auction prices vs. yield that I put together to show that this is indeed the case:

I will do the analysis with coupons at some stage.

However, in the meantime I note that I agree that new issues of a coupon bearing TIPS will have an issue price of close to 100, but a stripped TIPS (i.e., a zero coupon bond) will not have a price of 100. Since zero coupon bonds exist and are purchasable then using those in a model is a valid approach and the results also valid.
I don't think so. You can't buy stripped TIPS at auction (or anywhere else for that matter)--if you could, then the price would vary with yields as do bonds trading on secondary, and my duration matching problem would be solved.

Similarly, since you're dealing with a real life TIPS ladder, not a theoretical one where you can buy zero-coupon TIPS at auction, you must deal with the realities of auction pricing, where it's the coupon that's adjusted based on yield, not price.
StillGoing wrote: Fri Jun 28, 2024 12:43 pmSince for a given YTM, bonds with coupons have lower modified durations than the equivalent zero coupon bond, then prices change by less after a change in yield which I think is the point you were making in you other post (correct me if I'm wrong). I also note that I've been using yield and return interchangeably (which is acceptable for zero coupon bonds), but that the zero coupon yield is not the same as par yield and one needs to be converted to the other.
If I understand what you're saying, then no, it's not about duration at all. It's about auction prices being relatively fixed with variable coupons, and so duration matching just doesn't apply. For duration matching to apply, the cost of the liability you're matching must vary with yield as does the value of the bond portfolio you're using to match the duration of the liability.
If I make a calculation error, #Cruncher probably will let me know.
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StillGoing
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

Thank you for the recent comments. I was wrong in one assumption (about US treasury markets) and consequently wrong in my conclusions.

1) The (non)existence of stripped TIPS. Since https://www.treasurydirect.gov/marketab ... es/strips/, states "Treasury securities with a fixed-principal, such as notes, bonds, and TIPS are eligible and may be stripped." and Zwecher's book (Retirement Portfolios) incorporates them (in either coupon or principal form) I assumed that stripped TIPS were available to retail customers. This was my first mistake! Does anyone know why they are not available?

2) My second mistake, was then assuming that a ladder consisting of zero coupon TIPS was actionable (which, obviously it isn't if they are not available).

FWIW, I've redone my calculations assuming reinvested coupons and found that a 2 percentage point drop in total returns from 2.135% to 0.135% (with coupons of 2.124% and 0.135%) at the start of Year 1, means that the 35th rung is reduced to providing just under 1% income compared to over 3% income for the zero coupon version. In other words, I agree that the interest rate sensitivity of the extended ladder income is larger with coupons than without.

cheers
StillGoing
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### Re: How risky is interest rate risk in TIPS ladders longer than 30 years?

#Cruncher wrote: Fri Jun 28, 2024 5:01 pm
StillGoing wrote: Wed Jun 26, 2024 6:26 amConsider an example, where the retirees want to construct a ladder to 35 years ... However, at the start of retirement there are no TIPS available to cover the 31st to 35th 'withdrawals', so the retirees construct a ladder to 30 years with just under 90% of the portfolio (the payout rate on a 30 year ladder with 2.135% yield is pmt(2.135%,30,-100,0,1)=4.45% and therefore the 'premium' is required income 4.0/4.45=89.82%). The remaining part of the portfolio (10.18% of the initial portfolio) is invested in a 30 years TIPS, which when it matures 30 years later has grown, in real terms, to 19.18% (i.e., 10.18*power(1.02135,30) ) of the initial portfolio value. (underline added)
This would work if the TIPS maturing in 30 years had a zero coupon. But it fails badly for the real case where the TIPS maturing February 2054 has a 2-1/8% coupon. This TIPS value at maturity would not grow from 10.18% to 19.18% of the initial portfolio value. Since its yield is about the same as its coupon, it sells close to par and hardly grows at all in 30 years. If we started with the 30-year ladder and then used 10% of its cost to buy additional 2054 maturity, we'd end up collecting too much each year 2025-2053 and not enough in 2054.

The best way to proceed would be to build a ladder to cover 35 years by buying about six times the amount in 2054 as one would for a 30-year ladder. [1] The coupon interest thrown off every year by the additional purchase of the 2054 substantially reduces the amount needed of TIPS maturing in 2025-2053.

Thank you for all this useful information - I'll have a proper look shortly.

I note that if coupons were to be reinvested and (unrealistically) yields remained constant for the next 30 years, then that part of the portfolio would grow as for the zero coupon case. However, in the more realistic case, the price of the TIPS maturing in, for example, 2054 would increase with decreasing yield and consequently reinvesting the coupons would buy fewer bonds (and the eventually income would be less than expected) and vice versa.

cheers
StillGoing