Bond Returns: Realistic expectations

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Re: Bond Returns: Realistic expectations

Postby ogd » Fri Jul 26, 2013 11:53 am

billyt wrote:Ranger: There is another thing I don't understand about the scatter plots you posted: If you draw a 1:1 through the data, you will see that most of the time the return on the intermediate term bond fund is more than the rate on the 10-year treasury. I'm not sure if that makes sense.

The key here is that most of the time the yield curve is much flatter than today. So the 5-year is pretty close to the 10-year, and the bond index is 5 year plus credit risk.

Some random data points:
July 2010: 5yr T 1.76% 10 yr T 3.03% TBM 2.79%
July 2005: 5yr T 3.86 % 10yr T 4.08% TBM 4.29%
July 2000: 5yr T 6.18% 10yr T 6.04% (sic) TBM 7.02%
July 1995: 5yr T 6.10% 10yr T 6.42% TBM 6.56%

billyt wrote:Looking at the chart that simplegift posted almost all of the misfit (returns are higher than predicted) occurs before 1981.

Well, somewhere within the 10 years following the prediction. I think the early 80s are most likely to have caused the divergence, with those 12% compounded yields.
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Re: Bond Returns: Realistic expectations

Postby Ranger » Fri Jul 26, 2013 11:54 am

billyt wrote:Ranger: There is another thing I don't understand about the scatter plots you posted: If you draw a 1:1 through the data, you will see that most of the time the return on the intermediate term bond fund is more than the rate on the 10-year treasury. I'm not sure if that makes sense.


I am not an bond expert. But I won't be surprised by if Lehman Aggregate index returns are equal or higher than 10 year treasury even tho' duration is less. Index consists of Govies, MBS and ABS. So you need to add OAS (option adjusted spread) to equivalent duration govies.

I do not have access to bloomberg terminal, but when i had previously, OAS used to vary from 0.3 to 0.5%. Also there is an diversification effect between these three. Historical figures of diversification was around 5 to 10 basis points.
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Re: Bond Returns: Realistic expectations

Postby billyt » Fri Jul 26, 2013 11:59 am

Hi Epsilon:
My impression of what was done corresponds to your "how it should work" scenario, so maybe I am misunderstanding something. I think that the chart that kevin and simplegift posted compares the returns of intermediate term bond index to the initial YTM for the same index. Is that not the case? There is a good theoretical expectation that YTM should be predictive of returns based on the math. The empirical evidence seems to confirm this. Am I missing something?
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Re: Bond Returns: Realistic expectations

Postby Ranger » Fri Jul 26, 2013 12:09 pm

ogd wrote:
billyt wrote:Ranger: There is another thing I don't understand about the scatter plots you posted: If you draw a 1:1 through the data, you will see that most of the time the return on the intermediate term bond fund is more than the rate on the 10-year treasury. I'm not sure if that makes sense.

The key here is that most of the time the yield curve is much flatter than today. So the 5-year is pretty close to the 10-year, and the bond index is 5 year plus credit risk.
.


+1
I think we posted at the same time.

Good point about yield curve too.
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Re: Bond Returns: Realistic expectations

Postby billyt » Fri Jul 26, 2013 12:14 pm

OK, now it makes sense that the returns ought to be higher than the 10 year treasury rates on Ranger's plot. So in a sense it is not comparing apples to apples. But what about simplegifts plot? That is apples to apples, yes. It compares the yield prediction to the returns for the same index?
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Re: Bond Returns: Realistic expectations

Postby billyt » Fri Jul 26, 2013 12:28 pm

ogd: Ok, I think I get it. The greatest divergence between prediction and return occurs about 1976 (by eye). The actual returns are about 4% more than predicted. This is a result of interest rates more than doubling (6% to 14%) between 1976 and 1981. So it is clear that rising rates are nothing to be afraid of in terms of returns. Inflation, of course, is another matter. In 1981, I guess inflation and rates were pretty close, so real returns were near zero. Real returns are near zero now too. So there is not an enormous difference in real rates between 1981 and today.
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Re: Bond Returns: Realistic expectations

Postby Electron » Fri Jul 26, 2013 1:42 pm

Ranger wrote:I have updated the chart posted by Simplegift till 2012 here
viewtopic.php?f=10&t=120317&p=1758708#p1758708

Thanks for posting the updated chart. I just compared the results for 1950 and the two charts do not appear to be consistent. The chart posted by Simplegift shows the 10 year return higher than the initial yield, and the updated chart shows the 10 year return lower.

The updated chart does seem consistent with the table from Common Sense on Mutual Funds that I posted in this thread yesterday, although that analysis used Long Term Government bonds.

In that table, the compounded average return for the decade starting in 1950 was -0.1% which was 2.2% percentage points less than the projection of 2.1%.
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Re: Bond Returns: Realistic expectations

Postby billyt » Fri Jul 26, 2013 1:51 pm

I looked into this a little bit. Rangers chart compares intermediate term bond returns to 10 year treasury rates. The chart from John Bogle's site compares intermediate term bond returns to intermediate term rates, which seems like the right comparison.
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Re: Bond Returns: Realistic expectations

Postby Simplegift » Fri Jul 26, 2013 2:02 pm

billyt wrote:ogd: Ok, I think I get it. The greatest divergence between prediction and return occurs about 1976 (by eye). The actual returns are about 4% more than predicted. This is a result of interest rates more than doubling (6% to 14%) between 1976 and 1981. So it is clear that rising rates are nothing to be afraid of in terms of returns. Inflation, of course, is another matter.

Agreed. My takeaway from this discussion and charts is that, unless one thinks the Fed is going to let inflation get completely out of hand again (ala 1970-1980), then yield-to-maturity is going to be a good predictor of future bond returns. In fact, it may underestimate forward returns a bit during periods of rising rates. Thus, Kevin's objective in posting his original chart has been reinforced, in my view.
Cordially, Todd
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Re: Bond Returns: Realistic expectations

Postby billyt » Fri Jul 26, 2013 2:12 pm

Simplegift: Yes, I do agree that YTM is a good predictor of nominal bond fund returns. From Kevins chart there was still some question of predictability during long periods of rising rates. Your chart from Bogle's site answered that question to my satisfaction.
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Re: Bond Returns: Realistic expectations

Postby Ranger » Fri Jul 26, 2013 2:17 pm

Electron:


Sorry for the confusion. As billyt said I used 10 year rate to compare the data, since 5 year constant maturity data starts from 1962. I am not sure what is the proxy for 5 year constant maturity rate before that.
http://research.stlouisfed.org/fred2/series/DGS5/

Personally, I believe changes in 10 years treasury rate will be better predictor than 5 year rate because of most of credit spreads are priced out based on 10 year treasury.

It is best to use Vanguard chart since it compares apples to apples. My chart is more valid if some one evaluating the Bond index behavior based on 10 year treasury rates which is easier to observe daily.
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Re: Bond Returns: Realistic expectations

Postby Kevin M » Fri Jul 26, 2013 3:07 pm

I'm wondering about the discrepancy between the data from Common Sense on Mutual Funds posted by Electron, and the charts posted subsequently. For example, the former showed a return of essentially 0% for the decade starting 1950 (Electron shows -0.1% but in an online page from the book I see +0.1%), but the chart shared by Simplegift shortly after that shows a return of more than 2% for that decade.

Note also the differences in the direction of the prediction errors during periods of rising rates in the two data sets.

Is the difference due to the first data set using long-term bonds and the second using intermediate-term bonds?

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Re: Bond Returns: Realistic expectations

Postby Electron » Fri Jul 26, 2013 3:20 pm

Simplegift wrote:Finally ran across a chart below (courtesy of Mr. Bogle's Financial Market Research Center) that shows the long-term relationship between current bond yields and forward returns for the period starting in 1925. In this case, it's intermediate-term Treasury yields ..

It appears that prior to 1980 (a period of generally rising rates, post-1940), current yields tended to consistently underestimate forward returns a bit, sometimes significantly — but since 1980 (a period of generally falling rates), they've tracked each other more closely.

This is interesting because the table in Common Sense on Mutual Funds that I posted above shows the opposite for Long Term Government bonds. In that case, the initial yield was higher than the forward decade return in the 1950s, 1960s, and 1970s.

It appears that Intermediate Term maturities made a significant difference in periods of rising rates.
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Re: Bond Returns: Realistic expectations

Postby billyt » Fri Jul 26, 2013 3:20 pm

I would expect that long term bonds should exhibit the same general behavior, that is YTM is a good predictor of future returns. So a graph should be similar. However, a handful of randomly selected point returns (eg end of decade) might show different results because long-term bonds should have more volatile returns. It is difficult to compare a graph to point estimates. In the Bogle graph, there are a few points where the returns are lower than the predictions, in opposition to the general picture, and you might happen to sample those points when preparing a table. I would always rather see a graph than a table. A table looks at a few trees, a graph depicts the forest.
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Re: Bond Returns: Realistic expectations

Postby Electron » Fri Jul 26, 2013 3:51 pm

Kevin M wrote:I'm wondering about the discrepancy between the data from Common Sense on Mutual Funds posted by Electron, and the charts posted subsequently.

The answer is probably that the income stream rises faster with shorter term funds following an increase in rates. They say that most of the total return from bonds is related to the income stream over the long term. That includes reinvested income.

Common Sense on Mutual Funds includes a matrix table that really explains a lot if you spend some time and study it. It is Table 2.5 showing the effect of different Reinvestment Rates on Total Return. The table assumes a constant initial yield. The key parameters are Initial Yield, Terminal Yield, and Reinvestment Rate.

There are multiple versions of Common Sense on Mutual Funds and the charts have been updated.

Attached is a link to the Bond Model and Table Matrix.

http://my.safaribooksonline.com/book/pe ... he_bond_ma
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Re: Bond Returns: Realistic expectations

Postby ogd » Fri Jul 26, 2013 4:08 pm

Kevin M wrote:I'm wondering about the discrepancy between the data from Common Sense on Mutual Funds posted by Electron, and the charts posted subsequently. For example, the former showed a return of essentially 0% for the decade starting 1950 (Electron shows -0.1% but in an online page from the book I see +0.1%), but the chart shared by Simplegift shortly after that shows a return of more than 2% for that decade.

Note also the differences in the direction of the prediction errors during periods of rising rates in the two data sets.

Is the difference due to the first data set using long-term bonds and the second using intermediate-term bonds?

Kevin

Yes. The "Common Sense" data uses 20-year bonds, and a decade is not enough for those to recover from interest rate hits.

Do not be mislead by the "Total Bond Market Returns" -- it should be read as "Total Return of Bond Market".

Electron: without trying to be combative, there's a bit of data mining on your part here as well. I an not actually opposed to seeing even data-mined numbers from any period (it would be interesting), as long as the forward-looking period is longer than the duration of the bond portfolio.
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Re: Bond Returns: Realistic expectations

Postby Kevin M » Fri Jul 26, 2013 4:36 pm

Thanks for the link Electron. The Google books version preview I was seeing cut off a lot of what your link shows.

Minor observation: In the Table 2.4, the sign of the numbers in the Difference column is reversed for the last two rows (unless I am suffering from some form of dyslexia).

It's also now clear that he is using 20-year bonds as "long term".

Note than in looking at a 20-year bond over a 10-year time period, the terminal yield will have an impact on the return, unlike a bond held to maturity. Since a bond fund never matures, the terminal rate (rate at the end of the holding period or period being examined) will always have an impact. The reinvestment rate will have an impact in all cases (for bonds with non-zero coupons).

Looking at Table 2.5 is interesting. Would be nice to have something similar for 5-year and 10-year bonds. But for the 20-year, with an initial yield of 5% (Table 2.5, 10 years later), with a terminal yield of 7% and a reinvestment rate of 6%, total return is 3.8%, which seems at least roughly consistent with the numbers from Table 2.4, which you first posted. In general, if the reinvestment rate is equal to the terminal yield, and both are higher than the initial yield, the total return is always lower than the initial yield, and of course a lower reinvestment rate always results in even lower total return. By contrast, with reinvestment rate and terminal yield of 4% (the only number below the initial yield), total return is higher at 5.3%.

Does someone have access to or can someone create a similar chart for shorter-maturity bonds? Seems to me this would be valuable in helping our understanding of this topic.

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Re: Bond Returns: Realistic expectations

Postby Kevin M » Fri Jul 26, 2013 4:46 pm

Saw ogd's post after my last post.

Don't think Electron is data mining, but just presenting the data he found from John Bogle's book, but I totally agree with ogd's point about looking at periods closer to the duration or even maturity of the bonds.

Interesting that the Vanguard chart I posted uses aggregate bond market (call it roughly 5-year duration) over 10 years, while JB looks at 20-year bonds over 10-years! Most people seem to want to see aggregate bond market over a period equal to duration.

I assume JB used standard bond math to create Table 2.5, so I figure one of the bond and spreadsheet wizards here could do the same for a bond with a duration of 5 (or 5.5 or whatever) years, or even just a 5-year bond, which seems would be much closer to what folks here seem to think is more relevant.

Edit: But a 5-year bond over 5 years would not capture the effect of terminal value that would apply to an intermediate-term bond fund with no maturity, so ideally that would be built into the model (something like JB's table 2.5). I guess what might be useful is something like table 2.5 for a bond ladder that simulates Total Bond Market (for most Bogleheads, I'm guessing) and/or Intermediate-Term Treasury bond fund (for ogd and similarly minded compatriots).

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Re: Bond Returns: Realistic expectations

Postby Electron » Sat Jul 27, 2013 12:30 am

Kevin M wrote:Thanks for the link Electron. The Google books version preview I was seeing cut off a lot of what your link shows.

Minor observation: In the Table 2.4, the sign of the numbers in the Difference column is reversed for the last two rows (unless I am suffering from some form of dyslexia).

There appear to be several errors in the online book. The actual return for the 1950s in the original version of the book showed as -0.1%, and I believe the sign is missing in the online version. The Difference number of 2.2% would be consistent with 2.1% Initial Yield and -0.1% Actual Return.

The online version seems to have left out the sign for most of the Difference numbers in Table 2.4. The original version used a minus symbol for negative numbers which was all decades other than the 50s, 60s, and 70s. My earlier posts in this thread reversed all signs as I prefer it that way.

I also think there is an error in Matrix Table 2.5. The 8.2% in the upper right hand corner does not look right. It should be higher than the percentage to its left. That number is the same in both versions of the book.
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Re: Bond Returns: Realistic expectations

Postby Electron » Sat Jul 27, 2013 2:02 pm

Ranger wrote:I have updated the chart posted by Simplegift till 2012 here. viewtopic.php?f=10&t=120317&p=1758708#p1758708

Those are great charts.

I'm wondering if your spreadsheet models actual bonds paying semi-annual interest that is reinvested along with price changes in the bonds. The price changes would be difficult to model. The price of a bond changes after any change in rates, but it also changes gradually as the maturity date approaches.
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Re: Bond Returns: Realistic expectations

Postby Kevin M » Sat Jul 27, 2013 4:07 pm

ogd wrote:Yes. The "Common Sense" data uses 20-year bonds, and a decade is not enough for those to recover from interest rate hits.

If we want to judge by duration, it depends on the initial yield/coupon. Below shows yield (where coupon=yield) and modified duration for a 20-year bond.

Code: Select all
yield   mduration
2%   16.42
3%   14.96
4%   13.68
5%   12.55
6%   11.56
7%   10.68
8%   9.90
9%   9.20
10%   8.58


So at an initial yield and coupon of about 7.5%, a 20 year bond has a duration of about 10 years. So looking at 10-year returns for 20-year bonds assuming the historical average (in the ballpark of 7.5%) should satisfy those interested in a time period equal to duration (for long-term bonds).

But this does also highlight that for lower initial yields, duration is much longer. For current 20-year treasury yield of 3.3%, duration is close to 15 years.

Here are the same calculations for a 10-year bond:

Code: Select all
yield   mduration
2.00%   9.02
3.00%   8.49
4.00%   8.18
5.00%   7.79
6.00%   7.44
7.00%   7.11
8.00%   6.80
9.00%   6.50
10.00%   6.23


And for a 5-year bond:

Code: Select all
yield   mduration
2.00%   4.74
3.00%   4.58
4.00%   4.49
5.00%   4.38
6.00%   4.27
7.00%   4.16
8.00%   4.06
9.00%   3.96
10.00%   3.86


Note that the shorter the term of the bond, the closer duration is to term at a given yield/coupon.

I'm sure that this is obvious to bond experts, but for the rest of us it might be useful to keep in mind as part of this discussion.

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Re: Bond Returns: Realistic expectations

Postby Ranger » Sat Jul 27, 2013 4:32 pm

Electron wrote:I'm wondering if your spreadsheet models actual bonds paying semi-annual interest that is reinvested along with price changes in the bonds. The price changes would be difficult to model. The price of a bond changes after any change in rates, but it also changes gradually as the maturity date approaches.


Data was posted here in the same thread.
viewtopic.php?f=10&t=120317&p=1758708#p1758450

All i did was verified Lehman Aggregate index data from here https://indices.barcap.com/index.dxml and updated 2011 and 2012 figures. So the data includes total return of price and dividend reinvestment.
I was asking myself different question than OP was asking. OP's main objective to find Bond return expectations given the YTM today. There were many studies done before like Vanguard and others validating the assumptions. Here is another.
Image


I compared to ten year treasury because 1) most of the traders knows its history as back of their hands, 2) yields of TBM are more comparable to 10 years more so than 5 years and finally 5 year data was not available to me
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Re: Bond Returns: Realistic expectations

Postby Electron » Sat Jul 27, 2013 5:48 pm

Ranger wrote:Lehman Aggregate Index data

Thanks for the explanation on the charts. I had thought about deriving actual returns by modeling bonds with accurate semi-annual reinvestments. It did not look like an easy task when taking into account constant price changes in the bonds.

Here's a comment for everyone. After all the discussion on bonds, I decided to write down a few key bullets regarding bond funds.

1. When you buy shares in a bond fund the future return is unknown. However, you can estimate a range of possible future returns depending on the time held and the average maturity of the fund.

2. When you buy shares in a bond fund, you are purchasing a future income stream.

3. The monthly dividend paid by a bond fund typically changes over time. A long term bond fund has the most durable dividend, while a short term bond fund has the least durable dividend. A durable dividend is defined as a dividend that changes very slowly following changes in the prevailing interest rate.

4. Most of the total return in a bond fund over time is from the income stream. The reinvestment rate is a very significant factor in total return if one reinvests income.

5. The Net Asset Value of a bond fund typically changes over time.

6. Each purchase of bond fund shares has an associated cost basis and NAV. As a result, the income stream on any given lot of shares is related to the NAV at the time of purchase. More shares are purchased when the NAV has declined, and fewer shares are purchased when the NAV has risen.

7. A bond fund typically maintains a perpetual maturity.

8. The SEC Yield on a bond fund relates to bond fund shares at current NAV. In addition to the income stream and value of the shares at NAV, a holder of bond fund shares typically has a capital gain or loss at any given time after revaluing their shares to current NAV.
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Re: Bond Returns: Realistic expectations

Postby Kevin M » Sun Jul 28, 2013 3:32 pm

Hi Electron,

A couple of your points are relevant to the discussion in this thread. I think the OP actually states the most relevant point, which is that for the US aggregate bond index, YTM has been a pretty good guide for the following 10-year total return. We've also seen that this works pretty well for 20-year bonds (John Bogle) and 10-year bonds (latest chart by Ranger). Your point 1 gets at this without stating it directly, but also points out that there is some uncertainty in the estimate, as the charts show.

I think you must add a comment about terminal yield (i.e., change in rates) to your point 4:

Electron wrote:4. Most of the total return in a bond fund over time is from the income stream. The reinvestment rate is a very significant factor in total return if one reinvests income.

The terminal yield at the end of the holding period also can have a significant effect, although its importance diminishes for longer holding periods.

We see both effects from Table 2.5 from John Bogle's CSOMF:
Image

Note that at an initial yield of 5%, a 1 percentage point change in terminal yield has an even larger effect than a 1 percentage point change in reinvestment rate. A 1 pp increase to 6% in terminal yield decreases total return by 0.9 pp to 4.1%, while a 1 pp increase in reinvestment rate to 6% increases total return by 0.6 pp to 5.6%. Incidentally, duration for a 5% coupon bond sold at par is about 12.5 years.

I don't see that this chart justifies putting more emphasis on reinvestment rate than on terminal yield relative to initial yield. Obviously this only applies to a bond sold quite awhile before maturity, but as I said above, this seems relevant to bond funds, since (typical) bond funds always have a remaining term to maturity when you sell.

Looking at YTM vs. forward 10-year yields for 10-year bonds is not relevant when considering the impact of terminal yield, since the bond matures at par after 10 years, and the only cause of delta is reinvestment rate, so generally rising rates will obviously result in higher total return. The chart posted by Simplegift showing the YTM vs. following 10-year return is for 10 year bonds. The chart says "Intermediate-term Government Bond", but in the John Bogle speech from which the chart is taken, he mentions a yield of 3.3% for "intermediate treasuries", and on June 5, 2003, the date of the speech, the yield on the 10-year treasury was 3.33%, so I figure he considers 10-years treasuries intermediate term.

Still waiting to see something like table 2.5 for the aggregate bond index or some other intermediate-term bond index representing an intermediate-term bond fund, ideally for different holding periods (say 5 years and 10 years), using current initial yield. Bond gurus: Is that too hard to create?

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Re: Bond Returns: Realistic expectations

Postby ogd » Sun Jul 28, 2013 3:57 pm

Kevin M wrote:Still waiting to see something like table 2.5 for the aggregate bond index or some other intermediate-term bond index representing an intermediate-term bond fund, ideally for different holding periods (say 5 years and 10 years), using current initial yield. Bond gurus: Is that too hard to create?

You mean forward-looking from now? Yes. Here are the steps:
a) Pick a bond portfolio structure.
b) Pick an interest rate rising scenario.
c) Pick a yield curve shape all along the way.
d) Decide what the fund's strategy is as durations shorten with interest rates rising along the way.
e) Do a lot a transaction calculations.

Here are the problems with each:
a) Nobody will agree on this. The agg bond index is very complex and hard to simulate, and you don't know how its own composition adjusts to interest rates. An IT treasury fund is simpler, but then you'll be accused of datamining.
b) You have to be mindful as to what's realistic, particularly using data from high inflation periods. You'll inevitably get into inflation discussions anyway.
c) The behaviour of the yield curve is highly unintuitive, as I conceded in the "rolling returns" thread. It's only the past that can convince you that it flattens to match its own implied predictions, rather than staying sharp which would boost the bond fund a lot.
d) The fund may either allow duration to lessen, or lengthen maturities to keep the same duration, in which case its portfolio will be rather unrecognizable. The discussions on this will be interminable.
e) A few hours with a yield calculator need to be invested. Or a good spreadsheet, or a good program.

Personally, I don't have enough interest to undertake this at the moment, nor do I want to deal with endless discussions of choices a) to d). Why does the past behaviour not convince you? E.g. 2003 starting at 2% for the 5 year Treasury? It seems pretty clear that the YtM is a good predictor, and we can just leave it at that. It convinced me that the "rolling" boost from a steep yield curve tends to not last.

Also, I think you're making too much of reinvested interest. 10% (terminal) of 2% (reinvested) is only 0.2% annualized. It will barely matter. For a fund, reinvestment of capital will be the far greater effect. Edit: and for a bond held to maturity for a period close to the period considered -- you already know the outcome to the penny.
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Re: Bond Returns: Realistic expectations

Postby Electron » Sun Jul 28, 2013 4:24 pm

Kevin M wrote:Looking at YTM vs. forward 10-year yields for 10-year bonds is not relevant when considering the impact of terminal yield, since the bond matures at par after 10 years, and the only cause of delta is reinvestment rate, so generally rising rates will obviously result in higher total return.

Still waiting to see something like table 2.5 for the aggregate bond index or some other intermediate-term bond index representing an intermediate-term bond fund, ideally for different holding periods (say 5 years and 10 years), using current initial yield. Bond gurus: Is that too hard to create?

Thanks for your comments. I agree that my list should include a comment on terminal yield and possibly duration as well. There is a relationship since any change in rates will impact NAV and total return based on the duration of the portfolio.

I'm wondering if your first comment above is applicable to a bond mutual fund since it maintains a perpetual maturity. Holding an individual bond to maturity and dealing with the reinvestment of each coupon might look a little different.

I've been thinking about Table 2.5 and how it was generated. It appears that they made some assumptions that are not clear. I believe the table applies to a fund or index and not an individual bond.

As an example, let's say the initial yield was 5%, the reinvestment rate was 6%, and the terminal yield was 5%. It's not clear what happened along the way. This scenario may not even be realistic, as it implies that rates rose suddenly and stayed higher for ten years followed by a sudden decline in rates. There are probably many scenarios since the table deals with average reinvestment rate as mentioned in the book.
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Re: Bond Returns: Realistic expectations

Postby Electron » Sun Jul 28, 2013 6:35 pm

ogd wrote:I don't have enough interest to undertake this at the moment.

I agree that replicating Table 2.5 would be quite difficult.

I think investors would be very interested in a realistic range of returns in the bond index over the next 10 years. Perhaps we could just analyze two scenarios.

Case 1 would be deflation with interest rates dropping to 1% or less. Case 2 might be a strong economy and higher inflation with rates rising to 5% or higher. Select the percentages as desired.

Anyone care to project the ten year average return in the bond index for the two cases?
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Re: Bond Returns: Realistic expectations

Postby billyt » Sun Jul 28, 2013 6:43 pm

Electron: The historical evidence clearly shows that the future return of bond funds is very well estimated by the current yield. What more do you want to know?

The problem that we have now is that interest rates are low, not that they might increase.

If interest rates increase, bond funds will do better.

The wild card is inflation. So far no inflation. Tomorrow, who knows.

Stocks and TIPS should give you some inflation protection.
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Re: Bond Returns: Realistic expectations

Postby Kevin M » Sun Jul 28, 2013 9:09 pm

Electron wrote:I'm wondering if your first comment above is applicable to a bond mutual fund since it maintains a perpetual maturity. Holding an individual bond to maturity and dealing with the reinvestment of each coupon might look a little different.

No, it doesn't apply to a bond fund--I already made that point--so yes, holding a bond to maturity is completely different. As I said, it eliminates the impact of terminal yield, which is not the case for a bond fund.

Electron wrote:I've been thinking about Table 2.5 and how it was generated. It appears that they made some assumptions that are not clear. I believe the table applies to a fund or index and not an individual bond.

I don't think so. It seems pretty clear that it applies to a 20-year bond with an initial yield of 5%, held for 10 years.

Electron wrote:As an example, let's say the initial yield was 5%, the reinvestment rate was 6%, and the terminal yield was 5%. It's not clear what happened along the way.

I'm not sure, but I don't think it matters. The reinvestment rate tells us all we need to know about what happened along the way in terms of reinvested interest, and the terminal yield tells us all we need to know about impact on price. For this particular chart, I don't think the path matters. I think that's one of the beauties of this presentation.

If we think of the chart as representing a 10-year holding period, and we assume we bought the bond at par with a 5% coupon (the stated initial yield), the terminal yield is the only additional piece of data we need to calculate the price of the bond when we sell it, so that gives us the return component due to the difference in rates between purchase and sale.

We know what the coupon payments are, so we know that component of the return.

We know the average reinvestment rate, so that gives us the interest on interest component of the return.

What I was thinking of was something similar, but trying to respond to some of the criticisms of the applicability of this chart to an intermediate-term bond fund, like "10 years is not enough time for a 20-year bond to recover from an interest rate increase". OK, well let's use a shorter average maturity, closer to that of an intermediate-term bond fund.

A 10-year bond held for 10 years doesn't work because terminal yield is not relevant. I suspect we'd see similar complaints for a 10-year bond held for five years.

So I was just thinking of a simplified model, not necessarily with all the complexities of a bond fund

The first approximation could be a bond-thingy of some sort with a constant maturity of about 5 years or 7 years or whatever (TBM is 7.4 years, IT Treasury is 5.6 years). You start out with current yield, assume coupon=yield at time 0, and assume this gives you the coupon portion of your return. Then the two dimensions of the table give you the other return components over the selected time period. Terminal yield gives you the price change component, and average reinvestment rate gives you the interest-on-interest component.

I guess the major criticism of this model would be that it doesn't capture gradually changing coupon payments that you'd see as a bond fund rolls over it's bonds to ones with different coupon rates. Maybe a second order model could assume that the average coupon during the holding period was the average of the starting yield and the terminal yield.

I assume anything more complicated than this would get into some if not all of the complexities raised by ogd.

Anyway, perhaps this really warrants another post if anyone is interested in pursuing it, since the main purpose of this post has already been achieved. Current yield for the aggregate bond index is a pretty good predictor of following 10-year returns, but it's not perfect, and we don't really know whether it will be higher or lower, or by how much, but it's likely to be in the ballpark.

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Re: Bond Returns: Realistic expectations

Postby Electron » Mon Jul 29, 2013 12:30 am

Kevin M wrote:It seems pretty clear that it applies to a 20-year bond with an initial yield of 5%, held for 10 years.

I think you're correct that Table 2.5 was derived for an individual twenty year bond held for the following ten years. My initial thought was along those lines until I saw that the chart was labeled "Total Bond Market Return". Now in reading the text it appears that he used the table data as a model for bond market returns. One flaw might be that average maturity changes quite a bit in the bond as it matures, versus a more constant maturity in a fund or index. I'd also guess that Table 2.5 would be much more difficult to create for a fund or index as opposed to an individual bond.

The text in the book also mentions a fairly impressive figure. The simple bond model has a 0.93 correlation when comparing initial yield to the following ten year return. The simple three parameter stock forecasting model has a 0.54 correlation. It's possible that the 0.93 figure would be even higher for intermediate term bonds.

I agree that the initial yield provides a very reasonable ten year forecast generally within a few percentage points. However, on a percentage basis the forecast does not look quite as good.

Thanks for starting an excellent thread.
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Re: Bond Returns: Realistic expectations

Postby Kevin M » Mon Jul 29, 2013 1:38 am

Electron wrote:One flaw might be that average maturity changes quite a bit in the bond as it matures, versus a more constant maturity in a fund or index. I'd also guess that Table 2.5 would be much more difficult to create for a fund or index as opposed to an individual bond.

Definitely yes to the first statement, which is why I was hoping it might be feasible for someone to create something similar for a bond fund, even if it's a first-order or second-order approximation that doesn't capture all the intricacies of a bond fund. And also yes to the second statement, since for one thing, the average coupon rate isn't constant for a bond fund, so we can't even calculate the coupon component of the return, which is trivial for an individual bond.

Electron wrote:The text in the book also mentions a fairly impressive figure. The simple bond model has a 0.93 correlation when comparing initial yield to the following ten year return. The simple three parameter stock forecasting model has a 0.54 correlation. It's possible that the 0.93 figure would be even higher for intermediate term bonds.

A similar chart for intermediate-term bonds was shared earlier in the thread; it came from a speech given by John Bogle, and the R^2 was 0.91, so about the same.

Electron wrote:Thanks for starting an excellent thread.

You're welcome!

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Re: Bond Returns: Realistic expectations

Postby Electron » Mon Aug 12, 2013 1:48 pm

Kevin M wrote:Still waiting to see something like table 2.5 for the aggregate bond index or some other intermediate-term bond index representing an intermediate-term bond fund, ideally for different holding periods (say 5 years and 10 years), using current initial yield.

I was finally able to replicate Table 2.5 in Common Sense on Mutual Funds for the case of the 5% initial interest rate. Thanks for the suggestion on how to handle the coupon reinvestments. Attached are two charts using the same method for an initial interest rate of 2%.

The Long Term chart uses the same method as the book and holds a 20 year bond until 10 years from maturity. The Intermediate Term chart assumes a 15 year bond held until 5 years from maturity. In both cases ten additional bonds are added over the time period to handle all reinvestments. The next task is to decide if the results in the tables look realistic.

Image

Note that any calculator with the function Y to the X power can handle simple bond fund projections. Here is an example for the Bond Index currently paying 2% with a duration of 5.5 years. Invest $1.00 in the index today and assume that rates increase to 3% tomorrow. Based on the duration, the shares are now worth $0.945. If we compound 1.03 to the tenth power, we get 1.344. Multiply by $0.945 and the value of the shares after 10 years would be $1.27. Taking $1.27 to the 0.1 power results in 1.024 which indicates a compound return of 2.4%. That conflicts with the 1.7% return in the chart.

The case of 2% Reinvestment Rate and 3% Terminal Yield looks much better. Calculator results indicate 1.42% versus 1.4% in the chart.
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Re: Bond Returns: Realistic expectations

Postby Kevin M » Mon Aug 12, 2013 3:00 pm

As per our PMs, excellent job in working through all the nuances to construct these tables.

Although it's great to be able to look at different bond terms and interest rates, I don't think we should be surprised that the 15 year bond held for 10 years is not going to give the same results as a bond fund with a fairly constant duration of 5-6 years. For one thing, the modified duration of a 15-year bond with a coupon and yield of 2% is 12.9--much greater than 5.5, so the price hit in your scenario would be much greater. But for an individual bond, even that doesn't really matter, since we can compute the price of the bond at any combination of coupon, YTM and remaining term to maturity (95.4 with 2% coupon, 3% YTM, and 5 years to maturity), which is the kind of thing we can't do with a bond fund because of all of the unknowns over the ten years (e.g., yield curve, bond portfolio management, etc.).

Bottom line: I don't think any table 2.5 we construct for an individual bond (with coupons reinvested in more individual bonds) will give us results that approximate a bond fund or rolling bond ladder. I think that will require a more sophisticated model, even with some simplifying assumption, and the simplifying assumptions may be enough to make the model not very interesting.

Maybe start by thinking about a really simple model in which an 8 year bond is rolled over every year, so average maturity is about 7.5 years (close to TBM). To model that you need to make an assumption about the yield curve. Maybe use the current yield curve? There was another thread where a simplified model like this led the the conclusion that the expected return for the intermediate-term treasury bond fund was about twice the SEC yield, so obviously we have to be careful with these kinds of assumptions.

Note that even if you plug TBM numbers for YTM, average coupon, and average maturity, into the DURATION or MDURATION function, you get something closer to 6.5 than the 5.5 shown for TBM, showing another issue in trying to model the bond fund as a single bond.

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Re: Bond Returns: Realistic expectations

Postby Electron » Tue Aug 13, 2013 4:37 pm

Kevin M wrote:Although it's great to be able to look at different bond terms and interest rates, I don't think we should be surprised that the 15 year bond held for 10 years is not going to give the same results as a bond fund with a fairly constant duration of 5-6 years. For one thing, the modified duration of a 15-year bond with a coupon and yield of 2% is 12.9--much greater than 5.5, so the price hit in your scenario would be much greater.

I think the Table 2.5 bond model is lacking in multiple ways which includes reinvestment. One can force the 2% bond to be worth $100 at the end of the period and the 10 year return increases from 1.7% to only 2.09%. This is for the case of rates increasing from 2% to 3%. Compare that with the theoretical bond index return of 2.4% for the same case after 10 years. As you suggested, the model may need bonds maturing and rolling over to the higher rate so the cash flow for reinvestment increases.

The analysis for the bond index typically assumes that the NAV drops after a sharp rise in SEC yield, and that the investment then compounds steadily at the higher SEC yield for the next 10 years. Some of that return would be from an increase in NAV as bonds get closer to maturity. The model doesn't work in the same way. The SEC yield does incorporate yield to maturity.

One other interesting observation was made regarding the bond model. The model that matched Table 2.5 in the book for the 5% initial yield does not reproduce the published table for the 9% initial yield. Results were significantly different. The model seems quite a bit more rate sensitive so there must have been different assumptions in the 9% table.
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