Riding the yield curve, in action

Discuss all general (i.e. non-personal) investing questions and issues, investing news, and theory.
User avatar
Kevin M
Posts: 11287
Joined: Mon Jun 29, 2009 3:24 pm
Contact:

Re: Riding the yield curve, in action

Post by Kevin M » Fri Dec 19, 2014 10:19 pm

Actually, I'm saying just the opposite of "it's complicated".

If we look at individual bonds, it's quite simple. The original stlutz post used individual bonds, and the bond math was straightforward and verifiable.

A bond fund is made up of individual bonds, so there is no additional magic involved, and there are no additional sources of returns other than distributions and price change. We can put capital gains distributions in the price change category (since cap gains are reflected as price change before the distribution), which leaves dividend distributions. Dividend distributions are from coupon payments and amortization/accretion of premium/discount. No magic, no other sources of returns.

Although "roll yield" sounds really cool, it typically is not a term applied to bonds, which anyone can verify with a Google search. After accounting for coupon and amortization/accretion, all that is left is price change. So "roll yield" is just a fancy sounding name for a price increase during the holding period. I just don't see the need to introduce the additional complexification.

If the yield curve is steep, and remains steep, then of course you benefit from the price change as a bond "rolls down" the yield curve. This is just an aspect of being rewarded for term risk, which is a well-understood aspect of bonds. The catch is that we don't know what the future shape of the yield curve will be.

Now bond funds are a bit more mysterious than individual bonds, since we don't know exactly what's going on inside the bond funds. But if we dig into it, the performance of the bond fund must be explainable by the performance of the individual bonds held by the bond fund, and bond math must apply. I've explored some of the mysterious performance of bond funds in other threads, but this vague notion of "riding the yield curve" and "roll yield" have done nothing to increase my understanding. On the other hand, it's quite straightforward to do the bond math and compute the return from coupon payments and price change based on the constant parameters (e.g., coupon rate), and the variable parameters (e.g., YTM, term to maturity).

So, as stlutz did in the original thread, we should be able to build a model based on individual bonds, and use standard bond math to explain the performance of the simulated bond fund. If we can't, then it's just because there's something about the individual bonds that we don't understand (yet).

Kevin
Wiki ||.......|| Suggested format for Asking Portfolio Questions (edit original post)

User avatar
Kevin M
Posts: 11287
Joined: Mon Jun 29, 2009 3:24 pm
Contact:

Re: Riding the yield curve, in action

Post by Kevin M » Sat Dec 20, 2014 4:49 pm

It's always a bit puzzling to me when ogd criticizes my posts as being "wrong", "dangerous", or "not offering any clarifications", so I thought I'd review this thread to see what might be the reason for the latest criticism, and I remain puzzled. Basically in the reply that was criticized as not offering any clarification (toward the end of the last page) I summarized much of what has already been said in this thread by others, and added a little editorial comment that we can explain all of this with conventional bond concepts and bond math without introducing the futures terminology of "roll yield".

The point about bond returns consisting of coupon payments and price change that can be explained with conventional bond math was made by stlutz in this post: Bogleheads • View topic - Riding the yield curve, in action
stlutz wrote: I don't know that there is really a debate as much as an exploration of how the math of a bond portfolio works. The original post where I started the discussion simply pointed out that absent any changes in interest rates, there are *two* sources of bond returns: a) interest b) capital appreciation <snip>
The point that there is nothing magical about a bond fund that can't be explained by the performance of the individual bonds was made by stlutz here: stlutz
stlutz wrote:<snip> it is also conversely true that there is no magic that a fund has that individual bonds do not.
Member alexfrey posted some of the most cogent replies, making some of the same points I've made (except for the use of that unfortunate term "roll yield"):
Bogleheads • View topic - Riding the yield curve, in action
alexfrey wrote:<snip> just wanted to point out that ex-ante (looking-forward) expected roll-yield can be quite different from ex-post calculated roll yield.

In particular, you can always calculate a roll yield for a past period, which could be positive or negative. But it isn't strictly clear that you should expect roll yield to be positive in the future, even if the yield curve is positively sloped. A positively sloped yield curve can indicate the expectation that rates will increase in the future. If the "expectations theory" of the yield curve is correct, then there is actually a (loose) no-arbitrage condition in which, for instance, buying a ten year bond should return the same as buying a five year bond and then rolling it over at the expected five-year rate five years from now.
ogd agreed with this, and since if A = B and B = C, A = C, ogd agrees with me:
Bogleheads • View topic - Riding the yield curve, in action
ogd wrote: I fully agree with this. I don't expect roll yield to persist even starting from a steep yield curve, because if it flattens on schedule you will never get a value gain when you roll over a bond. I was pointing out in my latest update that the curve has been flattening, although behind schedule.
But unfortunately went on to use present tense, which is one of my objections:
ogd wrote:What I'm saying is, if you feel tempted to avoid bonds or go short because times are uncertain in bond land, it's worth understanding that you're getting paid quite a bit more for holding them now
As I've pointed out, you cannot know that "you are getting paid", you can only know that you have gotten paid. Stating it in the present tense implies that you know that you will continue to get paid, which implies that you can predict the future. In doing so, ogd not only implies something that I disagree with, but contradicts ogd's own statements elsewhere--even in the same reply.

I also disagree with the implication that there is any schedule for yield curve flattening. There would be if the current shape of the yield curve was 100% due to the expectations hypothesis, and if the expectations hypothesis held. The problem is that we don't know how much of the yield curve is due to expectations theory and how much to the competing liquidity preference theory. I suspect that there actually is agreement on this point, but it's slipping into language that implies that anyone is any good at predicting future interest rates that I find troublesome.

Another informative reply by alexfrey (and a minor disagreement from ogd):
Bogleheads • View topic - Riding the yield curve, in action
ogd wrote:
alexfrey wrote:Today the 10 yr is at 2.54% and the 5 yr at 1.64%. But what matters to the fund is not the five year rate today, but the five year rate five years from now when they go to flip their bond. We can calculate more or less what the market expects the five year rate might be five years from now using the expectations theory of interest rates -- and it's about 3.44%. (See: http://en.wikipedia.org/wiki/Expectation_hypothesis). So a fund that buys a 10 yr at 2.54% and then sells it 5 years later at 3.44% would actually see a realized negative roll yield.
Hmmm. While we are on the same page, I think you have this detail wrong. The expectation for the 5 year 5 years from now is about 2.54% (minus a risk premium), i.e. little no gain but no loss either.
I'd like to weigh in on this one, since I've spent significant time studying the term structure of interest rates theories since my earlier participation in this thread and the earlier related threads. I summarize much of my investigation here: Bogleheads • View topic - Yield Curve Investigations). In that thread, I address this topic directly here: Bogleheads • View topic - Yield Curve Investigations. Per standard academic approach, I use zero coupon rates in that post, but the numbers will be in the same ballpark for constant maturity Treasuries (the yield curve most commonly referred to). At the time the 5-year zero rate was about 1.7%, the 10-year rate was about 2.7%, and the 5-year forward 5-year rate was about 3.3%, so based on standard expectations theory, using a formula from a paper published by the Federal Reserve Board (FRB), alexfrey's numbers look correct to me.

Where I disagree somewhat with alexfrey is that this forward rate represents the market expectation. The reason is that we don't know how much of the forward rate is based on expectations theory and how much on liquidity-preference theory (aka, term risk, aka interest-rate risk). So ogd had almost the right idea, except that ogd got the sign reversed. I think a more accurate statement would have been that the expectation was 2.54% based on expectations theory plus a risk premium of 3.44% - 2.54% = 0.9% (more accurately 0.9 percentage points or 90 basis points) based on liquidity preference theory.

However it seems somewhat ludicrous that we know how much of the forward rate is due to expectations and how much due to liquidity preference. I don't believe term structure of interest rates theory is advanced enough to tell us that, but this may just be something I haven't seen any papers on yet.

In this post,
Bogleheads • View topic - Riding the yield curve, in action, alexfrey shows us the calculation of the forward rate:
alexfrey wrote: I get 3.45% if I actually run the calc in absence of a risk premium. My calculation is: =(1.0254 ^ 10 / 1.0164^5)^ (1/5)-1. This is solving for the five year rate five years from now that would make an investor indifferent between buying a ten year today and buying a five year with the expectation of rolling it over five years from now. 2.54% is the current 10 yr rate, 1.64% is the current five-year rate.
This is a different formula than presented in the FRB paper, but actually is the same formula I had derived before finding the formula in the FRB paper, and they produce the same results, so I assume one formula can be solved to produce the other.

This post by member The Dan illustrates the risk of thinking in terms of roll yield:
Bogleheads • View topic - Riding the yield curve, in action
The Dan wrote:Even though the roll bonus has gotten smaller, it is still pretty good. The 2.5% total return from rolling from 5 to 4 years still beats most bank CDs, and the treasury interest is exempt from state taxes to boot.
Again, the problem is thinking in present tense, and assuming that the shape of the yield curve remains static. Even though ogd has cautioned against this, the use of the present tense propagates this misguided thinking.

And this is just plain wrong:
The Dan wrote:I have been buying treasuries this year in the 3- and 5-year area of the curve, where it has been steepest. As long as the extremely short-term securities (i.e. 1-month) are still yielding near 0%, there will be a roll bonus, even if the magnitude and the exact position along the yield curve changes.
What happens at the short end of the curve (e.g., 1-month) has nothing to do with whether or not there will be a "roll yield" (aka, price change) benefit by buying say a 5-year Treasury and selling it after a year or two. What matters is the yield for the term to maturity when you sell the Treasury (e.g., 4-year yield one year later for a 5-year Treasury). The 4-year yield could rise enough to wipe out any price gain while the 1-month rate stayed the same. So it's not the overall shape of the yield curve that matters, but just the yield at the particular point for your particular security at the end of the holding period.

In this post, Bogleheads • View topic - Riding the yield curve, in action, ogd goes back and forth between making some very sensible statements, and slipping back into misleading present-tense statments:
ogd wrote: Being able to pick up roll yield does require the capability to sell an instrument for a price that reflects market yields at its remaining maturity.
Makes sense, except no need to call it "roll yield" when "price change" is precisely what it is.
ogd wrote: However, not all duration is rewarded the same and presently rolling five years to four makes more money than a 10 year Treasury ladder at steady state;
Maybe it "made" more money, but saying it "makes" more money implies that we can continue to make money using the strategy, and we just don't know that.
ogd wrote:CDs can still beat that but if we look back at the February yield curve and its reward of about 3.8% for rolling ten year Treasuries after one year, there's no safe fixed instrument that can beat that, period.
OK, we look back at the past, then for some reason slip into present tense again ("can beat that" instead of "beat that in the past"). A 10-year Treasury is not a "safe fixed instrument"; the reward was gained by taking term risk and by market timing (selling after one year). Jeez, if we knew we could earn 3.8% safely with this strategy, enough of us would do it that the price of the 10-year Treasury would be driven up until the opportunity disappeared.
ogd wrote:I think it's undeniable that a steep yield curve provides a lot of potential energy that can be harnessed, and it's not just a mind trick.
It absolutely is deniable. Using the phrase "potential energy that can be harnessed" sounds mystical and magical, instead of simply acknowledging that one is taking term risk, and making a bet that the yield curve will not move against them. I don't know if it's a mind trick, but it certainly obfuscates the fundamentals of risk and expected return in the bond world.
ogd wrote:The real ding against the curve riding story is that the yield curve steepness can't be expected to persist; at the very least, it's unreliable.
Yes! A point I've made over and over in these threads.
ogd wrote:Which is why I would not trade the "bird in the hand" of higher CD yields for projected rewards that might get diminished in short order, like they have been last year, and I do prefer CDs at the moment.
On this we agree, but I've preferred CDs for the last four years, because I've received an average of 1 percentage point of premium in yield relative to Treasuries of comparable maturity, and I have zero confidence in my ability to predict interest rates (which is the same as being able to predict the future shape of the yield curve).
ogd wrote:And then there's the put option, which although balanced partially by the ability to sell appreciated Treasuries to buy stocks in a crisis, is still a net positive.
I like the put option too, but I've debunked the notion that Treasuries will always appreciate in a crisis in several posts, most recently and thoroughly here: Bogleheads • View topic - Bond Fund vs CDs - which to use?
ogd wrote:My intention with this thread was not really to show that funds are preferable to CDs, like the original post of stlutz, but really to show that the effect is real in practice, and to make the argument that an uncertain "interest rate environment" also makes us quite a bit money and should not be treated as pure risk. The rewards are quite real.
Of course the effect can be real in practice; we know that from the bond math, but then there's that present tense again, and yes, it is pure risk. If it weren't, it would be arbitraged away.

In closing, I'd like to point out that "riding the yield curve" is not a result; it's an active bond management strategy. It falls under the general category of interest rate forecasting, and the subcategory of horizon analysis. See pages 472-473 of "Investments", Third Edition, by Bodie, Kane and Marcus. Here they summarize the key points that I've tried to make:
BKM wrote:If the yield curve is upward sloping and if it is projected that the curve will not shift during the investment horizon, then as bond maturities fall with the passage of time, their yields also will fall as they "ride" the yield curve toward the lower yields of shorter-term bonds. The decrease in yields will contribute to capital gains on the bonds.
<snip>
Of course you should always be skeptical of an apparent free lunch. Although extending maturity may increase the expected rate of return, that improvement may come at the price of additional risk. This, in fact, is the trade-off the portfolio manager is accepting if the yield curve is sloping upward because of a liquidity premium. The higher expected returns on the longer-term assets are no more than risk premiums.

The danger of riding the yield curve is that the yield curve will in fact rise over time. Indeed, according to the expectations hypothesis, an upward-sloping curve is evidence that market participants expect interest rates to be rising over time.
Hopefully this post has offered some clarifications to someone.

Kevin
Wiki ||.......|| Suggested format for Asking Portfolio Questions (edit original post)

User avatar
Topic Author
ogd
Posts: 4875
Joined: Thu Jun 14, 2012 11:43 pm

Re: Riding the yield curve, in action

Post by ogd » Sat Dec 20, 2014 5:40 pm

Kevin M wrote:
ogd wrote: Hmmm. While we are on the same page, I think you have this detail wrong. The expectation for the 5 year 5 years from now is about 2.54% (minus a risk premium), i.e. little no gain but no loss either.
I'd like to weigh in on this one, since I've spent significant time studying the term structure of interest rates theories since my earlier participation in this thread and the earlier related threads. I summarize much of my investigation here: Bogleheads • View topic - Yield Curve Investigations). In that thread, I address this topic directly here: Bogleheads • View topic - Yield Curve Investigations. Per standard academic approach, I use zero coupon rates in that post, but the numbers will be in the same ballpark for constant maturity Treasuries (the yield curve most commonly referred to). At the time the 5-year zero rate was about 1.7%, the 10-year rate was about 2.7%, and the 5-year forward 5-year rate was about 3.3%, so based on standard expectations theory, using a formula from a paper published by the Federal Reserve Board (FRB), alexfrey's numbers look correct to me.
Yes, I agree. I had this wrong back then and I've understood it better since. There was a long vacation inbetween for myself and this thread, so I never corrected it.

As for the rest of your double post Kevin: the tone is getting too contentious and it's hard for me to reply productively. The point about the returns being past and not present, consider it registered and something I agree with; that the investigation into the effects of a yield curve needs to carefully use past tense even when theoretical is something I don't. The point that it's wrong to investigate at any higher level than talking about detailed bond price effects, despite the fact that in bond discussions here we tend to look at yield changes at fixed maturity points and ignore the effects of declining maturities, that I strongly disagree with. I think the result of refusing to have a higher level story about curve steepness is people throwing their arms in the air and declaring that bond math is bogus, because look at how much better funds have done than the conventional wisdom said they would. This is happening in a concurrent thread as we speak. We should have something to say in response that can be understood without bond portfolio simulation spreadsheets. Something like "it's because the yield curve was steep", which in turn "is because the markets were prematurely worried", but "you can't really expect this to last". Or some sort of interpretation of a bag of numbers.

Finally, I never said that funds do anything more special than individual bonds. This thread was intended to be about practical confirmation that funds indeed do work like this.

These agreements and disagreements registered, I am done with this sub-thread.

User avatar
Electron
Posts: 1959
Joined: Sat Mar 10, 2007 8:46 pm

Re: Riding the yield curve, in action

Post by Electron » Sat Oct 10, 2015 1:33 pm

This thread and concept must have been an eye-opener for many investors. In looking at the portfolio of Vanguard Intermediate Term Treasury Fund VFIUX, the holdings all have a maturity ranging from 3 years to 10 years. It is easy to see how selling bonds several years before maturity has enhanced the NAV performance of the fund over the last several years. The proceeds would then be reinvested in bonds of longer maturity.

Since VFIUX is actively managed, it would be interesting to know how the portfolio managers alter their strategy based on the yield curve, and whether they attempt to manage for total return and not just income.

Inverted yield curves are not seen very often, but this raises an interesting question. How would bond funds such as VFIUX react to an inverted yield curve? One could speculate that some bonds might be held to maturity in that case.

Lastly, has the yield curve effect in recent years enhanced the return of the Total Bond Index funds? I believe the Bond Index holds bonds until one year from maturity. Bonds previously trading at a premium or higher premium would be declining in price as maturity approached. It's also not clear how much a bond index fund deviates from the index as a result of sampling or other methods.
Electron

User avatar
Doc
Posts: 9350
Joined: Sat Feb 24, 2007 1:10 pm
Location: Two left turns from Larry

Re: Riding the yield curve, in action

Post by Doc » Sat Oct 10, 2015 2:00 pm

Electron wrote:This thread and concept must have been an eye-opener for many investors. In looking at the portfolio of Vanguard Intermediate Term Treasury Fund VFIUX, the holdings all have a maturity ranging from 3 years to 10 years. It is easy to see how selling bonds several years before maturity has enhanced the NAV performance of the fund over the last several years. The proceeds would then be reinvested in bonds of longer maturity.

Since VFIUX is actively managed, it would be interesting to know how the portfolio managers alter their strategy based on the yield curve, and whether they attempt to manage for total return and not just income.
The fund's index bogey is the Barclays US 5-10 Yr Treasury Index. So if it is holding a 3-10 portfolio they are making some decisions based on the yield curve.

Unless a fund's specifically uses "income" or dividends in their objective I would assume that they manage for total return.
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.

mindbogle
Posts: 140
Joined: Sun Feb 10, 2013 11:28 am

Re: Riding the yield curve, in action

Post by mindbogle » Sat Oct 10, 2015 2:13 pm

Electron wrote:This thread and concept must have been an eye-opener for many investors. In looking at the portfolio of Vanguard Intermediate Term Treasury Fund VFIUX, the holdings all have a maturity ranging from 3 years to 10 years. It is easy to see how selling bonds several years before maturity has enhanced the NAV performance of the fund over the last several years. The proceeds would then be reinvested in bonds of longer maturity.
You'll get a roll return in the presence of a time-constant upwardly sloping yield curve regardless of whether the bonds are held to maturity or not - just have to "roll" proceeds to maintain average maturity of the portfolio. It may help to limit the portfolio maturity range to the steepest section of the curve, but letting bonds mature does not in itself eliminate the "enhancement".

One way to visualize this - take a portfolio consisting of a 0-10 year ladder. Consider two ways of managing this portfolio:

1) Each bond is held to maturity. When it matures, a new 10-yr bond is purchased to maintain average maturity.
2) You have 10 1-yr rolling sub-portfolios: 0-1, 1-2, 2-3,...9-10. When the 1 year bond matures, you buy a new one year bond. When the 2-yr bond becomes a 1-yr bond, you sell and buy a new 2-yr bond..... when the 10-yr bond becomes a 9-yr bond, you sell and buy a new 10-yr bond.

Its obvious that the second strategy would benefit from a time-constant upward sloping yield curve. But after a little thought, it should become clear (at least to me!) that the two ways of managing this portfolio are equivalent in terms of composition and average maturity versus time. Therefore they will both benefit from the "roll return".

MB

User avatar
Topic Author
ogd
Posts: 4875
Joined: Thu Jun 14, 2012 11:43 pm

Re: Riding the yield curve, in action

Post by ogd » Sat Oct 10, 2015 6:24 pm

Electron wrote:Since VFIUX is actively managed, it would be interesting to know how the portfolio managers alter their strategy based on the yield curve, and whether they attempt to manage for total return and not just income.

Inverted yield curves are not seen very often, but this raises an interesting question. How would bond funds such as VFIUX react to an inverted yield curve? One could speculate that some bonds might be held to maturity in that case.
I would hope they manage on total return, and I would hope that they don't do anything too out of the ordinary.

Selling bonds before maturity isn't really the key aspect; like mindbogle says above, it's not even necessary, to profit from the yield curve -- the majority of that is because a fund replenishes duration, so it will beat a declining duration instrument (and its own SEC yield) if duration is rewarded. Selecting the most rewarding part of the curve is a relatively minor aspect, though I can't help feel good about that when the yields below three years are miserable and I as a small investor can get 1% in a savings account, which the market can't.

The way I'd formulate it is, "does the fund move its maturity range to favorable places". E.g. when it comes to the inverted yield curve, that doesn't tend to last too long so merely not turning over bonds would be too slow to move to a shorter range -- you'd want to actively do it. But now you have to wonder, is it really that obvious that you want to be short? We're used to thinking in these terms with our yield curve and threats of Fed, but last time we saw inversion, 2007, the long end would have been the fantastic idea, not the short end. An even more egregious case is the early 1980s...
Electron wrote:Lastly, has the yield curve effect in recent years enhanced the return of the Total Bond Index funds? I believe the Bond Index holds bonds until one year from maturity. Bonds previously trading at a premium or higher premium would be declining in price as maturity approached. It's also not clear how much a bond index fund deviates from the index as a result of sampling or other methods.
Yes, it did. Total Bond doesn't hold bonds to maturity, as can be seen for its 72% turnover and its maturity distribution (which would be close to linear if it did). Also, whether a bond is trading at a premium or discount is rather immaterial except for taxes -- if it fits your desired maturity distribution you keep it, otherwise you don't, it's just as good as market bonds. I would hope that Total Bond doesn't make market calls, and I don't consider the calls of VFIUX a "feature" -- I like it because the fees are low and it fits well in my portfolio.

User avatar
Kevin M
Posts: 11287
Joined: Mon Jun 29, 2009 3:24 pm
Contact:

Re: Riding the yield curve, in action

Post by Kevin M » Sat Oct 10, 2015 8:01 pm

Electron wrote:Since VFIUX is actively managed, it would be interesting to know how the portfolio managers alter their strategy based on the yield curve, and whether they attempt to manage for total return and not just income.
They definitely manage the portfolio around the yield curve. In one of the annual or semi-annual reports I read, they used a phrase something like "yield curve management" in reference to adding to (or subtracting from) the total return for the period under discussion. Also, I posted somewhere the change in term to maturity of their holdings between two annual or semi-annual reports--there was a significant change in the dollar volume at different terms to maturities.

At least one of my investing textbooks describes riding the yield curve as an active management strategy, so in this sense VFIUX is employing this strategy, whereas TBM is not. That's not to say that TBM or any other fund that holds a wide range of maturities does not benefit from a positively-sloped yield curve.

Kevin
Wiki ||.......|| Suggested format for Asking Portfolio Questions (edit original post)

User avatar
Electron
Posts: 1959
Joined: Sat Mar 10, 2007 8:46 pm

Re: Riding the yield curve, in action

Post by Electron » Sun Oct 11, 2015 3:09 pm

Thanks for the replies MB, Doc, ogd, and Kevin.

In reviewing this thread, it appears that bullet portfolios achieve the higher return with income and capital gains. That suggests that the ladder portfolios achieve the higher return with additional income. That makes sense if replenishing duration means replacing the bond being sold with a longer term bond that also provides a higher income.

When I mentioned NAV performance, I was thinking about VFIUX or any bullet portfolio operating for many years with a static and upward sloping yield curve. In that hypothetical environment, I believe the portfolio would generate steady income along with continuous capital gains and increasing NAV.

In regards to VFIUX, the prospectus states the following: "The Fund seeks to provide a moderate and sustainable level of current income. The Fund invests at least 80% of its assets in U.S. Treasury securities, which include bills, bonds, and notes issued by the U.S. Treasury. The Fund is expected to maintain a dollar-weighted average maturity of 5 to 10 years." Even though the Barclays 5-10 Year Treasury Index is shown in various reports, they make no mention of trying to match the performance of that index. The fund appears to have generally underperformed the index.

The latest Semiannual Report does mention the yield curve. "With the volatility in the market, we had some success in managing the yield curve exposure of the funds. The shifts in expectations about when the Fed would raise interest rates gave us the chance to position the funds tactically to benefit from the compression and widening of yields."

The Total Bond Index funds appear to have some notable differences. The Barclays Fact Sheet on the Aggregate Bond Index does indicate that all holdings have a maturity of one year or longer. That would be one factor in portfolio turnover. However, these funds must track the Total Bond Market.

All new Treasury, Government, and Corporate issues added to the index regardless of maturity must be added to the fund possibly dependent on the sampling algorithm. If cash on hand is not sufficient other holdings may need to be sold to effectively rebalance the fund. Large Treasury auctions include different maturities and the amounts vary over time. The number of long term Treasuries added to the index might be reduced at times. As a result, bonds sold one year before maturity really need to be reallocated across the entire maturity range. Unlike the managed bond fund, you can't necessarily buy the longest maturity or highest coupon.
Electron

User avatar
Doc
Posts: 9350
Joined: Sat Feb 24, 2007 1:10 pm
Location: Two left turns from Larry

Re: Riding the yield curve, in action

Post by Doc » Sun Oct 11, 2015 3:38 pm

Electron wrote:All new Treasury, Government, and Corporate issues added to the index regardless of maturity must be added to the fund possibly dependent on the sampling algorithm. If cash on hand is not sufficient other holdings may need to be sold to effectively rebalance the fund. Large Treasury auctions include different maturities and the amounts vary over time. The number of long term Treasuries added to the index might be reduced at times. As a result, bonds sold one year before maturity really need to be reallocated across the entire maturity range. Unlike the managed bond fund, you can't necessarily buy the longest maturity or highest coupon.
Maybe. Auctions are in general replacing existing issues which are maturing. The fund held these same maturing issues a year ago so except for the time lag the fund has the money available. The fund also has the cash from coupons. So the fund may not be buying the longest issue but it is maintaining its portfolio to resemble the total bond market it tries to index. You chose to address a (passively) active fund in your discussion but there are other index funds out there that limit themselves to a fixed maturity segment of the market. iShares 3-7 Year Treasury Bond ETF IEI is an example.
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.

User avatar
Electron
Posts: 1959
Joined: Sat Mar 10, 2007 8:46 pm

Re: Riding the yield curve, in action

Post by Electron » Sun Oct 11, 2015 5:57 pm

Doc wrote:Auctions are in general replacing existing issues which are maturing.
In recent years, outstanding Treasury debt has increased significantly.

The duration of the Aggregate Bond Index was 3.7 in 2009. The duration is currently 5.7 which is quite a large increase. The reason is apparently a large increase in the number of outstanding long term Treasury bonds. Corporations have also issued more long term bonds.

http://www.thestreet.com/story/12024489 ... funds.html
Electron

User avatar
Doc
Posts: 9350
Joined: Sat Feb 24, 2007 1:10 pm
Location: Two left turns from Larry

Re: Riding the yield curve, in action

Post by Doc » Mon Oct 12, 2015 9:00 am

From Electron's link:
In recent years, the Treasury decided to issue more long bonds because interest rates were low. By selling a 30-year bond, Washington could lock in puny rates for decades. As a result, the average maturity of federal debt increased from four years in 2008 to 5.3 years in 2012.
The increase in duration and Treasury component of TBM plus the inclusion of MBS and the "inability" to take advantage of the riding the yield curve tactic are all very good reasons not to use a TBM fund as you sole fixed income asset.

Simplicity is not a one sided decision.
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.

User avatar
magellan
Posts: 3472
Joined: Fri Mar 09, 2007 4:12 pm

Re: Riding the yield curve, in action

Post by magellan » Tue Oct 13, 2015 7:54 am

Johno wrote:Buying a 2.4% CD every year you eventually get a steady state of approx 2.5yr avg life yielding 2.4%, way above the 2.5 yr CD rate let alone treasury rate (~1.5 and .8 respectively now). That's the same effect as 'roll yield', but realized a different way. It's not as if it simply doesn't exist in any form with a CD, just like it's wrong to say the benefit of falling rates doesn't exist in any form with a CD.
I believe this also means that in a constant yield curve environment, a rolling treasury bond ladder that has the same duration as a treasury fund will have the same total return, despite always holding its treasuries to maturity. As Kevin said, in one case the return comes just from coupons while in the other it comes from a combination of coupons and capital gains.

As I understand it, the essential takeaway is that capital gains earned from selling premium bonds are not a unique source of return. These sales are just a way to immediately monetize guaranteed coupon payments that will be made in the future.

Does anyone disagree with this?

User avatar
Doc
Posts: 9350
Joined: Sat Feb 24, 2007 1:10 pm
Location: Two left turns from Larry

Re: Riding the yield curve, in action

Post by Doc » Tue Oct 13, 2015 8:33 am

magellan wrote:As I understand it, the essential takeaway is that capital gains earned from selling premium bonds are not a unique source of return. These sales are just a way to immediately monetize guaranteed coupon payments that will be made in the future.

Does anyone disagree with this?
Assuming we are addressing market premium which I think we are, there is a difference in tax treatment but this is a second order effect and is non existent in a tax-advantaged account.
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.

User avatar
Electron
Posts: 1959
Joined: Sat Mar 10, 2007 8:46 pm

Re: Riding the yield curve, in action

Post by Electron » Wed Oct 14, 2015 12:37 pm

Here is some data from the latest semiannual report for the Vanguard Intermediate Term Treasury fund. The portfolio changed quite a bit compared with the previous report. Note the higher percentage in the 5-7 year maturity range.

Code: Select all

Date          1-31-15  7-31-15

< 1 year       -4.5%    -4.4%
1-3 years       0.1%     0.3%
3-5 years      54.5%    48.7%
5-7 years      26.1%    33.7%
7-10 years     23.8%    21.7%

SEC Yield      1.36%    1.63% 
YTM            1.30%    1.70%
Bonds          81       91
Duration       5.3      5.3
The Factsheet for the U.S. Aggregate Bond Index is quite interesting to review. It is available at the link below in the section at the top. The document for the Float Adjusted Index is in the section marked Alternative Weight.

https://index.barcap.com/Home/Guides_and_Factsheets

The Aggregate Bond Index is rebalanced once per month to reflect issues entering or dropping out of the index. Even though investors consider the Total Bond Index to be a passive investment, the actual index may change every month.
Electron

User avatar
Electron
Posts: 1959
Joined: Sat Mar 10, 2007 8:46 pm

Re: Riding the yield curve, in action

Post by Electron » Tue Oct 20, 2015 2:54 pm

mindbogle wrote:You'll get a roll return in the presence of a time-constant upwardly sloping yield curve regardless of whether the bonds are held to maturity or not - just have to "roll" proceeds to maintain average maturity of the portfolio. It may help to limit the portfolio maturity range to the steepest section of the curve, but letting bonds mature does not in itself eliminate the "enhancement".
I think I now understand how a positive yield curve increases bond fund returns even when holding bonds to maturity. Here is a simple way to explain it that all bond investors should be able to understand. If this thinking is incorrect please let me know.

Bond Ladder 1 is a conventional bond ladder with maturities from 1 year to 10 years. Assume that the yield curve is upward sloping and remains unchanged for a long period of time. Maturing bonds are replaced every year with a new 10 year bond. After ten years all bonds in the ladder would be paying the same dollar amount which is the 10 year yield. This bond ladder is paying a relatively high yield at this point. Bond prices would typically increase to a premium for a period of time but would then return to par at maturity.

Bond Ladder 2 is now put together with bonds of each maturity purchased at current market prices. This ladder would initially generate substantially less income than Bond Ladder 1. However, the income would rise every year as maturing bonds are replaced with new 10 year bonds. The income would continue to rise until all bonds are paying the same dollar amount which is equivalent to the 10 year yield.

In the real world we won't have a static positive yield curve, but the principle described would still be applicable whenever the yield curve is positive.
Electron

User avatar
patrick013
Posts: 2823
Joined: Mon Jul 13, 2015 7:49 pm

Re: Riding the yield curve, in action

Post by patrick013 » Tue Oct 20, 2015 3:13 pm

Electron wrote:
In the real world we won't have a static positive yield curve, but the principle described would still be applicable whenever the yield curve is positive.
Here's some info about spreads for the yield curve assuming no recession,
no quantitative easing, and an adequate supply of bonds for sale.
These are historical averages with a normal yield curve.

10 yr TRSY - 2% over fed funds rate
30 yr TRSY - 3% over fed funds rate
10 yr Corp - 3% over fed funds rate
Prime Rate - 3% over fed funds rate

Interesting that intermediate bonds and bond funds do so well
as they are at the highest slope of the yield curve when the curve
is not a normal yield curve and somewhat flat.
age in bonds, buy-and-hold, 10 year business cycle

User avatar
Kevin M
Posts: 11287
Joined: Mon Jun 29, 2009 3:24 pm
Contact:

Re: Riding the yield curve, in action

Post by Kevin M » Tue Oct 20, 2015 7:47 pm

Electron wrote: Bond Ladder 2 is now put together with bonds of each maturity purchased at current market prices. This ladder would initially generate substantially less income than Bond Ladder 1.
If Bond Ladder 2 is just Bond Ladder 1 purchased from the original owner, the dollar income will be exactly the same. And the 1-year return of each ladder is exactly the same, since it's the same ladder, and 1-year return is computed the same. The coupon payments are the same (income return), and the price changes are the same (capital return).

I just stick with something like your BL1 example to try and understand it intuitively. If you buy a 10-year bond with a YTM of 2%, you're going to earn an average annual return of about 2% over the 10-year holding period (to maturity), with some uncertainty due to reinvestment rates. The return will be higher than average in the early years, and lower than average in the latter years (at least with current yield curve), but the average will be about 2%.

Now pump a new 10-year bond into the ladder very year for 10 years (again, we're assuming static yield curve). Every bond will continue to earn its average 10-year return of 2% for 10 years, therefore the ladder earns an annual return of about 2%.

Here's another viewpoint. Assume a 1-10 year ladder of par bonds is purchased, so price of each bond is 100 and coupon rate = YTM when purchased. With the current yield curve, every bond except the 1-year bond will earn a capital return from price appreciation, in addition to it's coupon. So each bond will earn it's initial YTM = coupon rate in one year, plus the capital appreciation. Therefore, the ladder annual return is higher than the ladder average YTM.

Kevin
Wiki ||.......|| Suggested format for Asking Portfolio Questions (edit original post)

User avatar
Electron
Posts: 1959
Joined: Sat Mar 10, 2007 8:46 pm

Re: Riding the yield curve, in action

Post by Electron » Wed Oct 21, 2015 1:28 pm

Kevin M wrote:If Bond Ladder 2 is just Bond Ladder 1 purchased from the original owner, the dollar income will be exactly the same. And the 1-year return of each ladder is exactly the same, since it's the same ladder, and 1-year return is computed the same. The coupon payments are the same (income return), and the price changes are the same (capital return).
If you put together a new ladder identical to Bond Ladder 1, the dollar income from the bonds may be the same but your return is less since you must pay a premium for most of the bonds. You might also be amortizing premium which effectively reduces the dollar income. Your yield for each bond under the 10 year maturity is less than it is for the holder of Ladder 1 relative to purchase price. However, if you hold the new ladder for 10 years the two ladders would become equivalent on a return basis for each holder.

It seems that holding a new ladder in this environment becomes an investment in itself with the return increasing until 10 years is reached. At that point each bond in the ladder pays you the ten year yield. This appears to be another way to look at riding the yield curve. The key seems to be that each bond has now locked in the 10 year yield for the holder. The dollar income rises for ten years. I'm looking at each bond relative to purchase price rather than what Excel shows for any arbitrary date.
Kevin M wrote:Here's another viewpoint. Assume a 1-10 year ladder of par bonds is purchased, so price of each bond is 100 and coupon rate = YTM when purchased. With the current yield curve, every bond except the 1-year bond will earn a capital return from price appreciation, in addition to it's coupon. So each bond will earn it's initial YTM = coupon rate in one year, plus the capital appreciation. Therefore, the ladder annual return is higher than the ladder average YTM.
I agree that the annual return is higher as a result of the capital appreciation but you would have to sell at that point to capture it. If you hold to maturity the premium disappears. However, my ladder examples show that income can rise until all bonds have locked in the ten year yield.
Electron

User avatar
Kevin M
Posts: 11287
Joined: Mon Jun 29, 2009 3:24 pm
Contact:

Re: Riding the yield curve, in action

Post by Kevin M » Wed Oct 21, 2015 3:44 pm

Electron wrote:
Kevin M wrote:If Bond Ladder 2 is just Bond Ladder 1 purchased from the original owner, the dollar income will be exactly the same. And the 1-year return of each ladder is exactly the same, since it's the same ladder, and 1-year return is computed the same. The coupon payments are the same (income return), and the price changes are the same (capital return).
If you put together a new ladder identical to Bond Ladder 1, the dollar income from the bonds may be the same but your return is less since you must pay a premium for most of the bonds.
First of all, you said:
Electron wrote: Bond Ladder 2 is now put together with bonds of each maturity purchased at current market prices. This ladder would initially generate substantially less income than Bond Ladder 1.
"dollar income from the bonds" = "income"; i.e., you just said "income", not "return".

Second of all, and more importantly, annual return also is the same! I know this is a head scratcher, but annual return is measured from time 0 to time + 1 year. Annual return for ladder 1 is not measured based on purchase price, but based on the coupons and bond prices as of time 0, whenever that is, which is exactly the same for ladders 1 and 2, since they are the same at time 0 (and all subsequent times).

This is a common source of confusion in calculating returns and yields; if interest rates have gone down, and bond prices up, people like to think of their return and yield as relative to purchase price, but that is not the way annual return and yield are computed. Whatever return the owner has already earned from bonds rolling down the yield curve is in the past, and is not relevant for measuring return going forward, and the price paid is irrelevant for computing YTM or current yield.

The value of each bond at t0 and t0 + 1 year is the same in ladders 1 and 2, since they are the same ladder! Therefore, each bond in the ladder (1 and 2, since they're the same) will have the same capital return from price appreciation. The coupon of each bond is the same in ladders 1 and 2 for each maturity, therefore they earn the same annual income return. Total return = capital return + income return, therefore total return is the same for each ladder.
Electron wrote:You might also be amortizing premium which effectively reduces the dollar income.
This is a purely conceptual exercise, since the assumption of static yield curve is unrealistic, so let's not complicate it with taxes before we get the basic concept down.
Your yield for each bond under the 10 year maturity is less than it is for the holder of Ladder 1 relative to purchase price.
Yield (or annual return) is not calculated based on purchase price unless we are calculating it on the date of purchase. You get yield to maturity from a yield curve or from a quote. Neither has anything to do with purchase price. Whoever offers to buy your bond at a specified price/YTM has no idea what you paid for it.
However, if you hold the new ladder for 10 years the two ladders would become equivalent on a return basis for each holder.
The annual return of each ladder is exactly the same, regardless of when the bonds were purchased.
It seems that holding a new ladder in this environment becomes an investment in itself with the return increasing until 10 years is reached. At that point each bond in the ladder pays you the ten year yield. This appears to be another way to look at riding the yield curve. The key seems to be that each bond has now locked in the 10 year yield for the holder.
This a good way to help understand how annual return can be higher than average YTM, but it is not necessary for the ladder to generate this higher return. This can be seen if you actually build a spreadsheet model, and instead of assuming you're getting the 10-year coupon for each maturity (currently 2.08% for a 10-year par bond), set the coupon to the YTM for each maturity. So the 5-year bond with YTM of 1.40% also has coupon yield of 1.40%.

In my model, making this change lowers the annual return from 2.08% to 2.05%, so much, much less difference than the uncertainty of the model (i.e., assuming a static yield curve, using a par-bond yield curve for non-par bonds, etc.), and possibly just due to rounding errors. The key is that although the coupon payments are lower on average with this model, the capital return is higher on average. In this model (coupon = YTM for each maturity), it is a tautology that the average annual coupon payment is exactly the same as average YTM (1.37%), but the average capital return is 0.68%, getting us to the 2.05% total return.

Switching back to the L1 model, in which each bond has the 10-year coupon of 2.08%, the average annual income return is ... wait for it ... 2.08%, and the average capital return is 0%. The average annual income return is 2.08% because the annual coupon payment for each bond is 2.08%. The capital return for each bond varies from -1.81% to +0.82%, but the average must be 0% for the ladder to earn a total return of 2.08%, and indeed it is.
The dollar income rises for ten years.
No, the dollar income from a populated ladder remains exactly the same each year. The dollar income is just the coupon payments, so regardless of how you get to the 10-year ladder, using same assumptions about coupon and YTM for each ladder, the dollar income is exactly the same. There are not two ladders, there is only one ladder with different assumptions about how you built the ladder.
I'm looking at each bond relative to purchase price rather than what Excel shows for any arbitrary date.
But this is not the way annual return is computed. The dates aren't arbitrary. The dates represent the start date and end date for the period for which you are computing return. What happened in the past is irrelevant.
I agree that the annual return is higher as a result of the capital appreciation but you would have to sell at that point to capture it.

That may seem intuitive, but it is not the case. That's like saying that the value of your stock fund (or bond fund) based on market price is an illusion, and that you must sell the fund to capture the market value. Yet I bet you carry the market value of your funds on your books, not the purchase values.

You can capture the premium either by selling, or just by holding the ladder and continuing to roll the maturing bonds to new 10-year bonds.

Just envision never selling, and just rolling the ladder for 100 years, or forever. Are your calculated annual returns in each of those years before you sell not real?
If you hold to maturity the premium disappears.

True, any premium (or discount) for a particular maturity disappears at maturity, but the value at maturity is the same as the value of the newly purchased 10-year par bond (100), and each maturing bond at priced at 100 is rolled into another new 10-year par bond priced at 100. In a rolling ladder with static yield curve, the capital appreciation for each bond as it rolls down the yield curve from year 0 to year 0 + 1 is exactly the same every year.
However, my ladder examples show that income can rise until all bonds have locked in the ten year yield.
This statement makes no sense to me. Really, the best way to understand this is to build a spreadsheet model, break out income return and capital return for each year, and try different assumptions about coupon rates (e.g., all coupon rates = 2.08%, or each coupon rate = YTM for its maturity).

In the way you're thinking about it, all bonds have locked in the 10-year coupon, but if you model it, you'll see that this is not required. Also in the way you're thinking about it, and the way I think about it for easy intuitive understanding, each bond must earn about its original 10-year YTM if held to maturity, and since all bonds are held to maturity, the ladder must earn about the YTM of the 10-year bond.

But again, if you model it as I suggest, it's easier to see that the coupon and YTM for each bond work together in such a way that the average annual return comes out to about the YTM of the 10-year bond, as long as you don't jack the coupon rates too far above par (if you jack up coupon to say 4.08% for all bonds, the average annual return increases to 2.45% in my model).

Kevin
Wiki ||.......|| Suggested format for Asking Portfolio Questions (edit original post)

User avatar
Electron
Posts: 1959
Joined: Sat Mar 10, 2007 8:46 pm

Re: Riding the yield curve, in action

Post by Electron » Thu Oct 22, 2015 6:07 pm

Kevin M wrote:No, the dollar income from a populated ladder remains exactly the same each year.
Kevin - Thanks for the detailed commentary which will take some time to review.

Doesn't the dollar income in fact increase for a time after creating a new ladder when the yield curve is positive? Assume that the new ladder is created with ten $1K bonds that have maturities from 1 year through 10 years and that the yield curve remains unchanged. Each bond will be purchased at par for this example. It would seem that the dollar income would rise until all bonds are paying the 10 year coupon. All the lower coupon bonds are eventually replaced with the 10 year coupon as each new 10 year bond rides down the ladder and yield curve. The ten yields could span a range such as 0.2% to 2% or anything you choose.

A retiree investing for income would be happy to have income increase which would not occur with a flat yield curve.

I realize that the situation changes after 10 years with the dollar income no longer increasing. The next question is whether the rise in income is an artifact of riding the yield curve or some other effect. It looks as though a new ladder and established ladder have somewhat different characteristics in this example.

The rise in income does make sense in the following regard: Initially we bought a wide range of coupons. We then bought only 10 year bonds over time so it would follow that the income should increase.

As a reminder to other readers these examples are hypothetical and the yield curve would not remain unchanged.
Electron

User avatar
Topic Author
ogd
Posts: 4875
Joined: Thu Jun 14, 2012 11:43 pm

Re: Riding the yield curve, in action

Post by ogd » Thu Oct 22, 2015 6:28 pm

Electron: all of the arguments above work just as well with zero coupon bonds. They are independent of coupons and income, except for the slight dependency of yield on coupon due to reinvestment consideration. The return of a ladder under the [unrealistic, as you note] static yield curve assumption ends up being the yield on its highest rung. I have a quick proof of this that I can supply via PM if you wish.

I don't want to make this thread about income, it's all about return as far as I'm concerned. Speaking of, will need to post an update soon now that we have a good couple of years of data.

User avatar
Kevin M
Posts: 11287
Joined: Mon Jun 29, 2009 3:24 pm
Contact:

Re: Riding the yield curve, in action

Post by Kevin M » Thu Oct 22, 2015 11:05 pm

Electron wrote: Doesn't the dollar income in fact increase for a time after creating a new ladder when the yield curve is positive? Assume that the new ladder is created with ten $1K bonds that have maturities from 1 year through 10 years and that the yield curve remains unchanged. Each bond will be purchased at par for this example. It would seem that the dollar income would rise until all bonds are paying the 10 year coupon. All the lower coupon bonds are eventually replaced with the 10 year coupon as each new 10 year bond rides down the ladder and yield curve. The ten yields could span a range such as 0.2% to 2% or anything you choose.
OK, for this scenario, yes. I was thinking more of the scenario in which all bonds have the same coupon rate, which would be the case for your ladder 1 scenario, and of course in that scenario, ladder income would increase as you add each additional bond to the ladder as you build it up.

But as ogd says, this isn't really the key point here, since it's really a distraction, and isn't relevant to the conceptual, steady state model. In the steady state, you can use any coupon rate from 0% to the par yield of the 10-year bond (currently about 2%) without changing the results much if at all. Like I said, jacking the coupon rates much above that increases the annual return somewhat--at least that's what my model shows.
A retiree investing for income would be happy to have income increase which would not occur with a flat yield curve.
I am a retiree, and although having income (cash flow) makes managing income/expense easier, I really don't pay much attention to it, since the important measure is total return. I'm still not taking RMDs, so whether the return in my IRA comes from interest/dividends or capital appreciation is absolutely irrelevant. I also reinvest interest in my taxable CDs, so again, income is really irrelevant in terms of cash flow. If my bonds and stocks don't generate enough cash flow to pay for residual expenses, I just sell shares.
The next question is whether the rise in income is an artifact of riding the yield curve or some other effect. It looks as though a new ladder and established ladder have somewhat different characteristics in this example.
I think you'll drive yourself crazy thinking like this. For me, my spreadsheet model is what turned the light bulb on, and playing around with different coupon rates made it clear that coupon rate doesn't matter much. From a total return perspective, there is no difference between a new ladder and an established ladder--they are the same ladder!

I can provide a link to a Google Sheets spreadsheet if you or anyone else wants to see and play with my model.

If ogd wants to try and keep this thread focused on the "in action" part, you can either start a new thread, or tap into one of the other threads in which we were discussing the theory of this. Feel free to use my Yield Curve Investigations thread if you'd like, since it is meant to host a wide-ranging discussion of yield curve topics, more focused on the theoretical aspects. I don't think we got much into the "riding the yield curve" topic there (I find one reply in which I mentioned it), but glad to bring that into it.

Kevin
Wiki ||.......|| Suggested format for Asking Portfolio Questions (edit original post)

User avatar
Topic Author
ogd
Posts: 4875
Joined: Thu Jun 14, 2012 11:43 pm

Re: Riding the yield curve, in action

Post by ogd » Wed Oct 28, 2015 1:40 am

I think we and Electron clarified this in a PM discussion; to summarize, the problem with a high coupon ladder is that the maturing face values are insufficient to buy premium bonds at the top, so one has to use part of the income received each year, which exactly accounts for the difference.

The equivalent for the "rolling" strategy is that each year you get higher coupons, but the capital appreciation is lower or negative.

If coupons are very high (like Kevin says) you also have to account for the fact that these bonds have slightly lower YtM, as the market (or bond math, really) prices in the higher returns from earlier reinvestment. Otherwise you end up with higher returns, which is not the case in practice.

As far as I'm concerned, the only difference between high and low coupon bonds has to do with taxes, but even that is priced in at least partially I'm sure.

User avatar
Doc
Posts: 9350
Joined: Sat Feb 24, 2007 1:10 pm
Location: Two left turns from Larry

Re: Riding the yield curve, in action

Post by Doc » Wed Oct 28, 2015 9:03 am

ogd wrote:As far as I'm concerned, the only difference between high and low coupon bonds has to do with taxes, but even that is priced in at least partially I'm sure.
As I understand the tax code market premium has to be amortized so there is no difference. With market discount (not OID) you may have a choice of annual accretion or deferred until the bond is sold/matures but it is still ordinary income. So the difference is small. (The rules prior to May 1 1993 were different.)

As an aside I don't belive a fund has the choice of deferring the tax on the market discount but must accrete it probably daily.
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.

User avatar
Electron
Posts: 1959
Joined: Sat Mar 10, 2007 8:46 pm

Re: Riding the yield curve, in action

Post by Electron » Sun May 15, 2016 4:47 pm

I noticed that the Vanguard Intermediate and Long Term Treasury funds have both paid capital gains distributions in recent years.

https://personal.vanguard.com/us/funds/ ... =INT#tab=4
https://personal.vanguard.com/us/funds/ ... =INT#tab=4

I'm curious if anyone has thought about the percentage of capital gains distributions related to the yield curve versus other factors. Both funds appear to have bullet type portfolios. It's surprising to many that longer term bonds continue to perform very well. Negative short term interest rates overseas and foreign buying could be one factor.

Here is a summary of income and capital gains distributions for calendar year 2015.

VUSUX - 2015 - Vanguard Long-Term Treasury Fund Admiral Shares
$0.36511 Income
$0.32020 Capital Gains

VFIUX - 2015 - Vanguard Intermediate-Term Treasury Fund Admiral Shares
$0.20035 Income
$0.09270 Capital Gains
Electron

User avatar
Topic Author
ogd
Posts: 4875
Joined: Thu Jun 14, 2012 11:43 pm

Re: Riding the yield curve, in action

Post by ogd » Mon May 16, 2016 5:07 pm

Electron wrote:I'm curious if anyone has thought about the percentage of capital gains distributions related to the yield curve versus other factors. Both funds appear to have bullet type portfolios.
Yes, although I wouldn't separate out "capital gains distributions" because it's an artifact of how the fund turns over bonds, a big factor in which is the tax treatment and tax-related regulations.

What I'd talk about instead is "return in excess of starting yield", which in my mind comes from the difference between a bond's yield at time T and yield at the time T+dt, taking into account that the bond has aged meanwhile (by dt)

So if at time T a bond of maturity M yielded X1% and a bond of maturity M-dt yielded X2%, then after dt a bond of maturity M-dt yielded X3%, I would say that:

* Return attributable to changes in the yield curve is "duration times (X2 - X3)%". Sanity check: if the yield curve hadn't moved at all, this return would be zero.
* Return attributable to yield curve shape is "duration times (X1 - X2)%". Sanity check: if the yield curve started flat, this return would be zero.

This is not an exact science because there is no "representative bond" for a fund, and it readjusts duration all the time without waiting for it to decrease 1 year. But it should be in the ballpark.

For example, for a 5 year Treasury in 2015 (dt = 1 year), and assuming the 4 year yields are the average of the easily available 5 year and 3 year yields:
* X1 is 1.61%, X2 is 1.34% , X3 is 1.535%
* Yield curve return is approximately +1.35%
* Yield change return is approximately -0.97% (Treasury yields went up slightly despite dropping to 1.2% - 1.3% twice during the year)

As for how much of that excess return is distributed as capital gains, it's hard to tell; remember that "as much as possible" is the best outcome for the fund's taxable shareholders, because income is worse than distributed capital gains. I'm sure the funds took advantage of those dips to 1.2%, just like I did personally (I moved to CDs, but would have been reasonably willing to go back at times if it was easy or I had new money to invest). It's instructive to compare taxable bond funds with tax-exempt funds; the latter seem to hang onto bond premiums as much as possible because it's the best thing to do for their shareholders (distributed CG are worse than tax-exempt dividends).

User avatar
patrick013
Posts: 2823
Joined: Mon Jul 13, 2015 7:49 pm

Re: Riding the yield curve, in action

Post by patrick013 » Mon May 16, 2016 6:05 pm

ogd wrote:
Electron wrote:I'm curious if anyone has thought about the percentage of capital gains distributions related to the yield curve versus other factors. Both funds appear to have bullet type portfolios.
So if at time T a bond of maturity M yielded X1% and a bond of maturity M-dt yielded X2%, then after dt a bond of maturity M-dt yielded X3%, I would say that:

* Return attributable to changes in the yield curve is "duration times (X2 - X3)%". Sanity check: if the yield curve hadn't moved at all, this return would be zero.
* Return attributable to yield curve shape is "duration times (X1 - X2)%". Sanity check: if the yield curve started flat, this return would be zero.
Another factor:

The Fidelity Interm TRSY fund's 10 year yield is higher than the
VG Interm TRSY fund's 10 year yield.

The Fidelity fund holds the bonds from 10 to 5 years, the VG fund
holds the same bonds from 10 to 3 years.

So, when the fund takes the gain on the shorter term bond in the fund
and trades up to the higher yielding long bond (10 year) does have an
effect on total return, cap gain reinvested and interest reinvested.
In this observation only about .6 % but could be larger if rates were
moving at greater amounts up or down.
age in bonds, buy-and-hold, 10 year business cycle

User avatar
Topic Author
ogd
Posts: 4875
Joined: Thu Jun 14, 2012 11:43 pm

Re: Riding the yield curve, in action

Post by ogd » Mon May 16, 2016 6:20 pm

patrick013 wrote: The Fidelity fund holds the bonds from 10 to 5 years, the VG fund
holds the same bonds from 10 to 3 years.
Yes -- however, I expect this difference to be captured in the duration. It's 1.3 years or so longer in the Fidelity fund, so it'll have higher returns in times like the recent past. In my equation, the duration and starting yield would be slightly different (both larger for Fidelity), while the dt would keep the same meaning of "a short interval" -- it's not the 7 years until replacement.

I actually don't expect the faster replacement to make a difference not captured in those two numbers. If the yield curve happens to be steeper where the Fidelity fund is centered, then yes, but if it's linear-ish then the effect will be similar.

User avatar
patrick013
Posts: 2823
Joined: Mon Jul 13, 2015 7:49 pm

Re: Riding the yield curve, in action

Post by patrick013 » Mon May 16, 2016 6:39 pm

It's meant as an addendum to your post, something the index fund does.
I think there are times when selling at 3 years could be better than
selling at 5 years and vice-versa cap gain wise. Also, trading up to
the 10 year bond could be better at the 3 year or the 5 year point
depending on what's in the yield curve at a later date. So what the
index fund normally does is going to effect the cap gains/interest/total return
whether it does it at one time or the other.

If the yield curve's slope changes cap gains should change, as you stated,
or just occur at the rate expected from the original yield curve.
age in bonds, buy-and-hold, 10 year business cycle

User avatar
Electron
Posts: 1959
Joined: Sat Mar 10, 2007 8:46 pm

Re: Riding the yield curve, in action

Post by Electron » Tue May 17, 2016 2:42 pm

Thanks ogd and patrick013 for the replies. I just wanted to confirm that the bullet portfolio strategy can result in additional distributed capital gains at times. The distributions were quite significant for the longer maturity fund.

I agree that the tax accounting and other factors may impact the actual distributions. In recent years I suspect many bonds were purchased at a premium and sometimes sold at an even higher premium. Assuming that the bond premiums are amortized, the cost basis of the premium bonds would have decreased during the amortization period. That could result in additional capital gains.

Earlier today I looked at all the taxable Vanguard Intermediate and Long Term bond funds along with the Total Bond Market Index fund. A few interesting things were noted.

The Total Bond Market fund distributes minimal capital gains and I suspect that is because bonds are held until one year from maturity unless a particular security is removed from the index. The ETF share class may be another factor.

All the bond funds showed unrealized appreciation which is shown on the Distributions tab.

A number of the Intermediate and Long Term bond funds made no capital gains distributions at all in 2015. Those funds happened to have an ETF share class available which is not the case for VFIUX and VUSUX. Having the ETF share class for a given fund could be an advantage for taxable investors. I believe that would allow the removal of lower cost basis securities from the portfolio during in-kind exchanges with the authorized participants.
Electron

Post Reply