How to model TIPS rates (and returns) pre-1997

[siamond]

It was pointed out several times in the past that our synthetic TIPS series in the Simba backtesting spreadsheet seem quite debatable (it was eyeballed from a chart, and the underlying model from Kothari was lost since then), and that we might want to revisit the topic. Here is where this Kothari estimate came from:
viewtopic.php?t=281
http://www.cfapubs.org/doi/pdf/10.2469/faj.v60.n1.2592

Vanguard VIPSX history provides (US) TIPS historical returns since 2001. VIPSX's benchmark is Bloomberg Barclays US Treasury TIPS, which started in 1997. So we can use those index returns from 1997 to 2000 for a solid estimate. The question now is what to do for 1972-1996 returns (or better 1970-1996), and is there a better way than guesses derived from the Kothari chart.

The following research from Jan Groen and Menno Middeldorp was discussed a couple of times on this forum:
http://libertystreeteconomics.newyorkfe ... tions.html

Checking the very last sentence, there is a link to a companion spreadsheet ("Interested readers can download the historical estimates of break-evens here"). See some preliminary thoughts from Gordoni2 on the matter:
viewtopic.php?t=144355

If we were to be able to derive nominal TIPS rates from this research for the time period of interest, then we should be able to use the bund fund model to derive returns, as we did for other bonds series. Note that we need nominal returns, hence nominal rates.

Anybody willing to take a stab at connecting the dots here?

[grok87]

It was pointed out several times in the past that our synthetic TIPS series in the Simba backtesting spreadsheet seem quite debatable (it was eyeballed from a chart, and the underlying model from Kothari was lost since then), and that we might want to revisit the topic. Here is where this Kothari estimate came from:
viewtopic.php?t=281
http://www.cfapubs.org/doi/pdf/10.2469/faj.v60.n1.2592

Vanguard VIPSX history provides (US) TIPS historical returns since 2001. VIPSX's benchmark is Bloomberg Barclays US Treasury TIPS, which started in 1997. So we can use those index returns from 1997 to 2000 for a solid estimate. The question now is what to do for 1972-1996 returns (or better 1970-1996), and is there a better way than guesses derived from the Kothari chart.

The following research from Jan Groen and Menno Middeldorp was discussed a couple of times on this forum:
http://libertystreeteconomics.newyorkfe ... tions.html

Checking the very last sentence, there is a link to a companion spreadsheet ("Interested readers can download the historical estimates of break-evens here"). See some preliminary thoughts from Gordoni2 on the matter:
viewtopic.php?t=144355

If we were to be able to derive nominal TIPS rates from this research for the time period of interest, then we should be able to use the bund fund model to derive returns, as we did for other bonds series. Note that we need nominal returns, hence nominal rates.

Anybody willing to take a stab at connecting the dots here?

sounds interesting. I'm in I guess

[longinvest]

The key to simulating a TIPS fund would be to build a pseudo-historical real yield curve. Thanks to FRED, we do have a historical nominal yield curve (with some holes).

Here's one relatively simple approach I would like to suggest. I have no idea how good or bad the results it would yield, when compared to real-world results (post-1997), but I think that it could serve as a basis for further improvements, if it is not good enough:

• Estimate inflation expectations by simply taking the the annualized inflation of the preceding three years.
• Calculate a zero-coupon nominal yield curve out of FRED's nominal yield curve. (This increases the duration at each point on the curve, but delivers a pure yield curve).
• Apply the estimated inflation expectation uniformely across the zero-coupon yield curve to construct a pseudo-historical zero-coupon real yield curve.
• Reconstruct a pseudo-historical normal real yield curve from the zero-coupon yield curve.
• Feed the resulting pseudo-historical normal real yield curve into the bond fund simulator and look at the results.

The main idea, in what I am proposing, is to apply the inflation expectation on a zero-coupon yield curve, not on a normal yield curve. Further improvements would consist on finding better ways to estimate inflation expectations and the addition of other factors (such as the impact of higher liquidity risk and the elimination of inflation risk).

What do you think?

[dcabler]

Gordoni2 actually did make the leap and generated nominal annual returns from the FRED paper, but as I recall this was done before you guys came up with the rate->returns methodology currently in use. Might want to contact him directly for his methodology/assumptions and see if you can adapt it.

[grok87]

Gordoni2 actually did make the leap and generated nominal annual returns from the FRED paper, but as I recall this was done before you guys came up with the rate->returns methodology currently in use. Might want to contact him directly for his methodology/assumptions and see if you can adapt it.

I think this is the post you are referencing?
viewtopic.php?f=10&t=144355&p=2147157#p2147157
and maybe this one?
viewtopic.php?f=10&t=179425

Looks like a lot of work has been put into this already and it would be a shame to reinvent the wheel.
It seems like it should be possible to come up with a series for real returns from 1972-1997 for:
1) a constant maturity 20-year tips portfolio
2) a constant maturity 10- year tips portfolio

I haven't read through the entire "Historical Bond Returns - Shiller: From Rates to Returns" thread yet but i will. I think the key assumption is to fill in the 19 year TIPS real yields and the 9 year TIPs real yields for each year. The key assumption is the local slope of the yield curve around the 20 year and 10 year points. It seems like it should be possible to build on the nominal yield curve slopes that were used in the previous analysis- ie the nominal and real yield curve slopes are probably not TOO different...

I'll copy in the folks on the other thread...

cheers,

[longinvest]

I haven't read through the entire "Historical Bond Returns - Shiller: From Rates to Returns" thread yet but i will. I think the key assumption is to fill in the 19 year TIPS real yields and the 9 year TIPs real yields for each year. The key assumption is the local slope of the yield curve around the 20 year and 10 year points. It seems like it should be possible to build on the nominal yield curve slopes that were used in the previous analysis- ie the nominal and real yield curve slopes are probably not TOO different...

I'll copy in the folks on the other thread...

Grok,

Please take the time to entirely read the first post of the "Historival Bond Returns..." thread. It explains important concepts behind its model.

longinvest

[dcabler]

Gordoni2 actually did make the leap and generated nominal annual returns from the FRED paper, but as I recall this was done before you guys came up with the rate->returns methodology currently in use. Might want to contact him directly for his methodology/assumptions and see if you can adapt it.

I think this is the post you are referencing?
viewtopic.php?f=10&t=144355&p=2147157#p2147157
and maybe this one?
viewtopic.php?f=10&t=179425

Looks like a lot of work has been put into this already and it would be a shame to reinvent the wheel.
It seems like it should be possible to come up with a series for real returns from 1972-1997 for:
1) a constant maturity 20-year tips portfolio
2) a constant maturity 10- year tips portfolio

I haven't read through the entire "Historical Bond Returns - Shiller: From Rates to Returns" thread yet but i will. I think the key assumption is to fill in the 19 year TIPS real yields and the 9 year TIPs real yields for each year. The key assumption is the local slope of the yield curve around the 20 year and 10 year points. It seems like it should be possible to build on the nominal yield curve slopes that were used in the previous analysis- ie the nominal and real yield curve slopes are probably not TOO different...

I'll copy in the folks on the other thread...

cheers,

From the first thread. He didn't post the nominal return series, so I contacted him and he kindly sent it to me. But I only asked for the final answer and that's what I got - not the methodology. But he used the breakeven data from the Groen & Middledorp paper to ultimately generate the return series. I haven't read the G&M paper in a while, but it already does most of the heavy lifting re nominal treasury rates and inflation expectations.

[grok87]

I haven't read through the entire "Historical Bond Returns - Shiller: From Rates to Returns" thread yet but i will. I think the key assumption is to fill in the 19 year TIPS real yields and the 9 year TIPs real yields for each year. The key assumption is the local slope of the yield curve around the 20 year and 10 year points. It seems like it should be possible to build on the nominal yield curve slopes that were used in the previous analysis- ie the nominal and real yield curve slopes are probably not TOO different...

I'll copy in the folks on the other thread...

Grok,

Please take the time to entirely read the first post of the "Historival Bond Returns..." thread. It explains important concepts behind its model.

longinvest

THanks longinvest,
I just read the first post and i opened up your spreadsheet. Looks like a lot of good work has been done already and we don't want to reinvent the wheel. Can you just plug in the 20 year real rates and the 10 year real rates from the New York Fed (Groen and Middledorp) paper
http://libertystreeteconomics.newyorkfe ... tions.html
(spreadsheet link a the bottom of the paper)
and come up with the annual real returns for a long term tips fund: 10-20 year maturity I guess?
cheers,

[grok87]

Gordoni2 actually did make the leap and generated nominal annual returns from the FRED paper, but as I recall this was done before you guys came up with the rate->returns methodology currently in use. Might want to contact him directly for his methodology/assumptions and see if you can adapt it.

I think this is the post you are referencing?
viewtopic.php?f=10&t=144355&p=2147157#p2147157
and maybe this one?
viewtopic.php?f=10&t=179425

Looks like a lot of work has been put into this already and it would be a shame to reinvent the wheel.
It seems like it should be possible to come up with a series for real returns from 1972-1997 for:
1) a constant maturity 20-year tips portfolio
2) a constant maturity 10- year tips portfolio

I haven't read through the entire "Historical Bond Returns - Shiller: From Rates to Returns" thread yet but i will. I think the key assumption is to fill in the 19 year TIPS real yields and the 9 year TIPs real yields for each year. The key assumption is the local slope of the yield curve around the 20 year and 10 year points. It seems like it should be possible to build on the nominal yield curve slopes that were used in the previous analysis- ie the nominal and real yield curve slopes are probably not TOO different...

I'll copy in the folks on the other thread...

cheers,

From the first thread. He didn't post the nominal return series, so I contacted him and he kindly sent it to me. But I only asked for the final answer and that's what I got - not the methodology. But he used the breakeven data from the Groen & Middledorp paper to ultimately generate the return series. I haven't read the G&M paper in a while, but it already does most of the heavy lifting re nominal treasury rates and inflation expectations.

cool. so you can post it i guess?

[siamond]

Looks like a lot of work has been put into this already and it would be a shame to reinvent the wheel.

For sure. I sent a PM to Gordoni2 when I issued my first post, asking him if he'd be kind enough to participate to this thread, so that we converge on a fully documented solution and hopefully reach a decent consensus.

[siamond]

[...] and come up with the annual real returns for a long term tips fund: 10-20 year maturity I guess?

Actually, I opened this thread by referring to the Simba backtesting spreadsheet, and a historical extension of the VIPSX series. So if we could stay focused on durations akin to what VIPSX does (i.e. ~ intermediate term), this would be great.

As a side note, in this temporary version of the Simba spreadsheet, I already included the 1997-2000 returns derived from the Barclays TIPS index. This should help comparing any fancy model we come up up with the reality of the recent years. I also have handy the full total return series (1997-2005) for the index itself.

[siamond]

The key to simulating a TIPS fund would be to build a pseudo-historical real yield curve. Thanks to FRED, we do have a historical nominal yield curve (with some holes).
[...]
* Feed the resulting pseudo-historical normal real yield curve into the bond fund simulator and look at the results.

The main idea, in what I am proposing, is to apply the inflation expectation on a zero-coupon yield curve, not on a normal yield curve. Further improvements would consist on finding better ways to estimate inflation expectations and the addition of other factors (such as the impact of higher liquidity risk and the elimination of inflation risk).

Sorry if I am slow, but I don't get it:
1. how does feeding a real yield curve in the bond fund simulator help? what we need at the end are nominal returns. I am missing a step, I guess?
2. the entire point of TIPS is to manage the risk of unexpected inflation like we saw in the 70s. Hoes does the proposed model capture that?

[longinvest]

1. how does feeding a real yield curve in the bond fund simulator help? what we need at the end are nominal returns. I am missing a step, I guess?

We will add realized inflation adjustments to principal and coupons during the year (as happens to real-wold TIPS). Sorry, this seemed so intuitive to me that I forgot to spell it out.

2. the entire point of TIPS is to manage the risk of unexpected inflation like we saw in the 70s. Hoes does the proposed model capture that?

Is it? I don't care what the point is. My objective is to get as realistic a real yield curve as possible. Then, I'll let the model calculate the returns.

[longinvest]

Can you just plug in the 20 year real rates and the 10 year real rates from the New York Fed (Groen and Middledorp) paper
http://libertystreeteconomics.newyorkfe ... tions.html
(spreadsheet link a the bottom of the paper)
and come up with the annual real returns for a long term tips fund: 10-20 year maturity I guess?
cheers,

A 20 to 11-year fund would have an average maturity of 15 years, and an average duration not much lower (given the small TIPS coupons). It might yield a pretty volatile set of returns, but it is doable.

As the Treasury issues TIPS of three maturities, 30-year, 10-year, and 5-year, I think that the simplest way to model the total market would be to simulate the returns of three TIPS funds, 30 to 2-year, 10 to 2-year, and 5 to 2-year, and use the average the three annual returns as a proxy for total TIPS market returns. As it happens, this would yield an average maturity of approximately 8 years with an average duration pretty close to that, relatively similar the actual TIPS market.

[siamond]

1. how does feeding a real yield curve in the bond fund simulator help? what we need at the end are nominal returns. I am missing a step, I guess?

We will add realized inflation adjustments to principal and coupons during the year (as happens to real-wold TIPS). Sorry, this seemed so intuitive to me that I forgot to spell it out.

The process you're suggesting starts from a nominal quantity, goes to a real quantity by subtracting 'expected inflation', churns over real numbers, and then we come back to a nominal quantity by adding the current year's inflation. It wasn't fully obvious to me that subtracting expected inflation at the beginning of the year, then adding current inflation at the end of the year, is the right thing to do.

So, if this is how TIPS work in the real world, then I guess this is how the risk of unexpected inflation is captured? Starting by subtracting expected inflation, then adjusting for actual inflation along the way?

My objective is to get as realistic a real yield curve as possible. Then, I'll let the model calculate the returns.

Ok, fair enough... Let's give it a try.

[siamond]

[...] Estimate inflation expectations by simply taking the the annualized inflation of the preceding three years.

I tested this in the past, I did a quick refresh, and all basic statistical metrics agree, using the past year inflation is a better simple model than the (annualized) preceding two years, which is a better model than the (annualized) preceding three years. Well, at least with US numbers from Prof. Shiller. Plus I would tend to think that the current inflation does map better to the average expectation of participants, just because they live in it, and have short-term memories.

I like your idea of using such simple model first, before getting in the weeds of the inflation expectations model suggested by the Groen article. Which by the way includes surprisingly (overly?) subdued numbers in the late 70s, which would clearly display the effect of the unexpected outcome in those years.

Finally, here is a nice post from DQYDJ, summarizing and comparing inflation expectations surveys. The numbers in the 70s (consumers and forecasters) do seem more realistic to me than Groen, I have to say, but maybe I'm reacting too much in hindsight.

[dcabler]

Here's another paper often referred to for generating synthetic TIPs series. It's mentioned in one of the threads siamond posted, but I think it's worthwhile to mention it by itself. From Ibbotson/Morningstar. See Appendix A. By the way, like siamond's suggestion above, they use the previous year's inflation rate as the expected inflation forecast.

http://corporate.morningstar.com/ib/doc ... tClass.pdf

[longinvest]

[...] Estimate inflation expectations by simply taking the the annualized inflation of the preceding three years.

I tested this in the past, I did a quick refresh, and all basic statistical metrics agree, using the past year inflation is a better simple model than the (annualized) preceding two years, which is a better model than the (annualized) preceding three years. Well, at least with US numbers from Prof. Shiller. Plus I would tend to think that the current inflation does map better to the average expectation of participants, just because they live in it, and have short-term memories.

Here's another paper often referred to for generating synthetic TIPs series. It's mentioned in one of the threads siamond posted, but I think it's worthwhile to mention it by itself. From Ibbotson/Morningstar. See Appendix A. By the way, like siamond's suggestion above, they use the previous year's inflation rate as the expected inflation forecast.

FRED provides constant-maturity yields for TIPS. I suggest we compare the synthetic TIPS yields calculated from nominal yields and one-year/three-year inflation to real-world historical TIPS yields during the periods covered by FRED. I also suggest to compare the synthetic returns using FRED yields to real-world historical returns. These comparisons should give us hints about being on the right track or not.

[longinvest]

The process you're suggesting starts from a nominal quantity, goes to a real quantity by subtracting 'expected inflation', churns over real numbers, and then we come back to a nominal quantity by adding the current year's inflation. It wasn't fully obvious to me that subtracting expected inflation at the beginning of the year, then adding current inflation at the end of the year, is the right thing to do.

So, if this is how TIPS work in the real world, then I guess this is how the risk of unexpected inflation is captured? Starting by subtracting expected inflation, then adjusting for actual inflation along the way?

In the real world, assuming that a TIPS is bought at par, one is guaranteed to receive the stated coupon in inflation-adjusted dollars, and the principal back in inflation-adjusted dollars. TIPS have a special feature in case of deflation: a TIPS will never pay back less than its initial principal in nominal dollars (and I think this applies to coupons, too). I call this a special feature, because Canadian real return bonds, on which TIPS were partly modeled, have no such deflation bonus; they simply pay their coupons and return their principal in inflation-adjusted dollars, which might be lower nominal amounts than the original nominal amounts on the day of issue.

Let's look at a small example. Imagine that I bought a hypothetical 1% 5-year $100 TIPS at par. Each year, this bond will pay me $1 in inflation-adjusted dollars and, at maturity, it will pay me back $100 in inflation-adjusted dollars:

(All amounts, below, are in nominal dollars).
End of Year 0: I invest $100.00 into a 1% 5-year TIPS.
During Year 1: Inflation is 2.5%.
End of Year 1: The principal is now $100.00 + 2.5% = $102.50. The 1% coupon is paid and I receive $102.50 X 1% = $1.03.
During Year 2: Inflation is 3%.
End of Year 2: The principal is now $102.50 + 3% = $105.58. The 1% coupon is paid and I receive $105.58 X 1% = $1.06.
During Year 3: Inflation is -1%.
End of Year 3: The principal is now $105.58 - 1% = $104.53. The 1% coupon is paid and I receive $104.53 X 1% = $1.05.
During Year 4: Inflation is 2%.
End of Year 4: The principal is now $104.53 + 2% = $106.62. The 1% coupon is paid and I receive $106.62 X 1% = $1.07.
During Year 5: Inflation is 2.5%.
End of Year 5: The principal is paid and I receive $106.62 + 2.5% = $109.29. The 1% coupon is paid and I receive $109.29 X 1% = $1.09.

As you can see, there's no such thing as "subtracting expected inflation at the beginning of the year, then adding current inflation at the end of the year". A single TIPS works exactly like a nominal bond (if you exclude the deflation bonus), except that its principal and its coupons are adjusted to inflation.

All the talk about "expected inflation" is just speculation about TIPS pricing, like people do with the pricing of stocks and nominal bonds. A bond is a contract to be paid certain amounts of money at specific times. When one buys a bond (nominal or TIPS) at par, premium, or discount, one knows its exact future cash flows in nominal or inflation-adjusted dollars, depending on the type of bond (excluding any deflation bonus). In other words, one knows the future internal rate of return of the investment at maturity as long as the bond is held until maturity and coupons are not reinvested (in nominal or inflation-adjusted dollars, depending on the type of the bond, and excluding any deflation bonus). Note that this does not tell us the future total return of the investment over the same period if coupons were reinvested in the same bond, which would require knowing the future market prices of the bond on coupon pay dates (or future yields, if you prefer).

What I am proposing is to 1) try constructing a synthetic real yield curve*, then 2) model a TIPS fund similarly to how we modeled a nominal bond fund based on a nominal yield curve, except for the implementation of the annual inflation increments on coupons and principal amounts. Assuming exact investment-maturity and sell-maturity real yields, cash flows of the modeled fund would be exact, leading to self-correcting returns. Of course, we won't have exact real yields, so the quality of our synthetic returns will be dependent on the quality of our synthetic real yields.

* This will require speculating on TIPS pricing in a world where they didn't exist.

[Kevin M]

Don't know if it's at all relevant, but the discussion about zero-coupon yields vs. par yields reminded me of this paper: FRB: Finance and Economics Discussion Series: Screen Reader Version - The U.S. Treasury Yield Curve: 1961 to the Present. The authors maintain a spreadsheet, available online (link in the paper), that has both zero-coupon and par yields in annual increments from 1-30 years.

Although this is for nominal bonds, one benefit is having the yields in annual increments, modeled in a consistent manner, as opposed to just the sample maturities provided for CMTs by FRED, so no linear interpolation is required for the missing CMT maturities. Just thought everyone should be aware of this resource.

Kevin

[dcabler]

Another paper which discusses creating a synthetic tips series. This one is a bit different than other methods I've seen. The primary subject of the paper isn't about creating a synthetic tips series per se, but there is info included starting on page 15 in the section "Inflation Linked Bonds". They also reference the Kothari paper, whose results they purchased from the authors - but it wasn't suitable to their study.

Enjoy:
https://www.enduringinvestments.com/pap ... -Paper.pdf

[stlutz]

For expected inflation, I would suggest considering using the historical data from the Philly Fed survey of professional forecasters. Their forecast of the GDP deflator has the most history and would thus be the most usable one.

https://www.philadelphiafed.org/researc ... files/pgdp

The problem of course that I would think that a 10 year TIPS is priced based on expectations of longer-term inflation as opposed to a 1 year forecast. But we can of course use the actual returns since 1997 compared to the inputs to see how well the model has projected actual returns.

[siamond]

They also reference the Kothari paper, whose results they purchased from the authors

Indeed, they stated in their paper:
<< We contacted the authors and were able to purchase their modeled monthly time series of annual year-on-year real and nominal returns for 5-year inflation-indexed bonds dating to mid-1953. >>

Well, with a bit of luck, they properly archived the Kothari model and might be willing to share (as a reminder, as was documented here, it appears that Prof. Kothari's team lost the data!).

Let me try to contact the folks at Enduring Investments, and see what goes...

[siamond]

For expected inflation, I would suggest considering using the historical data from the Philly Fed survey of professional forecasters.

Here is a more direct link to what I think is of interest:
https://www.philadelphiafed.org/researc ... -forecasts

In the same vein, here is one about consumers inflation expectations:
http://www.sca.isr.umich.edu/tables.html

[longinvest]

While thinking about how to best add TIPS simulation within the bond fund simulator spreadsheet, I realized that it would be much simpler to let the spreadsheet calculate real returns for TIPS. Then, to get nominal returns, one would simply multiply annual real returns by annual inflation factors. We don't need to simulate nominal coupon and principal increments*. This is so obvious!

* The only caveat is this will ignore real-world TIPS deflation bonuses. But, I don't think that we've had enough annual deflation periods, since the 1970s, for this to make a big enough difference. It would be lost in the noise of the much bigger inaccuracies of our synthetic returns.

[grok87]

While thinking about how to best add TIPS simulation within the bond fund simulator spreadsheet, I realized that it would be much simpler to let the spreadsheet calculate real returns for TIPS. Then, to get nominal returns, one would simply multiply annual real returns by annual inflation factors. We don't need to simulate nominal coupon and principal increments*. This is so obvious!

* The only caveat is this will ignore real-world TIPS deflation bonuses. But, I don't think that we've had enough annual deflation periods, since the 1970s, for this to make a big enough difference. It would be lost in the noise of the much bigger inaccuracies of our synthetic returns.

yup

[gordoni2]

I sent a PM to Gordoni2 when I issued my first post, asking him if he'd be kind enough to participate to this thread

Sorry, I'm only just getting up to speed on this discussion. Yes, I did some of what you might be after a while back. I was interested in using the Groen & Middeldorp yields as an extension of the Fred 10 year FII10 data for my AACalc asset allocator. The good news is the code I wrote is publicly available. The bad news is I wrote it in Java and it is rather icky. See the file HistReturns.java. The relevant code is load_fred_interest_rate("FII10", tips10, 10, 2, false), which uses bond_npv() as a helper function.

In short I converted the monthly twice-the-semi-annual-coupon-rate to an annual yield (assuming the Groen & Middeldorp yields follow the standard Treasury convention), converted monthly rates to monthly returns with the help of bond_npv(), and then collapsed the monthly returns to annual returns. Converting to monthly returns before collapsing to annual returns might help reduce longinvest's concerns about estimating a 9 year rate with a 10 year rate. Instead I estimate a 9 year 11 month rate with a 10 year rate, which is probably acceptable.

Since the results are only used internally, I don't have the resulting data readily available, although I could extract it by adding a print statement or two.

I didn't try to adjust for non-10-year TIPS, expense ratios, or nominal returns.

[longinvest]

For expected inflation, I would suggest considering using the historical data from the Philly Fed survey of professional forecasters.

Here is a more direct link to what I think is of interest:
https://www.philadelphiafed.org/researc ... -forecasts

In the same vein, here is one about consumers inflation expectations:
http://www.sca.isr.umich.edu/tables.html

OK, guys. I'm realizing that my earlier proposal to use trailing inflation (three or one year) was actually a pretty bad idea; it would transform our synthetic TIPS into clunky nominal bonds, by simply dephasing inflation factors between nominals and TIPS.

I like the idea of using actual inflation expectations recorded at the time. So, which series should we use? The Fed's or univ. of Michigan's?

[grok87]

For expected inflation, I would suggest considering using the historical data from the Philly Fed survey of professional forecasters.

Here is a more direct link to what I think is of interest:
https://www.philadelphiafed.org/researc ... -forecasts

In the same vein, here is one about consumers inflation expectations:
http://www.sca.isr.umich.edu/tables.html

OK, guys. I'm realizing that my earlier proposal to use trailing inflation (three or one year) was actually a pretty bad idea; it would transform our synthetic TIPS into clunky nominal bonds, by simply dephasing inflation factors between nominals and TIPS.

I like the idea of using actual inflation expectations recorded at the time. So, which series should we use? The Fed's or univ. of Michigan's?

i think we want to add the "actual" inflation to the "actual" real-return (well synthetic i guess) of the tips to get the "actual" nominal return of the tips.
I don't think inflation expectations come into it anymore once you have an annual or monthly series of real yield curves.

[longinvest]

I don't think inflation expectations come into it anymore once you have an annual or monthly series of real yield curves.

But, we need inflation expectations to derive a synthetic real yield curve out of the nominal yield curve, for pre-TIPS years.

[Quark]

I don't think inflation expectations come into it anymore once you have an annual or monthly series of real yield curves.

But, we need inflation expectations to derive a synthetic real yield curve out of the nominal yield curve, for pre-TIPS years.

Exactly.

Is there any model of inflation expectations that correlates well with the spread by nominal treasuries and TIPS at various maturities? If you want to model TIPS rates pre-1997, it would seem you'd need a model which does this.

My sense is that most current models of expectations (including surveys) generate numbers that are off from the TIPS spreads. For example, the Cleveland Fed model typically diverges from the TIPS spreads, by design (else they'd just use the spread to model inflation expectations). Similarly for surveys. I'm not sure how far off these models usually are. One could compare https://fred.stlouisfed.org/series/T10YIEM to the Excel spreadsheet linked in https://www.clevelandfed.org/our-resear ... tions.aspx

[longinvest]

My sense is that most current models of expectations (including surveys) generate numbers that are off from the TIPS spreads. For example, the Cleveland Fed model typically diverges from the TIPS spreads, by design (else they'd just use the spread to model inflation expectations).

Very interesting!

What would you suggest to use, to recreate a synthetic real yield curve in pre-TIPS years?

[Quark]

My sense is that most current models of expectations (including surveys) generate numbers that are off from the TIPS spreads. For example, the Cleveland Fed model typically diverges from the TIPS spreads, by design (else they'd just use the spread to model inflation expectations).

Very interesting!

What would you suggest to use, to recreate a synthetic real yield curve in pre-TIPS years?

I don't know. One reason TIPS were created was to get a market measure of inflation expectations / real interest rates.

Survey data may have the most history and may therefore be best. It may not be great, but I'm not sure if there's anything long term any that's better.

[siamond]

I like the idea of using actual inflation expectations recorded at the time. So, which series should we use? The Fed's or univ. of Michigan's?

My gut feeling is that we should use expectations defined by the very folks who might buy TIPS, hence consumers (the UMich data in other words). But frankly, I have no clue and we should experiment a bit and see what goes.

Longinvest, do you feel ready to assemble a model according to the multiple step-process you defined earlier (+ the realized inflation adjustment at the end)? If yes, let's just pick one expectation inflation series, and see what goes... At some point, we should close the loop, and ponder the Groen paper as well, but let's start by building the model, then we can play with the input parameters.

[longinvest]

Longinvest, do you feel ready to assemble a model according to the multiple step-process you defined earlier (+ the realized inflation adjustment at the end)? If yes, let's just pick one expectation inflation series, and see what goes... At some point, we should close the loop, and ponder the Groen paper as well, but let's start by building the model, then we can play with the input parameters.

Siamond,

Yes, I think I am ready, now. I needed to plan things, first, and I think it was worthwhile to do so. It might take me a few days. I'll make the spreadsheet available as soon as I have something usable.

[Quark]

I like the idea of using actual inflation expectations recorded at the time. So, which series should we use? The Fed's or univ. of Michigan's?

My gut feeling is that we should use expectations defined by the very folks who might buy TIPS, hence consumers (the UMich data in other words). But frankly, I have no clue and we should experiment a bit and see what goes.

My sense, confirmed by brief inspection, is that consumers over-expect inflation by a sizable margin, both as to actual inflation and as to TIPS spreads. http://www.sca.isr.umich.edu/files/tbmpx1px5.pdf I do not know if they are reliably wrong, that is, wrong in a way that can be easily corrected.

Also, are individual consumers really the prime owners of TIPS?

[siamond]

Yes, I think I am ready, now. I needed to plan things, first, and I think it was worthwhile to do so. It might take me a few days. I'll make the spreadsheet available as soon as I have something usable.

Cool. Thank you so much (as usual).

Also, are individual consumers really the prime owners of TIPS?

Well, the owners should be a mix of individual investors (a subset of consumers) and institutional investors (although I remember reading that many institutions were barred from investing in TIPS for a while when it all started in 1997). So this is very imperfect for sure. But I'd say it's better than forecasters...

Anyhoo, as I mentioned, I think we should just pick one series to begin with, and then we can experiment.

[dcabler]

One thing to note from the G&M paper as you're pondering how to put this together:

" Clearly measuring liquidity in the TIPS market prior to its creation isn’t possible; however, to generate a backcast we need to set a value for TIPS transaction volumes. Simply setting this value to zero would result in a large wedge between the backcasts and the actual TIPS rates in the period immediately after the TIPS bonds started to trade when the market was much less liquid. Instead, we define a level of TIPS transaction volumes that approximates stable market conditions. The aforementioned chart suggests that this was most likely the case between 2005 and mid-2008, as transaction volumes have been substantially more volatile both before and after this period."

[MIretired]

I like the idea of using actual inflation expectations recorded at the time. So, which series should we use? The Fed's or univ. of Michigan's?

My gut feeling is that we should use expectations defined by the very folks who might buy TIPS, hence consumers (the UMich data in other words). But frankly, I have no clue and we should experiment a bit and see what goes.

My sense, confirmed by brief inspection, is that consumers over-expect inflation by a sizable margin, both as to actual inflation and as to TIPS spreads. http://www.sca.isr.umich.edu/files/tbmpx1px5.pdf I do not know if they are reliably wrong, that is, wrong in a way that can be easily corrected.

Also, are individual consumers really the prime owners of TIPS?

Somewhat on the lines of this ^. Would someone kindly oblige me some, or point me a good place to read up on, on the following:

1. I'm thinking you want to know the prices(yields) and the full curve of all durations for would be TIPS pre-1997.
2. I always thought nom. treas. were indicators of future inflation--especially 10yr treas. Is this not an indicator of expected inflation in times past?
3. Where can I find out why people buy shorter term bonds in IG and treas. for less yield than inflation? Isn't this the phenom of something a little better than a MM rate, and that this is the result of lending supply and demand(asks and bids.)?
4. I looked through the UofM hist. infl expect. of consumers. And somebody on the board has many times posted the graph of expected inflation? every year of money managers?; where every year they over-expect the future #s. The graph looks like one side of a feather. So, you are expecting these kinds of expectations to provide a yield or spread on would be past TIPS?

Much obliged with any enlightenment or direction> Thanks.

[siamond]

They also reference the Kothari paper, whose results they purchased from the authors

Indeed, they stated in their paper:
<< We contacted the authors and were able to purchase their modeled monthly time series of annual year-on-year real and nominal returns for 5-year inflation-indexed bonds dating to mid-1953. >>

Well, with a bit of luck, they properly archived the Kothari model and might be willing to share (as a reminder, as was documented here, it appears that Prof. Kothari's team lost the data!).

Let me try to contact the folks at Enduring Investments, and see what goes...

I got lucky. I got in touch with Michael Ashton at Enduring Investments, who is an inflation specialist, hence very interested in TIPS! Mike was very helpful, dug up the data, and readily agreed to share it if the original authors, Prof. Kothari (MIT Sloan) and Prof. Shanken (Emory University) would also agree. So I reached out to them, very nice people, they gave their agreement (as well as the agreement to reproduce in our Simba spreadsheet), and I got the data from Mike - the simulation is monthly, starting in Jun-53 up to Dec-98. Unfortunately this provides very little overlap with actuals, so it is hard to assess the quality of the model.

It took a bit of help from Mike for me to understand that those are TTM numbers, so Dec-xx is the annual return for the corresponding year, which Prof. Shanken confirmed. And... whoever did the eyeballing of the main chart of the original article didn't realize that, and all numbers were time-shifted by 11 months, which changes the shape of the time series in a non-negligible manner.

Bottomline: I now have the full Kothari/Shanken data series, which we can use. Still some of those numbers look a little counter-intuitive, and I think we should continue to do our own research.

[dcabler]

They also reference the Kothari paper, whose results they purchased from the authors

Indeed, they stated in their paper:
<< We contacted the authors and were able to purchase their modeled monthly time series of annual year-on-year real and nominal returns for 5-year inflation-indexed bonds dating to mid-1953. >>

Well, with a bit of luck, they properly archived the Kothari model and might be willing to share (as a reminder, as was documented here, it appears that Prof. Kothari's team lost the data!).

Let me try to contact the folks at Enduring Investments, and see what goes...

I got lucky. I got in touch with Michael Ashton at Enduring Investments, who is an inflation specialist, hence very interested in TIPS! Mike was very helpful, dug up the data, and readily agreed to share it if the original authors, Prof. Kothari (MIT Sloan) and Prof. Shanken (Emory University) would also agree. So I reached out to them, very nice people, they gave their agreement (as well as the agreement to reproduce in our Simba spreadsheet), and I got the data from Mike - the simulation is monthly, starting in Jun-53 up to Dec-98. Unfortunately this provides very little overlap with actuals, so it is hard to assess the quality of the model.

It took a bit of help from Mike for me to understand that those are TTM numbers, so Dec-xx is the annual return for the corresponding year, which Prof. Shanken confirmed. And... whoever did the eyeballing of the main chart of the original article didn't realize that, and all numbers were time-shifted by 11 months, which changes the shape of the time series in a non-negligible manner.

Bottomline: I now have the full Kothari/Shanken data series, which we can use. Still some of those numbers look a little counter-intuitive, and I think we should continue to do our own research.

Very cool. Now I got the sense from their paper that they had also done some independent work. Perhaps they created a series of their own they'd like to share?...

[siamond]

Very cool. Now I got the sense from their paper that they had also done some independent work. Perhaps they created a series of their own they'd like to share?...

This is all thanks to you. Great pointer you provided. I assume that 'they' refers to Enduring Investments. Yes, they did some derivative math, but not something they were willing to share (they actually cleaned up the Kothari/Shanken spreadsheet from their own additions before sharing it with me).

Reading again the Kothari paper, it seems to me that those professors did quite a nice work. We were all turned off a bit by the 'eyeballing' thing, but now that this has been solved, this paper remains one of the best available (I think!). I asked them if any follow-up work was performed or planned, but alas, the answer was negative.

[dcabler]

Very cool. Now I got the sense from their paper that they had also done some independent work. Perhaps they created a series of their own they'd like to share?...

This is all thanks to you. Great pointer you provided. I assume that 'they' refers to Enduring Investments. Yes, they did some derivative math, but not something they were willing to share (they actually cleaned up the Kothari/Shanken spreadsheet from their own additions before sharing it with me).

Reading again the Kothari paper, it seems to me that those professors did quite a nice work. We were all turned off a bit by the 'eyeballing' thing, but now that this has been solved, this paper remains one of the best available (I think!). I asked them if any follow-up work was performed or planned, but alas, the answer was negative.

Yep I I meant Enduring investments. Anyway, I thought it was probably a bit of a long shot and that they probably wouldn't want to share.

[Tyler9000]

I got lucky. I got in touch with Michael Ashton at Enduring Investments, who is an inflation specialist, hence very interested in TIPS! Mike was very helpful, dug up the data, and readily agreed to share it if the original authors, Prof. Kothari (MIT Sloan) and Prof. Shanken (Emory University) would also agree. So I reached out to them, very nice people, they gave their agreement (as well as the agreement to reproduce in our Simba spreadsheet), and I got the data from Mike - the simulation is monthly, starting in Jun-53 up to Dec-98.

Great work, Siamond. I really appreciate your willingness to do the networking and legwork to chase down this kind of info.

[siamond]

Great work, Siamond. I really appreciate your willingness to do the networking and legwork to chase down this kind of info.

Thanks, Tyler. It's actually fun to do. In addition of using the corresponding 1970+ numbers in my working version of the Simba spreadsheet, I put the Kothari's monthly data series on Google Drive:
https://docs.google.com/spreadsheets/d/ ... ue&sd=true

As previously mentioned, I think we should continue to do our own research though.

EDIT: updated sharing link to the same file...

[stlutz]

It took a bit of help from Mike for me to understand that those are TTM numbers, so Dec-xx is the annual return for the corresponding year, which Prof. Shanken confirmed. And... whoever did the eyeballing of the main chart of the original article didn't realize that, and all numbers were time-shifted by 11 months, which changes the shape of the time series in a non-negligible manner.

So, I downloaded the working copy of the spreadsheet and the "new" numbers actually make a significant difference in portfolio backtesting balanced portfolios. By "significant" I mean that previously when you used to run various allocations in the spreadsheet there really weren't any cases where TIPS were advantageous over nominal bonds. Now however, there is a definite advantage to using a mix of TIPS and nominals.

The results are certainly more logical than they used to be (i.e. TIPS provide a noticeable advantage over nominals in the late 1970s).

The average return/CAGR/standard deviation of the new TIPS series is very close to the old numbers. But the equity correlation is lower, which changes the answer to the question of whether they would have been desirable to own or not.

[longinvest]

As promised a couple of weeks ago, I've developed a TIPS fund simulator to test various approaches for reconstructing synthetic TIPS returns.

Here are links to three versions of the spreadsheet, for those interested to play with it:

• Online: BogleheadsTIPSSimulator (Google Sheets).
• Download: BogleheadsTIPSSimulator.xlsx (in Microsoft Office Excel format).
• Download: BogleheadsTIPSSimulator.ods (in LibreOffice Calc format).

The spreadsheet currently uses trailing average 3-years inflation as inflation expectation to derive real yields from nominal yields. I will let others look at the results and comment on that. My own opinion (already expressed earlier in this thread) is that it's a pretty bad approach, from a theoretical point of view. (Yes, I'm criticizing my own initial suggestion).

Entries in the Inflation Expectations sheet are modifiable, so that people can easily test various expectations. Fund returns are then automatically calculated.


Just to reassure myself of the soundness of our fund model (which averages the returns of (30-2), (10-2), and (5-2) simulated funds to approximate the total market, see viewtopic.php?f=10&t=203092&p=3132364#p3113218), I did a quick check by replacing synthetic real yields, in the spreadsheet, with actual FRED (30, 20, 10, and 5) TIPS yields and filling the holes using linear approximations. The yield series start in 2003 (5 & 10 year), 2005 (20 year), and 2010 (30 year).

From the obtained synthetic returns, I built the following chart which compares growth of our synthetic Blended TIPS Fund with VIPSX and its index:


To me, this looks good enough, specially that we have very few annual yields (30,20,10,5-year) and approximate the others. In other words, I think that our model gives us good enough returns when given good historical yields.

The challenge will be to properly create synthetic real yields, if we wish to recover good enough synthetic returns.

For the curious, here's the result of using trailing average 3-year inflation as inflation expectation to derive synthetic real yields. It's the same chart as above, but using synthetic yields instead of historical (FRED) yields:

[/quote]

[siamond]

Thanks a lot, longinvest. This was quite the effort you did here.

Anybody willing to review the model? Quite obviously, it all depends on the key inputs, but if we could be comfortable with the mechanics of the model first with a peer review or two, this would be great, and then we can try to refine the inputs. Any taker?

[stlutz]

Was looking at the "Zero Coupon Real Yields" sheet and that raised a question in my mind as to the exact timing of the inflation adjustments to TIPS coupons.

Just to simplify my question, let's assume for the moment that interest is paid and inflation adjustments occur once per year instead of twice.

Suppose I buy a TIPS at $100 and it pays a coupon of 2%. In year 1, inflation is 5%. Is the interest payment in year 1 100*.02 = $2 or is it $100 * 1.05 *.02 = $2.10?

The model is based on the later which made me realize that I didn't know which way was correct.

[longinvest]

Just to simplify my question, let's assume for the moment that interest is paid and inflation adjustments occur once per year instead of twice.

Suppose I buy a TIPS at $100 and it pays a coupon of 2%. In year 1, inflation is 5%. Is the interest payment in year 1 100*.02 = $2 or is it $100 * 1.05 *.02 = $2.10?

The model is based on the later which made me realize that I didn't know which way was correct.

Stlutz,

TIPS coupons (as well as principal) are adjusted to inflation. So, the answer to your question is $100 X 1.05 X .02 = $2.10.

The spreadsheet model is a simplified model. Coupons are annual. Each year, a new fund rung of the longest maturity is bought at par with all available cash (all coupons + the proceeds of selling the shortest rung).

For simplicity, all fund calculations are made in inflation-adjusted dollars. Nominal returns are then recovered by applying inflation on top of the real return. For example: 3% real return + 2% inflation = (1.03 X 1.02) - 1 = 5.06%.

Note that the FRED TIPS yields that I used to validate the model are not included in the spreadsheet. Here are the links:

• https://fred.stlouisfed.org/series/FII30
• https://fred.stlouisfed.org/series/FII20
• https://fred.stlouisfed.org/series/FII10
• https://fred.stlouisfed.org/series/FII7
• https://fred.stlouisfed.org/series/FII5

Feel free to ask for additional clarifications.