Historical Bond Returns - [Simulating Total Bond Market]

[jmk]

[Moved into a new thread from: Historical Bond Returns - From Rates to Returns [Bond Fund Simulator] --admin LadyGeek]

While a big fan of Longinvest's bond fund simulator and methodology for treasuries, I've been troubled by the way it models Total Bond Market using Bond 10-2 (rolling 10 year treasury bonds sold 1 year prior to maturity). The rub is that unlike Treasuries, we know that the Barclays Capital US Aggregate Bond Index includes corporate bonds and mortgage back securities. Yet the longinvest model uses simulated yields solely from Shiller's treasury yields, and we have good reason to think that at least some of the index's returns in the corporate bonds are due to Credit and Beta. The good news is we have Shiller's stock data going back to 1871 which could be incorporated into the bond simulator. Nothing about Longinvest's model of simulated yield curves incorporates this Beta; so for fun I decided to give a quick run.

I first ran a return regression in Portfolio Visualizer for Vanguard Total Bond Fund against Sp500, Short term treasury index, Intermediate term treasury index and Long Term treasury index. This came up with VBMFX being cloned by 4.9% Sp500, 54.2% STT, 26.1% ITT, and 14.8% LTT. (Since they come from a snippet of history, these numbers should be taken with a grain of salt but will do for our purposes.)

Longinvest's bond simulator contains models for ITT (Bond 10-4 ten year treasuries sold three years from maturity) and many other funds. I used his Bond 4-2 for STT and his Bond30-11 for LTT. I then came up with a weighted average for the Factor Model (FM) based on weighted average of the funds above. (Here's my Google spreadsheetsheet , though the charts seem to get messed up if you download to excel.)

On its face, the Factor Model does seem to simulate Total Bond Fund moderately better than the Bond 10-2 used in the Simba spreadsheet. Here's the Telltale chart for 1976 on, comparing Longinvest 10-2 model versus the Factor Model, where 1.0 would mean total correspondence:


How much difference would this make going backwards? Quite a bit actually:


(What to make of the outlier of 1928? The two models differ by 50% that year, due to the record 48% stock return, but the actual difference is between 3.1% simulated returns for FM versus 0.7% for the 10-2 model--not quite as dramatic as the telltale chart shows.)

In fact, a case could be made for using units of Standard Deviation as the comparison to help normalize rather than telltale charts. Here's a chart showing the difference between 10-2 and Factor Model from AGG, shown in units of AGG's standard deviation:


And we see that there is indeed quite a difference between the two models going backwards, with half a sd or even a full sd difference not uncommon.


Could an even closer fit be had? Just in terms of correlation, substituting Bond 3-1 (3 year bonds sold at maturity) produced superficially better results (see second tab in spreadsheet). And further substituting for LTT a Bond 24-2 (24 year bonds sold a year prior to maturity) or Bond 20-2 for Longinvest's/Simba Bond 30-11 increases the overall correlation with AGG even further, to 0.959:

But visually the telltale doesn't really show that to be as meaningful as one might think; so I ended up just leaving the existing Longinvest/Simba LTT=30-11 and STT=4-2 since I liked the first telltale better.


So what to make of all this? Should the Simba Backtesting Spreadsheet substitute the Factor Model for Total Bond Fund rather than the existing Bond 10-2? Not necessarily. To state the obvious, the constitution of the Total Bond Index has changed over time with corporates representing different degrees of the index. Beta risk is not the same as credit risk. The simplicity of the initial model gets muddied as well. However, given the intuitive appeal of incorporating a little TSM into the simulation when we know TBM has lots of corporates, further investigation is warranted. I've included my spreadsheet if folks want to play around like I did.

[AlohaJoe]

I first ran a return regression in Portfolio Visualizer for Vanguard Total Bond Fund against Total Stock Index, Short term treasury index, Intermediate term treasury index and Long Term treasury index. This came up with VBMFX being composed of 4.9% TSM, 54.2% ITT, 26.1% STT, and 14.8% LTT.

Very nifty idea!

[siamond]

I first ran a return regression in Portfolio Visualizer for Vanguard Total Bond Fund against Total Stock Index, Short term treasury index, Intermediate term treasury index and Long Term treasury index. This came up with VBMFX being composed of 4.9% TSM, 54.2% ITT, 26.1% STT, and 14.8% LTT.

Adding a dollop of TSM in there is an interesting idea. So is the idea of using a combo of STT/ITT/LTT. I checked the % against the current distribution per effective maturity documented by Vanguard for VBMFX and the numbers are fairly well aligned.

Then I recreated jmk's model based on inputs clear of expense ratios (i.e. the S&P 500 TR USD; the 3-2 model for STT; the 10-4 model for ITT; the 30-11 model for LTT; comparing against the Barclays Aggregate index itself). Note that we agreed in previous posts to move to the 3-2 model for STTs (Simba will catch up soon). Here is the Telltale, first starting from 1976, then starting from 1987 (when VBMFX became available). Click to see a bigger display.



I agree, the proposed model looks pretty good. Although the simple 10-4 model (which is the one I am currently considering for the next Simba update) isn't far behind. And I have to say that a model with % numbers based on a multi-factor regression isn't entirely my cup of tea (correlation isn't causation, this seems quite empirical and would minimally require some form of out-of-sample testing to gain more confidence in it). Kudos for creativity though and I do see the logic behind the regression model. Other opinions?

PS. we can use rounder numbers, e.g. 5% S&P 500, 55% ITT, 25% STT and 15% LTT, the Telltale quality remains.

[jmk]

deleted duplicate

[jmk]

Then I recreated jmk's model based on inputs clear of expense ratios (i.e. the S&P 500 TR USD; the 3-2 model for STT; the 10-4 model for ITT; the 30-11 model for LTT; comparing against the Barclays Aggregate index itself). Note that we agreed in previous posts to move to the 3-2 model for STTs (Simba will catch up soon). Here is the Telltale, first starting from 1976, then starting from 1987 (when VBMFX became available). Click to see a bigger display.

Nice to see you replicated things! Note that in my model, substituting Bond 4-2 (ie 4 year bonds, sold 1 year from maturity) for the Bond 3-2 you used for STT got me better results. I also got better results by using Bond 3-1 than 3-2. (In the google sheet the graph is on the second tab drawn from the "Bond 3-to-1-jk" tab on the far right; it is my tab not Longinvest's--but I tried to duplicate LongInvest's methodology exactly.) I'll be curious what you think of either the 4-2 or 3-1 substitutions for STT.
You'll also notice a (new) "Bond 24-to-2-jk" which I experimented with as a substitute for Bond 30-to-11 for LTT; it produced even better correlation results but the Telltale didn't look as good do didn't end up using it.

And I have to say that a model with % numbers based on a multi-factor regression isn't entirely my cup of tea (correlation isn't causation, this seems quite empirical and would minimally require some form of out-of-sample testing to gain more confidence in it)

Agreed on testing with an outside sample-- wonder if Total International Bond Fund would be a way to do this. But do note it's not just number crunching: there is an intuitive appeal breaking down TBM into its components which we know, from financial theory, includes equity beta not currently incorporated. So even without factor regression we know the model needs to incorporate something more since Treasuries--no matter how well modeled--are not the same as corporates.

My own reluctance to use the FM model is that the AGG components seem to change over time. Can one even model an index where MBS go from a small to a large chunk, and the ratio treasury to corporate bonds changes? Who knows what changes are to come or what the ratio of corporate to treasuries were back to 1871 if index had existed?

image courtesy of Simplegift


jmk

[siamond]

I have to say that a model with % numbers based on a multi-factor regression isn't entirely my cup of tea (correlation isn't causation, this seems quite empirical and would minimally require some form of out-of-sample testing to gain more confidence in it)

Agreed on testing with an outside sample-- wonder if Total International Bond Fund would be a way to do this. But do note it's not just number crunching: there is an intuitive appeal breaking down TBM into its components which we know, from financial theory, includes equity beta not currently incorporated. So even without factor regression we know the model needs to incorporate something more since Treasuries--no matter how well modeled--are not the same as corporates.

Yes, I get that. This line of reasoning does justify exploring such a model, agreed. But still, it is quite a stretch of inject TSM in a Total-Bonds simulation! First thing would be to use actual indices for STT/ITT/LTT and see if the logic holds (which is very likely in the US). Then maybe explore the SBBI series (starting in 1926), comparing LT Corps with LT Treasuries + X% Large-Caps? But yes, I'd love to figure out a way to make it completely out-of-sample, using some international numbers, Japan might be a candidate? AlohaJoe, any view on this?

[jmk]

still, it is quite a stretch of inject TSM in a Total-Bonds simulation!

I hear you. BTW here's the PV analysis I used to get my weightings. I used actual vanguard funds, 1993-present, monthly, and only utilized the "returns based clone" (ignoring factor regressions); I then translated into the Longinvest-Simba bond simulator model like you did, though with different "funds".



PV returns based clone of VBMFX with VTSMX, VFITX, VUSTX, VFISX

One thing to note is we've already gone "out of sample", since the regression was formed on monthly 1993-present, and you and I went back to 1976 and found the same weightings work just as well. That surprised me, and is what prompted me to post.

Another perhaps more scientific tack would be to come at it from pure Fama-French factors. For instance, with very good p-stats

Code: Select all

Factor Performance Attribution in Basis Points
Factor regression results
Monthly Factor Premiums (BPS)	22.45	32.28	32.88	53.65	 
Name	Ticker	Start Date	End Date	Annual Alpha	                	 ITRM	LTRM   CDT	HY	    Total	R2
Vanguard Total Bond Market Index Inv	VBMFX	Feb 2010	Jul 2019	0.17%	13.41	2.98	  4.05	2.20	    24.07	97.8%

PV link

Where ITRM and LTRM are intermediate and long TERM rate risks, CDT is CREDIT-RISK, and HY is High-Yield Credit Risk. Not sure how far back these factors are tracked though nor if they're publicly available.

But this takes things in an entirely different direction. I kept it simple with the Vanguard returns regression, buildling on Simba existing methodology, and using the same Shiller data. And in theory should get to roughly the same place, and notably shares the same flaw of changing constituents through time.

[siamond]

First thing would be to use actual indices for STT/ITT/LTT and see if the logic holds (which is very likely in the US). [...]

I ran this one. Note that the Barclays US Treasury 3-10 Yr only started in 2003, so I spliced with the 10-4 model for earlier years, but I did use the Barclays STT and LTT indices since 1976. 'FM JMK' uses the models while 'FMx JMK' uses the Barclays indices. Results are pretty good.



As a separate side note, I took a look at the correlation between the VICSX/VCIT (Vanguard IT Corp) series and the VFIAX (LCB/S&P500) series and I get 0.47 when using annual numbers from Simba, which is remarkably high for a bonds fund. Also, its correlation with IT Bonds was 0.73 and with Total-Bonds was 0.88. Note that the IT Corp data series is formed as:
- Barclays US Corporate Invest Grade TR USD 1973-1998
- Bloomberg Barclays US Credit Corporate 5-10 Year TR USD 1999-2009
- Vanguard Intermediate-Term Corporate Bond Index Fund (VICSX) 2010+

I also took the monthly values of Barclays US Corporate Invest Grade (1973+), imported them in PortfolioVisualizer, and the monthly correlation with the US Market was 0.33, which remains a fairly decent value given the never-ending hiccups of the stock market.

One thing to note is we've already gone "out of sample", since the regression was formed on monthly 1993-present, and you and I went back to 1976 and found the same weightings work just as well. That surprised me, and is what prompted me to post.

Very good point. Still... I'd like more validation before jumping in!

[Tyler9000]

I first ran a return regression in Portfolio Visualizer for Vanguard Total Bond Fund against Total Stock Index, Short term treasury index, Intermediate term treasury index and Long Term treasury index. This came up with VBMFX being composed of 4.9% TSM, 54.2% ITT, 26.1% STT, and 14.8% LTT. (Since they come from a snippet of history, these numbers should be taken with a grain of salt but will do for our purposes.)

This is very clever. I see two discrete insights in your method.

The first is deducing the average weights of the different maturities in the total market fund, which is something I've been trying to figure out for a long time and undoubtedly improves the accuracy of the calculations. Nice work! Even if the percentages shift over time, finding the long-term average is a nice improvement. It would be nice to narrow that down to individual maturities for more granular results, but even these three buckets is still a step in the right direction.

The second is adding TSM to the calculations to account for what you call "equity beta". Personally I'm a lot more skeptical of that one, as I suspect the core differentiation you're seeing between the treasury and corporate data is really about credit quality. In general, from my own experiments I've noticed that the higher the credit quality of a corporate bond fund the closer it will perform to treasuries. Since most of the corporate bonds in BND are rated only A and below, I'd argue that the boost you're seeing is related to the lower credit rating of the average corporate bond rather than the bonds being directly tied to the stock market.

So while I'll have to stew on it for a while, my first impression is that I'd be on board with properly weighting the calculations with regard to the market sizes for each maturity (just like bond funds already do). But I'd be a lot more hesitant to add stock noise to the data (which bond funds most certainly do not).

[siamond]

Hm. There is something fishy here. I tried to recreate the return regression test with PV, which worked fine. Except that STT % and ITT % seemed inverted. I came back to jmk's posts (see below), and I noticed the same inversion between the 1st post and the second post (the pie chart).

I wonder if this isn't a display error with Portfolio Visualizer as the 'Factor Exposure Clone' list is not ordered in the same way as the 'Returns Based Clone', and we may have somehow instinctively corrected it...

I first ran a return regression in Portfolio Visualizer for Vanguard Total Bond Fund against Total Stock Index, Short term treasury index, Intermediate term treasury index and Long Term treasury index. This came up with VBMFX being composed of 4.9% TSM, 54.2% ITT, 26.1% STT, and 14.8% LTT.

BTW here's the PV analysis I used to get my weightings. I used actual vanguard funds, 1993-present, monthly, and only utilized the "returns based clone" (ignoring factor regressions); I then translated into the Longinvest-Simba bond simulator model like you did.



PV returns based clone of VBMFX with VTSMX, VFITX, VUSTX, VFISX

One thing to note is we've already gone "out of sample", since the regression was formed on monthly 1993-present, and you and I went back to 1976 and found the same weightings work just as well. That surprised me, and is what prompted me to post.

Also, using VFISX and VFITX is troublesome. Those are Vanguard's active bond funds. And as we discussed earlier in this thread, when comparing against the corresponding index funds, Vanguard kind of meandered between STT = 1-5 or 1-3 and also ITT = 5-10 or 3-10. And well, the 3-5 slice is 28% in the current distribution. So maybe PV actually got it right... Seems to me we should re-run the regression using stable and long-lived indices instead of such active funds.

[Tyler9000]

Hm. There is something fishy here. I tried to recreate the return regression test with PV, which worked fine. Except that STT % and ITT % seemed inverted. I came back to jmk's posts (see below), and I noticed the same inversion between the 1st post and the second post (the pie chart).

For reference, here's a Bloomberg PDF that gives a little more detail on the weightings of various maturities in a total treasury market fund (in the trailing 5 years leading up to 2017).

https://www.bbhub.io/indices/sites/2/20 ... easury.pdf

I would definitely expect any bond fund to be weighted towards the short end, but you need to look closely at the breakdown of the specific funds you're studying to know how to evaluate the numbers. And be sure to be on the lookout for maturity overlap between funds.

[jmk]

Adding TSM to the calculations to account for what you call "equity beta". Personally I'm a lot more skeptical of that one, as I suspect the core differentiation you're seeing between the treasury and corporate data is really about credit quality. In general, from my own experiments I've noticed that the higher the credit quality of a corporate bond fund the closer it will perform to treasuries. Since most of the corporate bonds in BND are rated only A and below, I'd argue that the boost you're seeing is related to the lower credit rating of the average corporate bond rather than the bonds being directly tied to the stock market.

You raise a good point Tyler, so let me explain how I ended up with TSM. The academic factor models for bond returns includes Term and Credit risk (with some models adding "high yield" credit risk), not generic Market Risk. And, as you note, the two aren't the same thing and TSM isn't ideally suited. At first I thought about using something like the Barclays High Yield index or even Small Value Stock Index as a proxy for credit risk component inherent in corporate bonds.

Indeed I got better matching (94.7%) by including ~15% Vanguard High-Yield fund over either TSM or VISVX.

Code: Select all

Returns Based Clone	VFISX=45.43%, VFITX=25.89%, VWEHX=14.63%, VUSTX=14.06%

PV regression analysis

And unsurprisingly the best returns-based matching of all (98.5% of VBMFX) occurred by including ~25% Vanguard Interm Corporate Bond Index:

Code: Select all

Returns Based Clone	VFISX=51.24%, VICSX=27.47%, VUSTX=11.92%, VFITX=8.06%, VWEHX=0.73%, VTSMX=0.58%

PV regression analysis

Notice as soon as VICSX enters the picture, TSM plays almost no role. My guess is that these bond funds worked better than TSM for the reason you cite: by targeting credit risk. And of course including corporate bonds are part of the component of VBMFX.

The rub is: we don't have this data going back to 1871, at least not in readily available formats. And the primary purpose is for Simba's backtesting spreadsheet. So, in the end I ended up with TSM (with only a 91.4% match) over Corporate bonds or High-Yield bond funds/indexes because

1. Sp500 is readily available in the same Shiller database used to get the bond yields for Longinvest bond simulator
2. the results of including TSM--while not nearly as close a match as using Corporate or High-Yield bonds funds--considerably improved the existing Bond10-2 treasury model.

In other words, simple and good enough.

However, if someone has access to data for Corporate intermediate bonds going back to 1871, we could use it in the simulator. I know Ibbotson has Long Term corporates back to 1927.

jmk

[jmk]

Hm. There is something fishy here. I tried to recreate the return regression test with PV, which worked fine. Except that STT % and ITT % seemed inverted. I came back to jmk's posts (see below), and I noticed the same inversion between the 1st post and the second post (the pie chart).

I wonder if this isn't a display error with Portfolio Visualizer as the 'Factor Exposure Clone' list is not ordered in the same way as the 'Returns Based Clone', and we may have somehow instinctively corrected it...

Actually it wasn't PV's fault, just a typo in my first post, which I just corrected. Luckily the attached google spreadsheet used the correct weightings (though I used 4-2 for STT and 10-2 for ITT). But... fascinating that you got good results using the "wrong" weightings and 3-2 for STT. It may be due to the overlapping funds. Do VFISX and VFITX not pretty-much track their indexes?

Jmk

[siamond]

But... fascinating that you got good results using the "wrong" weightings and 3-2 for STT. It may be due to the overlapping funds. Do VFISX and VFITX not pretty-much track their indexes?

I am pretty sure it was a case of two errors canceling each other... About your question, is was discussed at length earlier in this thread, VFISX and VFITX are active funds. They tracked their respective index in a somewhat loose manner most of the time, then shifted recently to get closer to slightly different indices. So those are basically moving targets.

I tried to get everything straight, using the Barclays 1-5, 5-10 and LTT indices, using S&P 500 (not TSM), injecting that in Portfolio Visualizer (1992+, monthly) and getting Returns Based Clone weights to mimic the Barclays Aggregate index. Then I used the corresponding bond fund models (5-2, 10-6 and 30-11) and looked at the Telltale charts and... they look ok-ish, but actually not as good as what we had before (when we used the moving targets!). And certainly no better than the much simpler 10-4 model.

I'll revisit the numbers later on, maybe I made a copy & paste mistake along the way...

[siamond]

I'll revisit the numbers later on, maybe I made a copy & paste mistake along the way...

I double-checked my numbers and didn't find any mistake. Then I found a way to narrow down the core issue. This has little to do with my switch to 1-5 (STT) and 5-10 (ITT) indices as 'return clones'. This has mostly to do with my switch to recreate/emulate the Barclays Aggregate Bond index instead of the VBMFX trajectory. We see the issue right away with PortfolioVisualizer's growth chart (less glaringly than using Telltale charts, but we do get the same message -- while bypassing a lot of my copy & paste, hence possible sources for error).

Here is VBMFX recreated by 'cloning' the returns of the various indices. Click to see a larger image. The orange line hugs the blue line pretty nicely. Looks pretty good (the telltale actually shows various imperfections along the way, but still, it is fairly decent).



Now here is the Barclays Aggregate Bond index 'recreated' with the same 4 components. See how the orange line diverges? And if you look closely, you see that the trajectory is really not a good match (which the corresponding telltale shows very clearly).



I think PV struggles when using our simple set of 4 indices (S&P500 + 3 bond indices) to reconstruct the Barclays Aggr Bond index because it just can't find fixed weights that would match the entire trajectory (kind of an in-sample/out-of-sample issue). It does succeed for VBMFX and this has to be pure luck. I meant, it should be the reverse way around! Somehow VBMFX tracking error (against its own index!) created the room for the 'returns clone' model to work better -- that is, for this period of time (1992-2018). This just makes no sense, except for a mathematical coincidence (two errors canceling each other). And then we simply cannot trust such a construct to extend well back in time.

Jmk, I applaud your creativity. This was a really nice try and I really appreciate that you contributed in such a constructive manner. But I'm afraid all we did was observe a case of curve fitting that worked until... it didn't work.

[Lee_WSP]

Okay, I've searched for more than five minutes, so I'm throwing in the towel.

How do I create a daily or monthly synthetic STRIPS dataset that I can use for monte carlo and/or backtesting simulations?

[jmk]

Now here is the Barclays Aggregate Bond index 'recreated' with the same 4 components. See how the orange line diverges? And if you look closely, you see that the trajectory is really not a good match (which the corresponding telltale shows very clearly).

Siamond, thank you for the thorough vetting of this. What I like about your methodology is it isolates a more fundamental problem located in the components chosen for the clone (most likely SP500) independent of any problem with re-translation into the particular Longinvest funds (e.g. STT=Bond 3-1 vs Bond 5-1 etc). (Can you provide the PV "link" to your clone test? Did you import the indexes yourself?)

An interesting side note is that Portfolio visualizer itself uses those active bond funds you dislike--VBISX and VFITX--in its own Asset based returns, along with FRED 2 and 5 year maturity treasuries before those funds existence:

Short Term Treasuries
FRED Interest Rate Data (2-year maturity) 1977-1991
Vanguard Short Term Treasury Fund (VFISX) 1992+
Intermediate Term Treasuries
FRED Interest Rate Data (5-year maturity) 1972-1991
Vanguard Intermediate-Term Treasury Fund (VFITX) 1992+

data sources for PV monthly asset class returns ; PV asset-class-returns

I'm afraid all we did was observe a case of curve fitting that worked until... it didn't work.

Rather than "give up" on the idea of using regression component analysis to produce weightings, let me suggest that our next step should be to test my revised hypothesis, discussed in my response to Tyler9000 above: The "fatal" flaw of utilizing SP500 is that market risk doesn't match credit risk. And Credit risk--from corporate bonds--is the primary difference between the Aggregate Bond Index and any mix of Treasuries. (In fact, the factor-based models of bond fund returns can be explained with just Term and Credit factors without any Market factor.)

What would make more sense--if we could find the data back into the previous century--would be to utilize the same Treasury components (what you call IXSTT5,IXITT5, IXLTT) together with a Corporate Bond index.

My crude testing showed an outstanding match substituting an intermediate (VICSX) or long-term (VWESX) corporate bond fund for SP500:
(PV run with VICSX PV run with VWESX)


]

(Notice--contrary to our other regressions--the factor-based clone is as good or better than the returns-based clone, adding credence that we're "on to" what's really going on.)

Now, granted, these use the crude funds you disapproved of. But I would argue it is worth testing, to incorporate the insight about credit-risk and because the results look very good on their face. I originally used TSM for convenience because it was within shiller; but if we could find any corporate bond index back to 1920s it might prove fruitful. I seem to recall Ibbotson has an index of long term corporate bonds back to 1927.

jmk

[Tyler9000]

The rub is: we don't have this data going back to 1871, at least not in readily available formats. And the primary purpose is for Simba's backtesting spreadsheet. So, in the end I ended up with TSM (with only a 91.4% match) over Corporate bonds or High-Yield bond funds/indexes because

1. Sp500 is readily available in the same Shiller database used to get the bond yields for Longinvest bond simulator
2. the results of including TSM--while not nearly as close a match as using Corporate or High-Yield bonds funds--considerably improved the existing Bond10-2 treasury model.

In other words, simple and good enough.

However, if someone has access to data for Corporate intermediate bonds going back to 1871, we could use it in the simulator. I know Ibbotson has Long Term corporates back to 1927.

jmk

I hear ya. And I've had the same frustration looking for historical corporate bond data. The best source I've found is the US Treasury, which has full corporate yield curves but only back to 1984.

I appreciate your attempts to find a workaround. Keep it up.

[SimpleGift]

...but if we could find any corporate bond index back to 1920s it might prove fruitful.

Not sure if helpful for your specific application, but FRED has a corporate bond series starting from 1919:

Moody's Seasoned Aaa Corporate Bond Yield

This data is monthly, yield only, and for bonds with maturities of 20 years and above.

[siamond]

...but if we could find any corporate bond index back to 1920s it might prove fruitful.

Not sure if helpful for your specific application, but FRED has a corporate bond series starting from 1919:

Moody's Seasoned Aaa Corporate Bond Yield

This data is monthly, yield only, and for bonds with maturities of 20 years and above.

Yes, I am aware, and I have to wonder if SBBI derived their LT Corp bonds returns from this FRED data series, but what we really need is an index (or yield) for IT corp or for total-corp. And as Tyler indicated, we've hit a wall on finding anything like that with deep history.

This being said, I am going to give it a try with jmk's regression technique using SBBI LT Corp instead of S&P 500. Maybe this could be good enough to refine the TBM model. If that is the case, then we could use those FRED yields, inject them in longinvest's spreadsheet and get our own LT Corp simulated series and a refined TBM model by the same token... Let me give it a try.

PS. for the record, Bloomberg Barclays US Corporate Bond TR USD starts in 1973. Which is pretty good, but we're looking for deeper history.

[siamond]

Here's a thread to discuss how to properly calculate historical bond returns using Prof. Shiller's historical interest rate data (which goes back to 1871). [...]

Longinvest, I have an inkling that discussions based on jmk's idea of using PV regression math to try to find a refined model for TBM are going to keep going for a while. And this is side-tracking a tad from the original intent of this thread.

Are you ok with that or would you prefer that we ask moderators to split the corresponding posts in a separate thread? I'm inclined to suggest the latter, but you initiated the thread, so... up to you!

[longinvest]

Longinvest, I have an inkling that discussions based on jmk's idea of using PV regression math to try to find a refined model for TBM are going to keep going for a while. And this is side-tracking a tad from the original intent of this thread.

Are you ok with that or would you prefer that we ask moderators to split the corresponding posts in a separate thread? I'm inclined to suggest the latter, but you initiated the thread, so... up to you!

I've been following this interesting discussion but, effectively, modelling TBM is beyond the intended scope this thread which was simply about going from treasury rates to returns. Modelling TBM involves things like taking into consideration the market weighting of different types of bonds (treasuries, corporate, mortgages, etc.), defaults (how to reconstruct/identify them in history and how to model their impact on returns), and possibly other things.

I agree with you that moving the TBM discussion into a separate thread would be a good idea; it's a complex topic that definitely deserves its own thread.

[LadyGeek]

I agree with you that moving the TBM discussion into a separate thread would be a good idea; it's a complex topic that definitely deserves its own thread.

I moved the discussion into a new thread (this one).

(Thanks to the member who reported the post and requested the separate thread.)

[jmk]

...but if we could find any corporate bond index back to 1920s it might prove fruitful.

Not sure if helpful for your specific application, but FRED has a corporate bond series starting from 1919:

Moody's Seasoned Aaa Corporate Bond Yield

This data is monthly, yield only, and for bonds with maturities of 20 years and above.

This might work! One could construct a simulated Long term corporate bond fund using Longinvest's methodology just as he did for Treasuries based on their yearly yields. It looked in my crude tests like LTC might work to capture the credit factor missing from treasury yields, so definitely worth exploring. Maybe we can implore Longinvest to add a tab "LTC" to his spreadsheet? If not, I can give it a go. One obvious problem is "20 years and above" is pretty vague!

[longinvest]

Not sure if helpful for your specific application, but FRED has a corporate bond series starting from 1919:

Moody's Seasoned Aaa Corporate Bond Yield

This data is monthly, yield only, and for bonds with maturities of 20 years and above.

This might work! One could construct a simulated Long term corporate bond fund using Longinvest's methodology just as he did for Treasuries based on their yearly yields. It looked in my crude tests like LTC might work to capture the credit factor missing from treasury yields, so definitely worth exploring. Maybe we can implore Longinvest to add a tab "LTC" to his spreadsheet? If not, I can give it a go. One obvious problem is "20 years and above" is pretty vague!

It's easy enough, for experimenting, to simply replace treasury yields with corporate yields in a copy of the bond fund simulator spreadsheet.

There's a reason why corporates tend to attract higher yields than treasuries: they sometimes default or lose their investment-grade rating. To properly simulate a corporate bond fund, one would need to simulate defaults and downgrades (and upgrades, too!).

[jmk]

There's a reason why corporates tend to attract higher yields than treasuries: they sometimes default or lose their investment-grade rating. To properly simulate a corporate bond fund, one would need to simulate defaults and downgrades (and upgrades, too!).

But if this produces better results than 10-2 or 10-4 it would be "good enough" even if we didn't incorporate downgrades, defaults etc.
Big if of course. And we wouldn't really want to use "Bond 30-11" to represent "above 20 years maturity" so would probably need to construct a new tab, something like 25-1 or 30-1 or 900-870?

[jmk]

Basic Yields of Corporate Bonds, 1900-1942, David Durand, Volume ISBN: 0-87014-448-0
Volume URL: http://www.nber.org/books/dura42-1, June 1942

[Alpha4]

I know this is a thread bump (since this thread was originally from late 2019), but I was thinking:

Since apparently the factor that corporate bonds have is "credit risk" and not market risk (i.e. stock market risk) per se....why not try some of the above modeling/simulations using either preferreds and/or high yield bonds instead of (or perhaps in addition to) TSM.

Either preferreds or junk bonds are closer to "pure" credit risk (the factor that corporate bonds have that Treasuries don't) than TSM's pure "market risk" or "market beta" characteristics; also, like corporate bonds (but unlike stocks) these two asset classes have some pure interest rate/term/duration risk as well.

For instance, the OP used TSM, STT, ITT, and LTT in their original factor and returns-based clone. What if one added preferreds? As per https://www.portfoliovisualizer.com/mat ... UAL_WEIGHT here are the results.

It does seem to match better during certain years (2008, 2009, 2013, 2021, 2022); also, it might--I have a source for preferred stock returns back to 1900 but haven't tried simulating it back that far--match better in years like 1928 and in the mid to late 1950s when stocks went gangbusters and that caused the cloned simulation to show a rather higher return than the 10-2 TBM model.

A similar simulation could be tried with, say, VWEHX as the fifth asset as well (and we can extend that back to 1926 if need be using the Ibbotson Associates junk bond monthly and annual TR series).

Also, how does this compare with the "simulated VICSX back to 1871" from the previous iterations of the Simba spreadsheet (and while we're at it, how were those VICSX numbers simulated...the returns for certain years in the 1930s seem a bit questionable to put it mildly)?

Thoughts?