Extending total bond index returns back to 1900

[siamond]

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

Side-tracking a tad from the bond simulator itself, Prof. McQuarrie (McQ on this forum) shared the following research paper with me:
https://papers.ssrn.com/sol3/papers.cfm ... id=3947293

Abstract:

The Lehman / Barclay’s / Bloomberg Aggregate Bond Index dates to the 1970s. Historical back tests of investment strategies and outcomes that extend past 1973 have had to use either long bonds or short Treasuries. In terms of capturing returns over a complete market cycle, both long and short bonds are problematic relative to a total bond index, which obtains its yield from across the entire maturity range while maintaining an intermediate duration. This paper assembles eight bond series to simulate returns on a total bond index from 1900 to 1973. The individual series are for government bonds and corporate bonds, and for long, longer intermediate, shorter intermediate, and short maturities. Both the individual series and an equal-weighted composite are presented in down-loadable form. Some of the series have been previously compiled from observed prices while others were compiled specifically for this project using multiple sources. A brief interpretation of the behavior of the total bond index relative to its components is offered.

I suspect most people who have been interested in this bond simulator thread will find this paper interesting!

[Tyler9000]

I suspect most people who have been interested in this bond simulator thread will find this paper interesting!

Thanks for sharing! And to Prof. McQuarrie to compiling it all. Having more high-quality total bond data is really helpful.

[McQ]

Thanks for those kind words all!

In fairness, i should point out that the new Total Bond series is a work in progress, with limitations.

1. Some of the 8 series are based on observed returns: long corporate, long Treasuries, short intermediate Treasuries, long intermediate Treasuries (these last two merged before the early 1930s, there weren't enough). "Observed" means price at time1, price time2, coupon, annual frequency, large sample of the largest bonds (corporate).

2. Intermediate Corporate, short and long, come from yield interpolation. No allowance for defaults and downgrades in the 1930s (long corporates do reflect these events). Based on Durand (1942), a key cite: https://www.nber.org/system/files/chapt ... /c9269.pdf

3. Short corporate likewise from yields, short Treasuries only from 1960.

Last, equal weighting is probably false: long bonds dominated until well after WW II.

The appendix to the paper has the annual returns for each series. You can pop these into a spreadsheet and do as you will.

Happy to answer queries.

PS: I recently posted a series of blogs on the CFA Institute site (free), laying out the history of the US bond (and stock) markets, which might help with the lay of the land: https://blogs.cfainstitute.org/investor ... rket-data/

That's the first of three posts, the third about to appear.

[longinvest]

The appendix to the paper has the annual returns for each series. You can pop these into a spreadsheet and do as you will.

Happy to answer queries.

McQ, do you have a link to a thread dedicated to your paper?

I think that it would be preferable to keep this thread about the bond fund simulator linked in the first post which models bond funds using self-correcting calculations (see the first post for details).

[McQ]

The appendix to the paper has the annual returns for each series. You can pop these into a spreadsheet and do as you will.

Happy to answer queries.

McQ, do you have a link to a thread dedicated to your paper?

I think that it would be preferable to keep this thread about the bond fund simulator linked in the first post which models bond funds using self-correcting calculations (see the first post for details).

No dedicated thread at present, but I'd want to respect your wishes on the matter. Ask moderators to decide, with a copy of the request to Siamond? The mention came from him.

[LadyGeek]

No dedicated thread at present, but I'd want to respect your wishes on the matter. Ask moderators to decide, with a copy of the request to Siamond? The mention came from him.

There is now. I moved this discussion into a new thread.

[longinvest]

McQ, I've yet to read your 29-pages paper. Some answers could probably be found in it. But, as you've graciously offered to answer queries, here I go.

1. Some of the 8 series are based on observed returns: long corporate, long Treasuries, short intermediate Treasuries, long intermediate Treasuries (these last two merged before the early 1930s, there weren't enough). "Observed" means price at time1, price time2, coupon, annual frequency, large sample of the largest bonds (corporate).

How close or far are the observations in general? Weeks, months, or years apart? What are the resulting challenges for calculating accurate time-weighted returns?

2. Intermediate Corporate, short and long, come from yield interpolation. No allowance for defaults and downgrades in the 1930s (long corporates do reflect these events). Based on Durand (1942), a key cite: https://www.nber.org/system/files/chapt ... /c9269.pdf

Are exact (published) buy and sell yields used to calculate returns, or are some yields approximated and, if so, how (linear, other)?

For examples, some people use a published 10-year yield for year [X] along with a 10-year yield for year [X + 1] to derive a return for a 10-year bond bought in year [X], due to the unavailability of a published 9-year yield for year [X + 1]. In this situation, the 9-year yield is approximated using a 10-year yield instead. How, exactly, are returns derived from yields in your paper?

Last, equal weighting is probably false: long bonds dominated until well after WW II.

Did you compare returns derived using your methodology (1 & 2 & 3 of your post + equal weighting) with the returns of VBMFX for the period from 1987 (first full year of VBMFX) until 2020 (as your paper was published in 2021)? How close or far are the results?

Finally, do you happen to have an open spreadsheet with all the inputs (yields, prices, etc.) and the formulas used to derive outputs (which are the returns for various series included in your paper)?

[McQ]

McQ, I've yet to read your 29-pages paper. Some answers could probably be found in it. But, as you've graciously offered to answer queries, here I go.

1. Some of the 8 series are based on observed returns: long corporate, long Treasuries, short intermediate Treasuries, long intermediate Treasuries (these last two merged before the early 1930s, there weren't enough). "Observed" means price at time1, price time2, coupon, annual frequency, large sample of the largest bonds (corporate).

How close or far are the observations in general? Weeks, months, or years apart? What are the resulting challenges for calculating accurate time-weighted returns?

2. Intermediate Corporate, short and long, come from yield interpolation. No allowance for defaults and downgrades in the 1930s (long corporates do reflect these events). Based on Durand (1942), a key cite: https://www.nber.org/system/files/chapt ... /c9269.pdf

Are exact (published) buy and sell yields used to calculate returns, or are some yields approximated and, if so, how (linear, other)?

For examples, some people use a published 10-year yield for year [X] along with a 10-year yield for year [X + 1] to derive a return for a 10-year bond bought in year [X], due to the unavailability of a published 9-year yield for year [X + 1]. In this situation, the 9-year yield is approximated using a 10-year yield instead. How, exactly, are returns derived from yields in your paper?

Last, equal weighting is probably false: long bonds dominated until well after WW II.

Did you compare returns derived using your methodology (1 & 2 & 3 of your post + equal weighting) with the returns of VBMFX for the period from 1987 (first full year of VBMFX) until 2020 (as your paper was published in 2021)? How close or far are the results?

Finally, do you happen to have an open spreadsheet with all the inputs (yields, prices, etc.) and the formulas used to derive outputs (which are the returns for various series included in your paper)?

My goodness—29 pages must be some kind of record (for brevity) for me on SSRN.com!

One reason for the brevity: I wrote this total bond paper in service to another one, on RMDs, a more typical 67 page effort: https://papers.ssrn.com/sol3/papers.cfm ... id=4001986. I needed to test whether a balanced mix using total bonds rather than long bonds could extend inflation-adjusted RMD-style withdrawals for a longer period during the crucible of the 1960s (answer: yes).

In general, I think you will find my total bond returns too coarse-grained and approximate for your purposes. (Another argument for exporting discussion of it to another thread.)

But here are some answers to your questions

1. No data collected after 1972, so no later comparisons possible

2. Keep in mind that the focus was on observing bond prices (midpoint of the January high and low prices, from the Commercial & Financial Chronicle, and then NY Times after 1963). These were collected at an annual frequency, so returns are January2 price / January1 price, plus coupon divided by January1 price.

3. Where yields had to be used, the standard formula for price extraction from successive yields was applied (annual).

4. Yields, when used, came from the Durand 1942 paper (link up thread). Although I think you’ll find his methodology somewhere between approximate and, uh, imaginative, the paper was an early pioneer in the study of term structure and is well worth reading to understand the bond market pre WW II, and the sort of flat yield curves that used to be quite common before the Fed got into yield curve management to support the war effort.

5. No single spreadsheet, and not much info in the several sheets other than prices (I’ve never been interested in bond yields, just holding period returns).

Can’t remember if Siamond already has Robert Shiller’s GS 10 measure of bond returns in Simba already (available at Shiller web site). It’s a simulation of 10-year Treasury returns from yields, and much closer to what you have attempted, I believe. Just a caution that before 1920 the GS 10 is ... (trying to be polite here), ah … constructed from suspect inputs. More later on that point if anyone cares (short answer: Macaulay's yields, used by Shiller (and Siegel), are not observed but...something else.)

Best.

[siamond]

Can’t remember if Siamond already has Robert Shiller’s GS 10 measure of bond returns in Simba already (available at Shiller web site). It’s a simulation of 10-year Treasury returns from yields, and much closer to what you have attempted, I believe. Just a caution that before 1920 the GS 10 is ... (trying to be polite here), ah … constructed from suspect inputs. More later on that point if anyone cares (short answer: Macaulay's yields, used by Shiller (and Siegel), are not observed but...something else.)

The GS10 series isn't in Simba, nobody expressed a need for it, plus its 'suspicious' nature has been indeed pointed out in the past.

[McQ]

Can’t remember if Siamond already has Robert Shiller’s GS 10 measure of bond returns in Simba already (available at Shiller web site). It’s a simulation of 10-year Treasury returns from yields, and much closer to what you have attempted, I believe. Just a caution that before 1920 the GS 10 is ... (trying to be polite here), ah … constructed from suspect inputs. More later on that point if anyone cares (short answer: Macaulay's yields, used by Shiller (and Siegel), are not observed but...something else.)

The GS10 series isn't in Simba, nobody expressed a need for it, plus its 'suspicious' nature has been indeed pointed out in the past.

"Nobody expressed a need for it" is valuable information to me.

For the record, the Shiller GS-10 measure is unexceptional from 1954--simply the 10-year Constant Maturity series yields re-expressed as returns--I doubt there is a better 10-year simulation in Simba, or anywhere else--for that period.

From 1920 to 1954, the underlying yield series has a longer maturity than 10 years, but otherwise, just as good a simulation of 10+ year returns.

For that matter, from about 1897 to 1920 the source data is not really problematic, except for being municipal bonds, combined into an index with unknown maturities and coupons.

The fictive quality only appears prior to that point, especially in the 1870s and 1880s.

[Northern Flicker]

The makeup of the total bond market has changed so much since 1900 that I think treasury yields/returns make up a better historical sample. For instance, MBS are much more recent.

[Northern Flicker]

Another point is that corporate bond portfolios were riskier 100 years ago, so that credit spreads likely tended to be higher than today. Between that, and the lack of MBS for the total bond market, treasury portfolio backtests are likely to be more generalizable. Even there, some differences across different points in history include going off the gold standard (making deflation less common) and the emergence of the USD as the primary reserve currency (downward pressure on borrowing costs).