Historical Bond Returns - From Rates to Returns [Bond Fund Simulator]

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Kevin M
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by Kevin M » Tue Feb 23, 2016 2:58 pm

I should also mention that the 3-10 year ladder (rolled monthly) has the smallest geometric mean (aka CAGR aka average annualized return) error relative to VFITX. Here are the geometric means and errors

5.59%, n/a - VFITX
5.35%, +0.23% - 4-10 fund
5.23%, +0.36% - 4-10 ladder
5.46%, +0.12% - 3-10 ladder

(Discrepancies due to rounding).

I probably should be expressing the errors with the opposite sign, but at any rate, VFITX had the highest geometric mean, with the 3-10 year ladder the least amount below it.

Note that this is highly dependent on time period. By knocking off 2015, we get these values for geomean

6.02% - VFITX
6.20% - 4-10 fund
5.95% - 4-10 ladder
6.20% - 3-10 ladder

So I don't think the geometric mean statistics are as valuable.

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by Fryxell » Sun Jul 10, 2016 3:28 pm

I have some thoughts on this. Siamond suggested I share them here. I recently downloaded the latest Simba data. I noticed that 5-year treasury returns going back to 1871 were added. As some of you may know, I have a Google spreadsheet for backtesting, and I had come up with my own synthetic returns. I noticed a huge difference between my estimates and those in the Simba spreadsheet. This didn't make sense to me because from 1871 to 1872 the 10-year rate barely changed, from 5.32% to 5.36%, and the 1-year rate was 6.35%. Surely, I thought, the returns on a 5-year treasury should be between the returns on a 1-year treasury (6.35%) and a 10-year zero-coupon treasury (which I estimated at 4.96%). It didn't make sense to me that the return could have been so much lower—2.46%.

The returns in Simba for the years 1871-80 go as follow:

2.46, 3.46, 8.00, 9.58, 5.53, 5.22, 4.72, 5.56, 3.06, 5.15.

Here are the estimates I came up with:

5.73, 5.85, 7.56, 7.87, 6.97, 5.56, 5.21, 5.13, 5.04, 5.92.

The big difference in the first year caught my attention so I decided to investigate. First, my methodology was to assume a zero-coupon 10-year treasury was bought in January 1871 and sold in January 1872. I assumed the 9-year interest rate in 1872 was the same as the 10-year interest rate, which shouldn't be far from the mark. My method matches historical 10-year bond returns since 1926 very well. In order to synthesize returns for a 5-year treasury, I weighed a portfolio of 1-year treasuries and a zero-coupon 10-year treasury such that they would average out to a duration of 5 years. This turns out to be 44.44% 10-year Zeros and 55.55% 1-year treasuries.

I looked up the Boglehead Fund Simulator to see what was going on. I haven't yet fully figured out how this spreadsheet works but I think I figured out the reason for the discrepancy. The fund simulator creates a synthetic yield curve by assuming a linear distribution from the 1-year to the 10-year points, which sounds reasonable enough. From 1871 to 1872, the 10-year rate increased from 5.32% to 5.36%. The 1-year rate increased from 6.35% to 7.81%, which is a huge increase. As a result, the fund simulator assumes that rates increased significantly even for the 5-year point. This is probably why the fund simulator shows a much lower return than my own estimate.

So I see a possible problem with this. I understand the fund simulator matches the SSBI data pretty well. But this data only goes back to 1926. Financial market conditions were very different in the 1800s. In the late 1800s there was often deflation (because of the gold standard), and long bonds typically returned more than bills. This appears to be partly because persistent deflation may have made investors demand a premium for holding bills, and because banks "were permitted to issue circulating bank notes against government bonds held as reserves." See my source here, page 31:

http://www.jeremysiegel.com/index.cfm/f ... D/6159.cfm

So here is my thought: Financial market conditions were very different in the 1800s. So just because the fund simulator matches the SSBI data very well does not mean that it matches what happened in the 1800s. It seems quite possible that the yield curve was very steep in the late 1800s, though I do not know this for a fact. If so, the fund simulator may be generating inaccurate return estimates.

Here are some facts relating to this that I can glean from my own backtesting spreadsheet. From 1871 to 1925, these were the inflation-adjusted compound average growth rates for the following assets (with inflation-adjusted Sharpe ratios in parentheses--I used the 1-year treasury data as a stand-in for bills to calculate the Sharpe ratio):

Gold: -1.1% (-0.72)
10 Year Treasury: 3.6% (-0.08)
S&P 500: 6.7% (0.15)
1-Year Treasury: 4.3%
Portfolio 60% S&P 500, 40% 10-year treasuries: 5.7% (0.13)
Portfolio 60% S&P 500, 40% 1-year treasuries: 6.0% (0.16)

So note what happens. A balanced 60/40 Boglehead portfolio has a lower Sharpe ratio than the S&P 500. This is a long 55-year period! This is longer than the number of years we have in the Simba spreadsheet since 1972. Boglehead principles seem to break down in an era where long-term bonds provide lower returns than cash. A balanced boglehead portfolio reduced returns and reduced the Sharpe ratio. If we use 1-year treasuries instead of 10-year treasuries, then the returns are reduced and the Sharpe ratio is barely up from that of the S&P 500.

In other words, the assumptions we are used to making in the post-1926 world may not entirely hold in the pre-1926 world. Similarly, it could be that the yield curve assumptions we currently make may not hold pre-1926. Could the yield curve have been particularly steep around the 1-year point prior to 1926? Is there any data on the yield curve prior to 1926, so that we can confirm or deny this?

Furthermore, if Boglehead principles break down prior to 1926, anyone using the spreadsheet should be cautioned about this, or he may come to erroneous conclusions.

A paper on the yield curve in the 1800s that may be of interest: http://papers.ssrn.com/sol3/papers.cfm? ... id=1596461
Last edited by Fryxell on Sun Jul 10, 2016 4:52 pm, edited 1 time in total.

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by Fryxell » Sun Jul 10, 2016 4:07 pm

I found a paper that provides graphs of yield curves for corporate bonds from 1900 to 1929 (page 18):

https://www.google.com/url?sa=t&rct=j&q ... 0881,d.eWE

It seems that in some years a linear approximation is not far off the mark, but that in other years the curve was very steep and faltlined before the 10-year mark.

Note that the pre-1929 data exhibits persistently negative or flat yield curves, whereas the post-1929 data exhibits mostly positive yield curves. An implication is that if the simulated fund is trying to "roll down the yield curve," that this would detract from the fund returns in the pre-1929 data. A long-term bond being rolled down the yield curve would tend to accumulate a measure of negative price return from rolling down a steeply inverted yield curve, in addition to offering a lower yield than the 1-year bond. I would suppose that an intelligent fund manager would have either preferred to hold the 1-year bond, or avoided rolling down the yield curve all the way down to the 1-year point, by selling before the point where the yield curve steepened. In other words, a hypothetical bond fund pre-1926 might have been operated in a different manner than modern funds because of the inverted yield curves. Something to think about...

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by longinvest » Sun Jul 10, 2016 5:09 pm

Fryxell,

Interesting. But, as to the accuracy of the simulator spreadsheet, please take the time to read my previous posts in this thread.

While the 10-2 and 10-1 funds use approximate (linear aproximation) 2 to 9-year yields, they actually model a ladder construction with accurate cash flows (assuming Shiller's 10 and 1-year yields are trustworthy). I explained how this makes for self-correcting reconstructed total-returns.

Note that the simulator does not market-weight a fund's holdings. It really models a ladder-like fund where all coupons and maturing principals are used, yearly, to buy a new bond. This is likely to model an individual investor's bond investment, at the time, by minimizing transactions on the secondary market. The 10-1 fund is actually a ladder, where all bonds are kept until maturity. The 10-2 fund only sells bonds one year before maturity.

Note that funds like 10-3 or 10-4 funds do not exhibit the self-correcting property, because we have no accurate 2 and 3-year yields for the 1800s.
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by midareff » Tue Jul 12, 2016 7:38 am

https://fred.stlouisfed.org/series/IRLTLT01USM156N 1955 forward on the Ten from the FRED.

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by longinvest » Tue Jul 12, 2016 7:48 am

midareff wrote:https://fred.stlouisfed.org/series/IRLTLT01USM156N 1955 forward on the Ten from the FRED.
Midareff,

The bond fund contains all available* FRED 1, 2, 3, 5, 7, 10, 20, and 30-year yields (January average) since 1954, and uses them. You might want to inspect the bond fund simulator spreadsheet. A link to an online version is included in the original post (OP) of this thread.

* Some yields are missing in various years. There are holes in FRED's data set. The spreadsheet uses a linear approximation to estimate missing yields. For example, the earliest 30-year yield available is in 1978 and there are no 30-year yields for the 2003 to 2006 period.
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by midareff » Tue Jul 12, 2016 7:53 am

longinvest wrote:
midareff wrote:https://fred.stlouisfed.org/series/IRLTLT01USM156N 1955 forward on the Ten from the FRED.
Midareff,

The bond fund contains all available* FRED 1, 2, 3, 5, 7, 10, 20, and 30-year yields (January average) since 1954, and uses them. You might want to inspect the bond fund simulator spreadsheet. A link to an online version is included in the original post (OP) of this thread.

* Some yields are missing in various years. There are holes in FRED's data set. The spreadsheet uses a linear approximation to estimate missing yields.
The question was (from siamond): " Oh, and you were right, I didn't extend the LTGB (Long-Term Gov. Bonds) series to pre-1972 years. The current simulator can only do 1954+ though, which is why I didn't bother. If you have ideas on how to get to the earlier years, please discuss in the bond fund simulator thread."

I was responding to his request for LTGB specifically, not bond fund data. In retrospect I should have prefaced the post, my bad.

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by longinvest » Tue Jul 12, 2016 8:13 am

midareff wrote: The question was (from siamond): " Oh, and you were right, I didn't extend the LTGB (Long-Term Gov. Bonds) series to pre-1972 years. The current simulator can only do 1954+ though, which is why I didn't bother. If you have ideas on how to get to the earlier years, please discuss in the bond fund simulator thread."

I was responding to his request for LTGB specifically, not bond fund data. In retrospect I should have prefaced the post, my bad.
Midareff,

The bond fund simulator does provide a model for a LTGB ladder-like fund based on FRED's 10 and 20-year rates available starting in 1954.

It works as follows. Each year, all bonds with 10 years left to maturity are sold. The proceeds are combined with all distributed coupons to buy new 20-year bonds (at par with coupons equal to the 20-year yield). All cash flows are precise (except for the bootstrap period). The annual NAV is estimated using a linear approximation of 11 to 19-year yields.

Note that it is a ladder-like construction; the weighting of maturities does not necessarily reflect market weight. So, returns (even if self-correcting over time) might not necessarily reflect those of a market-weighted LTGB fund. But, they should give a good-enough estimate of the real historical returns of a ladder-like LTGB fund working like the model.

Look for the tab labeled "Bond Fund (20 to 11-year)" in the simulator spreadsheet.
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by siamond » Tue Jul 12, 2016 8:35 am

midareff wrote:The question was (from siamond): " Oh, and you were right, I didn't extend the LTGB (Long-Term Gov. Bonds) series to pre-1972 years. The current simulator can only do 1954+ though, which is why I didn't bother. If you have ideas on how to get to the earlier years, please discuss in the bond fund simulator thread."

I was responding to his request for LTGB specifically, not bond fund data. In retrospect I should have prefaced the post, my bad.
I meant earlier years than 1954...

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by siamond » Tue Jul 12, 2016 8:39 am

While we are at it... Midareff also suggested on the Simba thread to do something with corporate bonds based on:
midareff wrote:AAA Corporates going back to 1920: https://fred.stlouisfed.org/series/AAA
Longinvest, any thought about that?

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by longinvest » Tue Jul 12, 2016 8:56 am

siamond wrote:While we are at it... Midareff also suggested on the Simba thread to do something with corporate bonds based on:
midareff wrote:AAA Corporates going back to 1920: https://fred.stlouisfed.org/series/AAA
Longinvest, any thought about that?
Siamond,

It says: "Averages of daily data. Copyright, 2016, Moody's Investor Services. Reprinted with permission. Moody's tries to include bonds with remaining maturities as close as possible to 30 years. Moody's drops bonds if the remaining life falls below 20 years, if the bond is susceptible to redemption, or if the rating changes."

I see two difficulties:
  • Do we have permission from Moody's (though FRED's permission) to distribute the data in our spreadsheet?
  • The yield is an average over various long maturities. How can we make use of that to model a fund? Do we simply build a 30-year ladder and assume the yield to be a 30-year yield? This would require a 30-year bootstrap, taking us to 1950 before we start getting fully self-correcting returns.
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by longinvest » Tue Jul 12, 2016 9:08 am

I forgot that we have Shiller's 1-year rates. So, we can make a linear approximation!

The main thing to clarify is the copyright thing, though. Any idea?
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by midareff » Tue Jul 12, 2016 9:10 am

Averages of daily data. Copyright, 2016, Moody's Investor Services. Reprinted with permission. Moody's tries to include bonds with remaining maturities as close as possible to 30 years. Moody's drops bonds if the remaining life falls below 20 years, if the bond is susceptible to redemption, or if the rating changes.

Does this help?

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by longinvest » Tue Jul 12, 2016 9:19 am

midareff wrote:Averages of daily data. Copyright, 2016, Moody's Investor Services. Reprinted with permission. Moody's tries to include bonds with remaining maturities as close as possible to 30 years. Moody's drops bonds if the remaining life falls below 20 years, if the bond is susceptible to redemption, or if the rating changes.

Does this help?
I already cited this. It doesn't say if we have permission to reprint.

Also, just with 20-to-30-like yields, how do we model a "long-term" fund? We don't have the 10-year yields assuming we intend to sell bonds with 10 years to maturity.

Of course, we can model a 30-year (or maybe 25-year, the average of 20 and 30) ladder that keeps its bonds until maturity, as we do have some 1-year yields to help use approximate other yields; they're not necessarily 1-year AAA yields, but I don't expect much difference between 1-year AAA yields and government yields for such a short maturity. The ladder would benefit from the self-correcting property. But 25-years is a long time for self-correction to take place...
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by midareff » Tue Jul 12, 2016 9:23 am

longinvest wrote:
midareff wrote:Averages of daily data. Copyright, 2016, Moody's Investor Services. Reprinted with permission. Moody's tries to include bonds with remaining maturities as close as possible to 30 years. Moody's drops bonds if the remaining life falls below 20 years, if the bond is susceptible to redemption, or if the rating changes.

Does this help?
I already cited this. It doesn't say if we have permission to reprint.

Also, just with 20-to-30-like yields, how do we model a "long-term" fund? We don't have the 10-year yields assuming we intend to sell bonds with 10 years to maturity.

Of course, we can model a 30-year (or maybe 25-year, the average of 20 and 30) ladder that keeps its bonds until maturity, as we do have some 1-year yields to help use approximate other yields; they're not necessarily 1-year AAA yields, but I don't expect much difference between 1-year AAA yields and government yields for such a short maturity. The ladder would benefit from the self-correcting property. But 25-years is a long time for self-correction to take place...
Was just trying to be helpful. I'll leave the tough questions to you.

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by longinvest » Tue Jul 12, 2016 9:30 am

On the positive side, our ladder-like construction, even if we kept bonds until maturity, should have a pretty high duration, as all coupons are reinvested in new long bonds, tilting the weighting of maturities, within the ladder, towards longer maturities. So, it shouldn't be too bad an estimate of a long-term fund.

The main question is the copyright one. On that front, I notice that FRED writes:
Suggested Citation:

Board of Governors of the Federal Reserve System (US), Moody's Seasoned Aaa Corporate Bond Yield© [AAA], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/AAA, July 11, 2016.
So, I guess that it should be OK to simply include this with the data.

Any opinion?
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by midareff » Tue Jul 12, 2016 12:35 pm

longinvest wrote:On the positive side, our ladder-like construction, even if we kept bonds until maturity, should have a pretty high duration, as all coupons are reinvested in new long bonds, tilting the weighting of maturities, within the ladder, towards longer maturities. So, it shouldn't be too bad an estimate of a long-term fund.

The main question is the copyright one. On that front, I notice that FRED writes:
Suggested Citation:

Board of Governors of the Federal Reserve System (US), Moody's Seasoned Aaa Corporate Bond Yield© [AAA], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/AAA, July 11, 2016.
So, I guess that it should be OK to simply include this with the data.

Any opinion?
I suspect published US Federal Reserve reports are public realm data and may not be subject to copyright protections. In any event I believe the source quote would be more than sufficient.

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by LadyGeek » Tue Jul 12, 2016 2:49 pm

^^^ Yes, there is no copyright on government sites. However... that's a general statement and exceptions may apply.

Like for the data: Research Division Terms and Conditions
Some Information contained on this site may be copyrighted by its owner, and permission to use such copyrighted materials must be obtained from the owner and cannot be obtained from the Federal Reserve Bank of St. Louis.
I'm guessing there's a legal contract in place which allows the Fed to display the data.
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by longinvest » Tue Jul 12, 2016 3:50 pm

LadyGeek wrote:^^^ Yes, there is no copyright on government sites. However... that's a general statement and exceptions may apply.

Like for the data: Research Division Terms and Conditions
Some Information contained on this site may be copyrighted by its owner, and permission to use such copyrighted materials must be obtained from the owner and cannot be obtained from the Federal Reserve Bank of St. Louis.
I'm guessing there's a legal contract in place which allows the Fed to display the data.
LadyGeek,

What's your take on FRED's "Suggested Citation"? Do you think it means that we can include it in our spreadsheet, or do we have to get permission from Moody's?
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by siamond » Tue Jul 12, 2016 7:42 pm

Hm, before discussing legalities too much, maybe we should discuss goals first. There is no corporate-bonds data series in the Simba spreadsheet except for high-yield corporates (tracking the VWHEX fund).

If we were to add something new, I'd venture to guess that the most useful would Intermediate-Term Corporate Bonds (something akin to VICSX, which tracks the Barclays US 5-10 Year Corp Index). Trouble is this Moody AAA series would seems more of a match for Long-Term Corporate Bonds (something akin to VLTCX, which tracks the Barclays US 10+ Year Corp Index). I kind of doubt many investors are interested in the LT Corp Bonds... Opinions?

(in addition, both VICSX and VLTCX have a pretty short life, they were created in 2010, so any historical returns before that would not be entirely 'real')

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by Kevin M » Wed Jul 13, 2016 10:48 am

Agreed that intermediate-term corporates would be more applicable to typical Boglehead, but any investment-grade corporates, including long-term, could be useful in evaluating the historical credit-risk premium. Credit risk in investment grade corporates is significantly less than high-yield corporates. Of course this is potentially useful only to the extent maturity/duration of the corporate bonds used is close to available Treasury bond maturity/duration.

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by Tyler9000 » Wed Jul 13, 2016 2:18 pm

siamond wrote:If we were to add something new, I'd venture to guess that the most useful would Intermediate-Term Corporate Bonds (something akin to VICSX, which tracks the Barclays US 5-10 Year Corp Index).
Agreed. I'm not going to turn down good data of any type, but intermediate US corporate bonds and global bonds are highest on my personal wish list.

BTW, this looks promising: https://fred.stlouisfed.org/series/BAMLCC0A0CMTRIV#0

It appears to track US investment-grade corporate bonds starting in 1973.

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by siamond » Wed Jul 13, 2016 8:33 pm

Tyler9000 wrote:[BTW, this looks promising: https://fred.stlouisfed.org/series/BAMLCC0A0CMTRIV#0

It appears to track US investment-grade corporate bonds starting in 1973.
It does look promising. It's a mix of all possible maturities, I guess? All the description says is that an investment grade rating is required.

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by Tyler9000 » Wed Jul 13, 2016 9:45 pm

siamond wrote:It's a mix of all possible maturities, I guess? All the description says is that an investment grade rating is required.
My assumption is that it's sorta like a total bond market fund (BND) where by buying the whole market the average maturity works out to the intermediate range. So it's not a perfect match for VICSX that only holds bonds between 5-10 years maturity, but I expect it would track somewhat closely. I briefly looked and wasn't immediately discouraged, but someone should dig into that in more detail.

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by siamond » Wed Jul 13, 2016 10:41 pm

Tyler9000 wrote:My assumption is that it's sorta like a total bond market fund (BND) where by buying the whole market the average maturity works out to the intermediate range. So it's not a perfect match for VICSX that only holds bonds between 5-10 years maturity, but I expect it would track somewhat closely. I briefly looked and wasn't immediately discouraged, but someone should dig into that in more detail.
Here is a quick comparison for the few years of existence of VICSX (should subtract the 0.10% ER to the BofA returns to compare apples to apples), 2015 is weird, the rest is a reasonable match:

Code: Select all

	Total Return	  VICSX **
2010	 9.52%		 8.02%
2011	 7.51%		 7.94%
2012	10.37%		11.39%
2013	-1.46%		-1.79%
2014	 7.51%		 7.45%
2015	-0.63%		 0.93%
	                 ** Since inception on 03/02/2010

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by siamond » Thu Jul 14, 2016 2:58 pm

I found another source, the Barclays index tracking US Corporates at large:
https://index.barcap.com/indices/action ... 4e8cafcf0b

Annoyingly enough, this doesn't always match with the BofA numbers... Sometimes by a mile...

Code: Select all

	    BofA	Barclays
2002	10.17%	 1.68%
2003	 8.31%	 8.15%
2004	 5.41%	10.31%
2005	 1.97%	10.12%
2006	 4.38%	 8.24%
2007	 4.64%	 5.39%
2008	-6.82%	 4.56%
2009	19.76%	-4.94%
2010	 9.52%	18.68%
2011	 7.51%	 9.00%
2012	10.37%	 9.82%
2013	-1.46%	-1.53%
2014	 7.51%	 7.46%
2015	-0.63%	-0.92%

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by LadyGeek » Thu Jul 14, 2016 3:55 pm

siamond wrote:I found another source, the Barclays index tracking US Corporates at large:
https://index.barcap.com/indices/action ... 4e8cafcf0b
The link is broken (Resource Not Found). I'd try to locate it for you, but I don't know which index you are referring to (the complete bond list: Barclays - Index Products)
LadyGeek wrote:^^^ Yes, there is no copyright on government sites. However... that's a general statement and exceptions may apply.

Like for the data: Research Division Terms and Conditions
Some Information contained on this site may be copyrighted by its owner, and permission to use such copyrighted materials must be obtained from the owner and cannot be obtained from the Federal Reserve Bank of St. Louis.
I'm guessing there's a legal contract in place which allows the Fed to display the data.
To supplement the earlier discussion, all 3 of the St. Louis Fed's Corporate Bonds interest rate suppliers have copyright notices.

Finding a suitable proxy is a good approach.

Barclays' Terms of use appears promising.
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by siamond » Thu Jul 14, 2016 3:58 pm

LadyGeek wrote:
siamond wrote:I found another source, the Barclays index tracking US Corporates at large:
https://index.barcap.com/indices/action ... 4e8cafcf0b
The link is broken (Resource Not Found). I'd try to locate it for you, but I don't know which index you are referring to.
Hm. Strange. The link works fine for me, with direct access to a PDF file.

Anyhoo, here is the Barclays page where the link to the US Corporate Index PDF file can be found:
https://index.barcap.com/Home/Guides_and_Factsheets

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Tyler9000
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by Tyler9000 » Thu Jul 14, 2016 4:31 pm

As I understand it, modeling a bond fund simply from interest rate changes doesn't benefit from Longinvest's slick ladder method, but perhaps it can be close enough as a starting point. If so, there's a good source for AAA corporate bond rates on Quandl: https://www.quandl.com/data/MOODY/AAAYL ... Bond-Yield

Their Terms & Conditions are extremely accomodating. For example:
Can I redistribute or share Quandl data?

You can redistribute or share free data on Quandl without restriction. We think that it's best practice to cite your sources but it's not compulsory.

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by patrick013 » Thu Jul 14, 2016 9:21 pm

This is a recent 30 year study ending in 2012. So, VCIT, VG's Interm
Corp Bond ETF could have some loss statistically speaking. The
risk is there but certainly less than a high yield bond fund. The
average estimated default loss for VCIT for it's BBB- bonds would
be .30 % per year.

Image
age in bonds, buy-and-hold, 10 year business cycle

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by longinvest » Sat Jul 30, 2016 7:28 am

I have uploaded version 1.10 of the spreadsheet.

It is available online and to download from the links in the first post: viewtopic.php?f=10&t=179425#p2717165

Changes:
  • Added bond funds (2-year), (3 to 2-year), (4 to 2-year), and (20 to 2-year).
  • Removed obsolete funds.
As usual, comments are welcome.

Enjoy!
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by siamond » Sat Jul 30, 2016 9:34 am

Nice job, longinvest, thank you.

I took the VFISX (Vanguard Short-Term Treasury Fund Investor fund) numbers that we have in the Simba spreadsheet, and compared to the 4-2, 3-2, and 2-2 new bond fund models, and assembled a telltale chart. I adjusted the VFISX returns by adding back its ER to compare apples to apples. Here it is.

Image

The blue line looks really nice starting from 1990, and very poor before that. This is actually NOT surprising, as the data sources for the ST Treasuries column in the Simba spreadsheet are currently:
IFA website (IFA 2F, added back expenses): 1972-1991
Vanguard Short Term Treasury (VFISX) 1992+


Doubts were expressed by several fellows (notably dcabler) about the validity of using IFA 2F to 'emulate' VFISX, and I think this telltale chart tends to demonstrate that those doubts were correct. So I plan to replace the pre-1992 numbers by the 4-2 bond fund (and extend them to 1871 while I am at it) in the next Simba update. Feedback? Any theoretical reason for which this might be a good or not-so-good idea?

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by longinvest » Sat Jul 30, 2016 9:46 am

siamond wrote: Doubts were expressed by several fellows (notably dcabler) about the validity of using IFA 2F to 'emulate' VFISX, and I think this telltale chart tends to demonstrate that those doubts were correct. So I plan to replace the pre-1992 numbers by the 4-2 bond fund (and extend them to 1871 while I am at it) in the next Simba update. Feedback? Any theoretical reason for which this might be a good or not-so-good idea?
Awesome analysis as always, Siamond! :happy

My suggestion would be to use the annual 40/60 weighed-average of the 4-2 and 3-2 bond fund returns, instead of the returns of either of these two emulated funds. I am not making the suggestions based on the TellTale chart, but to better match the average maturity of VFISX (which is currently 2.2 years). The 4-2 fund has an average maturity of 2.5 years and the 3-2 fund has an average maturity of 2 years. A 40/60 allocation would have the proper average maturity. (It's OK to go 50/50, if you want; that would be good enough). Anyway, it's just a suggestion.
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by siamond » Sat Jul 30, 2016 9:52 am

longinvest wrote:My suggestion would be to use the annual 40/60 weighed-average of the 4-2 and 3-2 bond fund returns, instead of the returns of either of these two emulated funds. I am not making the suggestions based on the TellTale chart, but to better match the average maturity of VFISX (which is currently 2.2 years). The 4-2 fund has an average maturity of 2.5 years and the 3-2 fund has an average maturity of 2 years. A 40/60 allocation would have the proper average maturity. (It's OK to go 50/50, if you want; that would be good enough). Anyway, it's just a suggestion.
Yes, I pondered about something like that for a minute or two, but this seems a tad too complicated (remember, somebody other than us will have to maintain this stuff at some point). Also I would observe that VFISX tracks the Barclays US 1-5 Year Treasury Index. And unsurprisingly, the average maturity for the index is 2.9yrs (and average duration 2.8yrs). It seems to me that the current avg maturity for VFISX might be a tactical decision from Vanguard, and should reverse to the index at some point. Therefore keeping the 4-2 mapping is both simpler and more logical. Am I making sense?

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by longinvest » Sat Jul 30, 2016 10:03 am

siamond wrote: Yes, I pondered about something like that for a minute or two, but this seems a tad too complicated (remember, somebody other than us will have to maintain this stuff at some point). Also I would observe that VFISX tracks the Barclays US 1-5 Year Treasury Index. And unsurprisingly, the average maturity for the index is 2.9yrs (and average duration 2.8yrs). It seems to me that the current avg maturity for VFISX might be a tactical decision from Vanguard, and should reverse to the index at some point. Therefore keeping the 4-2 mapping is both simpler and more logical. Am I making sense?
I didn't know that! I fully agree with your assessment.
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by stlutz » Sat Jul 30, 2016 10:07 am

Vanguard reports the current average maturity of this fund to be 2.2 years:

https://personal.vanguard.com/us/funds/ ... IntExt=INT

As a point of comparision, I took a look at the 2006 annual report and the average maturity was 2.1:

https://personal.vanguard.com/us/funds/ ... IntExt=INT

In 2010 is was 2.2:

https://www.sec.gov/Archives/edgar/data ... sfinal.htm

So, the trend seems very consistent. The 3-2 series is probably the better fit to this particular fund. And most other short term fund alternatives out there (e.g. SHY, SCHO, VGSH etc.) use 1-3 year maturities. The exception would be Fidelity's Spartan ST fund which uses a 1-5 maturity range.

FWIW.

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by longinvest » Sat Jul 30, 2016 10:21 am

stlutz wrote:The 3-2 series is probably the better fit to this particular fund.
<Off Topic>

Without commenting on this suggestion, I can point out that starting in 1954, the 3-2 fund has precise cash flows (e.g. benefits from self-correcting returns, except for the bootstrap period). As 4-year yields are approximated from other yields, the 4-2 does not benefit from self-correcting returns. But, overall, it's a relatively moot point, because no real-life fund works exactly like the simulated model.

The main benefit of a simulated fund with self-correcting returns is that it gives us peace of mind, in that we're getting good-enough reconstructed returns. I think that Siamond's TellTale charts, in this thread, demonstrate that our model is good enough. So, I wouldn't make this a criterion to select between the 4-2 and 3-2 funds. :wink:

</Off Topic>
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by Tyler9000 » Sat Jul 30, 2016 10:48 am

siamond wrote:Feedback? Any theoretical reason for which this might be a good or not-so-good idea?
I think using the Longinvest calculations makes great sense, and like the idea of keeping the treasury sources consistent. My first thought was to make sure the average maturity is correct, but you guys are already on that.

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by siamond » Sat Jul 30, 2016 12:55 pm

stlutz wrote:Vanguard reports the current average maturity of this fund to be 2.2 years:

https://personal.vanguard.com/us/funds/ ... IntExt=INT

As a point of comparison, I took a look at the 2006 annual report and the average maturity was 2.1:

https://personal.vanguard.com/us/funds/ ... IntExt=INT

In 2010 is was 2.2:

https://www.sec.gov/Archives/edgar/data ... sfinal.htm

So, the trend seems very consistent. The 3-2 series is probably the better fit to this particular fund. And most other short term fund alternatives out there (e.g. SHY, SCHO, VGSH etc.) use 1-3 year maturities. The exception would be Fidelity's Spartan ST fund which uses a 1-5 maturity range.
Well, the crux of the problem is that Simba 'ST Treasury' data series currently mixes two types of maturities:
- 20 years are based on the IFA 2F fund, which, in the period of interest, is mostly mapped to the ML US Treasury Index 1-3 Years.
=> actually IFA 2F for 1972-77 is based on Five-Year T-Notes, and the telltale chart does match in those years
- 25 years are based on VFISX, which tracks the Barclays US 1-5 Year Treasury Index

So clearly, we need the 1972-1991 'synthetic' numbers to better match VFISX, as opposed to other flavors of ST Treasuries. Hence a 1-5yrs maturities fund. Now the numbers you found about VFISX history are a little bit troubling indeed. Also, when looking at the performance of VFISX against its Barclays index, they didn't do too good in the past 10 years, and this is probably due to the shortened duration (many analysts have been expecting interest raises every year for quite a while!).

Hm. this isn't too clear cut. Maybe there is some wisdom in longinvest's suggestion to do it 50/50, but I feel that we're splitting hairs, and that we really should align ourselves with the index of reference (and Vanguard should too!).

PS. slutz, your link to the 2006 annual report doesn't appear to be correct. Mind providing the right one?

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by LadyGeek » Sat Jul 30, 2016 1:22 pm

siamond wrote:PS. slutz, your link to the 2006 annual report doesn't appear to be correct. Mind providing the right one?
Here's the link: Vanguard Fixed Income Securities Funds (Form N-CSR), February 1, 2006 - January 31, 2007

Use the SEC's EDGAR database, then enter ticker symbol "VFISX" and dig through the pages to find the report. Click on the "Document" icon (for the filing of 2007-03-30) , then the first filename (fixedincomefinal.htm) which will open to the report.
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by siamond » Sat Jul 30, 2016 1:43 pm

LadyGeek wrote:Use the SEC's EDGAR database, then enter ticker symbol "VFISX" and dig through the pages to find the report. Click on the "Document" icon (for the filing of 2007-03-30) , then the first filename (fixedincomefinal.htm) which will open to the report.
Ah, cool, I finally found my way thanks to you... Here a link to all relevant reports about VFISX between 2006 and now. Sadly, 2006 is the first year being archived, and we were already in a time of relatively low interest rates by then. I sampled the various reports, and slutz is right, there is a clear pattern around 2.2yrs (the distribution is usually around 2/3rd 1-3yrs and 1/3rd 3-5yrs). Not sure why.

PS. this made me refine a bit my telltale chart, with better estimates for the historical ERs (which went from 0.26 to 0.20 between 2006 and now), but this doesn't really change the story, the 4-2 fund continues to map better. Which now puzzles me.

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by longinvest » Sat Jul 30, 2016 2:27 pm

siamond wrote:PS. this made me refine a bit my telltale chart, with better estimates for the historical ERs (which went from 0.26 to 0.20 between 2006 and now), but this doesn't really change the story, the 4-2 fund continues to map better. Which now puzzles me.
Don't forget that a real-life index fund is way more diversified than our bond fund model. For one thing, the real-life fund is probably market-weighted, and it is exposed to a much wider variety of maturities (within the target maturity range), and yields (all year long). The model only uses FRED's average January yields.

More interesting is to compare the returns of the fund with its index. If the fund's tracking error is low, then the problem is that our model does not capture all the subtleties of the Short-Term Treasury bond market. That's fine with me; I never expected the model to behave half as good as it does, given its utter simplicity. All I wanted was a good enough ballpark estimate of past returns (in periods for which we don't have real-life fund returns, nor index returns, only yields for a small set of maturities).

Added: Actually, I just realized that VFISX is actively managed. Who tells you that vanguard doesn't have terrific bond traders who are making a killing buying the Treasuries that mom and pop are dumping on the market to go hide into CDs?

Go with the 4-2 fund; that's what you want*. :wink:

* You made a convincing argument as to why use a single fund's return, instead of the average of 3-2 and 4-2, and between both, 4-2 seems to better reflect past returns.
Last edited by longinvest on Sat Jul 30, 2016 2:58 pm, edited 2 times in total.
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by stlutz » Sat Jul 30, 2016 2:38 pm

the 4-2 fund continues to map better. Which now puzzles me.
I think I see what is happening. I honestly haven't followed this thread super-closely. But if you are updating your numbers annually, then it is only a 4-2 fund at the beginning of the year. By the end of the year it is a 3-1 fund. So, on average your maturity is about 2.5 years, which is pretty close to the VG fund's actual.

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by longinvest » Sat Jul 30, 2016 2:42 pm

stlutz wrote:
the 4-2 fund continues to map better. Which now puzzles me.
I think I see what is happening. I honestly haven't followed this thread super-closely. But if you are updating your numbers annually, then it is only a 4-2 fund at the beginning of the year. By the end of the year it is a 3-1 fund. So, on average your maturity is about 2.5 years, which is pretty close to the VG fund's actual.
4-2 fund: 2.5 years
3-2 fund: 2 years

It would be nice, though, just for curiosity, to see the 50/50 4-2/3-2 on the TellTale chart. :wink:
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by siamond » Sat Jul 30, 2016 3:54 pm

longinvest wrote:
stlutz wrote:
the 4-2 fund continues to map better. Which now puzzles me.
I think I see what is happening. I honestly haven't followed this thread super-closely. But if you are updating your numbers annually, then it is only a 4-2 fund at the beginning of the year. By the end of the year it is a 3-1 fund. So, on average your maturity is about 2.5 years, which is pretty close to the VG fund's actual.
4-2 fund: 2.5 years
3-2 fund: 2 years
Aaah... I had missed that.
longinvest wrote:It would be nice, though, just for curiosity, to see the 50/50 4-2/3-2 on the TellTale chart. :wink:
All righty, I tried, but this doesn't help, 4-2 remains better. And simple. And closer to what the index should be. And now makes sense to me. Ok, then, 4-2 does seem the way to go. Many thanks for the useful contributions.

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by longinvest » Thu Aug 11, 2016 8:48 pm

I have uploaded version 1.11 of the spreadsheet.

It is available online and to download from the links in the first post: viewtopic.php?f=10&t=179425#p2717165

Changes:
  • Added bond fund (30 to 11-year), using a flat yield curve for pre-FRED years.
As usual, comments are welcome.

Enjoy!
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by longinvest » Thu Aug 11, 2016 9:17 pm

Recently, I realized that I had mistakenly removed bond fund (30 to 11-year), in version 1.10, as it was used in Simba's spreadsheet for long-term treasuries (LTT) returns from 1972 to 1986, inclusively.

(Siamond: For some reason, Simba's spreadsheet seems to include incorrect LTT returns from 1954 to 1971.)

I've added back bond fund (30 to 11-year) in version 1.11, but I simulated the entire 1871-2015 history by using a flat yield curve (using 10-year yield) for years for which longer yields are not available. The idea is that the average maturity (and duration) of the bond fund will still be appropriate.

To check of the validity of the flat curve approximation, here's the a growth chart (logarithmic scale) of three versions of the fund from 1954 to 2016:
  • Old: returns of version 1.9 (the fund is bootstrapped in 1954)
  • New: returns of version 1.11 (the fund is bootstrapped in 1871)
  • Flat: returns using a flat curve using 10-year yields for the entire history (the fund is bootstrapped in 1871)
Image

As expected, the differences due to bootstrapping are minimal (blue and red lines).

As for the flat yield-curve version (yellow), we see that it has a relatively similar volatility and general shape of returns as the other two. It lags a little in returns, but this is to be expected in a period where 30-year yields were higher than 10-year yields.

I would say that using a flat yield curve should be good enough to get an approximation when 20 and 30-year yields are missing.

What do you think?
Last edited by longinvest on Thu Aug 11, 2016 10:12 pm, edited 1 time in total.
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by LadyGeek » Thu Aug 11, 2016 9:26 pm

Can you explain what is meant by "bootstrap period"?

Is there is a formula that should be modified for a "bootstrap"? No bootstrap dates are indicated on any of the worksheets.

I'm using the LibreOffice Calc version.
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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by Tyler9000 » Thu Aug 11, 2016 9:31 pm

longinvest wrote: (Siamond: For some reason, Simba's spreadsheet seems to include incorrect LTT returns from 1954 to 1971.)
I just noticed that, too. It appears that they're off by a factor of 100, so I suspect that it's just a translation issue that didn't account for the percentage conversion.

Nice work, Longinvest. What's your opinion on the accuracy of the pre-1954 data when the best we have is 10-year returns and we're assuming it's flat up to 30? And any thought to continuing the linear trend below the 10-year data point above that, or does that just assume way too much?

(my apologies if I'm just being dense or if you already covered this)
Last edited by Tyler9000 on Thu Aug 11, 2016 9:55 pm, edited 7 times in total.

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Re: Historical Bond Returns - Shiller: From Rates to Returns

Post by longinvest » Thu Aug 11, 2016 9:32 pm

LadyGeek wrote:Can you explain what is meant by "bootstrap period"?

Is there is a formula that should be modified for a "bootstrap"? No bootstrap dates are indicated on any of the worksheets.

I'm using the LibreOffice Calc version.
LadyGeek,

The bootstrap period corresponds to the cells colored yellow, in the "Payments" and "Value (approximation)" columns.

Here's the idea. In 1871, we want to start a fund which contains 20 rungs of 30, 29, ..., 11 year maturities. The problem is that we don't know what the coupons of 19 of these rungs should be, as we don't have the 30-year yields of 1870, 1869, and previous years (even when using a flat curve). So, the fund is started (what I call "bootstrapped") by assuming that all the rungs were issued at the 1871 30-year yield. It's like if for all years before 1871, the yield curve was fixed.

You might note that this has not much impact on returns. See how the red and blue lines are close, even though they're not bootstrapped identically. When you look at their annual returns, in 1954, for example, one says 3.56%, the other says 3.21%. But these differences don't show up on the growth chart, because the differences due to bootstrapping mostly cancel out.
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