Covering the TIPS gap years with bracket year duration matching

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protagonist
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Re: Covering the TIPS gap years with bracket year duration matching

Post by protagonist »

bikechuck wrote: Fri Jan 24, 2025 12:58 pm isn't this a two sided coin?
Indeed, it is a two-sided coin. "Reinvestment risk" could also turn into "Reinvestment opportunity", so I don't make as much of an issue of 'reinvestment risk" per se, as do many others.

However, I view the case of TIPS as an exception, if, like me, your purpose of investing in TIPS is to guarantee asset preservation against unpredictable future events.

At today's yields, TIPS not only fulfill that goal, but also provide a nice real return on top of that goal, likely leaving you with greater spending power in the future than you have today. Yields could go up, but they could also turn negative when you want to reinvest.

For that reason, I would avoid reinvestment risk and lock in today's yields, regardless of whether or not they will be better in the future (something we have no way of knowing). Either way, if your goal is similar to mine, your ladder will have nicely met your goal.
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Kevin M
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Calculations for for covering 2036-2039

Post by Kevin M »

Sharing some of the work I've done on calculating how many excess bracket year TIPS to hold for duration matching of 2036-2040. I'll share an overview in this post, and go into more detail in subsequent posts. This is not something I'd expect anyone else to do, but I felt compelled to do it due to dissatisfaction from what I can do with the tips ladder building tools alone; this is primarily because tipsladder.com assumes the bracket year excess bonds are held as long as possible--i.e., the 2034s or 2035s until maturity, and the 2040s until the 2034s or 2035s mature, which is not what we typically intend to do with duration matching.

I calculated the duration matching weightings for the excess of either Jan 2034 and Feb 2040 or Jan 2035 and 2040. For the former it's 0.41 and 0.59, and for the latter it's 0.48 and 0.52 respectively. These weightings are based on current Schwab ask quotes. I haven't yet calculated the weightings for Jul 2034 and Feb 2040. For me, the relevant weightings currently are for Jan 2034, since that's where I hold my lower-bracket excess, and I haven't yet decided if I'm going to switch to Jan 2035 for my lower bracket year holdings.

I ran tipsladder.com with these parameters:

Image

I could pick any choice for the first parameter, since I'll be replacing the values for 2036-2039 in a later step, and tweaking the number of bonds for earlier years as necessary.

I then selected the Funded Years view, and downloaded it to a CSV file, which I then uploaded to a spreadsheet. The downloaded file contains many more fields than those shown on the webpage, which is a big aid to subsequent steps. Here is the way it looked at this point, with a couple of uninteresting columns hidden:

Image

I then modified the spreadsheet to calculate the values in all the fields except Year Funded, CUSIP, and Bond Count. At this point I no longer rely on tipsladder.com for any further calculations.

I modified the rows for 2034 and 2035 to use the actual values for the Jan 2034 and Jan 2035. When I did this, the Jan 2035 was not yet available in TipsLadder.com, but it is now.

The next steps are to make changes to the 2036-2039 rows such that they contain values as if these TIPS were issued today and settle on T+1. Here are those steps for each row, working from 2039 down to 2036, since this minimizes bond count tweaking due to interest from later bonds.
  • Delete CUSIP.
  • Set maturity date to Jan 1 of the Year Funded.
  • Set yield using linear interpolation between the Jan 2035 and Feb 2040 ask yields.
  • Set the coupon to what it would be at auction based on the yield.
  • Set inflation adjusted principal to 1,000.00, since the index ratio at auction would be very close to 1.
  • Tweak the Bond count so that it is the minimum to get the real total income to at least $100K (consistent with the tipsladder.com settings I chose).
  • Calculate the adjusted ask cost per bond based on the yield.
  • Calculate Purchase cost as adjusted cost per bond times bond count. Accrued interest is set to 0, so Total cost equals Purchase cost.
After this I tweaked the bond count for earlier years to get the appropriate real total income; this is not required for subsequent calculations, but it provides a more accurate total ladder cost.

Here's the result:

Image

Then I added some rows with calculations to determine the excess bracket year number of bonds:

Image

I know this is slim on explanations, but I wanted to get it out today since the calculations are based on today's yields, although I pulled the TipsLadder.com data a couple of days ago. More explanations to follow, and of course questions are welcome in the meantime.
If I make a calculation error, #Cruncher probably will let me know.
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Kevin M
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Re: Covering the TIPS gap years with bracket year duration matching

Post by Kevin M »

I want to start adding some explanations and clarifications to my previous post. I'll start with the last part of the post.

To aid in the explanations, I'll unhide one of the columns that were hidden in the screenshot in the previous post, the Adjusted Ask Cost column. I also realized that for completeness I should include accrued interest in calculating total costs. I've also added rows to show totals for the 2034 and 2040, which include both the excess values and the values to actually fund 2034 and 2040. Finally, I mistakenly hid the 2040 row in the previous post's screenshot.

Image

The Gap years total Purchase cost of 347,315 in cell I29, is simply the sum of the Purchase cost values for the gap years:

Code: Select all

=SUM(I15:I18)
Since the effect of duration matching is for the excess bracket year amounts to simulate owning the gap years as if they were part of the ladder, we want the total excess purchase cost of the bracket years to equal the estimated purchase cost of the theoretical gap year TIPS. So this is the value we start with.

The 2034 excess calculated purchase cost of 140,857 in cell I30 is the Jan 2034 excess bracket weight times the Gap years total excess purchase cost. We saw in the previous post that the 2034 excess weight is 0.41, but that's a rounded value, and in the calculation I reference the cell of that sheet directly, and so use the unrounded value:

Code: Select all

=I29*DurWtGapJan2034!G11
For those unfamiliar with spreadsheet syntax, DurWtGapJan2034 is the name of the sheet in which the duration weight calculations are done, and cell G11 in that sheet contains the excess 2034 weight.

The 2040 excess calculated purchase cost of 206,457 in cell I31 is the total calculated purchase cost minus the calculated 2034 cost:

Code: Select all

=I29-I30
The calculated 2034 excess bond count of 141 in cell C30 is the calculated 2034 excess purchase cost divided by the 2034 adjusted purchase cost, rounded to a whole number:

Code: Select all

=ROUND(I30/(H13))
Similarly, the 2040 excess bond count of 144 in cell C31 is the calculated 2040 excess purchase cost divided by the 2040 adjusted purchase cost, rounded to a whole number:

Code: Select all

=ROUND(I31/H19)
Since we can only buy a whole number of bonds, the actual costs will be a bit different than the calculated costs, and rows 34-35 are used to calculate those costs. For example, the actual cost of 140,613 for the excess 2034s in cell I33 is calculated as

Code: Select all

=C33*H13
Accrued interest is then calculated and added to get the total costs in column K.

The total funded year plus excess values are calculated in rows 37 and 38. For example, the bond count total for the 2034s is

Code: Select all

=SUM(C30,C13)
Of course it is fairly straightforward to scale these numbers for a desired annual real income of something other than $100K.
If I make a calculation error, #Cruncher probably will let me know.
MtnBiker
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Re: Calculations for for covering 2036-2039

Post by MtnBiker »

Kevin M wrote: Fri Jan 31, 2025 7:30 pm This is not something I'd expect anyone else to do, but I felt compelled to do it due to dissatisfaction from what I can do with the tips ladder building tools alone; this is primarily because tipsladder.com assumes the bracket year excess bonds are held as long as possible--i.e., the 2034s or 2035s until maturity, and the 2040s until the 2034s or 2035s mature, which is not what we typically intend to do with duration matching.

I calculated the duration matching weightings for the excess of either Jan 2034 and Feb 2040 or Jan 2035 and 2040. For the former it's 0.41 and 0.59, and for the latter it's 0.48 and 0.52 respectively.
Tipsladder.com has evolved so that now it can only cover the 2036-2039 gap using 2035s and 2040s. So, I haven't been able to use it to compare to your results covering 2036-2040 using 2034s and 2040s.

But I can report that using Tipsladder.com also calculates the duration matching weightings for the excess of Jan 2035 and 2040 to be 0.48 and 0.52, respectively. I'm not sure what the benefit would be to go through these lengthy spreadsheet operations to get the same result Tipsladder.com would give in 5 or 10 minutes without touching a spreadsheet?

Duration matching weightings of 0.41 and 0.59 for the excess of Jan 2034 and Feb 2040 for covering 2036-2039 is basically the same as one would calculate using n/6 weights. So, I'm not understanding why you are expressing dissatisfaction with results from tipsladder.com.
_______________________________________
Here are results I got from Tipsladder.com:
2040 - Need 63/0 (2040/2035)
2039 - Need 50/17 (2040/2035)
2038 - Need 38/34 (2040/2035)
2037 - Need 24/51 (2040/2035)
2036 - Need 13/68 (2040/2035)
2035 - Need 0/85 (2040/2035)
Note: the number for each gap year is just linear interpolation of the number held in the bracket years.
Total of excess holdings: 126/170 (2040/2035)
Total cost of excess holdings: 182K/170K (2040/2035)
Excess holding ratio based on cost: 0.52/0.48 (2040/2035)
2040 - Dur=12.79, Income=100.2K
2039 - Dur=12.07, Income=100.0K
2038 - Dur=11.34, Income=100.8K
2037 - Dur=10.58, Income=99.8K
2036 - Dur=9.83, Income=99.9K
2035 - Dur=9.01, Income=100.8K
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Kevin M
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Re: Covering the TIPS gap years with bracket year duration matching

Post by Kevin M »

To further illustrate a source of my discomfort in relying solely upon tipsladder.com for my calculations, consider the following:

Image

The values in column T show the real interest income downloaded from tipsladder.com, and the values in column M are calculated in my spreadsheet. Note that the values for the 2040-2047 are the same, but the values for the gap year TIPS are quite different. The reason is that tipsladder.com considers only interest from 2040 and later maturities as contributing to interest income for the gap years (for this download I chose an option for which only 2034s are used to cover the gap years). This does not compute, since the gap year coupons also will contribute to interest income for the funded year as well as for earlier maturities; the latter is why we see the delta increase for earlier gap years.

Using my own spreadsheet allows me to use my own assumptions about gap year coupons and how they would contribute to interest income. Not only does this have an impact on assumptions for gap year costs, but it also can affect quantities bought for earlier maturities. I can then easily vary my assumptions to see the impact on the values for gap and earlier maturities.

It well could be that one would end up with similar results with a simpler approach, but I won't know that unless I'm able to model things in a way in which I completely understand the inner workings of the model.
If I make a calculation error, #Cruncher probably will let me know.
MtnBiker
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Re: Covering the TIPS gap years with bracket year duration matching

Post by MtnBiker »

For the case where Jan 2035 covers 2035 and duration matched holdings of 2035/2040 cover 2036-2039 (same case as in my previous post), this is the annual real interest income that I see in Tipsladder.com:

2034 $20,084
2035 $15,868
2036 $12,957
2037 $12,368
2038 $11,391
2039 $10,026
2040 $8,274
2041 $6,286

These tipsladder.com real interest values aren't that far off from your values. Of course, one needs to use the manual tool to duration match the gap year properly before the interest payments stabilize to reasonable values. (Obviously, as you showed, the real interest in each gap year will be way off before duration matching.)

Note that my values match your values in 2040 and 2041, as they should.

You are correct that tipsladder.com fails to consider interest from the lower bracket year (2035 excess holdings in my example) as contributing to interest income for the gap years. This slightly underestimates the interest in the lower bracket year (2035) and the earlier gap years. (2036 is underestimated the most, and 2039 is hardly affected at all.) But as you can see, the error is small enough that it only makes a difference of one or two or three bonds per year (for 2035, 2036, and 2037) in this example with 100K of annual real income.

For the average investor with 20K or 30K or real income, I think tipsladder.com is good enough. The annual tipsladder.com real interest amount error is probably lost in the noise caused by the 1K per single bond granularity. I hope you eventually reach this same conclusion.
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Raspberry-503
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Re: Covering the TIPS gap years with bracket year duration matching

Post by Raspberry-503 »

My head hurts as I'm trying to figure out how many 2034-2040s I need to swap for 2035-2040, knowing that my ladder stops in 2038. EVery time I think I understand the explanations above, I seem to get confused.
The rates of the 2035 and 2040 are the same so that helps

Using 1/N am I correct that the percentage IN DOLLARS of each bookend for each year would be:

Code: Select all

        2035  2040
2035	100%	   0%
2036	80%     20%
2037	60%     40%
2038	40%     60%
Is that close enough? what would the relationship be using McCaulay durations?
exodusing
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Re: Covering the TIPS gap years with bracket year duration matching

Post by exodusing »

Kevin M wrote: Sun Feb 02, 2025 8:14 pmThe reason is that tipsladder.com considers only interest from 2040 and later maturities as contributing to interest income for the gap years (for this download I chose an option for which only 2034s are used to cover the gap years). This does not compute, since the gap year coupons also will contribute to interest income for the funded year as well as for earlier maturities; the latter is why we see the delta increase for earlier gap years.
Where is this extra gap year interest income coming from? Bonds maturing 2040 and later are generating interest income for 2036-2039. What else is generating interest income for those years? The 9,251 annual interest from 2040 and later TIPS won't generate additional interest unless invested in something.
MtnBiker
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Re: Covering the TIPS gap years with bracket year duration matching

Post by MtnBiker »

exodusing wrote: Mon Feb 03, 2025 6:05 am Where is this extra gap year interest income coming from? Bonds maturing 2040 and later are generating interest income for 2036-2039. What else is generating interest income for those years? The 9,251 annual interest from 2040 and later TIPS won't generate additional interest unless invested in something.
If each gap year is funded by a mixture of 2034s and 2040s, the proceeds from the 2034s (whether held to maturity and reinvested or sold early and swapped for the actual gap year) produce interest too.
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Re: Covering the TIPS gap years with bracket year duration matching

Post by MtnBiker »

Raspberry-503 wrote: Mon Feb 03, 2025 12:48 am My head hurts as I'm trying to figure out how many 2034-2040s I need to swap for 2035-2040, knowing that my ladder stops in 2038. EVery time I think I understand the explanations above, I seem to get confused.
The rates of the 2035 and 2040 are the same so that helps

Using 1/N am I correct that the percentage IN DOLLARS of each bookend for each year would be:

Code: Select all

        2035  2040
2035	100%	   0%
2036	80%     20%
2037	60%     40%
2038	40%     60%
Is that close enough? what would the relationship be using McCaulay durations?
Your table is correct for showing how to use the N/5 relationship to compute how many 2035-2040 (in dollars) to swap for 2036-2038.

If swapping January 2034-2040 for 2035-2038, the relationship (in dollars) to use is N/6:
(I assume you don't hold any July 2034s.)

Code: Select all

        2034  2040
2034	100%	   0%
2035	83%     17%
2036	67%     33%
2037	50%     50%
2038	33%     67%
If using McCaulay durations, the relationships are virtually identical, since, as you noted, the coupon rates for all these issues are about the same. See the original post.
exodusing
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Re: Covering the TIPS gap years with bracket year duration matching

Post by exodusing »

MtnBiker wrote: Mon Feb 03, 2025 8:29 am
exodusing wrote: Mon Feb 03, 2025 6:05 am Where is this extra gap year interest income coming from? Bonds maturing 2040 and later are generating interest income for 2036-2039. What else is generating interest income for those years? The 9,251 annual interest from 2040 and later TIPS won't generate additional interest unless invested in something.
If each gap year is funded by a mixture of 2034s and 2040s, the proceeds from the 2034s (whether held to maturity and reinvested or sold early and swapped for the actual gap year) produce interest too.
Yes, but if you were to figure cash flow today, based on interest from existing TIPS and maturity proceeds from existing TIPS, then you just get the cash flow shown by tipsladder. You only get more during the gap years (or elsewhere) if you reinvest some or all of that cash flow. No?
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Raspberry-503
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Re: Covering the TIPS gap years with bracket year duration matching

Post by Raspberry-503 »

MtnBiker wrote: Mon Feb 03, 2025 9:02 am If swapping January 2034-2040 for 2035-2038, the relationship (in dollars) to use is N/6:
(I assume you don't hold any July 2034s.)

Code: Select all

        2034  2040
2034	100%	   0%
2035	83%     17%
2036	67%     33%
2037	50%     50%
2038	33%     67%
If using McCaulay durations, the relationships are virtually identical, since, as you noted, the coupon rates for all these issues are about the same. See the original post.
I do have 91282CJY8 Jan 2024s (in excess). Last year was the first year I exchanged (purchased actually)to cover the gap years and I bought 2024s and 2040s
so I need to figure out how many to keep and how many to sell (and how many 2040s) to buy 91282CML2 Jan 2025s
Is there a reason 2035 should be covered with a mix of 2034s and 2035s? I ma be even more confused than I thought
MtnBiker
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Re: Covering the TIPS gap years with bracket year duration matching

Post by MtnBiker »

exodusing wrote: Mon Feb 03, 2025 9:21 am
MtnBiker wrote: Mon Feb 03, 2025 8:29 am

If each gap year is funded by a mixture of 2034s and 2040s, the proceeds from the 2034s (whether held to maturity and reinvested or sold early and swapped for the actual gap year) produce interest too.
Yes, but if you were to figure cash flow today, based on interest from existing TIPS and maturity proceeds from existing TIPS, then you just get the cash flow shown by tipsladder. You only get more during the gap years (or elsewhere) if you reinvest some or all of that cash flow. No?
Yes, you only get more interest than shown in tipsladder during the gap years if you reinvest the proceeds from the excess lower bracket year (2034) holdings (that are held expressly for the purpose of providing partial funding of a gap year beyond 2034). Since the purpose of the excess 2034s is to fund 2035-2039, it will necessarily be reinvested in something at some time. Whatever form that reinvestment may take, it will throw off some amount of interest in the gap years.

Tipsladder knows the difference between 2034s funding the 2034 year and individual blocks of excess holdings to cover each of the individual gap years. But, in its present form, tipsladder ignores the fact that interest will be generated from reinvestment of the excess 2034s in the time period from 2034 to each gap year. Thus, tipsladder is not a perfect model for the duration-matched swaps being discussed in this thread.

It is fair to debate whether the model is or isn't "good enough" to fit any one's particular situation. Even though I know it is imperfect, the errors (failure to account for interest from reinvestment during the gap years) are small enough that I find tipsladder to be "good enough" to model my particular situation.
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Re: Covering the TIPS gap years with bracket year duration matching

Post by MtnBiker »

Raspberry-503 wrote: Mon Feb 03, 2025 10:03 am
MtnBiker wrote: Mon Feb 03, 2025 9:02 am If swapping January 2034-2040 for 2035-2038, the relationship (in dollars) to use is N/6:
(I assume you don't hold any July 2034s.)

Code: Select all

        2034  2040
2034	100%	   0%
2035	83%     17%
2036	67%     33%
2037	50%     50%
2038	33%     67%
If using McCaulay durations, the relationships are virtually identical, since, as you noted, the coupon rates for all these issues are about the same. See the original post.
I do have 91282CJY8 Jan 2024s (in excess). Last year was the first year I exchanged (purchased actually)to cover the gap years and I bought 2024s and 2040s
so I need to figure out how many to keep and how many to sell (and how many 2040s) to buy 91282CML2 Jan 2025s
Is there a reason 2035 should be covered with a mix of 2034s and 2035s? I ma be even more confused than I thought
I tried to answer your question from the perspective of someone who holds excess TIPS maturing in January 2034 and February 2040 for the purpose of funding one or more gap years. The proportions shown in the table that I presented above shows the proportions (in dollars) to put toward any particular gap year. The proportions are the same regardless of whether you fill one gap year or all four using the proceeds from sale of the excess bracket year holdings.

If you have additional money from some other source to buy the 2035s directly, that is just fine. Ignore the 2034/2040 ratio for buying 2035 if you are buying with new money. But if you are buying 2035s using proceeds from sale of 2034s and 2040s, the ratio listed is a way to do it in a duration-matched manner (hedging against interest rate risk).

Tipsladder.com may be helpful for visualizing how much to swap to get a particular real income amount each year.
Last edited by MtnBiker on Mon Feb 03, 2025 10:43 am, edited 1 time in total.
exodusing
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Re: Covering the TIPS gap years with bracket year duration matching

Post by exodusing »

MtnBiker wrote: Mon Feb 03, 2025 10:24 am
exodusing wrote: Mon Feb 03, 2025 9:21 am
Yes, but if you were to figure cash flow today, based on interest from existing TIPS and maturity proceeds from existing TIPS, then you just get the cash flow shown by tipsladder. You only get more during the gap years (or elsewhere) if you reinvest some or all of that cash flow. No?
Yes, you only get more interest than shown in tipsladder during the gap years if you reinvest the proceeds from the excess lower bracket year (2034) holdings (that are held expressly for the purpose of providing partial funding of a gap year beyond 2034). Since the purpose of the excess 2034s is to fund 2035-2039, it will necessarily be reinvested in something at some time. Whatever form that reinvestment may take, it will throw off some amount of interest in the gap years.

Tipsladder knows the difference between 2034s funding the 2034 year and individual blocks of excess holdings to cover each of the individual gap years. But, in its present form, tipsladder ignores the fact that interest will be generated from reinvestment of the excess 2034s in the time period from 2034 to each gap year. Thus, tipsladder is not a perfect model for the duration-matched swaps being discussed in this thread.

It is fair to debate whether the model is or isn't "good enough" to fit any one's particular situation. Even though I know it is imperfect, the errors (failure to account for interest from reinvestment during the gap years) are small enough that I find tipsladder to be "good enough" to model my particular situation.
Yes, the plan is to reinvest some of the 2034s to gap years when gap year TIPS become available and those as yet unannounced TIPS will throw off cash flow during gap years, eventually all of them. Earlier years may also change, although probably not by much.

I continue to find my plan to use #Cruncher's spreadsheet to be good enough. As mentioned, I currently intend to fill it in as if I was starting today (i.e., a multiple of one for 2034 and three for each of 2035 and 2040), then reallocate bracket years as appropriate, at least for the 2035s (it would also have me do some minimal trading in other years, which I will ignore). I'll need Feb 15 interest to have sufficient funds for the 2035s. Just selling enough 2034s and 2040s to fund one year of 2035s would also work and would decrease trading costs (bid-ask spread) by a bit, as you've noted. There may also be an on-the-run premium. It's not clear to me that doing anything more sophisticated would make enough difference to matter, although I'm open to being convinced.
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Re: Covering the TIPS gap years with bracket year duration matching

Post by MtnBiker »

exodusing wrote: Mon Feb 03, 2025 10:43 am Yes, the plan is to reinvest some of the 2034s to gap years when gap year TIPS become available and those as yet unannounced TIPS will throw off cash flow during gap years, eventually all of them. Earlier years may also change, although probably not by much.

I continue to find my plan to use #Cruncher's spreadsheet to be good enough. As mentioned, I currently intend to fill it in as if I was starting today (i.e., a multiple of one for 2034 and three for each of 2035 and 2040), then reallocate bracket years as appropriate, at least for the 2035s (it would also have me do some minimal trading in other years, which I will ignore). I'll need Feb 15 interest to have sufficient funds for the 2035s. Just selling enough 2034s and 2040s to fund one year of 2035s would also work and would decrease trading costs (bid-ask spread) by a bit, as you've noted. There may also be an on-the-run premium. It's not clear to me that doing anything more sophisticated would make enough difference to matter, although I'm open to being convinced.
It sounds like you understand this stuff better than I do. I don't have anything to add.

I haven't looked at #Cruncher's spreadsheet lately. I would note that his spreadsheet in past years handled interest in the gap years in strange ways that was more confusing than tipsladder. In that earlier version, putting in a multiple of one for 2034 and three for each of 2035 and 2040 would not have resulted in the desired duration-matched 50-50 mix in dollars of excess bracket year holdings. I know that he has recently updated the spreadsheet to include another "psuedo" excess holding that is supposed to allow more accurate treatment of gap-year interest. I haven't made any effort to check that out. If you have any comments on the accuracy/utility of the new version of the spreadsheet, please feel free to report back.
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Raspberry-503
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Re: Covering the TIPS gap years with bracket year duration matching

Post by Raspberry-503 »

MtnBiker wrote: Mon Feb 03, 2025 10:40 am
Raspberry-503 wrote: Mon Feb 03, 2025 10:03 am

I do have 91282CJY8 Jan 2024s (in excess). Last year was the first year I exchanged (purchased actually)to cover the gap years and I bought 2024s and 2040s
so I need to figure out how many to keep and how many to sell (and how many 2040s) to buy 91282CML2 Jan 2025s
Is there a reason 2035 should be covered with a mix of 2034s and 2035s? I ma be even more confused than I thought
I tried to answer your question from the perspective of someone who holds excess TIPS maturing in January 2034 and February 2040 for the purpose of funding one or more gap years. The proportions shown in the table that I presented above shows the proportions (in dollars) to put toward any particular gap year. The proportions are the same regardless of whether you fill one gap year or all four using the proceeds from sale of the excess bracket year holdings.

If you have additional money from some other source to buy the 2035s directly, that is just fine. Ignore the 2034/2040 ratio for buying 2035 if you are buying with new money. But if you are buying 2035s using proceeds from sale of 2034s and 2040s, the ratio listed is a way to do it in a duration-matched manner (hedging against interest rate risk).

Tipsladder.com may be helpful for visualizing how much to swap to get a particular real income amount each year.
We must be missing each other somewhere, sorry. I don't have extra money to buy additional TIPS, I did last year to buy 2040s and 2034s but now it needs to be "self funded". i.e. sell excess bookend year TIPS already in the ladder to buy the missing years. We are in 2025, and Jan 2035 TIPS are available, why is 2035 not 100% covered by 2035 TIPS? The percentages you show are what I used last year to determine the split between 2034s and 2040s. Now I want to sell excess 2034s (year 2034 will indeed be 100% 2034 TIPS)) and buy 2035s to cover 2035 and the missing years in the right proportion.
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Re: Covering the TIPS gap years with bracket year duration matching

Post by exodusing »

MtnBiker wrote: Mon Feb 03, 2025 11:02 am
exodusing wrote: Mon Feb 03, 2025 10:43 am Yes, the plan is to reinvest some of the 2034s to gap years when gap year TIPS become available and those as yet unannounced TIPS will throw off cash flow during gap years, eventually all of them. Earlier years may also change, although probably not by much.

I continue to find my plan to use #Cruncher's spreadsheet to be good enough. As mentioned, I currently intend to fill it in as if I was starting today (i.e., a multiple of one for 2034 and three for each of 2035 and 2040), then reallocate bracket years as appropriate, at least for the 2035s (it would also have me do some minimal trading in other years, which I will ignore). I'll need Feb 15 interest to have sufficient funds for the 2035s. Just selling enough 2034s and 2040s to fund one year of 2035s would also work and would decrease trading costs (bid-ask spread) by a bit, as you've noted. There may also be an on-the-run premium. It's not clear to me that doing anything more sophisticated would make enough difference to matter, although I'm open to being convinced.
It sounds like you understand this stuff better than I do. I don't have anything to add.

I haven't looked at #Cruncher's spreadsheet lately. I would note that his spreadsheet in past years handled interest in the gap years in strange ways that was more confusing than tipsladder. In that earlier version, putting in a multiple of one for 2034 and three for each of 2035 and 2040 would not have resulted in the desired duration-matched 50-50 mix in dollars of excess bracket year holdings. I know that he has recently updated the spreadsheet to include another "psuedo" excess holding that is supposed to allow more accurate treatment of gap-year interest. I haven't made any effort to check that out. If you have any comments on the accuracy/utility of the new version of the spreadsheet, please feel free to report back.
I might have a good understanding how to implement a plan, but I'm not sure if my plan could be improved in a meaningful manner. Intuitively it makes sense to me to reallocate what I own now to what I'd own if I started from scratch today, especially if bid-ask spreads are not meaningful (I can figure that out by looking at pricing and the answers seems to be 11-25 basis points) and there's not much of an on-the-run premium (less clear how to estimate that unless there's a discontinuity when comparing to an interpolation of the 2034s and 2040s, which I don't see when I graph the TIPS yield curve).

The latest version of #Cruncher's spreadsheet includes the Jan 2035s, which is all I need beyond what there was earlier. As I noted upthread, I added columns to compute the difference between what I hold and what I "should" hold (needed minus already held and the cost of those TIPS). I filled in my existing holdings (using Python, but it's straightforward enough to do manually), then changed the multiples for the existing 2034s, the new Jan 2035s and the existing 2040s as indicated. The spreadsheet then shows what to buy and sell.
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Re: Covering the TIPS gap years with bracket year duration matching

Post by MtnBiker »

Raspberry-503 wrote: Mon Feb 03, 2025 11:12 am
We must be missing each other somewhere, sorry. I don't have extra money to buy additional TIPS, I did last year to buy 2040s and 2034s but now it needs to be "self funded". i.e. sell excess bookend year TIPS already in the ladder to buy the missing years. We are in 2025, and Jan 2035 TIPS are available, why is 2035 not 100% covered by 2035 TIPS? The percentages you show are what I used last year to determine the split between 2034s and 2040s. Now I want to sell excess 2034s (year 2034 will indeed be 100% 2034 TIPS)) and buy 2035s to cover 2035 and the missing years in the right proportion.
2035 will be covered 100% by 2035 after you buy it. Before you buy it, it is covered by the bookend years in the proportions shown. I am suggesting that you sell excess 2034s and excess 2040s in the proportions shown (in dollars) and use the proceeds to buy the 2035s. Does that make sense?

You don’t need to sell or buy anything to cover the other missing years in the right proportions (assuming you held the right proportions from the beginning). As long as you keep 2034 and 2040 as the bookends, the proportions held for each gap year never changes.

If, at some point in the future, you want to sell all the excess 2034s and part of the 2040s, and change to some other bookend year, then we could discuss that option then. For now, let’s leave that option on the table until we agree on the basics.
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Re: Covering the TIPS gap years with bracket year duration matching

Post by exodusing »

MtnBiker wrote: Mon Feb 03, 2025 12:51 pm
Raspberry-503 wrote: Mon Feb 03, 2025 11:12 am
We must be missing each other somewhere, sorry. I don't have extra money to buy additional TIPS, I did last year to buy 2040s and 2034s but now it needs to be "self funded". i.e. sell excess bookend year TIPS already in the ladder to buy the missing years. We are in 2025, and Jan 2035 TIPS are available, why is 2035 not 100% covered by 2035 TIPS? The percentages you show are what I used last year to determine the split between 2034s and 2040s. Now I want to sell excess 2034s (year 2034 will indeed be 100% 2034 TIPS)) and buy 2035s to cover 2035 and the missing years in the right proportion.
2035 will be covered 100% by 2035 after you buy it. Before you buy it, it is covered by the bookend years in the proportions shown. I am suggesting that you sell excess 2034s and excess 2040s in the proportions shown (in dollars) and use the proceeds to buy the 2035s. Does that make sense?

You don’t need to sell or buy anything to cover the other missing years in the right proportions (assuming you held the right proportions from the beginning). As long as you keep 2034 and 2040 as the bookends, the proportions held for each gap year never changes.

If, at some point in the future, you want to sell all the excess 2034s and part of the 2040s, and change to some other bookend year, then we could discuss that option then. For now, let’s leave that option on the table until we agree on the basics.
It seems there are a couple of choices when you reallocate.

One is whether to hold the excess TIPS in the 2034s or the 2035s. Obviously you'd sell more 2034s if you want to hold the excess in the 2035s rather than leave them in the 2034s. I suppose there are intermediate solutions, but that just complicates things.

The other is how to determine how much to reallocate. One method is to use percentages as MtnBiker illustrates. The other is to use tipsladder.com or #Cruncher's spreadsheet to figure out how you'd allocate if starting today (subject to the decision about where to hold the excess TIPS). This is likely a less important decision.
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Re: Covering the TIPS gap years with bracket year duration matching

Post by MtnBiker »

exodusing wrote: Mon Feb 03, 2025 11:18 am
I might have a good understanding how to implement a plan, but I'm not sure if my plan could be improved in a meaningful manner. Intuitively it makes sense to me to reallocate what I own now to what I'd own if I started from scratch today, especially if bid-ask spreads are not meaningful (I can figure that out by looking at pricing and the answers seems to be 11-25 basis points) and there's not much of an on-the-run premium (less clear how to estimate that unless there's a discontinuity when comparing to an interpolation of the 2034s and 2040s, which I don't see when I graph the TIPS yield curve).
I took a look at quotes at Vanguard at about 2PM EST. A snapshot of what I saw for selling and buying in a quantity of 5 or more was something like this:

January 2034, Sell at yield of 2.061
January 2035, Buy at a yield of 2.082
February 2040, Sell at a yield of 2.228

Linear interpolation between 2034 and 2040 would indicate a "fair" sell yield for 2035s would be about 2.088. If one can buy at 2.082, then the "cost" of the swap is only about 0.6 bps in yield. I'm not seeing any "on the run" premium in those numbers. (The situation looked quite different at this time a year ago; the buy yield for January 2034 was well below the sell yield of the April 2032 that I was trying to swap.)
exodusing wrote: Mon Feb 03, 2025 11:18 am The latest version of #Cruncher's spreadsheet includes the Jan 2035s, which is all I need beyond what there was earlier. As I noted upthread, I added columns to compute the difference between what I hold and what I "should" hold (needed minus already held and the cost of those TIPS). I filled in my existing holdings (using Python, but it's straightforward enough to do manually), then changed the multiples for the existing 2034s, the new Jan 2035s and the existing 2040s as indicated. The spreadsheet then shows what to buy and sell.
The reality check that I would suggest doing before acting on the spreadsheet instructions, is to verify that what you will have after you have done the buys and sells looks right. The duration-matched excess 2035/2040 bracket year holdings ratio should be approximately 50/50 in dollars. If it is not, then something is wrong with using multipliers of 3 and 3 for 2035 and 2040.

In this post, viewtopic.php?p=8213677#p8213677, and preceding posts referenced within that post, #Cruncher explains how to use the "pseudo 2/15/2035 TIPS" for covering the gap years. My understanding is that multipliers used should be 3, 2, and 1 for 2035, pseudo 2/15/2035 TIPS, and 2040, respectively.
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Re: Covering the TIPS gap years with bracket year duration matching

Post by exodusing »

MtnBiker wrote: Mon Feb 03, 2025 1:42 pm
exodusing wrote: Mon Feb 03, 2025 11:18 am
I might have a good understanding how to implement a plan, but I'm not sure if my plan could be improved in a meaningful manner. Intuitively it makes sense to me to reallocate what I own now to what I'd own if I started from scratch today, especially if bid-ask spreads are not meaningful (I can figure that out by looking at pricing and the answers seems to be 11-25 basis points) and there's not much of an on-the-run premium (less clear how to estimate that unless there's a discontinuity when comparing to an interpolation of the 2034s and 2040s, which I don't see when I graph the TIPS yield curve).
I took a look at quotes at Vanguard at about 2PM EST. A snapshot of what I saw for selling and buying in a quantity of 5 or more was something like this:

January 2034, Sell at yield of 2.061
January 2035, Buy at a yield of 2.082
February 2040, Sell at a yield of 2.228

Linear interpolation between 2034 and 2040 would indicate a "fair" sell yield for 2035s would be about 2.088. If one can buy at 2.082, then the "cost" of the swap is only about 0.6 bps in yield. I'm not seeing any "on the run" premium in those numbers. (The situation looked quite different at this time a year ago; the buy yield for January 2034 was well below the sell yield of the April 2032 that I was trying to swap.)
I'm glad that doing the math gives the same answer as looking at the yield curve.
MtnBiker wrote: Mon Feb 03, 2025 1:42 pm
exodusing wrote: Mon Feb 03, 2025 11:18 am The latest version of #Cruncher's spreadsheet includes the Jan 2035s, which is all I need beyond what there was earlier. As I noted upthread, I added columns to compute the difference between what I hold and what I "should" hold (needed minus already held and the cost of those TIPS). I filled in my existing holdings (using Python, but it's straightforward enough to do manually), then changed the multiples for the existing 2034s, the new Jan 2035s and the existing 2040s as indicated. The spreadsheet then shows what to buy and sell.
The reality check that I would suggest doing before acting on the spreadsheet instructions, is to verify that what you will have after you have done the buys and sells looks right. The duration-matched excess 2035/2040 bracket year holdings ratio should be approximately 50/50 in dollars. If it is not, then something is wrong with using multipliers of 3 and 3 for 2035 and 2040.

In this post, viewtopic.php?p=8213677#p8213677, and preceding posts referenced within that post, #Cruncher explains how to use the "pseudo 2/15/2035 TIPS" for covering the gap years. My understanding is that multipliers used should be 3, 2, and 1 for 2035, pseudo 2/15/2035 TIPS, and 2040, respectively.
I'm getting 52/48 in dollars based on Friday's pricing.

I'm not clear to me what's going on with that post. If nothing else, 3-3 makes more intuitive sense than 3-2-1 (putting 5x to 2035 and 1x to 2040), which would seem to overweight the earlier TIPS and therefore not be as good at duration matching.
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Re: Covering the TIPS gap years with bracket year duration matching

Post by Kevin M »

exodusing wrote: Mon Feb 03, 2025 6:05 am
Kevin M wrote: Sun Feb 02, 2025 8:14 pmThe reason is that tipsladder.com considers only interest from 2040 and later maturities as contributing to interest income for the gap years (for this download I chose an option for which only 2034s are used to cover the gap years). This does not compute, since the gap year coupons also will contribute to interest income for the funded year as well as for earlier maturities; the latter is why we see the delta increase for earlier gap years.
Where is this extra gap year interest income coming from? Bonds maturing 2040 and later are generating interest income for 2036-2039. What else is generating interest income for those years? The 9,251 annual interest from 2040 and later TIPS won't generate additional interest unless invested in something.
Once you've filled the gap years, you'll be receiving interest from those bonds as well as from the longer maturities. For example, for Jan 2036 you'll not only receive one coupon payment for that bond in 2036, but you'll also receive two coupon payments each in 2036 from the 2037-2039 bonds, as well as any longer maturity bonds in your ladder.

The largest component of real interest income for all but the latest funded year in the ladder is interest from the longer maturity bonds. The total real interest income for each funded year is the sum of the last year's interest for the bond maturing in the funded year and the annual interest for all of the longer-maturity bonds in the ladder. Indeed, in my spreadsheet I have separate columns for each of these components (not shown in the screenshots).

Those who want to fill the gaps as early as possible will have them filled by early 2029 (after the Jan 2039 is issued). Even those who wait until the 2034s or 2035s mature would (or could) fill them then, so by 2036 you'd be receiving interest income from the later gap years.

The more interest income you have for a funded year, the less real principle you need to get your desired annual real amount/income.

Of course we don't know what the coupons will be for the gap years, but we know that they'll be greater than 0 (at least 0.125%). One can make whatever assumptions they want, including the ones made by the ladder building tools.
If I make a calculation error, #Cruncher probably will let me know.
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Re: Covering the TIPS gap years with bracket year duration matching

Post by Kevin M »

MtnBiker wrote: Mon Feb 03, 2025 8:29 am
exodusing wrote: Mon Feb 03, 2025 6:05 am Where is this extra gap year interest income coming from? Bonds maturing 2040 and later are generating interest income for 2036-2039. What else is generating interest income for those years? The 9,251 annual interest from 2040 and later TIPS won't generate additional interest unless invested in something.
If each gap year is funded by a mixture of 2034s and 2040s, the proceeds from the 2034s (whether held to maturity and reinvested or sold early and swapped for the actual gap year) produce interest too.
Not what I was talking about, which I just now explained in my reply to exodusing.

Interest from the 2034 (or 2035 or whatever the lowest bracket year is) contributes real interest income to earlier funded years, and thus reduces the amount of principal required in those years. It's maturities greater than the funded year that add interest income to the funded year.
If I make a calculation error, #Cruncher probably will let me know.
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Re: Covering the TIPS gap years with bracket year duration matching

Post by MtnBiker »

exodusing wrote: Mon Feb 03, 2025 2:08 pm
MtnBiker wrote: Mon Feb 03, 2025 1:42 pm
The reality check that I would suggest doing before acting on the spreadsheet instructions, is to verify that what you will have after you have done the buys and sells looks right. The duration-matched excess 2035/2040 bracket year holdings ratio should be approximately 50/50 in dollars. If it is not, then something is wrong with using multipliers of 3 and 3 for 2035 and 2040.

In this post, viewtopic.php?p=8213677#p8213677, and preceding posts referenced within that post, #Cruncher explains how to use the "pseudo 2/15/2035 TIPS" for covering the gap years. My understanding is that multipliers used should be 3, 2, and 1 for 2035, pseudo 2/15/2035 TIPS, and 2040, respectively.
I'm not clear to me what's going on with that post. If nothing else, 3-3 makes more intuitive sense than 3-2-1 (putting 5x to 2035 and 1x to 2040), which would seem to overweight the earlier TIPS and therefore not be as good at duration matching.
In the earlier version of the spreadsheet, the problem with using multipliers of 3 and 3 for 2035 and 2040 would be that 2035 was assigned too much interest income and therefore a multiplier of 3 for 2035 resulted in buying too little excess principal for 2035.

I think the new version may be intended to fix that issue. The "pseudo 2/15/2035 TIPS" has the characteristics of the 2040, so my understanding is that putting 2x in "pseudo 2/15/2035" and 1x in 2040 is the way the new version handles 2x excess 2040 (to be sold early) and 1x maturing in 2040.
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Re: Covering the TIPS gap years with bracket year duration matching

Post by exodusing »

MtnBiker wrote: Mon Feb 03, 2025 2:39 pm
exodusing wrote: Mon Feb 03, 2025 2:08 pm

I'm not clear to me what's going on with that post. If nothing else, 3-3 makes more intuitive sense than 3-2-1 (putting 5x to 2035 and 1x to 2040), which would seem to overweight the earlier TIPS and therefore not be as good at duration matching.
In the earlier version of the spreadsheet, the problem with using multipliers of 3 and 3 for 2035 and 2040 would be that 2035 was assigned too much interest income and therefore a multiplier of 3 for 2035 resulted in buying too little excess principal for 2035.

I think the new version may be intended to fix that issue. The "pseudo 2/15/2035 TIPS" has the characteristics of the 2040, so my understanding is that putting 2x in "pseudo 2/15/2035" and 1x in 2040 is the way the new version handles 2x excess 2040 (to be sold early) and 1x maturing in 2040.
A new long-term ladder from tipsladder.com would fund 2035 and 2040 with approximately equal cost, which is what setting 2035 and 2040 at 3x with #Cruncher's spreadsheet would do. 3-2-1 would put only about 14% into the 2040.

The pseudo 2/15/2035 has coupon, yield and price numbers that are very similar to the 1/15/2035 TIPS while CPI adjusted principal is the same as the 2040.
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Re: Covering the TIPS gap years with bracket year duration matching

Post by MtnBiker »

exodusing wrote: Mon Feb 03, 2025 3:01 pm
MtnBiker wrote: Mon Feb 03, 2025 2:39 pm

In the earlier version of the spreadsheet, the problem with using multipliers of 3 and 3 for 2035 and 2040 would be that 2035 was assigned too much interest income and therefore a multiplier of 3 for 2035 resulted in buying too little excess principal for 2035.

I think the new version may be intended to fix that issue. The "pseudo 2/15/2035 TIPS" has the characteristics of the 2040, so my understanding is that putting 2x in "pseudo 2/15/2035" and 1x in 2040 is the way the new version handles 2x excess 2040 (to be sold early) and 1x maturing in 2040.
A new long-term ladder from tipsladder.com would fund 2035 and 2040 with approximately equal cost, which is what setting 2035 and 2040 at 3x with #Cruncher's spreadsheet would do. 3-2-1 would put only about 14% into the 2040.

The pseudo 2/15/2035 has coupon, yield and price numbers that are very similar to the 1/15/2035 TIPS while CPI adjusted principal is the same as the 2040.
Ok, I hope it works for you.
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Re: Covering the TIPS gap years with bracket year duration matching

Post by #Cruncher »

exodusing wrote: Thu Jan 23, 2025 8:00 am My plan for reallocating after the auction of the 2035s:
  1. List my current holding in #Cruncher's spreadsheet.
  2. Set the Multiplier for Jan 2034s to 1, the Jan 2035s to 3 and the Jan 2040s to 3.
  3. Set Sell Excess Bonds to TRUE.
  4. Set DARA to an amount which minimizes trading (spread between Held and Needed). This is higher than my original DARA due to subsequent inflation, etc. I inserted new columns R and S. R is P-0 (needed minus held) and S is the value of the R TIPS. I checked my DARA by summing column R (sum of bonds to buy/sell), then using Goal Seek to see what DARA results in 0 trades.
  5. Within the first few weeks of February sell 2034s and 2040s to buy 2035s. If I'm a bit short, I'll wait until Feb 15 for interest payments from other TIPS.
I've made up an illustration of exodusing's approach. In February 2024 Sam built a 30,000 constant dollar per year ladder with rungs running from 2025-2054. He used the 2/23/2024 version of my TIPS Ladder Builder Excel workbook. He kept all the default parameters except he entered "3.5" in the "Multiplier" column for the January 2034 and February 2040 maturities. This was to provide excess collections to later fund the five years 2035-2039 when TIPS maturing in those years became available.

Now, in February 2025 Sam wants to shift the excess Jan 2034's to the newly issued January 2035's. To fund this he will sell all but one rung of the Jan 2034's and some of the excess Feb 2040's. To determine exactly how much to sell of the Jan 2034's and Feb 2040's and how much to buy of the Jan 2035's Sam makes the following modifications to the "Ladder" sheet of the current 1/31/2035 version of the workbook:
  • Enter the number of TIPS 2026-2054 from last year's 2/23/2024 version of the workbook ("Total" column Q) in the "Already Held" (column O) of the current version of the workbook. (This is not a simple copy and paste of all 29 values because the current workbook version has new rows for new TIPS.)
  • Enter the following in the "Multiplier" column (N):
    • Jan 2034: 1
    • Jan 2035: 3
    • Feb 2040: 3
    • Other rows that have a value entered in the "Already Held" column: 1
    • All other rows: <blank> (The "Multiplier" column should total 29.)
  • Replace cell G1 (Real $ Base Date) with "2/26/2024", the date from the previous year's workbook. This will change cell G2 (Ref CPI on Base Date) to "306.78807". This will set new purchases to be in terms of the same constant dollar date as was the ladder built the previous year.
  • Change cell O2 (Sell Excess Bonds) to TRUE (selected from a drop-down menu).
  • Change cell T1 (Display) to "Buy Or Sell" (selected from a drop-down menu).
Here is the resulting list of the needed purchases and sales from the "ToPaste" sheet.

Code: Select all

Buy Or Sell Bonds                                                       --- Proceeds in 2/26/2024 Dollars ---
                        Ask                              Nbr                        Final Previous      Total
  Matures   Coupon     Price    Yield    CUSIP    Mult  Bnds      Cost   Principal Coupon  Coupons   Proceeds
 1/15/2029  0.875%   96.43750  1.815%  9128285W6     1    -1     -1,206     -1,215     -5      -32     -1,252
 1/15/2030  0.125%   91.81250  1.865%  912828Z37     1     1      1,126      1,192      1        6      1,199
 1/15/2031  0.125%   89.87500  1.937%  91282CBF7     1    -1     -1,089     -1,179     -1       -7     -1,187
 
 1/15/2034  1.750%   96.96875  2.123%  91282CJY8     1   -46    -45,826    -45,910   -402   -6,427    -52,739
 1/15/2035  2.125%   99.71875  2.155%  91282CML2     3    62     61,878     60,271    640   11,527     72,439
 2/15/2040  2.125%   98.06250  2.279%  912810QF8     3   -10    -14,459    -14,194   -151   -4,223    -18,568

                                              Total -->    5        424     -1,034     83      844       -107
  Total only 3 bonds Jan 2034, Jan 2035, & Feb 2040 -->    6      1,593        168     88      877      1,132
The "Bnds" column in the table shows that Sam should sell 46 of the January 2034's and 10 of the February 2040's; and use the proceeds to buy 62 of the new January 2035's. It also shows selling one Jan 2029 and one Jan 2031 and buying one Jan 2030. If these three small transactions are ignored, the bottom line shows a net cost of $1,593 and a net increase in proceeds of $1,132. (The cost is based on the 1/31/2025 WSJ Quotes and the proceeds are in 2/26/2024 constant dollars.)

I didn't have to modify cell B2 (Desired Annual Real Amount -- DARA) nor add columns as exodusing did in point # 4 quoted above. Sam can continue this process next February entering the following multipliers:
Jan 2035: 1
Jan 2036: 2.5
Feb 2040: 2.5

I don't imagine this process is as accurate as the ones presented by Kevin M and MtnBiker in this thread. But I think it is adequate.
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Re: Covering the TIPS gap years with bracket year duration matching

Post by protagonist »

#Cruncher wrote: Tue Feb 04, 2025 1:58 pm
exodusing wrote: Thu Jan 23, 2025 8:00 am My plan for reallocating after the auction of the 2035s:
  1. List my current holding in #Cruncher's spreadsheet.
  2. Set the Multiplier for Jan 2034s to 1, the Jan 2035s to 3 and the Jan 2040s to 3.
  3. Set Sell Excess Bonds to TRUE.
  4. Set DARA to an amount which minimizes trading (spread between Held and Needed). This is higher than my original DARA due to subsequent inflation, etc. I inserted new columns R and S. R is P-0 (needed minus held) and S is the value of the R TIPS. I checked my DARA by summing column R (sum of bonds to buy/sell), then using Goal Seek to see what DARA results in 0 trades.
  5. Within the first few weeks of February sell 2034s and 2040s to buy 2035s. If I'm a bit short, I'll wait until Feb 15 for interest payments from other TIPS.
I've made up an illustration of exodusing's approach. In February 2024 Sam built a 30,000 constant dollar per year ladder with rungs running from 2025-2054. He used the 2/23/2024 version of my TIPS Ladder Builder Excel workbook. He kept all the default parameters except he entered "3.5" in the "Multiplier" column for the January 2034 and February 2040 maturities. This was to provide excess collections to later fund the five years 2035-2039 when TIPS maturing in those years became available.

Now, in February 2025 Sam wants to shift the excess Jan 2034's to the newly issued January 2035's. To fund this he will sell all but one rung of the Jan 2034's and some of the excess Feb 2040's. To determine exactly how much to sell of the Jan 2034's and Feb 2040's and how much to buy of the Jan 2035's Sam makes the following modifications to the "Ladder" sheet of the current 1/31/2035 version of the workbook:
  • Enter the number of TIPS 2026-2054 from last year's 2/23/2024 version of the workbook ("Total" column Q) in the "Already Held" (column O) of the current version of the workbook. (This is not a simple copy and paste of all 29 values because the current workbook version has new rows for new TIPS.)
  • Enter the following in the "Multiplier" column (N):
    • Jan 2034: 1
    • Jan 2035: 3
    • Feb 2040: 3
    • Other rows that have a value entered in the "Already Held" column: 1
    • All other rows: <blank> (The "Multiplier" column should total 29.)
  • Replace cell G1 (Real $ Base Date) with "2/26/2024", the date from the previous year's workbook. This will change cell G2 (Ref CPI on Base Date) to "306.78807". This will set new purchases to be in terms of the same constant dollar date as was the ladder built the previous year.
  • Change cell O2 (Sell Excess Bonds) to TRUE (selected from a drop-down menu).
  • Change cell T1 (Display) to "Buy Or Sell" (selected from a drop-down menu).
Here is the resulting list of the needed purchases and sales from the "ToPaste" sheet.

Code: Select all

Buy Or Sell Bonds                                                       --- Proceeds in 2/26/2024 Dollars ---
                        Ask                              Nbr                        Final Previous      Total
  Matures   Coupon     Price    Yield    CUSIP    Mult  Bnds      Cost   Principal Coupon  Coupons   Proceeds
 1/15/2029  0.875%   96.43750  1.815%  9128285W6     1    -1     -1,206     -1,215     -5      -32     -1,252
 1/15/2030  0.125%   91.81250  1.865%  912828Z37     1     1      1,126      1,192      1        6      1,199
 1/15/2031  0.125%   89.87500  1.937%  91282CBF7     1    -1     -1,089     -1,179     -1       -7     -1,187
 
 1/15/2034  1.750%   96.96875  2.123%  91282CJY8     1   -46    -45,826    -45,910   -402   -6,427    -52,739
 1/15/2035  2.125%   99.71875  2.155%  91282CML2     3    62     61,878     60,271    640   11,527     72,439
 2/15/2040  2.125%   98.06250  2.279%  912810QF8     3   -10    -14,459    -14,194   -151   -4,223    -18,568

                                              Total -->    5        424     -1,034     83      844       -107
  Total only 3 bonds Jan 2034, Jan 2035, & Feb 2040 -->    6      1,593        168     88      877      1,132
The "Bnds" column in the table shows that Sam should sell 46 of the January 2034's and 10 of the February 2040's; and use the proceeds to buy 62 of the new January 2035's. It also shows selling one Jan 2029 and one Jan 2031 and buying one Jan 2030. If these three small transactions are ignored, the bottom line shows a net cost of $1,593 and a net increase in proceeds of $1,132. (The cost is based on the 1/31/2025 WSJ Quotes and the proceeds are in 2/26/2024 constant dollars.)

I didn't have to modify cell B2 (Desired Annual Real Amount -- DARA) nor add columns as exodusing did in point # 4 quoted above. Sam can continue this process next February entering the following multipliers:
Jan 2035: 1
Jan 2036: 2.5
Feb 2040: 2.5

I don't imagine this process is as accurate as the ones presented by Kevin M and MtnBiker in this thread. But I think it is adequate.
For now, I am sticking with the old idea...I have appropriately overweighted 2034 and 2040 over the past year or two to fund the gap years.
2035: fill my desired 2035 allocation with approx. 5/6 from 34 AND 1/6 FROM 40
2036: 4/6 2/6
2037: 3/6 3/6
2038: 2/6 4/6
2039: 1/6 5/6

Easy peasy, (I don't have much of an idea about how much money I will need or want to spend in 2039....)

If you guys worked out a much better plan, I am all ears.

Any excess unspent funds that I have at the end of any given year I will currently spread between existing ladder years. I will be 88 in 2040. If yields are still favorable going forward from 2030, and if I am still in good health in 2030, I might choose to extend my ladder with existing funds at that time. I already have a few 41s and 42s.
"The truth cannot force its way in, when something else is occupying its place." | -Ludwig Wittgenstein
exodusing
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Re: Covering the TIPS gap years with bracket year duration matching

Post by exodusing »

#Cruncher wrote: Tue Feb 04, 2025 1:58 pm
exodusing wrote: Thu Jan 23, 2025 8:00 am My plan for reallocating after the auction of the 2035s:
  1. List my current holding in #Cruncher's spreadsheet.
  2. Set the Multiplier for Jan 2034s to 1, the Jan 2035s to 3 and the Jan 2040s to 3.
  3. Set Sell Excess Bonds to TRUE.
  4. Set DARA to an amount which minimizes trading (spread between Held and Needed). This is higher than my original DARA due to subsequent inflation, etc. I inserted new columns R and S. R is P-0 (needed minus held) and S is the value of the R TIPS. I checked my DARA by summing column R (sum of bonds to buy/sell), then using Goal Seek to see what DARA results in 0 trades.
  5. Within the first few weeks of February sell 2034s and 2040s to buy 2035s. If I'm a bit short, I'll wait until Feb 15 for interest payments from other TIPS.
I've made up an illustration of exodusing's approach. In February 2024 Sam built a 30,000 constant dollar per year ladder with rungs running from 2025-2054. He used the 2/23/2024 version of my TIPS Ladder Builder Excel workbook. He kept all the default parameters except he entered "3.5" in the "Multiplier" column for the January 2034 and February 2040 maturities. This was to provide excess collections to later fund the five years 2035-2039 when TIPS maturing in those years became available.

Now, in February 2025 Sam wants to shift the excess Jan 2034's to the newly issued January 2035's. To fund this he will sell all but one rung of the Jan 2034's and some of the excess Feb 2040's. To determine exactly how much to sell of the Jan 2034's and Feb 2040's and how much to buy of the Jan 2035's Sam makes the following modifications to the "Ladder" sheet of the current 1/31/2035 version of the workbook:
  • Enter the number of TIPS 2026-2054 from last year's 2/23/2024 version of the workbook ("Total" column Q) in the "Already Held" (column O) of the current version of the workbook. (This is not a simple copy and paste of all 29 values because the current workbook version has new rows for new TIPS.)
  • Enter the following in the "Multiplier" column (N):
    • Jan 2034: 1
    • Jan 2035: 3
    • Feb 2040: 3
    • Other rows that have a value entered in the "Already Held" column: 1
    • All other rows: <blank> (The "Multiplier" column should total 29.)
  • Replace cell G1 (Real $ Base Date) with "2/26/2024", the date from the previous year's workbook. This will change cell G2 (Ref CPI on Base Date) to "306.78807". This will set new purchases to be in terms of the same constant dollar date as was the ladder built the previous year.
  • Change cell O2 (Sell Excess Bonds) to TRUE (selected from a drop-down menu).
  • Change cell T1 (Display) to "Buy Or Sell" (selected from a drop-down menu).
Here is the resulting list of the needed purchases and sales from the "ToPaste" sheet.

Code: Select all

Buy Or Sell Bonds                                                       --- Proceeds in 2/26/2024 Dollars ---
                        Ask                              Nbr                        Final Previous      Total
  Matures   Coupon     Price    Yield    CUSIP    Mult  Bnds      Cost   Principal Coupon  Coupons   Proceeds
 1/15/2029  0.875%   96.43750  1.815%  9128285W6     1    -1     -1,206     -1,215     -5      -32     -1,252
 1/15/2030  0.125%   91.81250  1.865%  912828Z37     1     1      1,126      1,192      1        6      1,199
 1/15/2031  0.125%   89.87500  1.937%  91282CBF7     1    -1     -1,089     -1,179     -1       -7     -1,187
 
 1/15/2034  1.750%   96.96875  2.123%  91282CJY8     1   -46    -45,826    -45,910   -402   -6,427    -52,739
 1/15/2035  2.125%   99.71875  2.155%  91282CML2     3    62     61,878     60,271    640   11,527     72,439
 2/15/2040  2.125%   98.06250  2.279%  912810QF8     3   -10    -14,459    -14,194   -151   -4,223    -18,568

                                              Total -->    5        424     -1,034     83      844       -107
  Total only 3 bonds Jan 2034, Jan 2035, & Feb 2040 -->    6      1,593        168     88      877      1,132
The "Bnds" column in the table shows that Sam should sell 46 of the January 2034's and 10 of the February 2040's; and use the proceeds to buy 62 of the new January 2035's. It also shows selling one Jan 2029 and one Jan 2031 and buying one Jan 2030. If these three small transactions are ignored, the bottom line shows a net cost of $1,593 and a net increase in proceeds of $1,132. (The cost is based on the 1/31/2025 WSJ Quotes and the proceeds are in 2/26/2024 constant dollars.)

I didn't have to modify cell B2 (Desired Annual Real Amount -- DARA) nor add columns as exodusing did in point # 4 quoted above. Sam can continue this process next February entering the following multipliers:
Jan 2035: 1
Jan 2036: 2.5
Feb 2040: 2.5

I don't imagine this process is as accurate as the ones presented by Kevin M and MtnBiker in this thread. But I think it is adequate.
On a general level, I continue to believe that reallocating to the holdings you would have if you created a ladder from scratch makes the most sense (ignoring years for which the changes would be small). This would seem to be 2034x1, 2035x3 and 2040x3, both for cash flow and duration matching purposes. Possible downsides are trading costs (bid-ask spreads), but these seem minimal, and an on-the-run premium for the 2035s, but evidence in this thread suggests there's little if any.

To all, what would be a significantly better approach?

On a spreadsheet implementation level, your suggestions do seem simpler than my steps. FWIW, I modified DARA because I bought TIPS on multiple dates and didn't have a single refcpi date to use. Both approaches should come to approximately the same place, so far as I can tell. Also, minimizing trading has a certain appeal. I put the extra columns in the Ladder page to have everything on one page - the extra columns are the same as the number of bonds and cost columns from the ToPaste sheet.

Thank you for commenting and for the great spreadsheet.
MtnBiker
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Re: Covering the TIPS gap years with bracket year duration matching

Post by MtnBiker »

For those of you who are ready to swap to 2035s, reallocate completely, or whatever, a shout out and word of thanks to kaesler for upgrading Tipsladder.com to handle such operations:
kaesler wrote: Tue Feb 04, 2025 5:05 pm
kaesler wrote: Sat Feb 01, 2025 10:52 am
I’m working today on adding the ability to reduce the size of a pre-owned holding in the manual “Build” page. This should allow modeling the use-case of selling one’s 2034s and 2040s to buy the newly minted 2035s.

It will show you the effect on your ladder and also estimate proceeds from sale of the pre-owned bonds.
This is now implemented and deployed. You may have to refresh your browser to get the new app version.

It works like this:
  • Load up your existing TIPS portfolio on the "Analyse" page, most conveniently from a previously saved CSV file
  • "Extend to ladder", which takes you to the "Build" page seeded with your existing ladder
  • Add new bonds, e.g. 2035s
  • Remove old bonds, e.g. some 2034s and 2040s, by reducing the bond count beside the CUSIP
  • When you have the ladder with the desired properties (they are updated as you go at the bottom of the page), download the buy and sell lists and execute the trades.
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Kevin M
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cash flow matching vs duration matching

Post by Kevin M »

In this post I want to clarify some bond portfolio management concepts, and discuss the relevance to and impact on TIPS ladders, and of course also the relevance to duration matching to cover the gap years.

Two common techniques to immunize a bond portfolio against interest rate risk are cash flow matching and duration matching. In either case, the thing we are matching is a liability at some point in the future. The idea behind an immunization technique is to be able to reliably fund the liability regardless of changes in the bond portfolio yields.

A typical TIPS ladder uses cash flow matching. The liabilities we are matching are the real expenses we want to cover with the TIPS ladder real cash flows. The real cash flow of a TIPS ladder for a particular funded year consists of the coupons paid in that year (from all TIPS in the ladder) and the proceeds from the TIPS that mature in that year. With this approach, bond durations can pretty much be ignored, since the real cash flows will reliably match the expected real liabilities.

Many others on this forum use one or more TIPS funds to cover their expected real liabilities. Since a fund never matures, and the coupon income is not as reliable as with a ladder, cash flow matching cannot be used, so duration matching is used instead. The portfolio of one or more funds is constructed such that the average duration of the fund(s) matches the average duration of the liabilities. The latter is roughly half of the term of the liabilities, so the average duration of 30 years of expenses is about 15 years, and we would want the average duration of the fund(s) to be about 15 years. Of course this requires switching and rebalancing the funds as the average duration of the liabilities decreases.

Having gap years in our TIPS ladder creates a problem for cash flow matching, since there are no TIPS available to provide the cash flows for the gap years. The solution proposed in this thread is to add a a duration matching component to our predominantly cash flow matched ladder. Using two bracket year TIPS maturities to match the average duration of the gap year TIPS is kind of analogous to using two funds to match the average duration of our expected liabilities. Using this analogy, the costs of the gap year TIPS are the liabilities funded by the duration matched bracket year TIPS holdings.

If we don't fund the gap years until the lower bracket year TIPS (e.g., 2034 or 2035) mature, then cash flow matching is reliable for the earlier funded years (e.g., 2025-2033/4), since the coupon cash flows are known for those years; i.e., we'll receive the known coupon payments from the 2034/5 and 2040 for those years. However, if we sell some bracket year TIPS to fund the gap years earlier, that introduces some uncertainty in the cash flows for the earlier funded years, since we will no longer be receiving all of the known coupons from the bracket year TIPS, but instead will be receiving some of the unknown coupon payments from the as-yet-to-be issued gap year TIPS.

I want to emphasize that this cash flow matching issue for earlier years is largely separate from the duration matching solution for the gap years. Indeed, this cash flow matching issue can be avoided entirely by simply holding the bracket years TIPS until the earlier bracket year TIPS mature, and although this may introduce a bit more uncertainty in the effectiveness of the duration matching solution due to possible non-linear yield curve shifts in the bracket/gap-year maturity range, one can view these as separate issues, and decide on which issue is of more concern. Furthermore, reviewing the duration matching calculations described in my first few posts in this thread should make it clear that the only actual TIPS involved in these calculations are the bracket year TIPS--other TIPS in the ladder are not involved, since they are not part of the duration matching portfolio.

Another issue with duration matching as described in this thread, and that already has been discussed, is that we can't reliably match the excess bracket year TIPS portfolio to the liabilities comprised by the gap year TIPS because the gap year TIPS prices don't move inversely to yields, and this is required for duration matching to work according to duration matching math. For example, if yields increase, instead of the gap year TIPS providing more value in the form of reduced prices, corresponding to the reduced prices of our bracket year TIPS, that value is delivered as higher coupons, since the price of newly issued TIPS remains relatively fixed at about 100 (percent of face value). The issue with this is that that higher coupon value is distributed across all the earlier maturity TIPS in the ladder, which introduces the cash flow matching issue alluded to above.

It may be possible to reduce the resulting cash flow matching issue with some additional ladder trades, but again, cash flow matching for the overall ladder is separate from duration matching the excess bracket year TIPS portfolio and expected gap year TIPS liabilities.
If I make a calculation error, #Cruncher probably will let me know.
MtnBiker
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Re: Covering the TIPS gap years with bracket year duration matching

Post by MtnBiker »

Seems like just semantics, but Bobcat2 says using two funds to match liabilities is duration targeting, not duration matching.

Quote from: https://www.perplexity.ai/search/compar ... U8kDIcn5cQ follows:
Duration matching and duration targeting are two strategies used in fixed-income portfolio management to manage interest rate risk. While both approaches aim to align a portfolio's duration with a specific target, they differ in their implementation and precision.

Duration matching involves precisely aligning the duration of a bond portfolio with the investor's investment horizon or the duration of their liabilities. This strategy aims to completely eliminate interest rate risk by ensuring that any changes in interest rates affect both assets and liabilities equally. For example, if an investor has a 10-year investment horizon, they would construct a portfolio with an exact 10-year duration.

Duration targeting, on the other hand, is a more flexible approach. It involves maintaining a portfolio duration close to, but not necessarily exactly matching, a target duration. This strategy allows for some deviation from the target, which can be beneficial in terms of portfolio management flexibility and potentially capturing additional returns.

Key Differences
Precision: Duration matching is more precise, aiming for an exact match between portfolio duration and the target. Duration targeting allows for some deviation from the target duration.

Flexibility: Duration targeting offers more flexibility in portfolio management, as it doesn't require constant rebalancing to maintain an exact duration match.

Risk Management: Duration matching theoretically eliminates all interest rate risk, while duration targeting may leave some residual interest rate risk.

Implementation: Duration matching often requires more frequent portfolio adjustments to maintain the exact match, especially as time passes and the investment horizon shortens. Duration targeting may require less frequent adjustments.

Potential Returns: Duration targeting may allow for potentially higher returns by providing more flexibility in security selection and portfolio composition.

While duration matching offers more precise risk management, duration targeting is often easier to implement and maintain, especially for individual investors or smaller portfolios. The choice between the two strategies depends on the investor's risk tolerance, investment goals, and resources available for portfolio management.
I kind of doubt that what we are doing to cover the gap years is precise enough to truly qualify as duration matching, but it seems more precise than duration targeting with several bond funds.
MtnBiker
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Re: cash flow matching vs duration matching

Post by MtnBiker »

Kevin M wrote: Fri Feb 07, 2025 5:54 pm It may be possible to reduce the resulting cash flow matching issue with some additional ladder trades, but again, cash flow matching for the overall ladder is separate from duration matching the excess bracket year TIPS portfolio and expected gap year TIPS liabilities.
My understanding is that cash flow matching of the overall ladder can be simultaneously achieved together with covering the gap with duration matching. These goals need not be separate.

All that is needed is to move past the restrictive concept implied by the OP that only two bracket years TIPS can be used for duration matching. You make the following statement:
Furthermore, reviewing the duration matching calculations described in my first few posts in this thread should make it clear that the only actual TIPS involved in these calculations are the bracket year TIPS--other TIPS in the ladder are not involved, since they are not part of the duration matching portfolio.
The highlighted part is true only if you choose to limit the duration matching calculations to the two bracket year TIPS. Limiting the duration matching to two bracket years guarantees that cash flow cannot be matched as yields change.

But there is no fundamental reason to use only two TIPS in the duration matching algebra. If three (or more) TIPS are used for duration matching a gap year swap, duration matching can be achieved with better cash flow matching than when using only two TIPS. Adding the third (or more) TIPS helps solve the coupon shift/cash flow issue while maintaining duration matching.

In other words, if "some additional ladder trades" to smooth ARA are planned to be done as part of the swap for the gap year, those additional trades MUST be included in the duration matching calculation.
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Re: Covering the TIPS gap years with bracket year duration matching

Post by Jaylat »

Just filled the 2035 rung of my TIPS ladder. In doing so there were two options, (1) buy only the amount needed for the 2035 ring and leave the rest of the excess TIPS in 2034’s or (2) sell all of the excess 2034 TIPS and move them into 2035 TIPS. I chose the latter for the following reasons:

In general, it’s better to narrow the gap in years to be filled in the TIPS ladder, as it reduces the potential interest rate risk that might be incurred in future duration matching. If the shape of the yield curve changes, a 4-year gap is slightly less risky than a 5-year gap;

The 2034 TIPS were close to par (for me) so minimal tax consequences from selling them at a gain or loss;

The 2035 TIPS have the same 2.125% coupon as the 2040 TIPS, so buying and selling those two TIPS simultaneously didn’t affect the income stream.

The negative of selling all the excess 2034 TIPS and buying additional 2035 TIPS is the potentially higher trading cost incurred as you move the excess TIPS from one year to the next. You have multiple larger trades, each with a bid/ask spread each year. The spread is pretty low at this point, though, and there’s no guarantee that future bid/ask spreads will be as tight.

That was my logic. Not saying this is the right way to do it, just what seemed to work for me as to how to best manage my TIPS portfolio given the current situation.
bpg1234
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Re: Covering the TIPS gap years with bracket year duration matching

Post by bpg1234 »

Jaylat wrote: Fri Feb 07, 2025 10:11 pm Just filled the 2035 rung of my TIPS ladder. In doing so there were two options, (1) buy only the amount needed for the 2035 ring and leave the rest of the excess TIPS in 2034’s or (2) sell all of the excess 2034 TIPS and move them into 2035 TIPS. I chose the latter for the following reasons:

In general, it’s better to narrow the gap in years to be filled in the TIPS ladder, as it reduces the potential interest rate risk that might be incurred in future duration matching. If the shape of the yield curve changes, a 4-year gap is slightly less risky than a 5-year gap;

The 2034 TIPS were close to par (for me) so minimal tax consequences from selling them at a gain or loss;

The 2035 TIPS have the same 2.125% coupon as the 2040 TIPS, so buying and selling those two TIPS simultaneously didn’t affect the income stream.

The negative of selling all the excess 2034 TIPS and buying additional 2035 TIPS is the potentially higher trading cost incurred as you move the excess TIPS from one year to the next. You have multiple larger trades, each with a bid/ask spread each year. The spread is pretty low at this point, though, and there’s no guarantee that future bid/ask spreads will be as tight.

That was my logic. Not saying this is the right way to do it, just what seemed to work for me as to how to best manage my TIPS portfolio given the current situation.
Interesting, so if you sell all the excess 2034s in this scenario and bracket year now moves to 2035 (with excess in 2035 for filling the future gap years) does one still need to sell any of the 2040s bracket year at this point?
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Raspberry-503
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Re: Covering the TIPS gap years with bracket year duration matching

Post by Raspberry-503 »

bpg1234 wrote: Sat Feb 08, 2025 3:44 pm
Jaylat wrote: Fri Feb 07, 2025 10:11 pm Just filled the 2035 rung of my TIPS ladder. In doing so there were two options, (1) buy only the amount needed for the 2035 ring and leave the rest of the excess TIPS in 2034’s or (2) sell all of the excess 2034 TIPS and move them into 2035 TIPS. I chose the latter for the following reasons:

In general, it’s better to narrow the gap in years to be filled in the TIPS ladder, as it reduces the potential interest rate risk that might be incurred in future duration matching. If the shape of the yield curve changes, a 4-year gap is slightly less risky than a 5-year gap;

The 2034 TIPS were close to par (for me) so minimal tax consequences from selling them at a gain or loss;

The 2035 TIPS have the same 2.125% coupon as the 2040 TIPS, so buying and selling those two TIPS simultaneously didn’t affect the income stream.

The negative of selling all the excess 2034 TIPS and buying additional 2035 TIPS is the potentially higher trading cost incurred as you move the excess TIPS from one year to the next. You have multiple larger trades, each with a bid/ask spread each year. The spread is pretty low at this point, though, and there’s no guarantee that future bid/ask spreads will be as tight.

That was my logic. Not saying this is the right way to do it, just what seemed to work for me as to how to best manage my TIPS portfolio given the current situation.
Interesting, so if you sell all the excess 2034s in this scenario and bracket year now moves to 2035 (with excess in 2035 for filling the future gap years) does one still need to sell any of the 2040s bracket year at this point?
Likely, the 2035s were funded by a duration-matched mix of 2034s and 2040s, so you would sell some 2040s and more 2034s to buy the 2035s
bpg1234
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Re: Covering the TIPS gap years with bracket year duration matching

Post by bpg1234 »

Raspberry-503 wrote: Sat Feb 08, 2025 4:48 pm
bpg1234 wrote: Sat Feb 08, 2025 3:44 pm
Interesting, so if you sell all the excess 2034s in this scenario and bracket year now moves to 2035 (with excess in 2035 for filling the future gap years) does one still need to sell any of the 2040s bracket year at this point?
Likely, the 2035s were funded by a duration-matched mix of 2034s and 2040s, so you would sell some 2040s and more 2034s to buy the 2035s
Option 2 is to sell ALL the excess 2034s and put in 2035s which would more than accommodate my required 2035 TIPS amount with available excess there for future gap years. So my question is do I still need to sell 2040s based on the duration-maxed percentages (say 16% of 2040 TIPS) and buy additional 2035s?

In thinking about this some more I guess I would still need to do this so to have enough excess 2035s to cover the additional gap years based on the duration-matched percentages.
MtnBiker
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Re: Covering the TIPS gap years with bracket year duration matching

Post by MtnBiker »

bpg1234 wrote: Sat Feb 08, 2025 4:58 pm So my question is do I still need to sell 2040s based on the duration-maxed percentages (say 16% of 2040 TIPS) and buy additional 2035s?

In thinking about this some more I guess I would still need to do this so to have enough excess 2035s to cover the additional gap years based on the duration-matched percentages.
Correct. My attempt at finding a duration-matched mix of 2035s and 2040s went like this:

https://www.bogleheads.org/forum/viewt ... 3#p8241363
Jaylat
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Re: Covering the TIPS gap years with bracket year duration matching

Post by Jaylat »

Raspberry-503 wrote: Sat Feb 08, 2025 4:48 pm
bpg1234 wrote: Sat Feb 08, 2025 3:44 pm
Interesting, so if you sell all the excess 2034s in this scenario and bracket year now moves to 2035 (with excess in 2035 for filling the future gap years) does one still need to sell any of the 2040s bracket year at this point?
Likely, the 2035s were funded by a duration-matched mix of 2034s and 2040s, so you would sell some 2040s and more 2034s to buy the 2035s
Yes, I started out with 3.5x of DARA (the desired annual real amount) in each of 2034 and 2040’s, which consists of 1.0x DARA for the year itself, plus another 2.5x excess to fill the 5 gap years in between 2034 and 2040 (2.5 x 2 = 5). It looked like this:

2034 3.5x DARA
2040 3.5x DARA

Buying the 2035 itself (1.0x DARA), and moving the excess to 2035 (2.0 DARA) resulted in a total 2035 TIPS of 3.0 DARA. The 2040 TIPS were reduced from 3.5 DARA to 3.0 DARA. This consists of 1.0x DARA for 2035, plus another 2.0x excess to fill the 4 gap years (2.0 x 2 = 4).

I sold 2.5x DARA of 2034 TIPS and 0.5x DARA of 2040 TIPS, and bought 3.0x DARA of 2035 TIPS. So I ended up with:

2034 1.0x DARA (the final amount)
2035 3.0x DARA
2040 3.0x DARA

In my case, I don’t count the TIPS coupon payments as being part of prior year’s DARA, I’m only looking at the inflation adjusted principle amounts to determine DARA for each year. I allocate the TIPS coupon payments for paying taxes on the TIPS OID, as most of my TIPS are in taxable. That also simplifies the hedging calculations; you can treat the TIPS as being almost like zero coupon bonds, so that their maturity = duration.
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Kevin M
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Re: cash flow matching vs duration matching

Post by Kevin M »

Kevin M wrote: Fri Feb 07, 2025 5:54 pm Using two bracket year TIPS maturities to match the average duration of the gap year TIPS is kind of analogous to using two funds to match the average duration of our expected liabilities. Using this analogy, the costs of the gap year TIPS are the liabilities funded by the duration matched bracket year TIPS holdings.
As I wrote this, I wondered why I don't just use the average duration of the gap year TIPS in my calculations, since with my approach all I care about is the total excess amount to allocate to each bracket year TIPS. I just did the calculation that way, and I guess it should be no surprise that the end result is the same:

Image

The formulas in cells F12 and G12 are:

Code: Select all

=AVERAGE(F3:F6)
=(F$7-F12)/(F$7-F$2)
So the spreadsheet that works for my purposes can be simplified to:

Image
If I make a calculation error, #Cruncher probably will let me know.
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Kevin M
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Re: Covering the TIPS gap years with bracket year duration matching

Post by Kevin M »

Jaylat wrote: Fri Feb 07, 2025 10:11 pm Just filled the 2035 rung of my TIPS ladder. In doing so there were two options, (1) buy only the amount needed for the 2035 ring and leave the rest of the excess TIPS in 2034’s or (2) sell all of the excess 2034 TIPS and move them into 2035 TIPS. I chose the latter for the following reasons:

In general, it’s better to narrow the gap in years to be filled in the TIPS ladder, as it reduces the potential interest rate risk that might be incurred in future duration matching. If the shape of the yield curve changes, a 4-year gap is slightly less risky than a 5-year gap;

The 2034 TIPS were close to par (for me) so minimal tax consequences from selling them at a gain or loss;

The 2035 TIPS have the same 2.125% coupon as the 2040 TIPS, so buying and selling those two TIPS simultaneously didn’t affect the income stream.

The negative of selling all the excess 2034 TIPS and buying additional 2035 TIPS is the potentially higher trading cost incurred as you move the excess TIPS from one year to the next. You have multiple larger trades, each with a bid/ask spread each year. The spread is pretty low at this point, though, and there’s no guarantee that future bid/ask spreads will be as tight.

That was my logic. Not saying this is the right way to do it, just what seemed to work for me as to how to best manage my TIPS portfolio given the current situation.
Good summary of the tradeoffs of the two approaches, and of your reasoning for choosing one over the other.
If I make a calculation error, #Cruncher probably will let me know.
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Kevin M
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Re: Covering the TIPS gap years with bracket year duration matching

Post by Kevin M »

bpg1234 wrote: Sat Feb 08, 2025 4:58 pm
Raspberry-503 wrote: Sat Feb 08, 2025 4:48 pm Likely, the 2035s were funded by a duration-matched mix of 2034s and 2040s, so you would sell some 2040s and more 2034s to buy the 2035s
Option 2 is to sell ALL the excess 2034s and put in 2035s which would more than accommodate my required 2035 TIPS amount with available excess there for future gap years. So my question is do I still need to sell 2040s based on the duration-maxed percentages (say 16% of 2040 TIPS) and buy additional 2035s?

In thinking about this some more I guess I would still need to do this so to have enough excess 2035s to cover the additional gap years based on the duration-matched percentages.
There are multiple approaches to this, a couple of which have been shared in replies to your question. My approach would be to first calculate the excess costs of the 2035 and 2040 required to match the average modified duration of the 2036-2039 (gap years), given whatever assumptions you want to make about the yields and coupons for the gap years; I've already shared how to do this using the assumptions that I might make.

Since it sounds like you have more than you need to do this in your excess 2034s and 2040s, it's up to you what to do with this excess. One option would be to stick with the weightings for the excess 2035s and 2040s, so you'd be holding more of them than you'd theoretically need to cover the cost of the hypothetical gap year TIPS as if they were issued today. I'd lean toward this approach, with a view toward possibly evening out the cash flows of the earlier funded years once all the gap years had been filled (since the coupons of the gap years are uncertain).

Another approach might be to put more of the excess in the 2040 or 2035, depending on your view of the attractiveness of current yields; i.e., taking more price risk by overweighting the 2040s, or more reinvestment risk by overweighting the 2035s. Another approach might be to spread the excess across the ladder, perhaps adjusting cash flows to suit your personal situation.
If I make a calculation error, #Cruncher probably will let me know.
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