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

Discuss all general (i.e. non-personal) investing questions and issues, investing news, and theory.
Topic Author
longinvest
Posts: 4291
Joined: Sat Aug 11, 2012 8:44 am

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

Post by longinvest » Thu Aug 11, 2016 9:51 pm

Tyler9000 wrote: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?
I've shown what using 10-year yields and assuming it's flat up to 30 looks like, compared to using longer yields (when available) in the comparison growth chart:

Image

The yellow line is using 10-year yields. The red and blue lines are using FRED 10, 20 and 30-year yields. It gives us an idea of how "wrong" using a flat curve can be.
Tyler9000 wrote:And any thought to continuing the linear trend below the 10-year data point above that, or does that just assume way too much?
I wouldn't try to guess longer yields. The yield curve has had all kind of shapes, over history. Before the 1930s, 1-year yields were often higher than 10-year yields.

In a long-term bond fund, the movement of the overall curve is more important than the shape of the curve. That's what we see, with the yellow line. Even if the yield curve does not move completely in parallel, movements from year to year are often bigger than differences between 10 and 30-year yields. For example:
  • 1980: 10-year 10.80%, 20-year 10.65%, 30-year 10.60%
  • 1981: 10-year 12.57%, 20-year 12.29%, 30-year 12.14%
  • 1982: 10-year 14.59%, 20-year 14.57%, 30-year 14.22%


See how yields moved 2% per year, while differences in maturities accounted for a few basis points.
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

User avatar
Tyler9000
Posts: 531
Joined: Fri Aug 21, 2015 11:57 am

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

Post by Tyler9000 » Thu Aug 11, 2016 9:57 pm

longinvest wrote: I've shown what using 10-year yields and assuming it's flat up to 30 looks like, compared to using longer yields (when available) in the comparison growth chart:

(cool chart)

The yellow line is using 10-year yields. The red and blue lines are using FRED 10, 20 and 30-year yields. It gives us an idea of how "wrong" using a flat curve can be.
Ah -- I really was just being dense. :oops: I get the chart now -- I guess I just didn't expect the different method to be so similar!

And thanks for the movement vs. shape explanation -- that makes sense.
Last edited by Tyler9000 on Thu Aug 11, 2016 10:13 pm, edited 1 time in total.

Topic Author
longinvest
Posts: 4291
Joined: Sat Aug 11, 2012 8:44 am

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

Post by longinvest » Thu Aug 11, 2016 9:59 pm

Just to put a little more contrast, here's the same growth chart where I added the (10 to 2-year) fund:

Image
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

User avatar
LadyGeek
Site Admin
Posts: 64031
Joined: Sat Dec 20, 2008 5:34 pm
Location: Philadelphia
Contact:

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

Post by LadyGeek » Thu Aug 11, 2016 10:24 pm

Thank you, the concept is sinking in.

Can you highlight the "Rates by maturity (years) columns which repeat every 10 years and link to the Shiller data? This will make it easier to see where the formulas change and to help understand how the spreadsheet is constructed.

For example, "Bond Fund (30 to 11-year)" C6 (=$Shiller.E14/100) and L6 (= $Shiller.F14/100) are colored yellow, but V6 (=L6) and AF6 (=V6) are gray. Columns V and AF should be yellow.

The same comment applies to "Bond Fund (20 to 2-year)" and "Bond Fund (30 to 2-year)".
Wiki To some, the glass is half full. To others, the glass is half empty. To an engineer, it's twice the size it needs to be.

Topic Author
longinvest
Posts: 4291
Joined: Sat Aug 11, 2012 8:44 am

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

Post by longinvest » Fri Aug 12, 2016 5:38 am

LadyGeek wrote: For example, "Bond Fund (30 to 11-year)" C6 (=$Shiller.E14/100) and L6 (= $Shiller.F14/100) are colored yellow, but V6 (=L6) and AF6 (=V6) are gray. Columns V and AF should be yellow.
LadyGeek,

We have a different interpretation for colors. I know, it's my fault for not making mine explicit. :wink:
  • Light yellow: accurate yield (Shiller)
  • Light green: accurate yield (FRED)
  • Gray: approximate yield
It would be inaccurate to change the color of the V and AF columns, because they contain approximate yields (e.g. using the 10-year yield as 20-year yield and 30-year yield).
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

Topic Author
longinvest
Posts: 4291
Joined: Sat Aug 11, 2012 8:44 am

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

Post by longinvest » Fri Aug 12, 2016 7:51 am

OK. In a new version (1.12), I've improved the approximation for 20-year yields (1986-1993) and for 30-year yields for (2003-2006). The 20-year improvement was already in use in version 1.9, but I forgot to reuse it in version 1.11. As for 30-year yields, they were approximated too naively in both 1.9 and 1.11.

Instead of a growth chart, I'll show a TellTale chart of bond fund (30-11) versions 1.9 and 10-year-flat against version 1.12. It reveals the differences more clearly:

Image

In particular, we see that bootstrapping differences (blue line) were mostly immaterial*, but the naive approximation of 30-year yields (2003-2006) was probably too optimistic (it was a linear approximation of 2002 to 2007 30-year yields, ignoring what was happening at other maturities). The new approximation guides the 30-year yield approximation based on changes at the 20-year maturity. This gives much lower 30-year yields from 2003 to 2006, resulting in lower returns. That's why the blue line (version 1.9) is ahead by 3% in the latest part of the chart.

* Actually, the small differences we see are due to the fact that version 1.9 used a flat curve (from 10 to 30 years) using FRED's 20-year yield for 1954-1977, whereas version 1.12 uses a linear approximation for 11-year to 19-year yields, and only uses a flat curve between 20 and 30 years of maturity.

The yellow line displays the error due to flattening the yield curve at the 10-year maturity. The impact on long-term returns was not big, except in the last 10 years. Still, it's only a 0.22% annualized lag over 62 years. But, when looking at the growth chart in my previous posts, we can see that it somewhat increases volatility (the jumps up and down are sharper than with a more accurate non-flat yield curve).

The yellow line lag, in the last 10 years, is due to the widening of the gap between 10-year and 30-year yields. I don't know if such things happened a lot in pre-FRED years. So, we should really warn users about the fact that we're simply providing a gross approximation of historical returns. Our model is not identical to a real-life fund, we only have a few yields available (10-year yields, and sometimes 20 and 30-year ones), and we approximate most yields across the curve. It is not the most precise thing ever! Luckily, bond math seems to makes our model good enough to get some idea of historical returns; at least, this is what Siamond's previous comparisons with real fund returns have shown.
Last edited by longinvest on Sat Aug 13, 2016 7:09 am, edited 1 time in total.
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

Topic Author
longinvest
Posts: 4291
Joined: Sat Aug 11, 2012 8:44 am

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

Post by longinvest » Fri Aug 12, 2016 8:48 am

Here are the visual comparisons with VUSTX (using Simba's spreadsheet returns) in the 1987-2016 period.

Growth chart:

Image

TellTale chart (against VUSTX):

Image
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

User avatar
siamond
Posts: 5445
Joined: Mon May 28, 2012 5:50 am

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

Post by siamond » Fri Aug 12, 2016 8:41 pm

Tyler9000 wrote:
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.
:oops: :oops: :oops: :oops:

Ok, I fixed this bug in the Simba spreadsheet and updated the file on Google Drive (didn't bother changing the version number). I'll catch up later on with longinvest's latest model and the subsequent thoughts (been fishing with kids for 12 hours today, will do the same tomorrow, my weak brain isn't functioning right now!)

WasabiOsbourne
Posts: 308
Joined: Wed Mar 16, 2016 1:48 pm

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

Post by WasabiOsbourne » Fri Aug 12, 2016 9:47 pm

massive grunching here,

can't you just assume that you rolled the 10 year bond perpetually? i.e. just use the 10 year rate at the start and the end of the period?

depends what you want the output for............. if it's actuarial for an insurance company then it needs to be very precise with tons of assumptions and little nuanced transactions......if it's to have a decent idea of bond returns i would just use the 10 year rate at start and end....

Topic Author
longinvest
Posts: 4291
Joined: Sat Aug 11, 2012 8:44 am

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

Post by longinvest » Sat Aug 13, 2016 6:41 am

WasabiOsbourne wrote:massive grunching here,

can't you just assume that you rolled the 10 year bond perpetually? i.e. just use the 10 year rate at the start and the end of the period?

depends what you want the output for............. if it's actuarial for an insurance company then it needs to be very precise with tons of assumptions and little nuanced transactions......if it's to have a decent idea of bond returns i would just use the 10 year rate at start and end....
WasabiOsbourne,

Please read the first post of this thread. It explains, in details, what we do and why we do it. The simulator uses available 10 and 1-year yields (and intermediate yields, when FRED provides them) to calculate self-correcting returns for Bond Fund (10 to 2-year) starting in 1871, 145 years ago.

As for estimating Long-Term Treasury (LTT) returns during the period 1871-1953, for which we don't have yields for maturities longer than 10 years, version 1.12 of the simulator uses a flat curve from 10-year to 30-year yields, using the only available 10-year yield. In other words, 30-year bonds are bought at par with a coupon equal to the 10-year yield, and are sold 20 years later. (See Bond Fund (30 to 11-year) in the simulator).

The few posts above this one are about getting an idea of how different from the historical returns of an LTT bond fund operating similarly, but with actual historical coupons/yields, we can expect our synthetic returns to be. To estimate this, I've shown the returns of an LTT bond fund that uses the flat 10-year curve, and another that uses available FRED 10, 20, and 30-year yields in the period 1954-2016*. Please look at the resulting charts and read my comments about them.

* Unfortunately, there are holes in FRED's 20-year and 30-year yield series. Version 1.12 of the simulator improved the approximation of the missing yields in those holes.
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

User avatar
siamond
Posts: 5445
Joined: Mon May 28, 2012 5:50 am

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

Post by siamond » Mon Aug 15, 2016 2:19 pm

longinvest wrote:Here are the visual comparisons with VUSTX (using Simba's spreadsheet returns) in the 1987-2016 period. [...]

TellTale chart (against VUSTX):

Image
I ran those numbers as well, and this is pretty good, but not as good as this specific chart seems to imply. The VUSTX numbers take in account an expense ratio (currently at 0.20, probably a tad higher in earlier years), and should be adjusted upwards to directly compare with the bond funds numbers (which do not have an expense ratio subtracted). So the orange line actually steadily goes down on average if we were to compare apples to apples. But still, I am nitpicking and this is really good.

User avatar
siamond
Posts: 5445
Joined: Mon May 28, 2012 5:50 am

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

Post by siamond » Mon Aug 15, 2016 3:38 pm

Then I ran a test of the new 30-11 model (version 1.12), with a telltale against SBBI LTGB (which are defined as 20 years maturity). Hm, the results aren't fully convincing. I also included the 30-2 model in there, just out of curiosity.

Image

Topic Author
longinvest
Posts: 4291
Joined: Sat Aug 11, 2012 8:44 am

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

Post by longinvest » Mon Aug 15, 2016 4:01 pm

siamond wrote:Then I ran a test of the new 30-11 model (version 1.12), with a telltale against SBBI LTGB (which are defined as 20 years maturity). Hm, the results aren't fully convincing. I also included the 30-2 model in there, just out of curiosity.

Image
Siamond,

Don't forget that for the period 1926-1953, Fund (30-11) uses a flat curve using the 10-year yields. And after that, in period 1954-1977, it uses a flat curve for yields over 20-year. It's not until 1978 that we have the yields of all three maturities (10, 20, and 30 years), and even then, there are holes!

It is not surprising that Fund (30-11) would trail the returns of a real-life long-term government bonds when using a lower maturity (10 or 20-year) yield as 30-year yield. Yet, the relatively linear slope indicates that the general shape of the growth curve of Fund (30-11) should be quite similar to SBBI LTGB's growth curve. The annualized difference is approximately -0.64% for the 55 years spanning from 1926 to 1981 (for a cumulative lag of 30%).

I think that this good enough to get a general idea, given that we don't have better free data.
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

User avatar
siamond
Posts: 5445
Joined: Mon May 28, 2012 5:50 am

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

Post by siamond » Tue Aug 16, 2016 12:52 pm

longinvest wrote:Don't forget that for the period 1926-1953, Fund (30-11) uses a flat curve using the 10-year yields. And after that, in period 1954-1977, it uses a flat curve for yields over 20-year. It's not until 1978 that we have the yields of all three maturities (10, 20, and 30 years), and even then, there are holes! [...] I think that this good enough to get a general idea, given that we don't have better free data.
Yes, I understand that you're doing your best with the little data we have, and thank you for that. Let's look at a few statistical metrics when comparing to SBBI LTGB:

Code: Select all

1926-1953: R2=0.40  RMSE=3.54
1954-2015: R2=0.94  RMSE=2.95
1972-2015: R2=0.94  RMSE=3.19
I am not entirely sure the outcome is 'good enough' for inclusion in the Simba spreadsheet for the years 1926-1953, to be honest. Which obviously cast quite some doubt on the pre-1926 results.

Topic Author
longinvest
Posts: 4291
Joined: Sat Aug 11, 2012 8:44 am

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

Post by longinvest » Tue Aug 16, 2016 1:59 pm

siamond wrote:Let's look at a few statistical metrics when comparing to SBBI LTGB:

Code: Select all

1926-1953: R2=0.40  RMSE=3.54
1954-2015: R2=0.94  RMSE=2.95
1972-2015: R2=0.94  RMSE=3.19
I am not entirely sure the outcome is 'good enough' for inclusion in the Simba spreadsheet for the years 1926-1953, to be honest. Which obviously cast quite some doubt on the pre-1926 results.
Siamond,

I propose that we investigate this a bit more.

It would be interesting to look at the R2/RMSE for the following specific periods (in addition to the already provided 1926-1953 period):
  • 1954-1977: because Fund (30-11) returns use a semi-flat curve (flat above 20 years).
  • 1978-2015: because Fund (30-11) returns use a linear approximation based on FRED 10, 20, and 30-year yields (and some hole patching) .
It would also be interesting to look at the R2/RMSE for the same three periods, but using the following returns, calculated using a flat curve (10-year yield) and adding 0.5% to the calculated return:

Code: Select all

Year	Flat+0.5%
1926	9.01%
1927	3.98%
1928	0.14%
1929	8.52%
1930	3.09%
1931	-0.79%
1932	9.50%
1933	6.55%
1934	8.50%
1935	5.36%
1936	2.71%
1937	4.97%
1938	6.10%
1939	5.16%
1940	6.79%
1941	-5.09%
1942	2.81%
1943	2.82%
1944	4.69%
1945	5.70%
1946	1.76%
1947	-0.16%
1948	4.98%
1949	2.65%
1950	-1.00%
1951	1.38%
1952	0.89%
1953	8.90%
1954	0.98%
1955	-1.26%
1956	-4.72%
1957	9.69%
1958	-9.27%
1959	-4.97%
1960	18.56%
1961	0.96%
1962	8.21%
1963	-0.37%
1964	4.39%
1965	-0.94%
1966	5.52%
1967	-6.72%
1968	-0.24%
1969	-12.25%
1970	28.21%
1971	10.33%
1972	0.51%
1973	0.99%
1974	1.93%
1975	5.42%
1976	14.19%
1977	-0.05%
1978	-2.48%
1979	-5.08%
1980	-2.56%
1981	-1.04%
1982	53.59%
1983	1.24%
1984	14.57%
1985	32.92%
1986	32.69%
1987	-6.99%
1988	5.32%
1989	18.27%
1990	9.88%
1991	19.85%
1992	12.15%
1993	16.81%
1994	-12.98%
1995	33.64%
1996	-3.54%
1997	19.24%
1998	16.07%
1999	-14.46%
2000	25.56%
2001	7.09%
2002	18.51%
2003	3.29%
2004	3.76%
2005	2.21%
2006	0.73%
2007	19.30%
2008	22.49%
2009	-12.33%
2010	8.97%
2011	26.47%
2012	3.37%
2013	-10.58%
2014	18.96%
2015	-0.75%
Yes, we are cheating by adding 0.5% to the calculated flat-curve returns, but it will allow us to see if the calculated returns are a good fit to the shape of SBBI's returns, despite their average 0.5% yearly lag.

Note: I am not proposing to add 0.5% in Simba; I am merely suggesting to look if the general shape is similar (despite a lag).
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

User avatar
siamond
Posts: 5445
Joined: Mon May 28, 2012 5:50 am

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

Post by siamond » Tue Aug 16, 2016 4:53 pm

longinvest wrote:I propose that we investigate this a bit more.
Sure. Here is the telltale chart when adding your 'cheat' model.

Image

And here are the relevant stats.

Image

Topic Author
longinvest
Posts: 4291
Joined: Sat Aug 11, 2012 8:44 am

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

Post by longinvest » Tue Aug 16, 2016 5:10 pm

Siamond,

Thanks for all the work. The R2 and RMSE numbers don't look good for the cheat returns, even though the telltale looks quite good (specially that movements are amplified by starting the x axis at 0.2 instead of 0).

Bond fund (30-11) with no cheating adjustments has better numbers, even in the period 1926-1953. So, I guess we can forget about the pre-1954 flat curve.
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

Topic Author
longinvest
Posts: 4291
Joined: Sat Aug 11, 2012 8:44 am

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

Post by longinvest » Tue Aug 16, 2016 9:44 pm

Wait a minute! These R2/RMSE numbers measure the difference in annual returns; they don't measure the closeness of the growth shapes! This can be misleading. Just think about looking at two charts of stock returns, one using annual returns December 31 to December 31, and another using annual returns January 15 to January 15. We wouldn't expect similar numbers, for annual returns, yet, we would expect both growth charts to be somewhat similar (but not identical).

This is what we are dealing with, here. SBBI probably measures annual returns December 31 to December 31. Our model uses average January yields. There is an obvious mismatch. We want to look at the general growth chart shape, not at exact annual returns, specially for our pre-1954 LTT approximation using a flat curve.

Here's my suggestion.

To measure the closeness of shapes, the R2/RMSE should be calculated on the TellTale numbers, not on the annual return numbers.

In other words, we nee to calculate four TellTale sequences against SBBI's LTGB:
  • Flat-curve (10-year) returns (the one already shown)
  • A cheat version of SBBI Corp Bonds (to get similar CAGR to SBBI LTGB 1926-2015)
  • A cheat version of SBBI IT Bonds (to get similar CAGR to SBBI LTGB 1926-2015)
  • A cheat version of SBBI US Bills (to get similar CAGR to SBBI LTGB 1926-2015)
The cheat versions are all built using the same trick: find the constant annual adjustment so that the 1926-2015 cumulative returns are equal to SBBI LTGB (in other words, the 2016 TellTale number is 1).

By looking visually at the resulting TellTale charts, and numerically at their R2/RMSE, we'll get a better assessment of the closeness of growth chart shapes.
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

User avatar
siamond
Posts: 5445
Joined: Mon May 28, 2012 5:50 am

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

Post by siamond » Tue Aug 16, 2016 10:22 pm

longinvest wrote:Wait a minute! These R2/RMSE numbers measure the difference in annual returns; they don't measure the closeness of the growth shapes! This can be misleading. Just think about looking at two charts of stock returns, one using annual returns December 31 to December 31, and another using annual returns January 15 to January 15. We wouldn't expect similar numbers, for annual returns, yet, we would expect both growth charts to be somewhat similar (but not identical).
Ok, I see your point, although I find hard to believe that a half month shift would make much of a difference on bond annual returns. BUT. Checking the description of the LTGB series in the SBBI book, the issue might actually be more severe than you suspected, as they used bonds maturing in August, March, June, name it... I don't quite get it. Let's discuss a bit more by PM.

User avatar
siamond
Posts: 5445
Joined: Mon May 28, 2012 5:50 am

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

Post by siamond » Fri Aug 26, 2016 11:26 am

siamond wrote:Then I ran a test of the new 30-11 model (version 1.12), with a telltale against SBBI LTGB (which are defined as 20 years maturity). Hm, the results aren't fully convincing.
For reference, we opened a new thread about the pitfalls of using historical SBBI data (a single bond model) when pondering about a bond fund trajectory. Bottomline, this might not be the best comparison in the world.

User avatar
siamond
Posts: 5445
Joined: Mon May 28, 2012 5:50 am

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

Post by siamond » Fri Aug 26, 2016 11:34 am

One post on the SBBI thread which would probably be better discussed here:
longinvest wrote:Note that the differences between the 10-2 and 10-4 model don't change things much. They both behave as intermediate funds, but the 10-4 model is somewhat more volatile due to its longer average duration. I like the 10-2 model because it seems closer to the smooth behavior of total bonds, while the 10-4 model behaves more like an intermediate treasury fund. I personally invest in domestic nominal total bonds, thus my preference.
This is an interesting point as we have an Intermediate Term Treasury fund in Simba (anchored on VFITX) and we have a Total-Bond fund as well (anchored on VBMFX). So far, based on earlier discussions, I used the 10-4 model for historical returns for both, but maybe I oversimplified. Any more views on this?

Topic Author
longinvest
Posts: 4291
Joined: Sat Aug 11, 2012 8:44 am

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

Post by longinvest » Fri Aug 26, 2016 2:10 pm

siamond wrote:One post on the SBBI thread which would probably be better discussed here:
longinvest wrote:Note that the differences between the 10-2 and 10-4 model don't change things much. They both behave as intermediate funds, but the 10-4 model is somewhat more volatile due to its longer average duration. I like the 10-2 model because it seems closer to the smooth behavior of total bonds, while the 10-4 model behaves more like an intermediate treasury fund. I personally invest in domestic nominal total bonds, thus my preference.
This is an interesting point as we have an Intermediate Term Treasury fund in Simba (anchored on VFITX) and we have a Total-Bond fund as well (anchored on VBMFX). So far, based on earlier discussions, I used the 10-4 model for historical returns for both, but maybe I oversimplified. Any more views on this?
Image
Image

Just consider that the premium VBMFX had over Fund 10-2 (due to its sub-allocation to longer bonds and corporates) paid for its ER. :wink:

I know, it's cheating, but do we have anything better for 1871-1986?
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

AlohaJoe
Posts: 5402
Joined: Mon Nov 26, 2007 2:00 pm
Location: Saigon, Vietnam

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

Post by AlohaJoe » Tue Aug 30, 2016 11:52 pm

I would like to generate monthly bond returns from Shiller's monthly rate data (preferably for a synthetic intermediate fund). Any guidance on how I'd go about doing that? If just using the annual data return data longinvest has already calculated and linearly interpolating it across the 12 months of the year is "good enough" then I can go with that. But if using the monthly rate data isn't too much work, I'd be curious about how to make that happen. (I noticed that the spreadsheet uses annual rates instead of the monthly GS10 rates that Shiller now provides.)

I noticed way back on page 1 Lady Geek and longinvest had a few comments on the topic but ultimately decided it wasn't very useful in the context of the Bogleheads backtesting spreadsheet, which is fair enough.

Context: in http://www.caniretireyet.com/new-resear ... trategies/ Darrow Kirkpatrick shows that (with his model at least) using CAPE10 to rebalance has some merit. Just looking at the monthly S&P 500 returns it is clear that the CAPE10 signal varies through out the year. If you look at CAPE10 in February it could tell you to sell bonds; if you look at CAPE10 in November it could tell you to sell stocks.

I'm curious about whether this effect is enough to substantially affect his results. But since I'm looking at things on a monthly basis I (ideally) would have monthly bond fund returns as well.

User avatar
siamond
Posts: 5445
Joined: Mon May 28, 2012 5:50 am

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

Post by siamond » Fri Sep 02, 2016 10:37 pm

AlohaJoe wrote:I would like to generate monthly bond returns from Shiller's monthly rate data (preferably for a synthetic intermediate fund). Any guidance on how I'd go about doing that? If just using the annual data return data longinvest has already calculated and linearly interpolating it across the 12 months of the year is "good enough" then I can go with that. But if using the monthly rate data isn't too much work, I'd be curious about how to make that happen. (I noticed that the spreadsheet uses annual rates instead of the monthly GS10 rates that Shiller now provides.)
It would certainly be great to do the math on a monthly basis at least once, if only to truly convince ourselves that this might not be entirely necessary! :D

Well, I would suggest that you read (or re-read) the beginning of this thread, if I remember well, longinvest provided detailed explanations about the way he approached it, so you should be able to infer how to develop a monthly logic. Then there is always the Excel spreadsheet to be studied (although I know it is hard to get in the logic of a spreadsheet designed by somebody else). And finally, longinvest is always very responsive to PMs when being asked clarification questions (done it myself multiple times!).

Note that Shiller's monthly data is itself the result of quite some interpolation in the early years, and that you'll need FRED monthly data too. Good luck, it would indeed be great if you could do it with some programming as it would be unwieldy to try such a 'monthly' project with Excel.

User avatar
LadyGeek
Site Admin
Posts: 64031
Joined: Sat Dec 20, 2008 5:34 pm
Location: Philadelphia
Contact:

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

Post by LadyGeek » Sat Sep 03, 2016 9:00 am

siamond wrote:Note that Shiller's monthly data is itself the result of quite some interpolation in the early years, and that you'll need FRED monthly data too. Good luck, it would indeed be great if you could do it with some programming as it would be unwieldy to try such a 'monthly' project with Excel.
I'd like to suggest the "R" programming language for this endeavor. See the wiki: Using open source software for portfolio analysis

I'm not volunteering (for now), just making the suggestion.
Wiki To some, the glass is half full. To others, the glass is half empty. To an engineer, it's twice the size it needs to be.

User avatar
siamond
Posts: 5445
Joined: Mon May 28, 2012 5:50 am

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

Post by siamond » Mon Oct 31, 2016 4:48 pm

Let me bump again this discussion, before I act on it by updating the Simba spreadsheet. The core idea is to use the 10-4 model for the Intermediate-Term Treasuries (no change), while using the 10-2 model for the Total-Bonds (currently mapped to 10-4). That is, to model historical values before we have real-life fund returns to use. Sounds ok to me. Any more feedback?
longinvest wrote:
siamond wrote:One post on the SBBI thread which would probably be better discussed here:
longinvest wrote:Note that the differences between the 10-2 and 10-4 model don't change things much. They both behave as intermediate funds, but the 10-4 model is somewhat more volatile due to its longer average duration. I like the 10-2 model because it seems closer to the smooth behavior of total bonds, while the 10-4 model behaves more like an intermediate treasury fund. I personally invest in domestic nominal total bonds, thus my preference.
This is an interesting point as we have an Intermediate Term Treasury fund in Simba (anchored on VFITX) and we have a Total-Bond fund as well (anchored on VBMFX). So far, based on earlier discussions, I used the 10-4 model for historical returns for both, but maybe I oversimplified. Any more views on this?
Image
Image

Just consider that the premium VBMFX had over Fund 10-2 (due to its sub-allocation to longer bonds and corporates) paid for its ER. :wink:

I know, it's cheating, but do we have anything better for 1871-1986?

grok87
Posts: 9110
Joined: Tue Feb 27, 2007 9:00 pm

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

Post by grok87 » Sat Nov 12, 2016 8:30 am

new thread on TIPs real returns by year pre 1997
viewtopic.php?f=10&t=203092&p=3113058#p3113058
RIP Mr. Bogle.

Topic Author
longinvest
Posts: 4291
Joined: Sat Aug 11, 2012 8:44 am

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

Post by longinvest » Sat Nov 12, 2016 8:34 am

grok87 wrote:new thread on TIPs real returns by year pre 1997
viewtopic.php?f=10&t=203092&p=3113058#p3113058
I know. Please read this first post of this thread. Thanks.
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

User avatar
siamond
Posts: 5445
Joined: Mon May 28, 2012 5:50 am

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

Post by siamond » Sat Nov 12, 2016 10:37 am

siamond wrote:Let me bump again this discussion, before I act on it by updating the Simba spreadsheet. The core idea is to use the 10-4 model for the Intermediate-Term Treasuries (no change), while using the 10-2 model for the Total-Bonds (currently mapped to 10-4). That is, to model historical values before we have real-life fund returns to use. Sounds ok to me. Any more feedback?
Not seeing any disagreement on this, and since it makes a lot of sense to me, it's a go. I updated my working version of the Simba spreadsheet accordingly.

AlohaJoe
Posts: 5402
Joined: Mon Nov 26, 2007 2:00 pm
Location: Saigon, Vietnam

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

Post by AlohaJoe » Wed Dec 07, 2016 10:34 pm

I haven't (yet) got around to monthly returns (though looking back through this thread it looks like Kevin M and gordoni have independently done this already?)

But I did make partial progress by (re-)implementing the bond fund simulator that longinvest describes. It is in python, not a spreadsheet. You can see it here on github (as a jupyter notebook)

My results match longinvest's, which isn't surprising, but I figured I would mention it.

I did it primarily for my own fun & understanding. That said, there are some benefits of moving it out of a spreadsheet. For one, it is much easier to simulate various shapes of bond funds. For instance, look at the sheet longinvest needed for the 30-2 fund :shock:

When it is code, you can do that a bit easier since everything is generalised. You can also simulate things like a 28-14 or a 17-9 fund. (I have no idea why you'd want to...)

Image

You can scroll to the bottom of the linked github page if you're not interested in the implementation and just want to see various funds simulated.

Also, simply by replacing the CSV file of rates with a different one you can simulate different things. (Say, corporates or UK bonds.) Of course, getting that rate data is usually the tricky part.

MachineGhost
Posts: 108
Joined: Sat Feb 14, 2009 2:46 am

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

Post by MachineGhost » Thu Dec 08, 2016 2:27 am

longinvest wrote:It's not a question of method, but a question of having historical data for a longer time span! Simba's spreadsheet only contains data for the period spanning from 1972 to 2014, for a total of 43 years. Shiller's data set spans from 1871 to 2012, for a total of 142 years.
It's also junx data and there's no other data series that goes back to 1871 other than maybe real estate, so its mostly useless to add it to the simba spreadsheet, Not worth the time nor drama. Portfolios are all about correlations; what correlation can you have with a long return series all by itself?

MachineGhost
Posts: 108
Joined: Sat Feb 14, 2009 2:46 am

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

Post by MachineGhost » Thu Dec 08, 2016 2:32 am

longinvest wrote:Shiller has so conveniently provided annual data for 1871-2012. I'm just not sure I could do a better job than Shiller himself to calculate historical annual rates.
Pah, Shiller didn't even do it himself; he pilfered it from Cowles which has numerous issues with the data. No data provider provides the correct S&P data, but this issue is off topic and its boring.

I don't have time to read through a year of posts in this thread, but all you need to do is create a total return time series from the yields provided at FRED. It's very simple to do.

AlohaJoe
Posts: 5402
Joined: Mon Nov 26, 2007 2:00 pm
Location: Saigon, Vietnam

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

Post by AlohaJoe » Thu Dec 08, 2016 3:01 am

MachineGhost wrote:
longinvest wrote:Shiller has so conveniently provided annual data for 1871-2012. I'm just not sure I could do a better job than Shiller himself to calculate historical annual rates.
Pah, Shiller didn't even do it himself; he pilfered it from Cowles which has numerous issues with the data. No data provider provides the correct S&P data, but this issue is off topic and its boring.
Shiller's data comes from A History of Interest Rates by Sidney Homer, not the Cowles commission.
MachineGhost wrote:but all you need to do is create a total return time series from the yields provided at FRED. It's very simple to do.
How does one do this?

User avatar
midareff
Posts: 6946
Joined: Mon Nov 29, 2010 10:43 am
Location: Biscayne Bay, South Florida

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

Post by midareff » Thu Dec 08, 2016 10:45 am

siamond wrote:
siamond wrote:Let me bump again this discussion, before I act on it by updating the Simba spreadsheet. The core idea is to use the 10-4 model for the Intermediate-Term Treasuries (no change), while using the 10-2 model for the Total-Bonds (currently mapped to 10-4). That is, to model historical values before we have real-life fund returns to use. Sounds ok to me. Any more feedback?
Not seeing any disagreement on this, and since it makes a lot of sense to me, it's a go. I updated my working version of the Simba spreadsheet accordingly.

I want to say thank you for the time and effort you and (others as appropriate) have put into getting this done. Much appreciated .

Topic Author
longinvest
Posts: 4291
Joined: Sat Aug 11, 2012 8:44 am

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

Post by longinvest » Thu Dec 08, 2016 5:24 pm

AlohaJoe,
AlohaJoe wrote:I haven't (yet) got around to monthly returns (though looking back through this thread it looks like Kevin M and gordoni have independently done this already?)

But I did make partial progress by (re-)implementing the bond fund simulator that longinvest describes. It is in python, not a spreadsheet. You can see it here on github (as a jupyter notebook)
That's awesome!

Here's the answer to your question:
Bond Fund Simulator.ipynb wrote: Bootstrapping the Ladder
...
Why do we have a different face value for each one? Why not just $50 for each? Good question. I don't know. But that's what longinvest did in the spreadsheet, so I'm assuming there was a good reason for it :)
Imagine, for a moment, that the yield curve was flat and that the yield remained fixed over time. How could we build a ladder such that the growth of rungs is regular?

Let's do some math. We have a ladder of N rungs. The interest rate (thus, the coupon) is R. We build a ladder such that the rung maturing in one year has an X face value, the one maturing in 2 years has an X * (1 + R) face value, the one maturing in 3 years has an X * (1 + R)^2 face value, and so on. The rung maturing in N years will have an X * (1 + R)^(N - 1) face value.

One year later, we get the following payments:
  • The maturing capital of the shortest rung = X
  • The coupons of all N rungs = R * (X + X * (1 + R) + X * (1 + R)^2 + ... + X * (1 + R)^(N - 1))
We combine all these payments to buy a new rung maturing in N years. Our new rung is thus:
  • NewRung = X + R * (X + X * (1 + R) + X * (1 + R)^2 + ... + X * (1 + R)^(N - 1))
    = X * (1 + R * (1 + 1 * (1 + R) + 1 * (1 + R)^2 + ... + 1 * (1 + R)^(N - 1)))
    = X * (1 + R * (1 + (1 + R) + (1 + R)^2 + ... + (1 + R)^(N - 1)))
    = X * (1 + R * ((1 + R)^0 + (1 + R)^1 + (1 + R)^2 + ... + (1 + R)^(N - 1))) # Geometric Sum
    = X * (1 + R * ((1 - (1 + R)^N) / (1 - (1 + R))))
    = X * (1 + R * ((1 - (1 + R)^N) / -R))
    = X * (1 + 1 * ((1 - (1 + R)^N) / -1))
    = X * (1 + -1 + (1 + R)^N)
    = X * (1 + R)^N
Magically, our new rung is of size X * (1 + R)^N. Next year's rung will be X * (1 + R)^(N + 1), and so on. Exactly what we wanted. :happy
AlohaJoe wrote:My results match longinvest's, which isn't surprising, but I figured I would mention it.
That's actually quite important. I really like having two independent calculations done differently (macro-less spreadsheet and python program); this helps detecting any error in the spreadsheet or program.

I think that it would be nice to continue the parallel development of the spreadsheet and python program.

The spreadsheet has the advantage of being very transparent, accessible to people without any programming background. The program has the advantage of being easier to read entirely (for a programmer) and it's probably harder for a formula error to slip through undetected.

Thanks a lot!
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

MachineGhost
Posts: 108
Joined: Sat Feb 14, 2009 2:46 am

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

Post by MachineGhost » Thu Dec 08, 2016 5:36 pm

AlohaJoe wrote:Shiller's data comes from A History of Interest Rates by Sidney Homer, not the Cowles commission.
Longinvest was talking about the stock returns, not the bond. I don't know anything about the bonds.

Tickle me silly, I'm surprised to see there's rates provided back to 1871 also. Never mind then.
AlohaJoe wrote:How does one do this?
I believe either Shiller or Damordan provided the formula in their spreadsheet. Just convert it to 30-year or whatever CMT you're using. It's just a capital gain + yield for each year. If that is not suitable, then what is the TL;DR for this thread so far?

Topic Author
longinvest
Posts: 4291
Joined: Sat Aug 11, 2012 8:44 am

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

Post by longinvest » Thu Dec 08, 2016 5:49 pm

longinvest wrote:
Bond Fund Simulator.ipynb wrote: Bootstrapping the Ladder
...
Why do we have a different face value for each one? Why not just $50 for each? Good question. I don't know. But that's what longinvest did in the spreadsheet, so I'm assuming there was a good reason for it :)
Imagine, for a moment, that the yield curve was flat and that the yield remained fixed over time. How could we build a ladder such that the growth of rungs is regular?
...
Why seek regular rung growth? Let's look at how rungs used to grow before I selected the appropriate bootstrapping rung sizes (9-rungs fund):

viewtopic.php?f=10&t=179425#p2719999
longinvest wrote: Image
Do you see how the mesh is irregular in early years, all rungs seem to jump to a "next layer" every 9 years in early years? Eventually, with time, the growth gets regular.

Here's the growth of rungs after the change (10-rungs ladder):

viewtopic.php?f=10&t=179425&start=50#p2721188
longinvest wrote: Image
This time, there are no "layers". The growth is regular from the start.

As rung growth tends to converge towards regularity, I thought that it would be a good idea to bootstrap funds and ladders in a regular manner.
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

Topic Author
longinvest
Posts: 4291
Joined: Sat Aug 11, 2012 8:44 am

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

Post by longinvest » Thu Dec 08, 2016 5:53 pm

MachineGhost wrote:If that is not suitable, then what is the TL;DR for this thread so far?
MachineGhost,

I would suggest reading the first post of this thread in its entirety. I explained, in details, why we do things differently, and how we do them. As a bonus, we gain some interesting self-correcting returns property out of it (all explained in the first post).

Yes, it took me a few hours to write that first post. So, feel welcome to read it. :wink:
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

Topic Author
longinvest
Posts: 4291
Joined: Sat Aug 11, 2012 8:44 am

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

Post by longinvest » Thu Dec 08, 2016 6:11 pm

Siamond,

Our Bond Fund (30-11), representing long Treasuries, suffers from estimating 30-year yields as equal to the 10-year yield, for pre-FRED years. Would it be OK to cheat a little and bump it up, let's say by a constant 50 basis points relative to the 10-year yield, and compare the results to your historical SBBI LTT returns? Maybe this could provide a more realistic set of synthetic historical LTT returns. What do you think?
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

MachineGhost
Posts: 108
Joined: Sat Feb 14, 2009 2:46 am

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

Post by MachineGhost » Thu Dec 08, 2016 6:30 pm

longinvest wrote:
MachineGhost wrote:If that is not suitable, then what is the TL;DR for this thread so far?
MachineGhost,

I would suggest reading the first post of this thread in its entirety. I explained, in details, why we do things differently, and how we do them. As a bonus, we gain some interesting self-correcting returns property out of it (all explained in the first post).

Yes, it took me a few hours to write that first post. So, feel welcome to read it. :wink:
Okay, I've now read it twice. :wink: So correct me if I'm wrong, but you want to calculate a total return series based on riding the yield curve and not constant maturity to determine the capital gains or losses for each year?

If so, my first thought is why bother imputing and/or interpolating bogus yields? Indexed bond funds are already constant maturity and the additional complexity isn't needed if you can just use a CMT and weight the series to get the exact duration needed to match a fund.

And also, T-Bills don't pay a yield. You buy them at a discount to par and the yield is baked in at maturity. All other Treasuries pay interest twice a year not once.

Topic Author
longinvest
Posts: 4291
Joined: Sat Aug 11, 2012 8:44 am

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

Post by longinvest » Thu Dec 08, 2016 7:08 pm

MachineGhost,
MachineGhost wrote: Okay, I've now read it twice. :wink: So correct me if I'm wrong, but you want to calculate a total return series based on riding the yield curve and not constant maturity to determine the capital gains or losses for each year?
Not really.

Just imagine you're in the late 1800's. There are no such things as CDs or bond funds. You want a bond portfolio. What do you do? You can simply build a bond ladder.

Let's say that you're really rich, so that you don't add or subtract any significant amount from the portfolio; you're mostly letting it ride. If you have a 10-year ladder, each year you collect coupons and maturing principals to buy a new 10-year rung in your ladder. This is exactly how our bond ladder/fund model works, too. The difference between our model ladder and fund is that the ladder keeps its rungs until maturity and the fund sells its shortest rung at when it reaches a specific maturity.

Of course, in real life, coupons are paid twice a year. Maybe you can buy two rungs per year starting 6 months apart, so your 10-year ladder has 20 rungs. Yes, we cheat: our model is simplified. It assumes simple annual coupons. If you want to model the semi-annual coupons in a spreadsheet, go ahead*. Nobody is stopping you. If you think that this makes a big difference, I have bad news for you: it doesn't. The imprecision of the historical annual yields we have for the late 1800's and first half of the 1900's is way worse than any small error in our calculations. :wink:

* [Added]: In the process, you'll lose the self correcting property, though, as we only have annual yields.

Our model exposes its modeled fund to a collection of bonds of various maturities. So, when a specific part of the yield curve is affected by a change, but other parts are less affected, the fund will have a partial exposure to that change, like what happens in real funds like TBM (Total Bond Market).
MachineGhost wrote: If so, my first thought is why bother imputing and/or interpolating bogus yields? Indexed bond funds are already constant maturity and the additional complexity isn't needed if you can just use a CMT and weight the series to get the exact duration needed to match a fund.
I think that your understanding of indexed bond funds is flawed. Index bond funds have a maturity cut out (TBM sells bonds when they reach 1-year to maturity). The weighting of various maturities is based on market weight, not on trying to maintain a specific average maturity or duration.
MachineGhost wrote: And also, T-Bills don't pay a yield. You buy them at a discount to par and the yield is baked in at maturity. All other Treasuries pay interest twice a year not once.
Please take the time to model the difference in total returns between a T-Bill and a 1-year treasury with 2 coupons remaining with the exact same yield-to-maturity, and calculate the total 1-year return difference. If it strikes you as a significant difference, please come back reporting about it on this thread. :wink:
Last edited by longinvest on Thu Dec 08, 2016 7:29 pm, edited 1 time in total.
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

User avatar
siamond
Posts: 5445
Joined: Mon May 28, 2012 5:50 am

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

Post by siamond » Thu Dec 08, 2016 7:26 pm

longinvest wrote:Siamond,

Our Bond Fund (30-11), representing long Treasuries, suffers from estimating 30-year yields as equal to the 10-year yield, for pre-FRED years. Would it be OK to cheat a little and bump it up, let's say by a constant 50 basis points relative to the 10-year yield, and compare the results to your historical SBBI LTT returns? Maybe this could provide a more realistic set of synthetic historical LTT returns. What do you think?
So far, as you may have guessed or noticed, I stayed shy of including pre-1954 LTT returns in my working version of the Simba spreadsheet. Reason being that it did seem to me that your model is great, but the inputs are insufficient in this precise case (by lack of LT yields from FRED), and this would indeed lead to systematically skew (underestimating was indeed my guess) the pre-1954 LTT returns and be overly misleading.

I did have at the back of my mind to apply some kind of coarse correction, more or less equal to the average delta between ITT and LTT bonds for known years, but when I gave it a quick try, such delta proved so highly dependent on the start/stop years that I quickly gave up. This being said, yes, we could calibrate ourselves by looking at the CAGR delta between SBBI IT bonds and SBBI LT bonds between 1926 and 1953, which is 0.54. Interesting. :wink:

I am sure you have a solid rationale behind your '50 basis points' suggestion. Is it the same as what I just computed, or some other reasoning?

PS. let's discuss a bit more, but I still have a lot of reservations, as adjusting the CAGR is one more thing, but the trajectory (incl. std-deviation, correlation numbers with other assets, etc) would remain pretty much certainly wrong.

MachineGhost
Posts: 108
Joined: Sat Feb 14, 2009 2:46 am

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

Post by MachineGhost » Thu Dec 08, 2016 7:41 pm

Hmm, I came to this thread with different expectations than you appearing to be working with. I'm concerned only about Treasury total returns for the simba spreadsheet (and unclear why it is now a problem to investigate, admittedly, but I was pointed to this thread). I've no interest in backfilling corporate bonds, actively managed, multi-sector bond aggregates, etc. where all this extra complexity appears to be needed just to model how such real-world funds operate?

Yet, a pure Treasury index fund or individual bond ladder with a fixed duration of about 17 years is equivalent to the 30-year CMT yields converted to a total return time series. Why do I need to be concerned about your additional complexity? You actually appear to be making a claim that all bond yield to price conversion formulas are wrong because of a lack of actual real world yields for years 29 to 21, etc. When I buy a 30-year Treasury and it goes off the run and seasons into year 29, I don't look for a fictitinous 29-year Treasury rate to find out what its worth. All the necessary parameters were frozen in time when I bought the 30-year and are enough to determine its value at any later point in time. If that is not so, then please enlighten me.

EDIT: Just read this thread viewtopic.php?f=10&t=198245
I think I get it now. Fascinating! I had no idea SBBI was using fake returns pre-1977 when the CMT 20-year is available back a couple of decades. It's basically another sorry example of monopolistic data providers sitting on turds.

Topic Author
longinvest
Posts: 4291
Joined: Sat Aug 11, 2012 8:44 am

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

Post by longinvest » Thu Dec 08, 2016 8:30 pm

siamond wrote: I am sure you have a solid rationale behind your '50 basis points' suggestion. Is it the same as what I just computed, or some other reasoning?
Unfortunately, no I don't. It's was only a suggestion based on the difference in returns between SBBI and our synthetic returns extending the curve flatly using the longest available yield.

Our TIPS investigation started me thinking about the wall we hit with LTT's. I was just thinking that it might be fun to try a simple idea, but, to avoid data mining too much, I asked on this thread before starting the investigation.

Now that it has been stated on this thread, I just started looking at the historical difference between FRED's 30-year yields and 10-year yields. Here's what I found:

30-year yield minus 10-year yield
Image

That's not remotely stable. I think that my idea is dead already. :annoyed
Bogleheads investment philosophy | One-ETF global balanced index portfolio | VPW

User avatar
siamond
Posts: 5445
Joined: Mon May 28, 2012 5:50 am

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

Post by siamond » Thu Dec 08, 2016 8:43 pm

longinvest wrote:That's not remotely stable. I think that my idea is dead already. :annoyed
Yes, I reached a similar conclusion by other means. Nice try though. Definitely a sound winter storm activity. :wink:

AlohaJoe
Posts: 5402
Joined: Mon Nov 26, 2007 2:00 pm
Location: Saigon, Vietnam

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

Post by AlohaJoe » Thu Dec 08, 2016 9:17 pm

MachineGhost wrote:Tickle me silly, I'm surprised to see there's rates provided back to 1871 also. Never mind then.
Homer's book has rates going back much further than 1871; he shows rates going back to 1778 in the US (and further back elsewhere in the world). 1871 is just the earliest stock returns, so that's were Shiller cut off the data so he'd had matching returns for both assets.
AlohaJoe wrote:How does one do this?
I believe either Shiller or Damordan provided the formula in their spreadsheet. Just convert it to 30-year or whatever CMT you're using. It's just a capital gain + yield for each year. If that is not suitable, then what is the TL;DR for this thread so far?
Damodaran's method was discussed in the very first post of this thread, under "naive approach" along with the problems of using that approach.
Last edited by AlohaJoe on Thu Dec 08, 2016 9:28 pm, edited 1 time in total.

AlohaJoe
Posts: 5402
Joined: Mon Nov 26, 2007 2:00 pm
Location: Saigon, Vietnam

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

Post by AlohaJoe » Thu Dec 08, 2016 9:28 pm

MachineGhost wrote:Yet, a pure Treasury index fund or individual bond ladder with a fixed duration of about 17 years is equivalent to the 30-year CMT yields converted to a total return time series.
I don't believe this is the case, as explained in the first post of the thread. You can see the difference in volatility caused by longer duration by comparing Damodaran's estimate for a 1929 return to longinvest's.

Image

AlohaJoe
Posts: 5402
Joined: Mon Nov 26, 2007 2:00 pm
Location: Saigon, Vietnam

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

Post by AlohaJoe » Thu Dec 08, 2016 9:38 pm

MachineGhost wrote:EDIT: Just read this thread viewtopic.php?f=10&t=198245
I think I get it now. Fascinating! I had no idea SBBI was using fake returns pre-1977 when the CMT 20-year is available back a couple of decades. It's basically another sorry example of monopolistic data providers sitting on turds.
How does having CMT yield prior to 1977 help with the problem of returns? Ibbotson uses the yields you are talking about to compute the returns.

What you call "sitting on turds" here is the same approach you suggested we follow above. It is the same approach Damodaran takes, too.

MachineGhost
Posts: 108
Joined: Sat Feb 14, 2009 2:46 am

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

Post by MachineGhost » Thu Dec 08, 2016 9:52 pm

AlohaJoe wrote:Damodaran's method was discussed in the very first post of this thread, under "naive approach" along with the problems of using that approach.
Okay, well, I had problems with that "naive approach (don't remember the specifics, but I do know it would give an error when trying to work with 30-years) so eventually I just used a function in R. That models it as a "one bond" portfolio which is good enough for me since what is important is the duration for determining risk or exposure. If I had multiple bonds with different maturities, I would just average up the duration to get the net duration.

MachineGhost
Posts: 108
Joined: Sat Feb 14, 2009 2:46 am

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

Post by MachineGhost » Thu Dec 08, 2016 9:57 pm

AlohaJoe wrote:
MachineGhost wrote:Yet, a pure Treasury index fund or individual bond ladder with a fixed duration of about 17 years is equivalent to the 30-year CMT yields converted to a total return time series.

I don't believe this is the case, as explained in the first post of the thread. You can see the difference in volatility caused by longer duration by comparing Damodaran's estimate for a 1929 return to longinvest's.
Not sure why you don't agree. A 30-year CMT has a duration of about 17 and is not a bond fund. The first post only suggests the naive approach is not realistic which I don't use as mentioned previously. Lets use FLBIX for an example fund which has a duration of about 19 last I recall. That's essentially a 30-year CMT with a bit of leverage. Why would it be necessary to exactly reproduce the holdings of FLBIX rather than use a 30-year CMT time series and weight accordingly? The difference is marginal. All that matters is matching duration as that is where the volatility is from.

It's also my understanding from reading the Boglehead Wiki that they treat bond ladders and funds as exactly the same. I assumed that was the dogma.
Last edited by MachineGhost on Thu Dec 08, 2016 10:14 pm, edited 2 times in total.

Post Reply