Individual TIPS vs TIPS Funds

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Topic Author
Prudence
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Individual TIPS vs TIPS Funds

Post by Prudence »

I re-read Bonds vs Bond Funds in the Wiki. I have some questions regarding the material authored by Annette Thau.
1. Thau has this quotation in her discussion of a bond ladder: "Moreover, if you don't reinvest the interest, you won't get the full annualized yield that made you so excited to buy the bond in the first place." (Out of context). Suppose I buy a TIPS that matures in ten years with a yield-to-maturity of 2% and I do not reinvest any of the semi-annual coupon payments (maybe I spend them or put them under the mattress). Assuming I hold the bond until the maturity date, will I have earned two percent real?
2. Thau has this quotation in her discussion of duration: "So, you should always hold bond funds with a duration equal to or shorter than the expected need for your money (note that holding the duration shorter than your need for the money leaves you exposed to the risk of lower returns if interest rates fall)." Suppose I buy a TIPS bond fund with an average duration of 6.5 years. Assume that I will be holding this fund for at least 20 years. Is this the wrong move if I know I will be needing some of the money before the 6.5 years are up?
3. Thau has lots of material regarding zero coupon bonds. Our accounts are at Vanguard and Treasury Direct. How would I purchase a zero coupon inflation protected bond (i.e. a TIPS zero coupon bond) if there is such a thing?
dcabler
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Re: Individual TIPS vs TIPS Funds

Post by dcabler »

Prudence wrote: Thu Feb 08, 2024 2:15 pm I re-read Bonds vs Bond Funds in the Wiki. I have some questions regarding the material authored by Annette Thau.
1. Thau has this quotation in her discussion of a bond ladder: "Moreover, if you don't reinvest the interest, you won't get the full annualized yield that made you so excited to buy the bond in the first place." (Out of context). Suppose I buy a TIPS that matures in ten years with a yield-to-maturity of 2% and I do not reinvest any of the semi-annual coupon payments (maybe I spend them or put them under the mattress). Assuming I hold the bond until the maturity date, will I have earned two percent real?
2. Thau has this quotation in her discussion of duration: "So, you should always hold bond funds with a duration equal to or shorter than the expected need for your money (note that holding the duration shorter than your need for the money leaves you exposed to the risk of lower returns if interest rates fall)." Suppose I buy a TIPS bond fund with an average duration of 6.5 years. Assume that I will be holding this fund for at least 20 years. Is this the wrong move if I know I will be needing some of the money before the 6.5 years are up?
3. Thau has lots of material regarding zero coupon bonds. Our accounts are at Vanguard and Treasury Direct. How would I purchase a zero coupon inflation protected bond (i.e. a TIPS zero coupon bond) if there is such a thing?
TIPS zero coupon bonds are definitely allowed, but nobody is currently providing them.

Cheers.
miket29
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Re: Individual TIPS vs TIPS Funds

Post by miket29 »

Prudence wrote: Thu Feb 08, 2024 2:15 pm Suppose I buy a TIPS that matures in ten years with a yield-to-maturity of 2% and I do not reinvest any of the semi-annual coupon payments (maybe I spend them or put them under the mattress). Assuming I hold the bond until the maturity date, will I have earned two percent real?
yield-to-maturity is not the same as what is earned even though many people use them as synonyms. Yield-to-maturity is simply the interest rate that solves the present-value equation when setting the bond cost equal to the stream of interest payments and principal repayment at maturity. It does not take what happens to the coupon payments into account at all.

But what most people mean by "earned" (and I suspect you do as well) is how much they have at maturity if their initial investment "earned" some specified rate, meaning it compounded at this rate. In order for this to happen the coupon payments will need to grow at same the earning rate. In your question they do not, so you will earn something less than 2%.

An example might make this clearer. Take a 2-year bond paying 5% annually, an investment on which you expect to earn 5% compounded annually. If you purchase a $1000 bond at face value then in 2 years you will expect to have $1000 x 1.05 x 1.05 = $1102.50. How did the investment get there? One year after purchase you get a $50 coupon. Over the 2nd year if it is invested at 5% it grows to $52.50 and at the end of the 2nd year your bond pays back its face value plus the final coupon payment for a total of $1050. Adding them together gives $1102.50 If the coupon(s) along the way were not reinvested at 5% then you did not earn 5% on your investment. However the yield-to-maturity of this bond is 5% no matter what is done with the coupons, as you can verify at https://www.omnicalculator.com/finance/ ... 5!perc,n:2
IDpilot
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Re: Individual TIPS vs TIPS Funds

Post by IDpilot »

miket29 wrote: Thu Feb 08, 2024 5:03 pm
Prudence wrote: Thu Feb 08, 2024 2:15 pm Suppose I buy a TIPS that matures in ten years with a yield-to-maturity of 2% and I do not reinvest any of the semi-annual coupon payments (maybe I spend them or put them under the mattress). Assuming I hold the bond until the maturity date, will I have earned two percent real?
yield-to-maturity is not the same as what is earned even though many people use them as synonyms. Yield-to-maturity is simply the interest rate that solves the present-value equation when setting the bond cost equal to the stream of interest payments and principal repayment at maturity. It does not take what happens to the coupon payments into account at all.

But what most people mean by "earned" (and I suspect you do as well) is how much they have at maturity if their initial investment "earned" some specified rate, meaning it compounded at this rate. In order for this to happen the coupon payments will need to grow at same the earning rate. In your question they do not, so you will earn something less than 2%.

An example might make this clearer. Take a 2-year bond paying 5% annually, an investment on which you expect to earn 5% compounded annually. If you purchase a $1000 bond at face value then in 2 years you will expect to have $1000 x 1.05 x 1.05 = $1102.50. How did the investment get there? One year after purchase you get a $50 coupon. Over the 2nd year if it is invested at 5% it grows to $52.50 and at the end of the 2nd year your bond pays back its face value plus the final coupon payment for a total of $1050. Adding them together gives $1102.50 If the coupon(s) along the way were not reinvested at 5% then you did not earn 5% on your investment. However the yield-to-maturity of this bond is 5% no matter what is done with the coupons, as you can verify at https://www.omnicalculator.com/finance/ ... 5!perc,n:2
For a great discussion on this topic see this thread, viewtopic.php?t=389539
Topic Author
Prudence
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Re: Individual TIPS vs TIPS Funds

Post by Prudence »

IDpilot wrote: Thu Feb 08, 2024 7:10 pm
miket29 wrote: Thu Feb 08, 2024 5:03 pm
Prudence wrote: Thu Feb 08, 2024 2:15 pm Suppose I buy a TIPS that matures in ten years with a yield-to-maturity of 2% and I do not reinvest any of the semi-annual coupon payments (maybe I spend them or put them under the mattress). Assuming I hold the bond until the maturity date, will I have earned two percent real?
yield-to-maturity is not the same as what is earned even though many people use them as synonyms. Yield-to-maturity is simply the interest rate that solves the present-value equation when setting the bond cost equal to the stream of interest payments and principal repayment at maturity. It does not take what happens to the coupon payments into account at all.

But what most people mean by "earned" (and I suspect you do as well) is how much they have at maturity if their initial investment "earned" some specified rate, meaning it compounded at this rate. In order for this to happen the coupon payments will need to grow at same the earning rate. In your question they do not, so you will earn something less than 2%.

An example might make this clearer. Take a 2-year bond paying 5% annually, an investment on which you expect to earn 5% compounded annually. If you purchase a $1000 bond at face value then in 2 years you will expect to have $1000 x 1.05 x 1.05 = $1102.50. How did the investment get there? One year after purchase you get a $50 coupon. Over the 2nd year if it is invested at 5% it grows to $52.50 and at the end of the 2nd year your bond pays back its face value plus the final coupon payment for a total of $1050. Adding them together gives $1102.50 If the coupon(s) along the way were not reinvested at 5% then you did not earn 5% on your investment. However the yield-to-maturity of this bond is 5% no matter what is done with the coupons, as you can verify at https://www.omnicalculator.com/finance/ ... 5!perc,n:2
For a great discussion on this topic see this thread, viewtopic.php?t=389539
You are right about that excellent thread. Thank you. The issue is still hard to follow. It seems that YTM assumes nothing about what the investor does with the coupon payments during the holding period, which is exactly what I had understood. I don't intend to re-open this whole deal, but if I buy a TIPS with a two percent YTM, and hold it to maturity, I will have received two percent real (and I will receive 100% of my principal adjusted upwards if inflation is greater than zero). Correct?
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Svensk Anga
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Re: Individual TIPS vs TIPS Funds

Post by Svensk Anga »

Prudence wrote: Thu Feb 08, 2024 2:15 pm
3. Thau has lots of material regarding zero coupon bonds. Our accounts are at Vanguard and Treasury Direct. How would I purchase a zero coupon inflation protected bond (i.e. a TIPS zero coupon bond) if there is such a thing?
Treasury policy is for TIPS to have a minimum coupon rate of 0.125% even if the yield set at auction is negative. There are some outstanding issues with this rate. It is not zero coupon, but it is very close.

The inflation adjustment portion of TIPS return works essentially as a zero coupon bond. You don't receive the inflation adjustment until maturity (or until you sell the bond +/- bond price moves).
Topic Author
Prudence
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Re: Individual TIPS vs TIPS Funds

Post by Prudence »

Svensk Anga wrote: Thu Feb 08, 2024 9:21 pm
Prudence wrote: Thu Feb 08, 2024 2:15 pm
3. Thau has lots of material regarding zero coupon bonds. Our accounts are at Vanguard and Treasury Direct. How would I purchase a zero coupon inflation protected bond (i.e. a TIPS zero coupon bond) if there is such a thing?
Treasury policy is for TIPS to have a minimum coupon rate of 0.125% even if the yield set at auction is negative. There are some outstanding issues with this rate. It is not zero coupon, but it is very close.

The inflation adjustment portion of TIPS return works essentially as a zero coupon bond. You don't receive the inflation adjustment until maturity (or until you sell the bond +/- bond price moves).
Good points, thank you.
IDpilot
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Re: Individual TIPS vs TIPS Funds

Post by IDpilot »

Prudence wrote: Thu Feb 08, 2024 8:50 pm
IDpilot wrote: Thu Feb 08, 2024 7:10 pm
miket29 wrote: Thu Feb 08, 2024 5:03 pm
Prudence wrote: Thu Feb 08, 2024 2:15 pm Suppose I buy a TIPS that matures in ten years with a yield-to-maturity of 2% and I do not reinvest any of the semi-annual coupon payments (maybe I spend them or put them under the mattress). Assuming I hold the bond until the maturity date, will I have earned two percent real?
yield-to-maturity is not the same as what is earned even though many people use them as synonyms. Yield-to-maturity is simply the interest rate that solves the present-value equation when setting the bond cost equal to the stream of interest payments and principal repayment at maturity. It does not take what happens to the coupon payments into account at all.

But what most people mean by "earned" (and I suspect you do as well) is how much they have at maturity if their initial investment "earned" some specified rate, meaning it compounded at this rate. In order for this to happen the coupon payments will need to grow at same the earning rate. In your question they do not, so you will earn something less than 2%.

An example might make this clearer. Take a 2-year bond paying 5% annually, an investment on which you expect to earn 5% compounded annually. If you purchase a $1000 bond at face value then in 2 years you will expect to have $1000 x 1.05 x 1.05 = $1102.50. How did the investment get there? One year after purchase you get a $50 coupon. Over the 2nd year if it is invested at 5% it grows to $52.50 and at the end of the 2nd year your bond pays back its face value plus the final coupon payment for a total of $1050. Adding them together gives $1102.50 If the coupon(s) along the way were not reinvested at 5% then you did not earn 5% on your investment. However the yield-to-maturity of this bond is 5% no matter what is done with the coupons, as you can verify at https://www.omnicalculator.com/finance/ ... 5!perc,n:2
For a great discussion on this topic see this thread, viewtopic.php?t=389539
You are right about that excellent thread. Thank you. The issue is still hard to follow. It seems that YTM assumes nothing about what the investor does with the coupon payments during the holding period, which is exactly what I had understood. I don't intend to re-open this whole deal, but if I buy a TIPS with a two percent YTM, and hold it to maturity, I will have received two percent real (and I will receive 100% of my principal adjusted upwards if inflation is greater than zero). Correct?
Correct. You will receive two percent real on all the money you invested in the TIPS. No one knows what you will receive on the coupon payments the TIPS generate between the time you buy them and maturity of the TIPS.
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Prudence
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Re: Individual TIPS vs TIPS Funds

Post by Prudence »

IDpilot wrote: Fri Feb 09, 2024 8:01 am
Prudence wrote: Thu Feb 08, 2024 8:50 pm
IDpilot wrote: Thu Feb 08, 2024 7:10 pm
miket29 wrote: Thu Feb 08, 2024 5:03 pm
Prudence wrote: Thu Feb 08, 2024 2:15 pm Suppose I buy a TIPS that matures in ten years with a yield-to-maturity of 2% and I do not reinvest any of the semi-annual coupon payments (maybe I spend them or put them under the mattress). Assuming I hold the bond until the maturity date, will I have earned two percent real?
yield-to-maturity is not the same as what is earned even though many people use them as synonyms. Yield-to-maturity is simply the interest rate that solves the present-value equation when setting the bond cost equal to the stream of interest payments and principal repayment at maturity. It does not take what happens to the coupon payments into account at all.

But what most people mean by "earned" (and I suspect you do as well) is how much they have at maturity if their initial investment "earned" some specified rate, meaning it compounded at this rate. In order for this to happen the coupon payments will need to grow at same the earning rate. In your question they do not, so you will earn something less than 2%.

An example might make this clearer. Take a 2-year bond paying 5% annually, an investment on which you expect to earn 5% compounded annually. If you purchase a $1000 bond at face value then in 2 years you will expect to have $1000 x 1.05 x 1.05 = $1102.50. How did the investment get there? One year after purchase you get a $50 coupon. Over the 2nd year if it is invested at 5% it grows to $52.50 and at the end of the 2nd year your bond pays back its face value plus the final coupon payment for a total of $1050. Adding them together gives $1102.50 If the coupon(s) along the way were not reinvested at 5% then you did not earn 5% on your investment. However the yield-to-maturity of this bond is 5% no matter what is done with the coupons, as you can verify at https://www.omnicalculator.com/finance/ ... 5!perc,n:2
For a great discussion on this topic see this thread, viewtopic.php?t=389539
You are right about that excellent thread. Thank you. The issue is still hard to follow. It seems that YTM assumes nothing about what the investor does with the coupon payments during the holding period, which is exactly what I had understood. I don't intend to re-open this whole deal, but if I buy a TIPS with a two percent YTM, and hold it to maturity, I will have received two percent real (and I will receive 100% of my principal adjusted upwards if inflation is greater than zero). Correct?
Correct. You will receive two percent real on all the money you invested in the TIPS. No one knows what you will receive on the coupon payments the TIPS generate between the time you buy them and maturity of the TIPS.
Thank you. No one has given feedback on question #2 in my original post. Care to weigh in?
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jeffyscott
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Re: Individual TIPS vs TIPS Funds

Post by jeffyscott »

Prudence wrote: Thu Feb 08, 2024 2:15 pm 2. Thau has this quotation in her discussion of duration: "So, you should always hold bond funds with a duration equal to or shorter than the expected need for your money (note that holding the duration shorter than your need for the money leaves you exposed to the risk of lower returns if interest rates fall)." Suppose I buy a TIPS bond fund with an average duration of 6.5 years. Assume that I will be holding this fund for at least 20 years. Is this the wrong move if I know I will be needing some of the money before the 6.5 years are up?
I think it depends on when you need that portion of the money and how much of it you need. If you have a series of small withdrawals (e.g. 3-4% per year over 10+ years) from the fund, I don't think there will be much difference in the results between using a fund or a ladder of individual bonds. OTOH, if you put $500K in the fund and you plan to spend $300K of that in two years to buy a house, then there could be a very large difference in the results for the fund vs. a ladder that would include $300K in a two year bond.

BTW, I don't believe that part of the wiki, or much of the rest that you ascribe to Thau, is quoting anyone. Quotes are designated by italics (or " ").
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Prudence
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Re: Individual TIPS vs TIPS Funds

Post by Prudence »

jeffyscott wrote: Fri Feb 09, 2024 9:23 am
Prudence wrote: Thu Feb 08, 2024 2:15 pm 2. Thau has this quotation in her discussion of duration: "So, you should always hold bond funds with a duration equal to or shorter than the expected need for your money (note that holding the duration shorter than your need for the money leaves you exposed to the risk of lower returns if interest rates fall)." Suppose I buy a TIPS bond fund with an average duration of 6.5 years. Assume that I will be holding this fund for at least 20 years. Is this the wrong move if I know I will be needing some of the money before the 6.5 years are up?
I think it depends on when you need that portion of the money and how much of it you need. If you have a series of small withdrawals (e.g. 3-4% per year over 10+ years) from the fund, I don't think there will be much difference in the results between using a fund or a ladder of individual bonds. OTOH, if you put $500K in the fund and you plan to spend $300K of that in two years to buy a house, then there could be a very large difference in the results for the fund vs. a ladder that would include $300K in a two year bond.

BTW, I don't believe that part of the wiki, or much of the rest that you ascribe to Thau, is quoting anyone. Quotes are designated by italics (or " ").
Thank you. I agree with you. Also, I generally assume that there is a 50-50 chance that interest rates could increase or decrease in the future so the bond fund may not be negatively impacted by the fluctuations.
dbr
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Re: Individual TIPS vs TIPS Funds

Post by dbr »

Prudence wrote: Thu Feb 08, 2024 2:15 pm
2. Thau has this quotation in her discussion of duration: "So, you should always hold bond funds with a duration equal to or shorter than the expected need for your money (note that holding the duration shorter than your need for the money leaves you exposed to the risk of lower returns if interest rates fall)." Suppose I buy a TIPS bond fund with an average duration of 6.5 years. Assume that I will be holding this fund for at least 20 years. Is this the wrong move if I know I will be needing some of the money before the 6.5 years are up?
With all due respect to Thau this is terrible language. The statement about match of investment duration to timing of use is technically a valid discussion except that it overlooks that you and most of us "need" the money in small increments over the passage of long times. We also hold the bonds alongside stocks and we rely on the combination of both to fund retirement. This really makes the whole discussion about "need the money" completely nonsensical.

It is possible to analyze a life time of accumulation and disaccumulation of assets held as stocks and bonds, a period of perhaps 60 years, and still 30 years the day you retire, and try to parse out what duration you should be holding in some bond fund or funds, but it is really difficult to get that pinned down to any particular significance for the duration of that exact fund. In short, it doesn't matter what the duration is of the bonds in a stock/bond portfolio from which you steadily withdraw small amount over a long times. Especially it doesn't matter if you offset the generally lower returns of shorter bonds with a little more allocated to stocks, and vice versa.

You can't get hung up on bond math in isolation when in fact you are operating long term investments in combined assets.
IDpilot
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Re: Individual TIPS vs TIPS Funds

Post by IDpilot »

Prudence wrote: Fri Feb 09, 2024 8:07 am
IDpilot wrote: Fri Feb 09, 2024 8:01 am
Prudence wrote: Thu Feb 08, 2024 8:50 pm
IDpilot wrote: Thu Feb 08, 2024 7:10 pm
miket29 wrote: Thu Feb 08, 2024 5:03 pm yield-to-maturity is not the same as what is earned even though many people use them as synonyms. Yield-to-maturity is simply the interest rate that solves the present-value equation when setting the bond cost equal to the stream of interest payments and principal repayment at maturity. It does not take what happens to the coupon payments into account at all.

But what most people mean by "earned" (and I suspect you do as well) is how much they have at maturity if their initial investment "earned" some specified rate, meaning it compounded at this rate. In order for this to happen the coupon payments will need to grow at same the earning rate. In your question they do not, so you will earn something less than 2%.

An example might make this clearer. Take a 2-year bond paying 5% annually, an investment on which you expect to earn 5% compounded annually. If you purchase a $1000 bond at face value then in 2 years you will expect to have $1000 x 1.05 x 1.05 = $1102.50. How did the investment get there? One year after purchase you get a $50 coupon. Over the 2nd year if it is invested at 5% it grows to $52.50 and at the end of the 2nd year your bond pays back its face value plus the final coupon payment for a total of $1050. Adding them together gives $1102.50 If the coupon(s) along the way were not reinvested at 5% then you did not earn 5% on your investment. However the yield-to-maturity of this bond is 5% no matter what is done with the coupons, as you can verify at https://www.omnicalculator.com/finance/ ... 5!perc,n:2
For a great discussion on this topic see this thread, viewtopic.php?t=389539
You are right about that excellent thread. Thank you. The issue is still hard to follow. It seems that YTM assumes nothing about what the investor does with the coupon payments during the holding period, which is exactly what I had understood. I don't intend to re-open this whole deal, but if I buy a TIPS with a two percent YTM, and hold it to maturity, I will have received two percent real (and I will receive 100% of my principal adjusted upwards if inflation is greater than zero). Correct?
Correct. You will receive two percent real on all the money you invested in the TIPS. No one knows what you will receive on the coupon payments the TIPS generate between the time you buy them and maturity of the TIPS.
Thank you. No one has given feedback on question #2 in my original post. Care to weigh in?
dbr says it well!
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#Cruncher
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Re: Individual TIPS vs TIPS Funds

Post by #Cruncher »

IDpilot wrote: Fri Feb 09, 2024 8:01 am
Prudence wrote: Thu Feb 08, 2024 8:50 pm... if I buy a TIPS with a two percent YTM, and hold it to maturity, I will have received two percent real ... Correct?
Correct. You will receive two percent real on all the money you invested in the TIPS.
This is correct if the vague phrase, "will receive ...", refers to yield-to-maturity (YTM). YTM doesn't depend on how or even if coupons are reinvested. But if it refers to what I call Terminal Value Annual Return (TVAR) [1], it isn't necessarily correct. To illustrate, here is a comparison of two bonds both with a YTM of 2%. One has a 0-1/8% coupon and matures in 28 years while the other has a 1-1/2% coupon and matures a year later. [2] Row 9 in the table below [3] shows that if coupons are reinvested at 2%, the same as the YTM, the TVAR will also be 2% for both bonds.

Code: Select all

Row     Col A    Col B    Col C   Formula in Col B Copied to Col C
  2       YTM   2.000%
  3  Reinvest   2.000%  <===
  4    Coupon   0.125%   1.500%
  5      Term       28       29
  6     Price   60.098   89.078  =-100*PV($B2,B5,B4,1,0)
  7  Interest    4.631   58.188  =FV($B3,B5,-100*B4,0,0)
  8  Proceeds  104.631  158.188  =B7+100
  9      TVAR    2.00%    2.00%  =(B8/B6)^(1/B5)-1
But if coupons are only reinvested at a return of 1%, the TVAR of the 0-1/8% coupon bond will be higher than that of the 1-1/2% coupon bond.

Code: Select all

Row     Col A    Col B    Col C
  2       YTM   2.000%
  3  Reinvest   1.000%  <===
  4    Coupon   0.125%   1.500%
  5      Term       28       29
  6     Price   60.098   89.078
  7  Interest    4.016   50.176
  8  Proceeds  104.016  150.176
  9      TVAR    1.98%    1.82%
On the other hand, if the coupons were reinvested at 3%, the 1-1/2% coupon bond will have the higher TVAR.

Code: Select all

Row     Col A    Col B    Col C
  2       YTM   2.000%
  3  Reinvest   3.000%  <===
  4    Coupon   0.125%   1.500%
  5      Term       28       29
  6     Price   60.098   89.078
  7  Interest    5.366   67.828
  8  Proceeds  105.366  167.828
  9      TVAR    2.03%    2.21%
  1. See my Nov 2022 post for a description of TVAR.
  2. These roughly correspond to the TIPS maturing Feb 15, 2052 and Feb 15, 2053.
  3. Formulas for rows 6 and 7 use the Excel PV and FV functions and assume coupons are paid annually instead of semi-annually.
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Prudence
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Re: Individual TIPS vs TIPS Funds

Post by Prudence »

#Cruncher wrote: Fri Feb 09, 2024 12:23 pm
IDpilot wrote: Fri Feb 09, 2024 8:01 am
Prudence wrote: Thu Feb 08, 2024 8:50 pm... if I buy a TIPS with a two percent YTM, and hold it to maturity, I will have received two percent real ... Correct?
Correct. You will receive two percent real on all the money you invested in the TIPS.
This is correct if the vague phrase, "will receive ...", refers to yield-to-maturity (YTM). YTM doesn't depend on how or even if coupons are reinvested. But if it refers to what I call Terminal Value Annual Return (TVAR) [1], it isn't necessarily correct. To illustrate, here is a comparison of two bonds both with a YTM of 2%. One has a 0-1/8% coupon and matures in 28 years while the other has a 1-1/2% coupon and matures a year later. [2] Row 9 in the table below [3] shows that if coupons are reinvested at 2%, the same as the YTM, the TVAR will also be 2% for both bonds.

Code: Select all

Row     Col A    Col B    Col C   Formula in Col B Copied to Col C
  2       YTM   2.000%
  3  Reinvest   2.000%  <===
  4    Coupon   0.125%   1.500%
  5      Term       28       29
  6     Price   60.098   89.078  =-100*PV($B2,B5,B4,1,0)
  7  Interest    4.631   58.188  =FV($B3,B5,-100*B4,0,0)
  8  Proceeds  104.631  158.188  =B7+100
  9      TVAR    2.00%    2.00%  =(B8/B6)^(1/B5)-1
But if coupons are only reinvested at a return of 1%, the TVAR of the 0-1/8% coupon bond will be higher than that of the 1-1/2% coupon bond.

Code: Select all

Row     Col A    Col B    Col C
  2       YTM   2.000%
  3  Reinvest   1.000%  <===
  4    Coupon   0.125%   1.500%
  5      Term       28       29
  6     Price   60.098   89.078
  7  Interest    4.016   50.176
  8  Proceeds  104.016  150.176
  9      TVAR    1.98%    1.82%
On the other hand, if the coupons were reinvested at 3%, the 1-1/2% coupon bond will have the higher TVAR.

Code: Select all

Row     Col A    Col B    Col C
  2       YTM   2.000%
  3  Reinvest   3.000%  <===
  4    Coupon   0.125%   1.500%
  5      Term       28       29
  6     Price   60.098   89.078
  7  Interest    5.366   67.828
  8  Proceeds  105.366  167.828
  9      TVAR    2.03%    2.21%
  1. See my Nov 2022 post for a description of TVAR.
  2. These roughly correspond to the TIPS maturing Feb 15, 2052 and Feb 15, 2053.
  3. Formulas for rows 6 and 7 use the Excel PV and FV functions and assume coupons are paid annually instead of semi-annually.
This is clearly over my head, but, can you please add a scenario where there are no reinvestments (reinvestmented at zero percent perhaps?). I would like to see that to compare against your three scenarios.
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Re: Individual TIPS vs TIPS Funds

Post by jeffyscott »

dbr wrote: Fri Feb 09, 2024 10:39 am
Prudence wrote: Thu Feb 08, 2024 2:15 pm
2. Thau has this quotation in her discussion of duration: "So, you should always hold bond funds with a duration equal to or shorter than the expected need for your money (note that holding the duration shorter than your need for the money leaves you exposed to the risk of lower returns if interest rates fall)."
With all due respect to Thau this is terrible language.
Just FYI, as I noted above,
that doesn't appear to be a quote of Thau. I believe Prudence is quoting the wiki and the statement is not ascribed to anyone there.
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Re: Individual TIPS vs TIPS Funds

Post by IDpilot »

#Cruncher wrote: Fri Feb 09, 2024 12:23 pm
IDpilot wrote: Fri Feb 09, 2024 8:01 am
Prudence wrote: Thu Feb 08, 2024 8:50 pm... if I buy a TIPS with a two percent YTM, and hold it to maturity, I will have received two percent real ... Correct?
Correct. You will receive two percent real on all the money you invested in the TIPS.
This is correct if the vague phrase, "will receive ...", refers to yield-to-maturity (YTM). YTM doesn't depend on how or even if coupons are reinvested. But if it refers to what I call Terminal Value Annual Return (TVAR) [1], it isn't necessarily correct.
My comment did NOT refer to what you call Terminal Value Annual Return.
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Re: Individual TIPS vs TIPS Funds

Post by dbr »

In any case buying and holding to maturity a bond at a certain YTM means a certain very specific thing and "receive 2% real" is ambiguous. The problem is in the meaning of receive. I would say the expression is "good enough for government work" as it is a government bond after all. But if a person is going to sit down and count up all the transactions in and out to the penny, an investor may find that what they receive is a little bit different from what their idea of "received" is.
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Re: Individual TIPS vs TIPS Funds

Post by IDpilot »

Question on your interest computation below.
#Cruncher wrote: Fri Feb 09, 2024 12:23 pm
7 Interest 4.631 58.188 =FV($B3,B5,-100*B4,0,0)
You appear to be assuming a single coupon payment a year instead of the more typical, especially for treasuries, of semi-annual payments. If you account for semi-annual payments won't this be the formula to use?

FV($B3/2,B5*2,-100*B4/2,0,0)
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Re: Individual TIPS vs TIPS Funds

Post by IDpilot »

dbr wrote: Sat Feb 10, 2024 8:55 am In any case buying and holding to maturity a bond at a certain YTM means a certain very specific thing and "receive 2% real" is ambiguous. The problem is in the meaning of receive. I would say the expression is "good enough for government work" as it is a government bond after all. But if a person is going to sit down and count up all the transactions in and out to the penny, an investor may find that what they receive is a little bit different from what their idea of "received" is.
Geez guys ... all of what I wrote was,


Correct. You will receive two percent real on all the money you invested in the TIPS. No one knows what you will receive on the coupon payments the TIPS generate between the time you buy them and maturity of the TIPS.


It is pretty obvious that "received two percent real" is ONLY on the funds used to PURCHASE the TIP and has nothing to do with what happens with the coupons. Don't really know how to make it any clearer.
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Re: Individual TIPS vs TIPS Funds

Post by watchnerd »

Prudence wrote: Thu Feb 08, 2024 2:15 pm 3. Thau has lots of material regarding zero coupon bonds. Our accounts are at Vanguard and Treasury Direct. How would I purchase a zero coupon inflation protected bond (i.e. a TIPS zero coupon bond) if there is such a thing?
No such thing in the traditional finance space, only nominal STRIPS.

Such instruments do exist in the tokenized real world asset space.
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Re: Individual TIPS vs TIPS Funds

Post by watchnerd »

Svensk Anga wrote: Thu Feb 08, 2024 9:21 pm Treasury policy is for TIPS to have a minimum coupon rate of 0.125% even if the yield set at auction is negative. There are some outstanding issues with this rate. It is not zero coupon, but it is very close.

The inflation adjustment portion of TIPS return works essentially as a zero coupon bond. You don't receive the inflation adjustment until maturity (or until you sell the bond +/- bond price moves).
This is not correct.

Because the coupon pays out as a % of the adjusted principal, the coupons are also inflation-adjusted.

It's close to being de-facto true for very low coupons, but it's actually not a correct explanation of TIPS coupon payments.
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Re: Individual TIPS vs TIPS Funds

Post by jeffyscott »

IDpilot wrote: Sat Feb 10, 2024 9:18 am
dbr wrote: Sat Feb 10, 2024 8:55 am In any case buying and holding to maturity a bond at a certain YTM means a certain very specific thing and "receive 2% real" is ambiguous. The problem is in the meaning of receive. I would say the expression is "good enough for government work" as it is a government bond after all. But if a person is going to sit down and count up all the transactions in and out to the penny, an investor may find that what they receive is a little bit different from what their idea of "received" is.
Geez guys ... all of what I wrote was,


Correct. You will receive two percent real on all the money you invested in the TIPS. No one knows what you will receive on the coupon payments the TIPS generate between the time you buy them and maturity of the TIPS.


It is pretty obvious that "received two percent real" is ONLY on the funds used to PURCHASE the TIP and has nothing to do with what happens with the coupons. Don't really know how to make it any clearer.
So it sounds like you are thinking of it as some of the funds used purchased the TIPS principal and some of the funds used purchased each of the coupon payments. And each portion of those funds will earn 2% real for as long as it remains invested. Part of the funds will be invested for 6 months or less until the first coupon payment removes that portion, then the next bit will be invested until 6 months after that, etc., with the funds used to buy the final coupon and principal being invested until the TIPS matures.
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Re: Individual TIPS vs TIPS Funds

Post by TheTimeLord »

Since I didn't read the Wiki or much of anything else when I constructed my TIPS ladder I took what I now know is a road much less traveled and built my ladder based on the adjusted principle of the TIPS ignoring the coupon payments entirely. :oops:
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Re: Individual TIPS vs TIPS Funds

Post by watchnerd »

TheTimeLord wrote: Sat Feb 10, 2024 10:50 am Since I didn't read the Wiki or much of anything else when I constructed my TIPS ladder I took what I now know is a road much less traveled and built my ladder based on the adjusted principle of the TIPS ignoring the coupon payments entirely. :oops:
It's not like that's going to lead to a bad outcome.
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Re: Individual TIPS vs TIPS Funds

Post by TheTimeLord »

watchnerd wrote: Sat Feb 10, 2024 10:53 am
TheTimeLord wrote: Sat Feb 10, 2024 10:50 am Since I didn't read the Wiki or much of anything else when I constructed my TIPS ladder I took what I now know is a road much less traveled and built my ladder based on the adjusted principle of the TIPS ignoring the coupon payments entirely. :oops:
It's not like that's going to lead to a bad outcome.
No, it definitely won't. Given the coupons I bought and the length of the ladder I could reinvest the payments into additional rungs and it would self fund for a fair amount of time.
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Re: Individual TIPS vs TIPS Funds

Post by IDpilot »

jeffyscott wrote: Sat Feb 10, 2024 10:39 am
IDpilot wrote: Sat Feb 10, 2024 9:18 am
dbr wrote: Sat Feb 10, 2024 8:55 am In any case buying and holding to maturity a bond at a certain YTM means a certain very specific thing and "receive 2% real" is ambiguous. The problem is in the meaning of receive. I would say the expression is "good enough for government work" as it is a government bond after all. But if a person is going to sit down and count up all the transactions in and out to the penny, an investor may find that what they receive is a little bit different from what their idea of "received" is.
Geez guys ... all of what I wrote was,


Correct. You will receive two percent real on all the money you invested in the TIPS. No one knows what you will receive on the coupon payments the TIPS generate between the time you buy them and maturity of the TIPS.


It is pretty obvious that "received two percent real" is ONLY on the funds used to PURCHASE the TIP and has nothing to do with what happens with the coupons. Don't really know how to make it any clearer.
So it sounds like you are thinking of it as some of the funds used purchased the TIPS principal and some of the funds used purchased each of the coupon payments. And each portion of those funds will earn 2% real for as long as it remains invested. Part of the funds will be invested for 6 months or less until the first coupon payment removes that portion, then the next bit will be invested until 6 months after that, etc., with the funds used to buy the final coupon and principal being invested until the TIPS matures.
Nope. All of the funds are used to purchase the TIPS principal (keep it simple and assume no accrued interest). Your yield on those funds will be the yield to maturity. And since this is a TIPS it will be a real YTM. I make NO assumption about any interest earned on the coupons.

Quick example based on one of Cruncher's examples above,
YTM 2.00%
Coupon 0.125%
Term 28 years
Price 60.098
Total Coupons 3.50
Proceeds 103.50
Yield 2.0%
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Re: Individual TIPS vs TIPS Funds

Post by #Cruncher »

Prudence wrote: Fri Feb 09, 2024 1:36 pm... can you please add a scenario where there are no reinvestments (reinvestmented at zero percent perhaps?). I would like to see that to compare against your three scenarios.
I can think of three cases to model this and calculate a Terminal Value Annual Return (TVAR).
  • Coupons are reinvested at a 0% real rate.
  • Coupons are reinvested at a 0% nominal rate. (This is equivalent to sticking them in a mattress and not actually reinvesting them.) But since we are analyzing TIPS with a real return, we have to make an inflation assumption and convert 0% nominal to a real rate. for instance if we were to assume 2% inflation, the real reinvestment rate is about -2%.
  • The coupons are spent. But in this case, TVAR has little meaning. It would be better to ignore TVAR and just think of each collection of coupons and principal as a separate investment earning the YTM -- as mentioned in this post by jeffyscott.
Here are the results for each of these three cases:

Code: Select all

Coupon      0-1/8%   1-1/2%
Price       60.098   89.078
Reinvest    
  Rate        TVAR     TVAR
--------     -----    -----
   0%        1.96%    1.66%   Row 10
  -2%        1.93%    1.40%   Row 15
  n/a        1.84%    0.40%   Row 20
And here are the details of the calculation:

Code: Select all

Row          Col A    Col B    Col C   Formula in Column B Copied to Column C
  2            YTM   2.000%
  3         Coupon   0.125%   1.500%
  4           Term       28       29
  5          Price   60.098   89.078  =-100*PV($B2,B4,B3,1,0)

  7  Reinvest rate   0.000%
  8   Cum interest    3.500   43.500  =IF(ISNUMBER($B7),FV($B7,B$4,-100*B$3,0,0),0)
  9   Tot proceeds  103.500  143.500  =B8+100
 10           TVAR    1.96%    1.66%  =(B9/B$5)^(1/B$4)-1

Code: Select all

 12  Reinvest rate  -2.000%
 13   Cum interest    2.700   33.254  =IF(ISNUMBER($B12),FV($B12,B$4,-100*B$3,0,0),0)
 14   Tot proceeds  102.700  133.254  =B13+100
 15           TVAR    1.93%    1.40%  =(B14/B$5)^(1/B$4)-1

 17  Reinvest rate      n/a
 18   Cum interest       -        -   =IF(ISNUMBER($B17),FV($B17,B$4,-100*B$3,0,0),0)
 19   Tot proceeds  100.000  100.000  =B18+100
 20           TVAR    1.84%    0.40%  =(B19/B$5)^(1/B$4)-1
IDpilot wrote: Sat Feb 10, 2024 9:01 amYou appear to be assuming a single coupon payment a year instead of the more typical, especially for treasuries, of semi-annual payments. If you account for semi-annual payments won't this be the formula to use?
FV($B3/2,B5*2,-100*B4/2,0,0)
This is correct. TIPS do pay interest semi-annually. But I purposely assumed annual interest payments to simplify the calculations.
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Re: Individual TIPS vs TIPS Funds

Post by Prudence »

#Cruncher wrote: Sun Feb 11, 2024 8:01 am
Prudence wrote: Fri Feb 09, 2024 1:36 pm... can you please add a scenario where there are no reinvestments (reinvestmented at zero percent perhaps?). I would like to see that to compare against your three scenarios.
I can think of three cases to model this and calculate a Terminal Value Annual Return (TVAR).
  • Coupons are reinvested at a 0% real rate.
  • Coupons are reinvested at a 0% nominal rate. (This is equivalent to sticking them in a mattress and not actually reinvesting them.) But since we are analyzing TIPS with a real return, we have to make an inflation assumption and convert 0% nominal to a real rate. for instance if we were to assume 2% inflation, the real reinvestment rate is about -2%.
  • The coupons are spent. But in this case, TVAR has little meaning. It would be better to ignore TVAR and just think of each collection of coupons and principal as a separate investment earning the YTM -- as mentioned in this post by jeffyscott.
Here are the results for each of these three cases:

Code: Select all

Coupon      0-1/8%   1-1/2%
Price       60.098   89.078
Reinvest    
  Rate        TVAR     TVAR
--------     -----    -----
   0%        1.96%    1.66%   Row 10
  -2%        1.93%    1.40%   Row 15
  n/a        1.84%    0.40%   Row 20
And here are the details of the calculation:

Code: Select all

Row          Col A    Col B    Col C   Formula in Column B Copied to Column C
  2            YTM   2.000%
  3         Coupon   0.125%   1.500%
  4           Term       28       29
  5          Price   60.098   89.078  =-100*PV($B2,B4,B3,1,0)

  7  Reinvest rate   0.000%
  8   Cum interest    3.500   43.500  =IF(ISNUMBER($B7),FV($B7,B$4,-100*B$3,0,0),0)
  9   Tot proceeds  103.500  143.500  =B8+100
 10           TVAR    1.96%    1.66%  =(B9/B$5)^(1/B$4)-1

Code: Select all

 12  Reinvest rate  -2.000%
 13   Cum interest    2.700   33.254  =IF(ISNUMBER($B12),FV($B12,B$4,-100*B$3,0,0),0)
 14   Tot proceeds  102.700  133.254  =B13+100
 15           TVAR    1.93%    1.40%  =(B14/B$5)^(1/B$4)-1

 17  Reinvest rate      n/a
 18   Cum interest       -        -   =IF(ISNUMBER($B17),FV($B17,B$4,-100*B$3,0,0),0)
 19   Tot proceeds  100.000  100.000  =B18+100
 20           TVAR    1.84%    0.40%  =(B19/B$5)^(1/B$4)-1
IDpilot wrote: Sat Feb 10, 2024 9:01 amYou appear to be assuming a single coupon payment a year instead of the more typical, especially for treasuries, of semi-annual payments. If you account for semi-annual payments won't this be the formula to use?
FV($B3/2,B5*2,-100*B4/2,0,0)
This is correct. TIPS do pay interest semi-annually. But I purposely assumed annual interest payments to simplify the calculations.
Before buying a TIPS bond most investors will want to know what the YTM is, and many will want the YTM to be positive. OTOH, the TVAR cannot be calculated at purchase, so it is irrelevant to the investor at that time. Correct?
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Re: Individual TIPS vs TIPS Funds

Post by IDpilot »

Prudence wrote: Sun Feb 11, 2024 12:47 pm Before buying a TIPS bond most investors will want to know what the YTM is, and many will want the YTM to be positive. OTOH, the TVAR cannot be calculated at purchase, so it is irrelevant to the investor at that time. Correct?
You are correct that TVAR cannot be calculated at purchase. It can only be calculated after the bond matures. Conversely, YTM of a TIP can be calculated as soon as you know the purchase price.

The continuing issue is that some/many buyers of bonds don't understand what YTM is. Some believe that YTM is TVAR. They are thus disappointed when results fail to match their erroneous expectations.
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Re: Individual TIPS vs TIPS Funds

Post by beyou »

There are a lot of people here who like to tinker.
Personally I think when you do your tax return you'll be glad you went with a bond fund over individual bonds.
If you want simplicity go with a bond fund.
If you want control at the expense of simplicity, many do invest directly in TIPS and it's not that hard.
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Re: Individual TIPS vs TIPS Funds

Post by scifilover »

Something that seems to be missing in this discussion is the income tax effect of holding an actual TIP in a taxable account as opposed to holding a TIP fund. If you hold the fund, the inflation increase in the funds holding is distributed to you as taxable dividends. If you hold the TIP itself, the increases in the value of the TIP are used to calculate the amount of interest earned, BUT, the are also taxable each year even though you did not receive the increase in real cash!

I think that is why it is usually recommended to hold actual TIPs in a tax deferred account.

In my IRA, I hold both individual TIPs and TIP ETF funds. When there is inflation, the dividends on the funds go up to deliver the value of the inflation increase to you. When you hold the TIP, the value of the TIP goes up but you are not taxed because the increase is in the IRA. You can choose to invest the dividends in the same fund or invest them elsewhere or withdraw and pay the tax.

In July of 2014, in my IRA, I purchased a 10 year .0125 TIP. July of this year, the TIP will mature. The current value of the bond is almost exactly the net purchase price of the bond after discount times the Dept of Labor CPI increase over this time. Additionally, I have received 19 semi-annual payments based on .0125 x the value of the bond with the current CPI index increase since issue. These payments were tiny compared to the value of the bond.

The value of holding actual TIPs in a tax deferred account is that they are a real way to maintain the purchasing power of money over time.
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Re: Individual TIPS vs TIPS Funds

Post by jeffyscott »

scifilover wrote: Mon Feb 12, 2024 6:58 amIf you hold the TIP itself, the increases in the value of the TIP are used to calculate the amount of interest earned, BUT, the are also taxable each year even though you did not receive the increase in real cash!
Taxes are certainly a reason to prefer to hold TIPS or bonds in general in tax deferred. But I don't think this cash flow issue should be a factor in that decision.

I don't have any TIPS in taxable, but even if I did hold them there it's not like they would be 100% of what we do have in taxable. Furthermore, you would get the coupon payments and likely be able to pay the taxes on the inflation adjustment from that money. Ultimately there's also the option to sell some TIPS or other investments if you need more cash for taxes or for any other reason.

The individual TIPS I owned in a tax deferred account last year paid out about $1500 in coupon payments and the inflation adjustments were about $2660. So were they in taxable, I would owe Federal Income tax on $4160 and have $1500 in actual cash distributions. Unless my Federal tax bracket were 36% or higher, there would no issue at all. Since my actual tax bracket is 12%, rather than figuring out where to get the tax money, I would have to decide where to reinvest the extra $1000 from coupons that is not owed in taxes.

If they are held in taxable and you are worried about the potential need to sell some for taxes, you can choose some of the higher coupon issues to boost cash flow.
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Re: Individual TIPS vs TIPS Funds

Post by Prudence »

jeffyscott wrote: Mon Feb 12, 2024 8:21 am
scifilover wrote: Mon Feb 12, 2024 6:58 amIf you hold the TIP itself, the increases in the value of the TIP are used to calculate the amount of interest earned, BUT, the are also taxable each year even though you did not receive the increase in real cash!
Taxes are certainly a reason to prefer to hold TIPS or bonds in general in tax deferred. But I don't think this cash flow issue should be a factor in that decision.

I don't have any TIPS in taxable, but even if I did hold them there it's not like they would be 100% of what we do have in taxable. Furthermore, you would get the coupon payments and likely be able to pay the taxes on the inflation adjustment from that money. Ultimately there's also the option to sell some TIPS or other investments if you need more cash for taxes or for any other reason.

The individual TIPS I owned in a tax deferred account last year paid out about $1500 in coupon payments and the inflation adjustments were about $2660. So were they in taxable, I would owe Federal Income tax on $4160 and have $1500 in actual cash distributions. Unless my Federal tax bracket were 36% or higher, there would no issue at all. Since my actual tax bracket is 12%, rather than figuring out where to get the tax money, I would have to decide where to reinvest the extra $1000 from coupons that is not owed in taxes.

If they are held in taxable and you are worried about the potential need to sell some for taxes, you can choose some of the higher coupon issues to boost cash flow.
What if you owned a tips fund in taxable? How would the interest and inflation adjustments be done on your tax returns, using the same example?
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Re: Individual TIPS vs TIPS Funds

Post by jeffyscott »

Prudence wrote: Mon Feb 12, 2024 8:46 am What if you owned a tips fund in taxable? How would the interest and inflation adjustments be done on your tax returns, using the same example?
With a fund the inflation adjustments are distributed along with coupons and you choose to reinvest or not. Either way selling shares of a mutual fund, if you need cash for taxes or anything else would be trivial.

I'm not sure what you mean by the same example? But the TIPS index, based on SWRSX, distributions were 3.11% last year. So if had $134K invested, the distributions would be $4160 and the same taxes would apply to that $4160 as the $4160 from individual TIPS.
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