I’m definitely open to this. I hope to offer a solution but expect to be busy with other matters for a few months. So any concrete algorithmic ideas or GUI suggestions would be helpful. I’d like to solve the problem before all the gaps are filled.exodusing wrote: ↑Wed Oct 30, 2024 4:53 pm A suggestion to kaesler, author of tipsladder.com, is to add a function to figure out how to fill the gap years when a new gap year TIPS is issued.
Might someone propose a formula (or anything specific enough to be capable of being programmed) to help kaelser implement this. It's much harder to implement a concept than something specific. The enemy of a good plan is the dream of the perfect plan is probably applicable here.
Filling the TIPS gap years with bracket year duration matching
Re: Filling the TIPS gap years with bracket year duration matching
Re: Filling the TIPS gap years with bracket year duration matching
As a small first step I was planning to modify the manual ladder editor to remove, I.e. sell, preowned bond holdings, as part of the process. So you could model selling your old gapstraddling holdings and replacing them with the newly issued bonds. The tool would show the resultant ladder, including the net cost (or gain?) involved.kaesler wrote: ↑Wed Oct 30, 2024 5:42 pmI’m definitely open to this. I hope to offer a solution but expect to be busy with other matters for a few months. So any concrete algorithmic ideas or GUI suggestions would be helpful. I’d like to solve the problem before all the gaps are filled.exodusing wrote: ↑Wed Oct 30, 2024 4:53 pm A suggestion to kaesler, author of tipsladder.com, is to add a function to figure out how to fill the gap years when a new gap year TIPS is issued.
Might someone propose a formula (or anything specific enough to be capable of being programmed) to help kaelser implement this. It's much harder to implement a concept than something specific. The enemy of a good plan is the dream of the perfect plan is probably applicable here.
Re: Filling the TIPS gap years with bracket year duration matching
Perhaps we could focus on one thing at a time, starting with this. As I've explained, I don't see any sense in tracking the number of bonds originally allocated to buy each gap year. I'll reiterate the reasoning here.MtnBiker wrote: ↑Wed Oct 30, 2024 4:37 pm One should emphasize the importance of keeping a record of how many of each of the two bonds were purchased for each rung, so the user remembers how many to sell when the time comes to swap the bracket year bonds for newly issued bonds maturing in a particular gap year. (At that time, the user sells the specified mix of bracket years and uses the proceeds to buy the gap year.)
<snip>
Thoughts?
The only objective I see in duration matching to cover the gap years is to expose the TIPS ladder to approximately the risk/return profile that would exist if the gapyear TIPS were issued and then marketable at the time the ladder is built. If you see any other objectives, please share.
Given this, I see no other objective for the remaining excess bracket year TIPS as each gap year TIPS are issued and purchased. Therefore, the decision as to how many of each bracket year TIPS to sell to purchase the new gap year TIPS at issue or at some later time depends on how many excess TIPS for each bracket year should continue to be held to replicate the risk/return profile of the remaining gap year TIPS. The number to be sold can differ from that originally allocated because the cost of newly issued TIPS is relatively constant, while the value of the excess bracket year TIPS changes as a result of yield changes.
Although the cost of newly issued TIPS is relatively constant, the coupons of newly issued TIPS are not. Changes in coupons can affect the number of earlier maturity TIPS required compared to the number that were bought originally based on the bracket year coupons at the time. This could be relevant, for example, if bracket year yields increased significantly, since the lower than expected values of the bracket year TIPS originally targeted for buying the gap year TIPS might not be enough to buy the gap year TIPS. In this case, the higher gap year coupon could reduce the number of TIPS required in earlier years, and the excess could be sold to complete the purchase of the gap year TIPS.
Acknowledging a weakness in this argument, I haven't done the math to determine how big the yield/coupon change would need to be to change the values enough to change the number of TIPS involved. If TIPS could be bought in small enough increments, this would not be an issue. The larger the TIPS ladder value, the more likely that a given change in value would change the number of TIPS involved.
If I make a calculation error, #Cruncher probably will let me know.
Re: Filling the TIPS gap years with bracket year duration matching
We front loaded most of it before the Gap years, and are underweight on a years after the Gap years. It worked out well, because my husband has now been found to need a higher level of care, which will cost more money in the upcoming 10 years.
Re: Filling the TIPS gap years with bracket year duration matching
It seems to me that you build a ladder to meet specific needs with whatever is available at the time. Then, as time progresses, new issues allow for a better fit between your needs and available offerings. What matters at that point is the difference between what you have and what would be "ideal" to meet your needs. I don't see how the history of how you got where you are would matter at all.Kevin M wrote: ↑Thu Oct 31, 2024 5:53 pmPerhaps we could focus on one thing at a time, starting with this. As I've explained, I don't see any sense in tracking the number of bonds originally allocated to buy each gap year. I'll reiterate the reasoning here.MtnBiker wrote: ↑Wed Oct 30, 2024 4:37 pm One should emphasize the importance of keeping a record of how many of each of the two bonds were purchased for each rung, so the user remembers how many to sell when the time comes to swap the bracket year bonds for newly issued bonds maturing in a particular gap year. (At that time, the user sells the specified mix of bracket years and uses the proceeds to buy the gap year.)
<snip>
Thoughts?
The only objective I see in duration matching to cover the gap years is to expose the TIPS ladder to approximately the risk/return profile that would exist if the gapyear TIPS were issued and then marketable at the time the ladder is built. If you see any other objectives, please share.
You should certainly care whether or not it makes sense to change anything, but also doesn't need history. In my mind, determining the difference between "makes sense", doesn't make sense", and "may or may not make sense" is what is important  IOW, when to pull the trigger.
“Adapt what is useful, reject what is useless, and add what is specifically your own.” ― Bruce Lee
Re: Filling the TIPS gap years with bracket year duration matching
Since you and I both now have a pretty good understanding of the issues involved in making a swap, I doubt that you or I will come to much different conclusions on what to do when making a swap. We are probably saying much the same thing in slightly different ways.Kevin M wrote: ↑Thu Oct 31, 2024 5:53 pmPerhaps we could focus on one thing at a time, starting with this. As I've explained, I don't see any sense in tracking the number of bonds originally allocated to buy each gap year. I'll reiterate the reasoning here.MtnBiker wrote: ↑Wed Oct 30, 2024 4:37 pm One should emphasize the importance of keeping a record of how many of each of the two bonds were purchased for each rung, so the user remembers how many to sell when the time comes to swap the bracket year bonds for newly issued bonds maturing in a particular gap year. (At that time, the user sells the specified mix of bracket years and uses the proceeds to buy the gap year.)
<snip>
Thoughts?
The only objective I see in duration matching to cover the gap years is to expose the TIPS ladder to approximately the risk/return profile that would exist if the gapyear TIPS were issued and then marketable at the time the ladder is built. If you see any other objectives, please share.
Given this, I see no other objective for the remaining excess bracket year TIPS as each gap year TIPS are issued and purchased. Therefore, the decision as to how many of each bracket year TIPS to sell to purchase the new gap year TIPS at issue or at some later time depends on how many excess TIPS for each bracket year should continue to be held to replicate the risk/return profile of the remaining gap year TIPS. The number to be sold can differ from that originally allocated because the cost of newly issued TIPS is relatively constant, while the value of the excess bracket year TIPS changes as a result of yield changes.
Although the cost of newly issued TIPS is relatively constant, the coupons of newly issued TIPS are not. Changes in coupons can affect the number of earlier maturity TIPS required compared to the number that were bought originally based on the bracket year coupons at the time. This could be relevant, for example, if bracket year yields increased significantly, since the lower than expected values of the bracket year TIPS originally targeted for buying the gap year TIPS might not be enough to buy the gap year TIPS. In this case, the higher gap year coupon could reduce the number of TIPS required in earlier years, and the excess could be sold to complete the purchase of the gap year TIPS.
Acknowledging a weakness in this argument, I haven't done the math to determine how big the yield/coupon change would need to be to change the values enough to change the number of TIPS involved. If TIPS could be bought in small enough increments, this would not be an issue. The larger the TIPS ladder value, the more likely that a given change in value would change the number of TIPS involved.
I can explain where I am coming from by presenting an example. (The numbers I will use with be approximate, as the details aren't as important as the general concept.)
Let's suppose that in 2024 I bought about 20K of principal in bracket years targeted for producing income of 20K real at the 2037 maturity. At the time of the purchase in 2024, the duration of the 2034 was 8.5 and the duration of the 2040 was 13.2. I estimated that the duration of a 2037, if it existed, would be about midway between these, that is a duration of 10.9. Thus, I bought a 50/50 mix of 2034s and 2040s targeted for the 2037 rung with an average duration of 10.9. For about 20K cost, I would then buy 10 of the 2034s (for 10K) and 7 of the 2040s (also for about 10K). I would hold these until 2027, with the intent to swap for the 2037 when it becomes available.
You mention possibly selling more or less when time to make a swap, for the reason of making sure that the remaining bracket year holdings are the correct amounts needed to fill the remaining gap years. I would say that the amounts I bought in 2024 targeted for 2038 and 2039 are already the correct amounts for those gap years. But if you had a reason to fine tune the amounts held for 2038 and 2039, I wouldn't quibble about it.
But regardless of whether you sell more or less in the swap for 2037, I think you would agree that it is important to sell the 2034s and 2040s in the right proportion (about a 50/50 mix by cost). It wouldn't make any sense from a duration matching standpoint to sell all 2040s or all 2034s to fill the 2037 gap. Rather it would make sense to sell a mix that has an average duration close to the duration of the new 2037s when they are issued. I would expect the duration of the 2037 when issued to not be much different from the average duration of the 50/50 mix of 2034 and 2040 bracketyears that I have held with the intent of making the swap. If interest rates changed by +/ 1%, the coupon rate of the newly issued 2037s would be different enough to maybe shift the duration by +/ 0.5, or so. If you wanted to change the mix ratio sold to account for that, fine.
Let's further examine what happens if I proceed along the swap path that I initially described. Also suppose that the 10year interest rate in 2027 has risen by 1% (from 2% in 2024 to 3% in 2027). The average duration of the bracketyear holdings at the beginning of year 2027 will be about 9.0, so they will have lost about 9% of their value. So, if I sell the holdings and buy the 2037s using the proceeds, as planned, I will only be able to buy 18 bonds, with a principal of 18K (not 20K) and will have about $200 cash left over. However, the coupon rate for the 2037 will be 3%, compared to the average coupon rate of the bracketyear holdings of about 2%. Thus, I will be making up $180 (1% of the principal) for each of the 10 years that the 2037s are held. This $1800 in extra coupon payments, together with the $200 cash left over, is enough to make up the difference. (Duration matching worked in terms of maintaining the total payout, but the timing of the payments is off.) If I wanted to, I could do ARA smoothing by selling any 2 earlier bonds in years where the income is a bit higher than 20K and use that to buy 2 more 2037s to restore the 20K of principal at the 2037 maturity.
This is the logic that I am using to say that the average investor should keep track of how many of each of the two bonds were purchased for each rung, so the investor remembers how many to sell when the time comes to swap the bracket year bonds for newly issued bonds maturing in a particular gap year. If investors don't keep some sort of records of the original plan, how would they know how many to sell and in what ratio? Maybe record keeping wouldn't be needed it there was a tool available to analyze holdings and tell you how much to sell, but that tool doesn't exist yet. As far as I know, all we have today is a tool (tipsladder.com manual ladder builder) to tell us how much of each bracket year to buy now for each gap year.
At least in my mind, the concept of durationmatching the gap years is complication enough for the average investor at this point in time. The possible need for ARA smoothing is an additional complication that is somewhat speculative, as it won't even be needed if interest rate changes are small enough or if they average out over time. I say proceed with duration matching now and if ARA smoothing is needed after the five swaps, it can be implemented at that time.
EDIT: Whether ARA smoothing is essential will also depend on the individual needs of each investor. My purpose for holding a TIPS ladder is to supplement an income floor in retirement which is primarily from Social Security. In this example, an income floor of 70K/yr meets my needs (50K from SS and 20K from TIPS). The TIPS income will always be "grainy" at the 1K level because fractional bonds are unavailable. If, due to the gapyear coupon variations mentioned above, the income floor varies even more, say between 68K and 72K from year to year, or even 66K and 74K from year to year, it wouldn't affect my lifestyle or ability to sleep at night. ARA smoothing isn't particularly important to me, as other investments are available to fill in any minor divots in the income floor. Perfectly smooth income might be needed by others, and ARA smoothing can easily be implemented by them.
Re: Filling the TIPS gap years with bracket year duration matching
I agree that the end result is unlikely to be much different. I don't think we're saying quite the same thing, which I'll try to highlight in responding to some of your comments below. I would say that I'm coming at it from a more purely theoretical perspective, while you're coming at it from a "good enough", practical perspective.MtnBiker wrote: ↑Thu Oct 31, 2024 9:36 pmSince you and I both now have a pretty good understanding of the issues involved in making a swap, I doubt that you or I will come to much different conclusions on what to do when making a swap. We are probably saying much the same thing in slightly different ways.Kevin M wrote: ↑Thu Oct 31, 2024 5:53 pm
Perhaps we could focus on one thing at a time, starting with this. As I've explained, I don't see any sense in tracking the number of bonds originally allocated to buy each gap year. I'll reiterate the reasoning here.
The only objective I see in duration matching to cover the gap years is to expose the TIPS ladder to approximately the risk/return profile that would exist if the gapyear TIPS were issued and then marketable at the time the ladder is built. If you see any other objectives, please share.
Given this, I see no other objective for the remaining excess bracket year TIPS as each gap year TIPS are issued and purchased. Therefore, the decision as to how many of each bracket year TIPS to sell to purchase the new gap year TIPS at issue or at some later time depends on how many excess TIPS for each bracket year should continue to be held to replicate the risk/return profile of the remaining gap year TIPS. The number to be sold can differ from that originally allocated because the cost of newly issued TIPS is relatively constant, while the value of the excess bracket year TIPS changes as a result of yield changes.
Although the cost of newly issued TIPS is relatively constant, the coupons of newly issued TIPS are not. Changes in coupons can affect the number of earlier maturity TIPS required compared to the number that were bought originally based on the bracket year coupons at the time. This could be relevant, for example, if bracket year yields increased significantly, since the lower than expected values of the bracket year TIPS originally targeted for buying the gap year TIPS might not be enough to buy the gap year TIPS. In this case, the higher gap year coupon could reduce the number of TIPS required in earlier years, and the excess could be sold to complete the purchase of the gap year TIPS.
Acknowledging a weakness in this argument, I haven't done the math to determine how big the yield/coupon change would need to be to change the values enough to change the number of TIPS involved. If TIPS could be bought in small enough increments, this would not be an issue. The larger the TIPS ladder value, the more likely that a given change in value would change the number of TIPS involved.
(emphasis mine)
My point about this is that you can't accurately target the amount of the bracket year TIPS you purchase to the amount the gap year TIPS will cost when you buy them; your subsequent comments illustrate this. As I've said, what the bracket year TIPS do is simulate the risk and return of the gap year TIPS as if the existed and were marketable. You have a different way of thinking about this, which you clarify in your subsequent comments.
(emphasis mine)
No; again, the bracket year TIPS don't meet the objective of accurately filling the remaining gap years. The objective is to simulate the risk/return of the gap years as if they existed and were marketable.
Of course you will sell some mix of the bracket years, but I would pay no attention to the duration of the 2037s, and instead I would pay attention the the durations of the remaining gap years and the average duration of the remaining bracket years. A simpler, "good enough" approach might be to just ensure that about half of the excess TIPS dollar value continues to be held in each bracket year.MtnBiker wrote: ↑Thu Oct 31, 2024 9:36 pmBut regardless of whether you sell more or less in the swap for 2037, I think you would agree that it is important to sell the 2034s and 2040s in the right proportion (about a 50/50 mix by cost). It wouldn't make any sense from a duration matching standpoint to sell all 2040s or all 2034s to fill the 2037 gap. Rather it would make sense to sell a mix that has an average duration close to the duration of the new 2037s when they are issued.
MtnBiker wrote: ↑Thu Oct 31, 2024 9:36 pmLet's further examine what happens if I proceed along the swap path that I initially described. Also suppose that the 10year interest rate in 2027 has risen by 1% (from 2% in 2024 to 3% in 2027). The average duration of the bracketyear holdings at the beginning of year 2027 will be about 9.0, so they will have lost about 9% of their value. So, if I sell the holdings and buy the 2037s using the proceeds, as planned, I will only be able to buy 18 bonds, with a principal of 18K (not 20K) and will have about $200 cash left over.
Yes, and this is where the concept of targeting the dollars you'll need to buy the gap year fails. By "fails", I mean it fails to allow you to buy your DARA for that year. This highlights what I mean in saying I'm coming at it from a more purely theoretical point of view, which requires buying the DARA amount of each gap year. I understand that that may not be important to you or others, and that's fine. However, when I started the thread, that was my objective, and that's the objective that the faulty model seemed to meet.
So I'm saying that once the fault in the original model was identified, and I corrected the model for it, the original objective was no longer met. In thinking about this, I've framed what I think is a new objective that the duration matching approach does meet quite well.
(emphasis mine)MtnBiker wrote: ↑Thu Oct 31, 2024 9:36 pmHowever, the coupon rate for the 2037 will be 3%, compared to the average coupon rate of the bracketyear holdings of about 2%. Thus, I will be making up $180 (1% of the principal) for each of the 10 years that the 2037s are held. This $1800 in extra coupon payments, together with the $200 cash left over, is enough to make up the difference. (Duration matching worked in terms of maintaining the total payout, but the timing of the payments is off.)
This is a useful way to frame it, and perhaps it illustrates the practical result of simulating the risk/return of the gap year TIPS as if they were marketable. I like the way you state it in the emphasized sentence.
This is where the theoretical rubber meets the practical road. We can't achieve the exact DARA in any year, due to the minimum purchase limit of $1K face value. If the minimum face values was $100, we could come much closer. Although TD sells TIPS in $100 increments, you can't sell in any increment at TD, so you can't "rebalance" your ladder as part of filling a gap year. Your suggestion probably is as good as any other, although I'm sure there are other approaches that could make more sense depending on one's personal circumstances.
MtnBiker wrote: ↑Thu Oct 31, 2024 9:36 pmThis is the logic that I am using to say that the average investor should keep track of how many of each of the two bonds were purchased for each rung, so the investor remembers how many to sell when the time comes to swap the bracket year bonds for newly issued bonds maturing in a particular gap year. If investors don't keep some sort of records of the original plan, how would they know how many to sell and in what ratio? Maybe record keeping wouldn't be needed it there was a tool available to analyze holdings and tell you how much to sell, but that tool doesn't exist yet. As far as I know, all we have today is a tool (tipsladder.com manual ladder builder) to tell us how much of each bracket year to buy now for each gap year.
At least in my mind, the concept of durationmatching the gap years is complication enough for the average investor at this point in time.
With your original approach of holding n/6 excess 2040 TIPS, where n = 1 to 5 for each of the 2035 to 2039 gap years, and (6n)/6 of the 2034 (e.g., 5/6 2034s and 1/6 2040s for the 2035), which comes quite close to using actual duration calculations to determine the weights, the result is to hold 50% of 5*DARA extra each in the 2034s and 2040s. Using duration calculations based on today's yields the ratio is 0.49 2034s to 0.51 2040s, so 50/50 is close enough considering all the other variables and uncertainty.
How is this complicated, and how is it any more complicated to redo a variation of this simple calculation in figuring out how many bracket year TIPS to continue to hold in filling a gap year?
One answer I guess is that I've ignored coupons; i.e., it would be this simple if zerocoupon TIPS existed and we used them exclusively. Is it that complicated to factor the coupons into this calculation?
I agree with all of this.MtnBiker wrote: ↑Thu Oct 31, 2024 9:36 pmEDIT: Whether ARA smoothing is essential will also depend on the individual needs of each investor. My purpose for holding a TIPS ladder is to supplement an income floor in retirement which is primarily from Social Security. In this example, an income floor of 70K/yr meets my needs (50K from SS and 20K from TIPS). The TIPS income will always be "grainy" at the 1K level because fractional bonds are unavailable. If, due to the gapyear coupon variations mentioned above, the income floor varies even more, say between 68K and 72K from year to year, or even 66K and 74K from year to year, it wouldn't affect my lifestyle or ability to sleep at night. ARA smoothing isn't particularly important to me, as other investments are available to fill in any minor divots in the income floor. Perfectly smooth income might be needed by others, and ARA smoothing can easily be implemented by them.
In my case, I have a huge excess of 20252027 TIPS, yet I still have my tentative DARA or more in most rungs of my ladder; i.e., my ladder is much larger than it needs to be to meet the DARA I've been using. So, I'm considering using some of my excess 2025s or 2026s to buy the Jan 2035 early next year. I've already been using some excess 2025s to add to my longer rungstoday I sold some Jul 2025s to buy some 2045s at 2.26%. My marketvalue weighted duration now is 6.4 years, and it probably should be closer to 10 years.
I think we're pretty close to exhausting this discussion. You've presented your thinking well, and I think I understand it.
I haven't played with tipsladder.com lately. I want to do that, and also give some more thought to the "other interest from later coupons" issue, and how to modify the use of the #Cruncher ladder builder spreadsheet accordingly so that the market value of the TIPS in each of the bracket years corresponds more closely to what they should be based on the duration matching calculations.
If I make a calculation error, #Cruncher probably will let me know.
Re: Filling the TIPS gap years with bracket year duration matching
So Kevin before you close this thread I'm still not certain if I have enough of 2040 TIPS to cover the gap years with a 3.5x target of each. Presently I have accummulated 200 2034 TIPS and 125 2040 TIPS. So when you indicate 3.5x of each for the 7 year period (2 bracket years and 5 gap years) does that mean the same number of actual TIPS (say 200 TIPS of 2034s and 200 TIPS of 2040s) or do you base the number of 2040 TIPS required on the cost which is a lot higher per TIPS (so less actual 2040 TIPS needed) to get the 3.5x ratio?Kevin M wrote: ↑Fri Nov 01, 2024 6:15 pmI agree that the end result is unlikely to be much different. I don't think we're saying quite the same thing, which I'll try to highlight in responding to some of your comments below. I would say that I'm coming at it from a more purely theoretical perspective, while you're coming at it from a "good enough", practical perspective.MtnBiker wrote: ↑Thu Oct 31, 2024 9:36 pm
Since you and I both now have a pretty good understanding of the issues involved in making a swap, I doubt that you or I will come to much different conclusions on what to do when making a swap. We are probably saying much the same thing in slightly different ways.
(emphasis mine)
My point about this is that you can't accurately target the amount of the bracket year TIPS you purchase to the amount the gap year TIPS will cost when you buy them; your subsequent comments illustrate this. As I've said, what the bracket year TIPS do is simulate the risk and return of the gap year TIPS as if the existed and were marketable. You have a different way of thinking about this, which you clarify in your subsequent comments.
(emphasis mine)
No; again, the bracket year TIPS don't meet the objective of accurately filling the remaining gap years. The objective is to simulate the risk/return of the gap years as if they existed and were marketable.
Of course you will sell some mix of the bracket years, but I would pay no attention to the duration of the 2037s, and instead I would pay attention the the durations of the remaining gap years and the average duration of the remaining bracket years. A simpler, "good enough" approach might be to just ensure that about half of the excess TIPS dollar value continues to be held in each bracket year.MtnBiker wrote: ↑Thu Oct 31, 2024 9:36 pmBut regardless of whether you sell more or less in the swap for 2037, I think you would agree that it is important to sell the 2034s and 2040s in the right proportion (about a 50/50 mix by cost). It wouldn't make any sense from a duration matching standpoint to sell all 2040s or all 2034s to fill the 2037 gap. Rather it would make sense to sell a mix that has an average duration close to the duration of the new 2037s when they are issued.
MtnBiker wrote: ↑Thu Oct 31, 2024 9:36 pmLet's further examine what happens if I proceed along the swap path that I initially described. Also suppose that the 10year interest rate in 2027 has risen by 1% (from 2% in 2024 to 3% in 2027). The average duration of the bracketyear holdings at the beginning of year 2027 will be about 9.0, so they will have lost about 9% of their value. So, if I sell the holdings and buy the 2037s using the proceeds, as planned, I will only be able to buy 18 bonds, with a principal of 18K (not 20K) and will have about $200 cash left over.
Yes, and this is where the concept of targeting the dollars you'll need to buy the gap year fails. By "fails", I mean it fails to allow you to buy your DARA for that year. This highlights what I mean in saying I'm coming at it from a more purely theoretical point of view, which requires buying the DARA amount of each gap year. I understand that that may not be important to you or others, and that's fine. However, when I started the thread, that was my objective, and that's the objective that the faulty model seemed to meet.
So I'm saying that once the fault in the original model was identified, and I corrected the model for it, the original objective was no longer met. In thinking about this, I've framed what I think is a new objective that the duration matching approach does meet quite well.
(emphasis mine)MtnBiker wrote: ↑Thu Oct 31, 2024 9:36 pmHowever, the coupon rate for the 2037 will be 3%, compared to the average coupon rate of the bracketyear holdings of about 2%. Thus, I will be making up $180 (1% of the principal) for each of the 10 years that the 2037s are held. This $1800 in extra coupon payments, together with the $200 cash left over, is enough to make up the difference. (Duration matching worked in terms of maintaining the total payout, but the timing of the payments is off.)
This is a useful way to frame it, and perhaps it illustrates the practical result of simulating the risk/return of the gap year TIPS as if they were marketable. I like the way you state it in the emphasized sentence.
This is where the theoretical rubber meets the practical road. We can't achieve the exact DARA in any year, due to the minimum purchase limit of $1K face value. If the minimum face values was $100, we could come much closer. Although TD sells TIPS in $100 increments, you can't sell in any increment at TD, so you can't "rebalance" your ladder as part of filling a gap year. Your suggestion probably is as good as any other, although I'm sure there are other approaches that could make more sense depending on one's personal circumstances.
MtnBiker wrote: ↑Thu Oct 31, 2024 9:36 pmThis is the logic that I am using to say that the average investor should keep track of how many of each of the two bonds were purchased for each rung, so the investor remembers how many to sell when the time comes to swap the bracket year bonds for newly issued bonds maturing in a particular gap year. If investors don't keep some sort of records of the original plan, how would they know how many to sell and in what ratio? Maybe record keeping wouldn't be needed it there was a tool available to analyze holdings and tell you how much to sell, but that tool doesn't exist yet. As far as I know, all we have today is a tool (tipsladder.com manual ladder builder) to tell us how much of each bracket year to buy now for each gap year.
At least in my mind, the concept of durationmatching the gap years is complication enough for the average investor at this point in time.
With your original approach of holding n/6 excess 2040 TIPS, where n = 1 to 5 for each of the 2035 to 2039 gap years, and (6n)/6 of the 2034 (e.g., 5/6 2034s and 1/6 2040s for the 2035), which comes quite close to using actual duration calculations to determine the weights, the result is to hold 50% of 5*DARA extra each in the 2034s and 2040s. Using duration calculations based on today's yields the ratio is 0.49 2034s to 0.51 2040s, so 50/50 is close enough considering all the other variables and uncertainty.
How is this complicated, and how is it any more complicated to redo a variation of this simple calculation in figuring out how many bracket year TIPS to continue to hold in filling a gap year?
One answer I guess is that I've ignored coupons; i.e., it would be this simple if zerocoupon TIPS existed and we used them exclusively. Is it that complicated to factor the coupons into this calculation?
I agree with all of this.MtnBiker wrote: ↑Thu Oct 31, 2024 9:36 pmEDIT: Whether ARA smoothing is essential will also depend on the individual needs of each investor. My purpose for holding a TIPS ladder is to supplement an income floor in retirement which is primarily from Social Security. In this example, an income floor of 70K/yr meets my needs (50K from SS and 20K from TIPS). The TIPS income will always be "grainy" at the 1K level because fractional bonds are unavailable. If, due to the gapyear coupon variations mentioned above, the income floor varies even more, say between 68K and 72K from year to year, or even 66K and 74K from year to year, it wouldn't affect my lifestyle or ability to sleep at night. ARA smoothing isn't particularly important to me, as other investments are available to fill in any minor divots in the income floor. Perfectly smooth income might be needed by others, and ARA smoothing can easily be implemented by them.
In my case, I have a huge excess of 20252027 TIPS, yet I still have my tentative DARA or more in most rungs of my ladder; i.e., my ladder is much larger than it needs to be to meet the DARA I've been using. So, I'm considering using some of my excess 2025s or 2026s to buy the Jan 2035 early next year. I've already been using some excess 2025s to add to my longer rungstoday I sold some Jul 2025s to buy some 2045s at 2.26%. My marketvalue weighted duration now is 6.4 years, and it probably should be closer to 10 years.
I think we're pretty close to exhausting this discussion. You've presented your thinking well, and I think I understand it.
I haven't played with tipsladder.com lately. I want to do that, and also give some more thought to the "other interest from later coupons" issue, and how to modify the use of the #Cruncher ladder builder spreadsheet accordingly so that the market value of the TIPS in each of the bracket years corresponds more closely to what they should be based on the duration matching calculations.
Thanks in advance for any guidance.
bpg1234
Last edited by bpg1234 on Sat Nov 02, 2024 8:56 am, edited 3 times in total.
Re: Filling the TIPS gap years with bracket year duration matching
I understand and agree with most of what you presented in the previous post. However, you lost me with the highlighted portion of the following, and I hope you can clarify:
Periodic rebalancing is required when holding two TIPS mutual funds or ETFs to satisfy some future obligation which will need to be paid at a known time. This is because the duration of the obligation declines over time, but the durations of the two funds are nearly constant, thus requiring shifting holdings from the longer fund to the shorter fund over time to remain duration matched to the obligation. In the case of holding two bracket year TIPS to satisfy a future obligation, no such rebalancing is needed since the average duration of the two bracketyear TIPS declines in lock step with the declining duration of the obligation.
When redoing this simple calculation (as proposed in the highlighted text above) while making a swap, or after making a swap, how is the result going to change? If using the n/6 approximation based on original cost, n/6 before the swap is still n/6 after the swap. Assuming the actual years used as the bracket years aren't changing after the swap, I wouldn't expect the results to change enough after any swap (compared to what was originally calculated in 2024) to matter much, even if using actual durations instead of the n/6 approximation. Or am I missing something?
Please enlighten me as to why you think the simple calculation, or a variation thereof, needs to be redone at all after the swap. Are you thinking that the bracket years are going to change after the swap? If so, I agree completely that, of course, the calculations need to be redone after each swap and are not complicated. Obviously, after the first swap n/6 becomes n/5, then n/4, n/3 and so on. Is that why you need to recalculate?
EDIT: In the simple example of a swap to 2037s that I showed above, the objective to "simulate the risk/return of the gap years as if they existed and were marketable" was shown to be met based on my simple backoftheenvelope estimate of the total payout (including coupons). Only the timing (cash flow) of the stream of payments was perturbed. My example assumed no recalculations after the prior swaps for 2035s and 2036s. If the interest rate had been 2% at the time of the swap for 2037s in 2027, the total payout (and cash flows) would have been essentially the same as if the 2037s had existed in 2024 with a 2% coupon rate and held to maturity without needing temporary bracket year holdings.
You seem to be proposing some sort of additional recalculations/rebalancing steps after the 2035 and 2036 swaps. If the objective to "simulate the risk/return of the gap years as if they existed and were marketable" is met without rebalancing, why rebalance? Suppose one or more of those recalculations was done at some wildly different rate of interest/yield, like 0% or 4%. If the interest rate then returned to 2% in time for the swap to 2037s in 2027, would the total payout be the same as it would have been without the recalculations? If the objective is to hedge against parallel yield shifts, whatever intervening recalculations are done should not affect the result if parallel interest rate shifts occur in the intervening time before the swap. Or is the objective of the recalculations to somehow hedge against nonparallel yield shifts? (I am confused!)
END EDIT
(emphasis mine)Kevin M wrote: ↑Fri Nov 01, 2024 6:15 pm
With your original approach of holding n/6 excess 2040 TIPS, where n = 1 to 5 for each of the 2035 to 2039 gap years, and (6n)/6 of the 2034 (e.g., 5/6 2034s and 1/6 2040s for the 2035), which comes quite close to using actual duration calculations to determine the weights, the result is to hold 50% of 5*DARA extra each in the 2034s and 2040s. Using duration calculations based on today's yields the ratio is 0.49 2034s to 0.51 2040s, so 50/50 is close enough considering all the other variables and uncertainty.
How is this complicated, and how is it any more complicated to redo a variation of this simple calculation in figuring out how many bracket year TIPS to continue to hold in filling a gap year?
One answer I guess is that I've ignored coupons; i.e., it would be this simple if zerocoupon TIPS existed and we used them exclusively. Is it that complicated to factor the coupons into this calculation?
Periodic rebalancing is required when holding two TIPS mutual funds or ETFs to satisfy some future obligation which will need to be paid at a known time. This is because the duration of the obligation declines over time, but the durations of the two funds are nearly constant, thus requiring shifting holdings from the longer fund to the shorter fund over time to remain duration matched to the obligation. In the case of holding two bracket year TIPS to satisfy a future obligation, no such rebalancing is needed since the average duration of the two bracketyear TIPS declines in lock step with the declining duration of the obligation.
When redoing this simple calculation (as proposed in the highlighted text above) while making a swap, or after making a swap, how is the result going to change? If using the n/6 approximation based on original cost, n/6 before the swap is still n/6 after the swap. Assuming the actual years used as the bracket years aren't changing after the swap, I wouldn't expect the results to change enough after any swap (compared to what was originally calculated in 2024) to matter much, even if using actual durations instead of the n/6 approximation. Or am I missing something?
Please enlighten me as to why you think the simple calculation, or a variation thereof, needs to be redone at all after the swap. Are you thinking that the bracket years are going to change after the swap? If so, I agree completely that, of course, the calculations need to be redone after each swap and are not complicated. Obviously, after the first swap n/6 becomes n/5, then n/4, n/3 and so on. Is that why you need to recalculate?
EDIT: In the simple example of a swap to 2037s that I showed above, the objective to "simulate the risk/return of the gap years as if they existed and were marketable" was shown to be met based on my simple backoftheenvelope estimate of the total payout (including coupons). Only the timing (cash flow) of the stream of payments was perturbed. My example assumed no recalculations after the prior swaps for 2035s and 2036s. If the interest rate had been 2% at the time of the swap for 2037s in 2027, the total payout (and cash flows) would have been essentially the same as if the 2037s had existed in 2024 with a 2% coupon rate and held to maturity without needing temporary bracket year holdings.
You seem to be proposing some sort of additional recalculations/rebalancing steps after the 2035 and 2036 swaps. If the objective to "simulate the risk/return of the gap years as if they existed and were marketable" is met without rebalancing, why rebalance? Suppose one or more of those recalculations was done at some wildly different rate of interest/yield, like 0% or 4%. If the interest rate then returned to 2% in time for the swap to 2037s in 2027, would the total payout be the same as it would have been without the recalculations? If the objective is to hedge against parallel yield shifts, whatever intervening recalculations are done should not affect the result if parallel interest rate shifts occur in the intervening time before the swap. Or is the objective of the recalculations to somehow hedge against nonparallel yield shifts? (I am confused!)
END EDIT
I hope you like what you see when you try the tipsladder.com manual ladder builder. I find it to be a more intuitive method for filling the gap years. If the coupon payments were allocated to the gap and bracket years properly, it would be just about ideal (and could be automated). Please let us know what you learn.Kevin M wrote: ↑Fri Nov 01, 2024 6:15 pm I think we're pretty close to exhausting this discussion. You've presented your thinking well, and I think I understand it.
I haven't played with tipsladder.com lately. I want to do that, and also give some more thought to the "other interest from later coupons" issue, and how to modify the use of the #Cruncher ladder builder spreadsheet accordingly so that the market value of the TIPS in each of the bracket years corresponds more closely to what they should be based on the duration matching calculations.
Re: Filling the TIPS gap years with bracket year duration matching
Now that I've refreshed my knowledge of tipsladder.com, I think I'll stop using the multiplier terminology used for the #Cruncher ladder spreadsheetthat's where the "3.5X" terminology comes from. That multiplier approach doesn't work well anyway, for reasons that MtnBiker has explained; i.e., the interest assigned to the 2034 is way too much, so you end up buying way to little 2034 principal.bpg1234 wrote: ↑Fri Nov 01, 2024 9:31 pm So Kevin before you close this thread I'm still not certain if I have enough of 2040 TIPS to cover the gap years with a 3.5x target of each. Presently I have accummulated 200 2034 TIPS and 125 2040 TIPS. So when you indicate 3.5x of each for the 7 year period (2 bracket years and 5 gap years) does that mean the same number of actual TIPS (say 200 TIPS of 2034s and 200 TIPS of 2040s) or do you base the number of 2040 TIPS required on the cost which is a lot higher per TIPS (so less actual 2040 TIPS needed) to get the 3.5x ratio?
Thanks in advance for any guidance.
bpg1234
For duration matching using Jan 2034 and 2040, using current yields and the coupon assumptions I make, you end up needing pretty close to 50% of the total dollar value required for the gap years' principal in each of the 2034 and 2040. For example, say your DARA is $10K. Ignoring coupons, you'd need about $50K to buy the five gap years. Assuming about $2K in interest for each gap year, you'd need about $40K for the purchases.
Given these assumptions, you'd want about $20K of extra market value (cost when you first build the ladder) in each of the 2034 and 2040; of course you'd also want $10K of DARA for each of the 2034 and 2040 ladder years themselves.
Note that all calculations use market values, not quantity of TIPS.
If I make a calculation error, #Cruncher probably will let me know.

 Posts: 9873
 Joined: Sun Dec 26, 2010 11:47 am
Re: Filling the TIPS gap years with bracket year duration matching
Hypothetically, for every $10K of 2035s I buy, about 5/6 (approx. $8333) would come from sale of 2034s and about 1/6 (approx. $1667) would come from sale of 2040s. If the value of 2034s and 2040s change dramatically I would alter the amount of 2035s I purchase accordingly.
Precision is not important. Nor is it really possible, since you can't buy fractional TIPS. In the long run, small variations in approach will not affect one's bottom line enough to likely be consequential.
I don't know what my annual expenses will be in 2035, and I have no idea what my portfolio will be worth (I have other investments besides TIPS). A lot can happen between now and then.
Precision is not important. Nor is it really possible, since you can't buy fractional TIPS. In the long run, small variations in approach will not affect one's bottom line enough to likely be consequential.
I don't know what my annual expenses will be in 2035, and I have no idea what my portfolio will be worth (I have other investments besides TIPS). A lot can happen between now and then.
Last edited by protagonist on Wed Nov 06, 2024 6:55 am, edited 1 time in total.
Re: Filling the TIPS gap years with bracket year duration matching
What you end up actually swapping may not change, but I'd rather focus on the purpose of the remaining duration matching holdings in determining the quantity of each bracket year I swap.MtnBiker wrote: ↑Fri Nov 01, 2024 10:08 pm I understand and agree with most of what you presented in the previous post. However, you lost me with the highlighted portion of the following, and I hope you can clarify:
(emphasis mine)Kevin M wrote: ↑Fri Nov 01, 2024 6:15 pm
With your original approach of holding n/6 excess 2040 TIPS, where n = 1 to 5 for each of the 2035 to 2039 gap years, and (6n)/6 of the 2034 (e.g., 5/6 2034s and 1/6 2040s for the 2035), which comes quite close to using actual duration calculations to determine the weights, the result is to hold 50% of 5*DARA extra each in the 2034s and 2040s. Using duration calculations based on today's yields the ratio is 0.49 2034s to 0.51 2040s, so 50/50 is close enough considering all the other variables and uncertainty.
How is this complicated, and how is it any more complicated to redo a variation of this simple calculation in figuring out how many bracket year TIPS to continue to hold in filling a gap year?
One answer I guess is that I've ignored coupons; i.e., it would be this simple if zerocoupon TIPS existed and we used them exclusively. Is it that complicated to factor the coupons into this calculation?
<snip>
When redoing this simple calculation (as proposed in the highlighted text above) while making a swap, or after making a swap, how is the result going to change? If using the n/6 approximation based on original cost, n/6 before the swap is still n/6 after the swap. Assuming the actual years used as the bracket years aren't changing after the swap, I wouldn't expect the results to change enough after any swap (compared to what was originally calculated in 2024) to matter much, even if using actual durations instead of the n/6 approximation. Or am I missing something?
It's probably fine to do it the way you've outlined, in which case no calculations need to be redone. OTOH, with the way I'm thinking about it, one doesn't need to keep track of how many of each bracket year were originally intended to cover a particular gap year.MtnBiker wrote: ↑Fri Nov 01, 2024 10:08 pmPlease enlighten me as to why you think the simple calculation, or a variation thereof, needs to be redone at all after the swap. Are you thinking that the bracket years are going to change after the swap? If so, I agree completely that, of course, the calculations need to be redone after each swap and are not complicated. Obviously, after the first swap n/6 becomes n/5, then n/4, n/3 and so on. Is that why you need to recalculate?
I would want to recheck the duration weighting calculations to be sure, but assuming that they'll always end up resulting in something close to a 50/50 weighting by market value for each of the bracket years, that's a simple calculation to do.
Yes, and as I said, I appreciate that framing of it. It fleshes out the way I had been thinking about it, which was just that that if yields go up, the added value of a new TIPS is generated by the higher coupons rather than by a lower price, so a newly created ladder is less expensive, not because the newly issued TIPS are less expensive, but because less principal of the newly issued gap and earlier maturing TIPS must be purchased due to the higher coupon interest delivered for those rungs.MtnBiker wrote: ↑Fri Nov 01, 2024 10:08 pmEDIT: In the simple example of a swap to 2037s that I showed above, the objective to "simulate the risk/return of the gap years as if they existed and were marketable" was shown to be met based on my simple backoftheenvelope estimate of the total payout (including coupons). Only the timing (cash flow) of the stream of payments was perturbed.
I'm not thinking about rebalancing after, but just calculating how much market value should be retained in each of the bracket years before the swap, to determine how much of the bracket years should be sold to fund the swap. I'm not thinking in terms of rebalancing at all, but more in terms of where the cash comes from to fund a gap year purchase.
I probably answered this in my posts yesterday and today in New tool for building a TIPS ladder  Page 12  Bogleheads.org. It appears that we're on the same page about this now. #Cruncher's post in that thread opened my eyes to how he and kaesler have been thinking about using the bracket years to cover the gap yearsi.e., holding the bracket years to maturityrather than the way you, I, and probably others following this thread have been thinking about iti.e., selling some of each bracket year to buy each gap year in the year issued.MtnBiker wrote: ↑Fri Nov 01, 2024 10:08 pmI hope you like what you see when you try the tipsladder.com manual ladder builder. I find it to be a more intuitive method for filling the gap years. If the coupon payments were allocated to the gap and bracket years properly, it would be just about ideal (and could be automated). Please let us know what you learn.
If I make a calculation error, #Cruncher probably will let me know.
Re: Filling the TIPS gap years with bracket year duration matching
Quoted from another thread: viewtopic.php?p=8109443#p8109443
I am not yet convinced that duration matching will be preserved if one follows the procedure defined by the highlighted statement. I think you are suggesting doing "this exercise" multiple times, another time for each of the first four swaps. The first (original) "this exercise," as you laid it out, is to hedge against interest rate changes subsequent to the date that the bracket year holdings were chosen. The first time you do "this exercise,' you assure that the total real income achieved will be about the same as if you could buy all the gap years directly in 2024 at a 2% interest rate. Getting the bracket year holdings into the ideal initial 50/50 ratio based on original cost is the way this is achieved.
At a later date, the then present dollar values of the excess bracket year holdings will no longer be in a 50/50 mix since the interest rate will have changed. Assuming you are now ready to do the first swap, the target values for the remaining bracket holdings will no longer be 50/50 as one of the gap years will be out of the picture. What is that new target mix ratio? is the new target mix ratio to be based on the original cost or the now present value? Once you figure out the answers to those questions, you then sell whatever you need to bring the mix back to the new target value ratio after the first swap. Is the amount sold the correct mix to achieve duration matching for that gap year? When you complete "this exercise" at this later date when the interest rate is some other value, will you not be hedging against changes from this other interest rate for the remaining excess bracket holdings? Suppose you complete "this exercise" again when interest rates are 0%? Will the resulting real income be lower (closer to 0% yield) as a result? Are these fair questions or am I overthinking this and making it way more complicated than it is?
These are rhetorical questions. I don't know any of the answers. But I am fairly sure that even lacking this knowledge, I shouldn't have any worries about duration matching falling off the rails if I duration match each gap year individually. My method is easier for me to understand and makes more sense than complicating things by potentially allowing errors to creep in as excess holdings shift around between gap years as interest rates change.
EDIT: After thinking about this some more, I still don't know the answers to my questions but I'm willing to make a guess. My intuition is that if "this exercise" is repeated using the original cost of each bond, the result of your method should be equivalent to my method. That is, if interest rates swing from 2% to 0% while waiting to complete the swaps, the total ARA ultimately received will not be significantly affected. If using your method, my intuition says that if each one of the "this exercise" calculations is completed using the then present value of the bonds, that the final result may differ significantly if interest rates vary significantly over time. I would postulate that records of the original costs probably need to be kept in order for your method to satisfy the basic duration matching criteria. So, my thought is that some basic record keeping is probably needed for either method to work well. Please correct me if I'm wrong.
I am following you so far. Since a calculation of duration never entered the discussion, I assume you are using the zerocoupon, n/6 approximation. You have determined that the excess bracket year holdings should be selected in roughly a 50/50 mix by original cost when the ladder is built in 2024 at an existing interest rate of about 2%. By holding this exact mix of bracket year holdings (by number of bonds, not by subsequent cost), until 2029 when all 5 swaps can be completed together in one fell swoop, you will have achieved duration matching. The real income should be approximately preserved regardless of any intervening parallel interest rate shifts. So far, so good.Kevin M wrote: ↑Thu Nov 07, 2024 3:46 pmThere's what I think is an even easier way to do it. The key is that all that matters is that you have about half of the "cost" amount allocated for the gap years in each of the bracket years (e.g., 2034 and 2040).MtnBiker wrote: ↑Fri Oct 11, 2024 4:36 pm The most straightforward method that I am aware of at the present time is to use the manual version ("build ladder by hand") on tipsladder.com.
For the bracket years use bonds maturing in January 2034 and February 2040.
The duration for the Feb 2040 is 13.2.
The duration for the Jan 2034 is 8.5.
The duration of the missing gap years, with January maturities (if they were available today), would be very close to:
2039, Dur = 12.4
2038, Dur = 11.6
2037, Dur = 10.9
2036, Dur = 10.1
2035, Dur = 9.3
Use the manual tool to find the mix of Jan 2034s and Feb 2040s that have these average durations for each of these gap years. I found the following, based on the desire to receive 20K real income per year from 2034 to 2040.
2040: Need 13 of the 2040s. Dur = 13.2
2039: Need 11 of the 2040s and 3 of the 2034s, Dur = 12.4
2038: Need 9 of the 2040s and 5 of the 2034s, Dur = 11.9
2037: Need 7 of the 2040s and 8 of the 2034s, Dur = 11.1
2036: Need 4 of the 2040s and 12 of the 2034s, Dur = 10.1
2035: Need 2 of the 2040s and 15 of the 2034s, Dur = 9.3
2034: Need 18 of the 2034s, Dur = 8.5
You can try it yourself and see if you come up with something similar.
Start with any options that result in one of the 2034s (I'll use July here) being used for 2035 and 2036, and the 2040 being used for 2038 and 2039. The 2037 will be covered either by 2034 or 2040 to start. With my choices, using $10K desired annual income, this is what it looks like:
I focus on the third column from the left, the "Net purchase cost" column, since that will be close to the starting market values. We see that the 2035 and 2037 are covered by the 2034, and the 2038 and 2039 are covered by the 2040, as desired. The 2037 also is covered by the 2034, but we're going to modify that manually so that about half each of the excess purchase cost is held in each of the 2034 and 2040.
Without using a calculator or a spreadsheet, we can eyeball it and see that there's roughly $16,000 each of purchase cost allocated to the 2035/2036 and the 2038/2039. There's about $8K of the 2034 allocated to the 2037, so we'll edit that so there's about $4K each allocated to each of the 2034 and 2040, which turns out to be three 2040s and four 2034s:
Funded years now looks like this:
I might have bumped up the quantity by one for the 2038 before calculating what to do for the 2037, but I wanted this first pass to just start with the defaults, especially given the current shortcomings in the tool to meet our needs for gap year duration matching as we intend to use it.
This will work better if kaesler is able to implement a solution that allows us more flexibility in handling the gap years, as we've discussed, and the more analytical among us might want to use a spreadsheet or at least a calculator to fine tune the approach, but even this very rough approach probably comes close enough given the uncertainties involved in the duration matching approach.
(Emphasis added is mine.)Kevin M wrote: ↑Thu Nov 07, 2024 3:46 pm
Given the simplicity of this approach, there is no need to think in terms of allocating specific durationmatched quantities to each gap year, and it follows that there's no need to keep track of that. Simply repeat this exercise as each new gap year becomes available to determine how much should continue to be held in each bracket year, use whatever excess is required and available to fund the purchase of the gap year, and then optionally do any additional ladder tweaking that is desired (which may be none).
I am not yet convinced that duration matching will be preserved if one follows the procedure defined by the highlighted statement. I think you are suggesting doing "this exercise" multiple times, another time for each of the first four swaps. The first (original) "this exercise," as you laid it out, is to hedge against interest rate changes subsequent to the date that the bracket year holdings were chosen. The first time you do "this exercise,' you assure that the total real income achieved will be about the same as if you could buy all the gap years directly in 2024 at a 2% interest rate. Getting the bracket year holdings into the ideal initial 50/50 ratio based on original cost is the way this is achieved.
At a later date, the then present dollar values of the excess bracket year holdings will no longer be in a 50/50 mix since the interest rate will have changed. Assuming you are now ready to do the first swap, the target values for the remaining bracket holdings will no longer be 50/50 as one of the gap years will be out of the picture. What is that new target mix ratio? is the new target mix ratio to be based on the original cost or the now present value? Once you figure out the answers to those questions, you then sell whatever you need to bring the mix back to the new target value ratio after the first swap. Is the amount sold the correct mix to achieve duration matching for that gap year? When you complete "this exercise" at this later date when the interest rate is some other value, will you not be hedging against changes from this other interest rate for the remaining excess bracket holdings? Suppose you complete "this exercise" again when interest rates are 0%? Will the resulting real income be lower (closer to 0% yield) as a result? Are these fair questions or am I overthinking this and making it way more complicated than it is?
These are rhetorical questions. I don't know any of the answers. But I am fairly sure that even lacking this knowledge, I shouldn't have any worries about duration matching falling off the rails if I duration match each gap year individually. My method is easier for me to understand and makes more sense than complicating things by potentially allowing errors to creep in as excess holdings shift around between gap years as interest rates change.
EDIT: After thinking about this some more, I still don't know the answers to my questions but I'm willing to make a guess. My intuition is that if "this exercise" is repeated using the original cost of each bond, the result of your method should be equivalent to my method. That is, if interest rates swing from 2% to 0% while waiting to complete the swaps, the total ARA ultimately received will not be significantly affected. If using your method, my intuition says that if each one of the "this exercise" calculations is completed using the then present value of the bonds, that the final result may differ significantly if interest rates vary significantly over time. I would postulate that records of the original costs probably need to be kept in order for your method to satisfy the basic duration matching criteria. So, my thought is that some basic record keeping is probably needed for either method to work well. Please correct me if I'm wrong.
Re: Filling the TIPS gap years with bracket year duration matching
Also quoted from other thread:
Wouldn't you need to sell in order to get the indicated total income for each gap year, rather than just relying on TIPS maturing and interest being paid? If so, I find that suboptimal, especially if you're concerned about making it easy for a less finance oriented spouse or less cognitively coherent self during the gap years. That's why I'd rather sell bracket year TIPS when new 10 year TIPS are issued, even if I have to take a small hit due to trading costs and possible interest rate risk.
Wouldn't you need to sell in order to get the indicated total income for each gap year, rather than just relying on TIPS maturing and interest being paid? If so, I find that suboptimal, especially if you're concerned about making it easy for a less finance oriented spouse or less cognitively coherent self during the gap years. That's why I'd rather sell bracket year TIPS when new 10 year TIPS are issued, even if I have to take a small hit due to trading costs and possible interest rate risk.
 Raspberry503
 Posts: 1253
 Joined: Sat Oct 03, 2020 6:42 am
Re: Filling the TIPS gap years with bracket year duration matching
It's the first time I understand someone is advocating waiting till 2029 rather than exchanging gradually as new 2035+ TIPS become available. I don't understand the pros and cons, it just shows that I still don't understand what I should do to make sure I get the most of my ladder with what I have purchased already.MtnBiker wrote: ↑Thu Nov 07, 2024 9:43 pm I am following you so far. Since a calculation of duration never entered the discussion, I assume you are using the zerocoupon, n/6 approximation. You have determined that the excess bracket year holdings should be selected in roughly a 50/50 mix by original cost when the ladder is built in 2024 at an existing interest rate of about 2%. By holding this exact mix of bracket year holdings (by number of bonds, not by subsequent cost), until 2029 when all 5 swaps can be completed together in one fell swoop, you will have achieved duration matching. The real income should be approximately preserved regardless of any intervening parallel interest rate shifts. So far, so good.
Re: Filling the TIPS gap years with bracket year duration matching
To be clear, I don’t advocate waiting until 2029. It is one of many options but exchanging gradually is probably better for most folks. The gap is an annoying complication that is best eliminated sooner rather than later when cognitive decline might be an issue.Raspberry503 wrote: ↑Fri Nov 08, 2024 11:14 amIt's the first time I understand someone is advocating waiting till 2029 rather than exchanging gradually as new 2035+ TIPS become available. I don't understand the pros and cons, it just shows that I still don't understand what I should do to make sure I get the most of my ladder with what I have purchased already.MtnBiker wrote: ↑Thu Nov 07, 2024 9:43 pm I am following you so far. Since a calculation of duration never entered the discussion, I assume you are using the zerocoupon, n/6 approximation. You have determined that the excess bracket year holdings should be selected in roughly a 50/50 mix by original cost when the ladder is built in 2024 at an existing interest rate of about 2%. By holding this exact mix of bracket year holdings (by number of bonds, not by subsequent cost), until 2029 when all 5 swaps can be completed together in one fell swoop, you will have achieved duration matching. The real income should be approximately preserved regardless of any intervening parallel interest rate shifts. So far, so good.
Re: Filling the TIPS gap years with bracket year duration matching
By gradually do you mean annually, as new 10year TIPS are issued? What would you sell to buy the new TIPS?MtnBiker wrote: ↑Fri Nov 08, 2024 1:39 pmTo be clear, I don’t advocate waiting until 2029. It is one of many options but exchanging gradually is probably better for most folks. The gap is an annoying complication that is best eliminated sooner rather than later when cognitive decline might be an issue.
Is this your suggestion: viewtopic.php?p=8071818#p8071818
Re: Filling the TIPS gap years with bracket year duration matching
Calculation of duration is implicit. Although I didn't explicitly mention it in this particular post, I've previously pointed out that about half in each of the bracket years is a close approximation to the ratio that results from actual duration matching calculations, which results in 49% in 2034 and 51% in 2040. Or as a gap year example, the duration calculations for 2035 result in 82.9% in 2034, which is the same as 1/6 = 83.3% rounded to the closest percent.MtnBiker wrote: ↑Thu Nov 07, 2024 9:43 pm Quoted from another thread: viewtopic.php?p=8109443#p8109443
I am following you so far. Since a calculation of duration never entered the discussion, I assume you are using the zerocoupon, n/6 approximation.Kevin M wrote: ↑Thu Nov 07, 2024 3:46 pm
There's what I think is an even easier way to do it. The key is that all that matters is that you have about half of the "cost" amount allocated for the gap years in each of the bracket years (e.g., 2034 and 2040).
Start with any options that result in one of the 2034s (I'll use July here) being used for 2035 and 2036, and the 2040 being used for 2038 and 2039. The 2037 will be covered either by 2034 or 2040 to start. With my choices, using $10K desired annual income, this is what it looks like:
I focus on the third column from the left, the "Net purchase cost" column, since that will be close to the starting market values. We see that the 2035 and 2037 are covered by the 2034, and the 2038 and 2039 are covered by the 2040, as desired. The 2037 also is covered by the 2034, but we're going to modify that manually so that about half each of the excess purchase cost is held in each of the 2034 and 2040.
Without using a calculator or a spreadsheet, we can eyeball it and see that there's roughly $16,000 each of purchase cost allocated to the 2035/2036 and the 2038/2039. There's about $8K of the 2034 allocated to the 2037, so we'll edit that so there's about $4K each allocated to each of the 2034 and 2040, which turns out to be three 2040s and four 2034s:
Funded years now looks like this:
I might have bumped up the quantity by one for the 2038 before calculating what to do for the 2037, but I wanted this first pass to just start with the defaults, especially given the current shortcomings in the tool to meet our needs for gap year duration matching as we intend to use it.
This will work better if kaesler is able to implement a solution that allows us more flexibility in handling the gap years, as we've discussed, and the more analytical among us might want to use a spreadsheet or at least a calculator to fine tune the approach, but even this very rough approach probably comes close enough given the uncertainties involved in the duration matching approach.
I explained the duration matching calculations early in the thread. I don't assume zerocouponI use linear interpolation between the 2034 and 2040 yields to estimate a hypothetical yield for each gap year, and calculate the coupon based on the yield. The modified duration of each gap year is estimated from these values.
One thing to clarify is that the quantities shown for each gap year that I showed using tipsladder.com do not indicate the quantities that will be sold to fund that gap year when the bond is issued. Those are just convenient quantities to simplify the calculation of the quantities to buy for the middle gap year. All that matters is that we end up with the appropriate market value. So we wouldn't actually sell only 2034s to fund the 2035we'd probably sell closer to 5/6 of the required amount to buy it, or about $6,667 of the 2034 and $1,333 of the 2040 for $8K of principal (assuming $2K of coupons) for $10K DARA of the 2035. Of course we'll have to adjust these values due to the minimum amount of either bond we can purchase.
I don't assume the bracket year bonds are held until 2029. The idea remains that a gap year will be purchased in the year it is issued.MtnBiker wrote: ↑Thu Nov 07, 2024 9:43 pmYou have determined that the excess bracket year holdings should be selected in roughly a 50/50 mix by original cost when the ladder is built in 2024 at an existing interest rate of about 2%. By holding this exact mix of bracket year holdings (by number of bonds, not by subsequent cost), until 2029 when all 5 swaps can be completed together in one fell swoop, you will have achieved duration matching. The real income should be approximately preserved regardless of any intervening parallel interest rate shifts. So far, so good.
Kevin M wrote: ↑Thu Nov 07, 2024 3:46 pm Given the simplicity of this approach, there is no need to think in terms of allocating specific durationmatched quantities to each gap year, and it follows that there's no need to keep track of that. Simply repeat this exercise as each new gap year becomes available to determine how much should continue to be held in each bracket year, use whatever excess is required and available to fund the purchase of the gap year, and then optionally do any additional ladder tweaking that is desired (which may be none).
The new target mix ratio would be based on new duration matching calculations. The goal would be to retain the resulting ratios, based on then current market values, of the bracket year TIPS. This is no different than if you were building a new ladder at that time. Either way, the goal is to hold the market value of each of the gap year TIPS that continues to provide duration matching for the remaining gap years.MtnBiker wrote: ↑Thu Nov 07, 2024 9:43 pm(Emphasis added is mine.)
I am not yet convinced that duration matching will be preserved if one follows the procedure defined by the highlighted statement. I think you are suggesting doing "this exercise" multiple times, another time for each of the first four swaps. The first (original) "this exercise," as you laid it out, is to hedge against interest rate changes subsequent to the date that the bracket year holdings were chosen. The first time you do "this exercise,' you assure that the total real income achieved will be about the same as if you could buy all the gap years directly in 2024 at a 2% interest rate. Getting the bracket year holdings into the ideal initial 50/50 ratio based on original cost is the way this is achieved.
At a later date, the then present dollar values of the excess bracket year holdings will no longer be in a 50/50 mix since the interest rate will have changed. Assuming you are now ready to do the first swap, the target values for the remaining bracket holdings will no longer be 50/50 as one of the gap years will be out of the picture. What is that new target mix ratio? is the new target mix ratio to be based on the original cost or the now present value?
I haven't done so yet, but soon I'll run some calculations assuming the 2035 has been issued to determine what the ratio would be. I can do those calculations for different yields. I'm guessing that it's still close to 50/50, but that's just my intuition. Note that if there are five gap years, my intuition is that the approximate allocation to the earlier bracket year for the earliest gap year would be about 4/5 of the total market value of the excess bracket year TIPS. We'll see if the calculations support this.
As I've said before, I'm not thinking in terms of establishing the new ratio after the swap, but before the swap. That ratio will allow me to determine if I have an excess or shortfall in each bracket year. If I have an excess in both, then I sell enough in each to buy the earliest gap year, and maintain the new ratio for the bracket years. If I have a shortfall in both, then I sell as much as I can to go toward funding the earliest gap year and maintain enough in the bracket years to hopefully fund the remaining gap years, or I sell enough of the bracket years to fully fund the earliest gap year, and still maintain the new ratio in the bracket years, expecting a shortfall in funding later gap years. Of course I can add cash or do some ladder rebalancing to tweak all of this.
The idea with duration matching in general is that you're always hedging against future yield changes. In classic duration matching used to immunize a bond portfolio against future yield changes, periodic rebalancing is required as yields and durations change. We should expect the same to be true for this version of duration matching, which is why I expect to focus more on maintaining whatever mix of bracket years is required to duration match as I fund each gap year after its bond is issued.MtnBiker wrote: ↑Thu Nov 07, 2024 9:43 pmWhen you complete "this exercise" at this later date when the interest rate is some other value, will you not be hedging against changes from this other interest rate for the remaining excess bracket holdings? Suppose you complete "this exercise" again when interest rates are 0%? Will the resulting real income be lower (closer to 0% yield) as a result? Are these fair questions or am I overthinking this and making it way more complicated than it is?
Of course each of us can do whatever we want. I'm just trying to develop a sound theoretical basis for the duration matching approach to cover the gap years. Errors are more likely to creep in by not recalculating and adjusting the appropriate mix of bracket year bonds as each gap year is filled, just as if a bond portfolio intended to immunize against future yield changes is not periodically rebalanced, it can deviate from the appropriate mix of durations to continue to meet its objective.MtnBiker wrote: ↑Thu Nov 07, 2024 9:43 pmThese are rhetorical questions. I don't know any of the answers. But I am fairly sure that even lacking this knowledge, I shouldn't have any worries about duration matching falling off the rails if I duration match each gap year individually. My method is easier for me to understand and makes more sense than complicating things by potentially allowing errors to creep in as excess holdings shift around between gap years as interest rates change.
Given the minimum transaction limit of $1K face value, this may or may not be a practical concern in our case.
As explained above, duration calculations are always based on current yields and market values, so I can't think of why any record keeping is required using the approach I'm suggesting.MtnBiker wrote: ↑Thu Nov 07, 2024 9:43 pmEDIT: After thinking about this some more, I still don't know the answers to my questions but I'm willing to make a guess. My intuition is that if "this exercise" is repeated using the original cost of each bond, the result of your method should be equivalent to my method. That is, if interest rates swing from 2% to 0% while waiting to complete the swaps, the total ARA ultimately received will not be significantly affected. If using your method, my intuition says that if each one of the "this exercise" calculations is completed using the then present value of the bonds, that the final result may differ significantly if interest rates vary significantly over time. I would postulate that records of the original costs probably need to be kept in order for your method to satisfy the basic duration matching criteria. So, my thought is that some basic record keeping is probably needed for either method to work well. Please correct me if I'm wrong.
If I make a calculation error, #Cruncher probably will let me know.
Re: Filling the TIPS gap years with bracket year duration matching
I don’t understand the cons either, but obvious pro is that you would know coupon rates of all available TIPS and you (with help of tipsladder.com) would be able to come up with as close to perfect fill as possible. And not have to deal with any of the complex calculations being discussed in this thread.Raspberry503 wrote: ↑Fri Nov 08, 2024 11:14 amIt's the first time I understand someone is advocating waiting till 2029 rather than exchanging gradually as new 2035+ TIPS become available. I don't understand the pros and cons, it just shows that I still don't understand what I should do to make sure I get the most of my ladder with what I have purchased already.MtnBiker wrote: ↑Thu Nov 07, 2024 9:43 pm I am following you so far. Since a calculation of duration never entered the discussion, I assume you are using the zerocoupon, n/6 approximation. You have determined that the excess bracket year holdings should be selected in roughly a 50/50 mix by original cost when the ladder is built in 2024 at an existing interest rate of about 2%. By holding this exact mix of bracket year holdings (by number of bonds, not by subsequent cost), until 2029 when all 5 swaps can be completed together in one fell swoop, you will have achieved duration matching. The real income should be approximately preserved regardless of any intervening parallel interest rate shifts. So far, so good.
I mean, if you currently have a ladder providing for $60k/year, how much 2035 are you going to convert, $60k? Obviously less because you expect coupon payments from future 203639 buys to amount to something. How much less then, $56k, $58k? Can’t know until all pieces of the puzzle are on the board.
To be sure, for someone wanting to fill years as soon as the bonds become available, I don’t think it’s a big deal to later sell some years and buy others later to true up their ladder if desired. Just that it’s not possible to make the fill perfect in that case.
 Raspberry503
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Re: Filling the TIPS gap years with bracket year duration matching
If there is no real disadvantage/risk to waiting will 2029, I am more than willing to do so, I just was under the (mistaken?) assumption that swapping yearly was better.
Re: Filling the TIPS gap years with bracket year duration matching
One disadvantage is that if you suffer cognitive decline or the ladder is inherited by someone not facile with these things, the situation is more complicated than if one had to just sit back and watch TIPS mature and interest be paid.Raspberry503 wrote: ↑Fri Nov 08, 2024 6:23 pm If there is no real disadvantage/risk to waiting will 2029, I am more than willing to do so, I just was under the (mistaken?) assumption that swapping yearly was better.
Re: Filling the TIPS gap years with bracket year duration matching
Another reason not to wait too long to make the swaps is because duration matching works better when the interest rates of the bracket year holdings shift in a parallel manner. Nonparallel shifts (changes in the slope and shape of the yield curve) cannot be hedged against as well as parallel shifts. As the bracket years approach their respective maturities, they become relatively shorter term bonds. The short end of the real yield curve is subject to more gyrations that may tend to generate yield shifts more of the nonparallel variety as the remaining term of the bracketyear bonds shortens. These effects would argue for completing the swaps sooner when practical, while the bracket year bonds remain of the intermediate term variety.Raspberry503 wrote: ↑Fri Nov 08, 2024 6:23 pm If there is no real disadvantage/risk to waiting will 2029, I am more than willing to do so, I just was under the (mistaken?) assumption that swapping yearly was better.
Re: Filling the TIPS gap years with bracket year duration matching
Thanks for taking time to explain what you are proposing in detail. I think I’ve already made it abundantly clear that my opinion is that you are wasting your time doing this, but I will try to continue to follow along and keep an open mind. Hopefully other readers won’t be deterred from duration matching the gap by the unnecessary complexity of what you propose.Kevin M wrote: ↑Fri Nov 08, 2024 3:25 pm
The idea with duration matching in general is that you're always hedging against future yield changes. In classic duration matching used to immunize a bond portfolio against future yield changes, periodic rebalancing is required as yields and durations change. We should expect the same to be true for this version of duration matching, which is why I expect to focus more on maintaining whatever mix of bracket years is required to duration match as I fund each gap year after its bond is issued.
As I’ve said before, periodic rebalancing of two fixedduration bond funds is absolutely necessary for duration matching, but periodic rebalancing of two decliningduration bracket year holdings is not necessary. The only reason rebalancing would be needed is if the average duration of the two holdings drifts away from the desired duration that is trying to be matched. In the case of two bracket year bonds, their declining average duration automatically tracks the declining duration of the gap year to a precision that is close enough. (The n/6 approximation for the bracketyear mix is independent of time, and is independent of any temporal changes in yield and coupon rate, and is considered to be good enough.)
Re: Filling the TIPS gap years with bracket year duration matching
Yes, I plan to swap soon after (no longer than a year after) a new 10year TIPS is issued.exodusing wrote: ↑Fri Nov 08, 2024 2:12 pmBy gradually do you mean annually, as new 10year TIPS are issued? What would you sell to buy the new TIPS?MtnBiker wrote: ↑Fri Nov 08, 2024 1:39 pmTo be clear, I don’t advocate waiting until 2029. It is one of many options but exchanging gradually is probably better for most folks. The gap is an annoying complication that is best eliminated sooner rather than later when cognitive decline might be an issue.
Is this your suggestion: viewtopic.php?p=8071818#p8071818
Yes, my suggestion would be to sell using a schedule something like the example shown there: viewtopic.php?p=8071818#p8071818
and here: viewtopic.php?p=8072876#p8072876