Duration matching with TIPS funds instead of buying individual TIPs

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CULater
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Duration matching with TIPS funds instead of buying individual TIPs

Post by CULater » Mon Nov 05, 2018 11:34 am

My objective is to use TIPS in order to provide a given dollar amount in real (inflation adjusted) dollars in 10 years. I could simply purchase a TIP in that amount maturing in 10 years but the problem with that is that the return from TIP assumes that the interest thrown off is re-invested in the TIP and that is impractical. A zero-coupon TIP would be perfect, if it existed.

As an alternative, I'm looking into the idea of using a ST and LT TIPS fund in order to simulate the declining duration of a 10-year TIP. I've heard this method called "duration matching". For example, at the beginning I would weight the ST and LT TIPS funds in order to achieve an aggregate duration of 10 years. Then every year I would change the weighting to match the declining durations of 9, 8, 7 etc. years.

I know that Bobcat2 has discussed duration-matching in the past and am hopeful that he or someone else can comment on implementing this strategy as a replacement for investing in a single TIP (or other bond) and holding to maturity.
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Re: Duration matching with TIPS funds instead of buying individual TIPs

Post by PugetSoundguy » Mon Nov 05, 2018 11:43 am

Or you could buy a 10-year TIPS and put the interest payments into Vanguard's short-term TIPS fund. A bonus of this approach is that the expense ratio would be 0 for a large part of your investment, although simplicity is what would drive me to this approach.

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Re: Duration matching with TIPS funds instead of buying individual TIPs

Post by grok87 » Mon Nov 05, 2018 12:37 pm

CULater wrote:
Mon Nov 05, 2018 11:34 am
My objective is to use TIPS in order to provide a given dollar amount in real (inflation adjusted) dollars in 10 years. I could simply purchase a TIP in that amount maturing in 10 years but the problem with that is that the return from TIP assumes that the interest thrown off is re-invested in the TIP and that is impractical. A zero-coupon TIP would be perfect, if it existed.

As an alternative, I'm looking into the idea of using a ST and LT TIPS fund in order to simulate the declining duration of a 10-year TIP. I've heard this method called "duration matching". For example, at the beginning I would weight the ST and LT TIPS funds in order to achieve an aggregate duration of 10 years. Then every year I would change the weighting to match the declining durations of 9, 8, 7 etc. years.

I know that Bobcat2 has discussed duration-matching in the past and am hopeful that he or someone else can comment on implementing this strategy as a replacement for investing in a single TIP (or other bond) and holding to maturity.
May be of interest
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Re: Duration matching with TIPS funds instead of buying individual TIPs

Post by ThrustVectoring » Mon Nov 05, 2018 2:00 pm

If you just take the TIPS coupons in cash and reinvest at money market rates, the yield slippage will be probably be less than the trading costs of the TIPS funds. Coupons are at like 1% per year, the spread between cash and 10-year rates is like 1%, you hold the cash an average of 5 years or so, overall cost is 5% coupon amount * 1% yield spread = 0.5%. VAIPX has an expense ratio of 0.1%, so over ten years your overall cost is 1%.

So very very rough math says that you'll have like half the costs if you just buy the TIPS directly and dump the coupons into a money market fund. It's also simpler, since I believe you can just use Treasury Direct and put the coupons into a money market fund that way, so you have to do literally nothing.
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Re: Duration matching with TIPS funds instead of buying individual TIPs

Post by #Cruncher » Mon Nov 05, 2018 2:33 pm

CULater wrote:
Mon Nov 05, 2018 11:34 am
I could simply purchase a TIP in that amount maturing in 10 years but the problem with that is that the return from TIP assumes that the interest thrown off is re-invested in the TIP and that is impractical. A zero-coupon TIP would be perfect, if it existed.
The coupon on the latest 10-year TIPS, the 0.75% July 2028 is so low, the reinvestment rate on coupons will have little effect on the accumulated balance on the maturity date.

According to the WSJ TIPS Quotes 11/2/2018 the 0.75% July 2028 TIPS had a 1.145% yield to maturity. For simplicity if we assume the term were exactly 10 years and interest was paid annually, the price would be 96.288, calculated as follows with the Excel PV function:
96.288 = -PV(1.145%, 10, 0.75, 100, 0)

The following table shows that any real reinvestment rate from 0% to 2% would have little effect on the real value accumulated after 10 years:

Code: Select all

 Coupons
Reinvested  Value in
    At      10 Years   Return
----------  --------   ------
  0.000%     107.50    1.108% [*]
  0.500%     107.67    1.124%
  1.145%     107.90    1.145%
  1.500%     108.03    1.157%
  2.000%     108.21    1.174%
* Example calculations using Excel FV function:
107.50 = FV(0%, 10, -0.75, 0, 0) + 100
1.108% = (107.50 / 96.288) ^ (1 / 10) - 1

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Re: Duration matching with TIPS funds instead of buying individual TIPs

Post by nisiprius » Mon Nov 05, 2018 3:49 pm

I'm not sure I did the analysis correctly, but when I looked into this years ago I came away completely convinced that, no, holding an intermediate-term TIPS fund and a short-term TIPS fund and gradually shifting the allocation from intermediate-term to short-term is not at all equivalent to holding a rolling TIPS ladder, allowing them to mature, harvesting a portion of the proceeds, and reinvesting the rest.

It seemed to me that there was no way to get around the problem that at any given instant in time, most of the bonds in a TIPS fund are exposed to market valuation, fluctuation, and interest rate risk, whereas at the instant of maturity, an individual TIPS is not.

I also convinced myself that fussing about it was meaningless fine tuning.
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Re: Duration matching with TIPS funds instead of buying individual TIPs

Post by bobcat2 » Mon Nov 05, 2018 3:59 pm

nisiprius wrote:
Mon Nov 05, 2018 3:49 pm
I'm not sure I did the analysis correctly, but when I looked into this years ago I came away completely convinced that, no, holding an intermediate-term TIPS fund and a short-term TIPS fund and gradually shifting the allocation from intermediate-term to short-term is not at all equivalent to holding a rolling TIPS ladder, allowing them to mature, harvesting a portion of the proceeds, and reinvesting the rest.
This analysis is irrelevant for the question at hand. The OP, CULater, is asking about a non-rolling TIPS ladder, not a rolling TIPS ladder.

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Re: Duration matching with TIPS funds instead of buying individual TIPs

Post by Ping Pong » Mon Nov 05, 2018 4:09 pm

This is pretty simple. You buy the 10 year TIPS, and the coupons end up in your money market account. When you have enough cash to purchase one additional bond, you buy it on the secondary market. You'll be buying an additional bond of the maturity that you already own.

This is what I do, and it's easy peasy.

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Re: Duration matching with TIPS funds instead of buying individual TIPs

Post by dcabler » Mon Nov 05, 2018 4:16 pm

bobcat2 wrote:
Mon Nov 05, 2018 3:59 pm
nisiprius wrote:
Mon Nov 05, 2018 3:49 pm
I'm not sure I did the analysis correctly, but when I looked into this years ago I came away completely convinced that, no, holding an intermediate-term TIPS fund and a short-term TIPS fund and gradually shifting the allocation from intermediate-term to short-term is not at all equivalent to holding a rolling TIPS ladder, allowing them to mature, harvesting a portion of the proceeds, and reinvesting the rest.
This analysis is irrelevant for the question at hand. The OP, CULater, is asking about a non-rolling TIPS ladder, not a rolling TIPS ladder.

BobK
Hi Bobcat2 - when this went around last time this was discussed, I completely understood how to create the non-rolling ladder using 2 (or 3) funds. What I never quite figured out was how to calculate the amount to withdraw from the ladder each time it was required. I suppose one could assume a 0% real return, but that means a large withdrawal at the very end. Or one could go the 1/N approach, but that results in real withdrawals that are all over the place as interest rates change. What is the correct way to make the calculation?
Last edited by dcabler on Mon Nov 05, 2018 4:43 pm, edited 1 time in total.

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Re: Duration matching with TIPS funds instead of buying individual TIPs

Post by bobcat2 » Mon Nov 05, 2018 4:20 pm

The idea of combining ST & LT TIPS funds to duration match targeted income is intended for the case where one is spending from the funds every year over a series of years. If you simply need real assets at one particular point in time in the future, I agree with other posters that it's much easier to buy the TIPS that mature in the year the income is needed and reinvest the coupons in a MMF until you've accumulated enough in the MMF to buy additional TIPS maturing in the year needed.

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Re: Duration matching with TIPS funds instead of buying individual TIPs

Post by CULater » Mon Nov 05, 2018 4:32 pm

bobcat2 wrote:
Mon Nov 05, 2018 4:20 pm
The idea of combining ST & LT TIPS funds to duration match targeted income is intended for the case where one is spending from the funds every year over a series of years. If you simply need real assets at one particular point in time in the future, I agree with other posters that it's much easier to buy the TIPS that mature in the year the income is needed and reinvest the coupons in a MMF until you've accumulated enough in the MMF to buy additional TIPS maturing in the year needed.

BobK
Hi BobK - I've been revisiting the previous thread in which you discussed duration matching for liability targeted income. You advised that using this strategy as DIY should probably not go beyond age 85, in favor of turning one's attention to longevity protection by using an SPIA. I tend to agree with your rationale that this gets too tricky for advanced elderly to do. But, what if you have signed up for Dimensional or TIAA targeted income? How long are those plans designed to run, with the financial folks doing the TIPS duration matching? And does it seem OK to go further out than age 85 if you're not trying to DIY?
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Re: Duration matching with TIPS funds instead of buying individual TIPs

Post by Angst » Mon Nov 05, 2018 4:39 pm

CULater wrote:
Mon Nov 05, 2018 11:34 am
My objective is to use TIPS in order to provide a given dollar amount in real (inflation adjusted) dollars in 10 years. I could simply purchase a TIP in that amount maturing in 10 years but the problem with that is that the return from TIP assumes that the interest thrown off is re-invested in the TIP and that is impractical. A zero-coupon TIP would be perfect, if it existed.
You're overthinking this. To get "a given dollar amount in real (inflation adjusted) dollars in 10 years", buy a 10 year TIPS at auction and don't worry about the interest payments. Spend them, put them with the rest of your other savings, whatever, you will still (essentially) get in 10 years exactly what you say you want. The interest payments every 6 months are above and beyond the real return required to make your initial purchase whole in real terms 10 years later. The Treasury appears to set the interest rate at auction such that the price per bond is as close to $1,000 as possible. At maturity you'll receive the equivalent of $1,000 in today's (original auction date) dollars, plus one final interest payment.

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Re: Duration matching with TIPS funds instead of buying individual TIPs

Post by nisiprius » Mon Nov 05, 2018 4:59 pm

bobcat2 wrote:
Mon Nov 05, 2018 3:59 pm
nisiprius wrote:
Mon Nov 05, 2018 3:49 pm
I'm not sure I did the analysis correctly, but when I looked into this years ago I came away completely convinced that, no, holding an intermediate-term TIPS fund and a short-term TIPS fund and gradually shifting the allocation from intermediate-term to short-term is not at all equivalent to holding a rolling TIPS ladder, allowing them to mature, harvesting a portion of the proceeds, and reinvesting the rest.
This analysis is irrelevant for the question at hand. The OP, CULater, is asking about a non-rolling TIPS ladder, not a rolling TIPS ladder.

BobK
1) You're right.

2) I think my objection still holds. If you make periodic sales from a TIPS fund to buy something else, in this case a shorter-duration TIPS fund, you are exposed to market valuation and fluctuation on every transaction, with almost every bond in the fund's portfolio. You haven't immunized yourself against interest rate risk. You may well have reduced it, because of the averaging effect of making many periodic transactions, as well as some diversification because all of the bonds in the fund have different maturity dates. But it is still qualitatively different to sell a TIPS fund, five years from now, than to select bonds that mature at the time when you project you need the money and allow them to mature.
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Re: Duration matching with TIPS funds instead of buying individual TIPs

Post by stlutz » Mon Nov 05, 2018 7:33 pm

I think my objection still holds.
Last time we discussed this in detail I was convinced Bob K was wrong. So, I setup a spreadsheet that:

a) Had two "funds" holding a single TIPS issue--one long term and one short term.
b) Assumed that I take out an inflation-adjusted amount from my funds each year
c) Assumed random changes in the direction of rates and the shape of the yield curve
d) Maintained a duration-matched portfolio. That is, my average duration was always 1/2 of the time of the endpoint of my portfolio.

I reran a bunch of times with (c) generating new random patterns in interest rate changes with each simulation and you know what--it all worked out extremely close to how BobK said it would. In short, I set out to prove him wrong but I proved myself wrong instead.

Now, owning a single fund (e.g. VAIPX) that is not duration matched to your time horizon doesn't work out so neatly. Sometimes you run out of money early; sometimes it lasts longer than you need. In that case it depends on when rates changes and it what direction.

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Re: Duration matching with TIPS funds instead of buying individual TIPs

Post by OffGridder » Mon Nov 05, 2018 10:31 pm

nisiprius wrote:
Mon Nov 05, 2018 4:59 pm
bobcat2 wrote:
Mon Nov 05, 2018 3:59 pm
nisiprius wrote:
Mon Nov 05, 2018 3:49 pm
I'm not sure I did the analysis correctly, but when I looked into this years ago I came away completely convinced that, no, holding an intermediate-term TIPS fund and a short-term TIPS fund and gradually shifting the allocation from intermediate-term to short-term is not at all equivalent to holding a rolling TIPS ladder, allowing them to mature, harvesting a portion of the proceeds, and reinvesting the rest.
This analysis is irrelevant for the question at hand. The OP, CULater, is asking about a non-rolling TIPS ladder, not a rolling TIPS ladder.

BobK
1) You're right.

2) I think my objection still holds. If you make periodic sales from a TIPS fund to buy something else, in this case a shorter-duration TIPS fund, you are exposed to market valuation and fluctuation on every transaction, with almost every bond in the fund's portfolio. You haven't immunized yourself against interest rate risk. You may well have reduced it, because of the averaging effect of making many periodic transactions, as well as some diversification because all of the bonds in the fund have different maturity dates. But it is still qualitatively different to sell a TIPS fund, five years from now, than to select bonds that mature at the time when you project you need the money and allow them to mature.
Hi Nisiprius,
Do you still have an allocation to TIPS in your portfolio? I recall you gave up on managing a TIPS ladder and reallocated the funds to TIPS funds. If you still do, what is your allocation to TIPS and the duration? Your rationale would be appreciated. Thank you.
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Re: Duration matching with TIPS funds instead of buying individual TIPs

Post by #Cruncher » Tue Nov 06, 2018 12:23 pm

Angst wrote:
Mon Nov 05, 2018 4:39 pm
The Treasury appears to set the interest rate at auction such that the price per bond is as close to $1,000 as possible.
This is approximately true for the initial auction of a Treasury bond (nominal or TIPS). [*] But it is not the case for subsequent auctions of the same issue. For example, the reopening auction of the 10-year 0.75% July 2028 TIPS that (according to the tentative auction schedule) will take place later this month, is currently priced at a significant discount to par (96+19/32 according to the WSJ TIPS Quotes 11/5/2018). The auction price will be close to this If the bond's yield to maturity remains around 1.123%.

nisiprius wrote:
Mon Nov 05, 2018 4:59 pm
If you make periodic sales from a TIPS fund to buy something else, in this case a shorter-duration TIPS fund, you are exposed to market valuation and fluctuation on every transaction, ... You haven't immunized yourself against interest rate risk. You may well have reduced it, ... But it is still qualitatively different to sell a TIPS fund, five years from now, than to select bonds that mature at the time when you project you need the money and allow them to mature. (underline added)
Well said, NIsi! In my post, Re: Matching a TIPS bond ladder with ST and LT TIPS bond funds, I illustrate this with a hypothetical case. It shows that even when rebalancing to shorter duration funds every quarter, after four years of rates rising 1% per year, one would lose about 8% in market value.

stlutz wrote:
Mon Nov 05, 2018 7:33 pm
Last time we discussed this in detail I was convinced Bob K was wrong. So, I setup a spreadsheet … I reran a bunch of times ... generating new random patterns in interest rate changes with each simulation and you know what--it all worked out extremely close to how BobK said it would. In short, I set out to prove him wrong but I proved myself wrong instead. (underline added)
Since rising and falling interest rates have an opposite effect on the duration matching strategy, I'm not surprised your analysis with random changes has about the same results as bobcat2 predicts. But, if you're referring to the thread, Matching a TIPS bond ladder with ST and LT TIPS bond funds Bob specifically states (in this post):
Because you have duration matched you are immunized against changing interest rates in either direction.
But as Nisi states and I try to demonstrate, the duration matching with funds does not immunize against rising rates.


* At the initial auction of a Treasury note or bond (nominal or TIPS) the price will generally be at or slightly below par. This is because the coupon is set equal to or under the accepted yield in 1/8% increments. E.g., if the yield is 1.000% to 1.124%, the coupon would be set to 1%. An exception would be if the accepted yield is less than 0.125%. In this case the coupon will be set to the minimum 1/8% and the price will therefore be at a premium to par. (This happened to many 5-year and 10-year TIPS from 2011 - 2017.)

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Re: Duration matching with TIPS funds instead of buying individual TIPs

Post by CULater » Tue Nov 06, 2018 2:38 pm

But as Nisi states and I try to demonstrate, the duration matching with funds does not immunize against rising rates.
Profound if true, since the whole idea behind using TIPS effectively for liability matching is to immunize against both inflation and rising rates so that you have a safe, predictable real income being produced. This would mean the only way to assure this is to use a TIPs ladder, correct?
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