So do we care more about change in bond price or bond yield?

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Re: So do we care more about change in bond price or bond yi

Post by LadyGeek »

FYI - I added this thread to the wiki: Bond pricing and Bond yield (under "External links" in both)
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Re: So do we care more about change in bond price or bond yi

Post by ogd »

Kevin M wrote:So definitely less scatter for monthly and monthly-average regressions. Highest R^2 for the monthly-average, but there are only 11 data points (since I'm averaging over 30 trading days, not 30 calendar days).
Kevin: what I had in mind was a rolling, daily graph, which should give you many data points; however, it might in fact be very similar to the monthly graph. And have you tried geometric mean?

(Correct me if I'm wrong, but the "Daily price vs yield" graph is the same as the one before, and un-averaged, right?).
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Re: So do we care more about change in bond price or bond yi

Post by ogd »

Johno wrote:On liquidity I meant the difference between being able to realize the benefit of a drop in rates instantly (in a treasury or treasury futures contract sold at higher price after the rate decline) and having to receive it over time (the CD simply paying a higher rate than can be gotten after the rate decline). Again, I think that's how it should be viewed rather than 'the CD doesn't benefit from drop in rates'; on a term yield/opportunity cost basis it benefits/loses just as much as a similar duration treasury as rates move, except doesn't lose asmuch past a certain rate increase because of the put option.
Johno: could one sell short the matching Treasury to accelerate the timeline, after the rate drop, as if they were able to sell the CD at a higher price? The mechanism that's at my level is shorting a defined-maturity ETF, but that might be expensive and perhaps futures work better.

OTOH it just seems that the 5 year CDs are even better deals than the 1% savings accounts.
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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

ogd wrote: Kevin: what I had in mind was a rolling, daily graph, which should give you many data points; however, it might in fact be very similar to the monthly graph.
Ah, OK. That is easy to change for the price/yield chart:

Image

Interesting. R^2 a bit lower, and the estimated duration is further off. Many points line up nicely on the regression line, but still quite a few outliers. It will take a bit more work to redo the charts of the price/yield relationships over time, but that might be interesting. Right now I'm working on making the spreadsheet more flexible, and doing the analysis for Int-Term Inv-Grade bond fund.

As an aside, by using 30-trading-day rolling periods we are investigating price averaged over calendar periods that are longer, but not too much longer, than one month.
ogd wrote:And have you tried geometric mean?
I checked, and the values are the same to the penny. You only see differences if you look at the 3rd or 4th decimal place (i.e., 1/10 or 1/100 of a cent). I guess this is because the price values don't change enough over 30 trading days to see a difference. Not sure why you'd want to use geo mean anyway; although returns compound, I don't get thinking of price as compounding. Vanguard just uses average (mean) price over previous month for its calculation of distribution yield. At any rate, it doesn't make any difference.
ogd wrote:(Correct me if I'm wrong, but the "Daily price vs yield" graph is the same as the one before, and un-averaged, right?).
Correct. I just included it so we could easily compare the results for all three methods.

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Re: So do we care more about change in bond price or bond yi

Post by ogd »

Thanks. I would call this a satisfying match, considering the formula is inherently imprecise due to convexity. Anything that stands out about the outliers?
Kevin M wrote:I checked, and the values are the same to the penny. You only see differences if you look at the 3rd or 4th decimal place (i.e., 1/10 or 1/100 of a cent). I guess this is because the price values don't change enough over 30 trading days to see a difference. Not sure why you'd want to use geo mean anyway; although returns compound, I don't get thinking of price as compounding. Vanguard just uses average (mean) price over previous month for its calculation of distribution yield. At any rate, it doesn't make any difference.
Price is compounding by nature because you can always sell and buy in the middle. If you imagine two large +20% changes, your shares can't make only 40% when the shares of an investor who made 20% then sold to another investor who made the other 20% are now +48.4%. But you're right, it won't make a huge difference for low changes.
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Re: So do we care more about change in bond price or bond yi

Post by Johno »

ogd wrote:
Johno wrote:On liquidity I meant the difference between being able to realize the benefit of a drop in rates instantly (in a treasury or treasury futures contract sold at higher price after the rate decline) and having to receive it over time (the CD simply paying a higher rate than can be gotten after the rate decline). Again, I think that's how it should be viewed rather than 'the CD doesn't benefit from drop in rates'; on a term yield/opportunity cost basis it benefits/loses just as much as a similar duration treasury as rates move, except doesn't lose asmuch past a certain rate increase because of the put option.
1. could one sell short the matching Treasury to accelerate the timeline, after the rate drop, as if they were able to sell the CD at a higher price? The mechanism that's at my level is shorting a defined-maturity ETF, but that might be expensive and perhaps futures work better.

2. OTOH it just seems that the 5 year CDs are even better deals than the 1% savings accounts.
1. You could do that, but shorting a cash treasury as individual is hard to do at low transactions costs AFAIK, and the inverse ETF's have significantly higher ER's than the implied ER of rolling futures (which is on the order of 8 bps pa including commission and assuming a loss of 1/4 of 1/32, half the usual bid offer, on every trade). That doesn't include the roll yield effect though, which is going against you in today's curve if short the futures.

2. The key is that the 1% account has about as high a spread to the repo rate as the 5yr CD does to the 5yr treasury. Then you add the treasury futures return to the bank account return. So for example in the Dec 5yr note contract the underlying is the 1.5% of 2/28/19 treasury. It yields around 1.58% right now, repo rate might be .16% (implied in contract might be a little different), bank account might be .95% rather than 1%, but the net would match 2.3% of 5yr CD if you left 7% of the notional in margin at zero (way more than you have to, and 7% daily move in a 5yr note is gigantic). 1.58+.93*.95-.16=2.3. However rolling the futures in that direction gives you the roll pickup in addition, which I calced awhile ago to be over 1% pa for this contract, of course again only assuming the yc is stationary. But it lacks the put protection of the CD, so the yield comparison isn't completely fair. And it's taking more duration risk to capture the roll yield by continually moving back to a short range of maturities around 4.5 yrs (where the contract underlying is likely to be the way the formula works and w/ today's assortment of eligible notes) rather than just shrinking duration linearly in time w/ a single CD. But the roll effect is quite a lot in that part of the curve now. Again it parallels the bond fund discussion, qualitatively, and quantitatively the 5yr note futures/MMA combination would yield considerably more than the 5yr CD, counting roll effect, if or as long as that effect is near its present size.
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Re: So do we care more about change in bond price or bond yi

Post by ogd »

Thanks Johno. What I was actually thinking is to sell short a defined-maturity ETF like the Guggenheim or ishares corporates 201X. But I see now that there are no such Treasury fund, presumably because there isn't any particular reason you'd go long such a thing vs Treasury Direct.

Indeed, I called the 5 year CD a better deal than even the 1% savings because of the put option. The yield curve bonus is not something I was counting in the comparison because it's not something I'd be buying with my money, it might work out or it might not. More likely to work than not, probably.
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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

ogd wrote:Thanks. I would call this a satisfying match, considering the formula is inherently imprecise due to convexity.
There is no significant convexity visible in the graph, so I don't think convexity explains much. But we don't have a historical record of fund duration that I know of, so I don't really know what the average fund duration was over the last 17 months. I only know what Vanguard says it is now. We're in the ballpark, so I'm not really concerned about this.
ogd wrote:Price is compounding by nature because you can always sell and buy in the middle. If you imagine two large +20% changes, your shares can't make only 40% when the shares of an investor who made 20% then sold to another investor who made the other 20% are now +48.4%. But you're right, it won't make a huge difference for low changes.
Sorry, but I still don't buy it. Your example is discussing returns, not price.

Anyway, the 30-day price averaging idea was a good one. However, I've decided it makes more sense to use 30 calendar days instead of 30 trading days, since that's what's used for SEC yield; i.e., we want the price to be averaged over the same period the YTM is averaged. I've finished the analysis of VG int-term bond fund, and this approach significantly reduces the noise in the price/SEC-yield relationship.

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Re: So do we care more about change in bond price or bond yi

Post by ogd »

Kevin M wrote:ogd wrote:
Price is compounding by nature because you can always sell and buy in the middle. If you imagine two large +20% changes, your shares can't make only 40% when the shares of an investor who made 20% then sold to another investor who made the other 20% are now +48.4%. But you're right, it won't make a huge difference for low changes.

Sorry, but I still don't buy it. Your example is discussing returns, not price.
I was discussing price alone actually. To do this mathematically, using your variables above:

dP/P = -dSEC x D

solves to

P = K e^(-SEC x D)

, for some constant K, like all good compounding functions. Fundamentally, if a given absolute change in yield x causes a known relative change f(x) to any starting price, then additive changes to yield must translate to compounding changes in price. So arithmetic mean in one corresponds to geometric mean in the other; not that it matters much here. End of academic interlude :mrgreen:
Kevin M wrote:Anyway, the 30-day price averaging idea was a good one. However, I've decided it makes more sense to use 30 calendar days instead of 30 trading days, since that's what's used for SEC yield; i.e., we want the price to be averaged over the same period the YTM is averaged. I've finished the analysis of VG int-term bond fund, and this approach significantly reduces the noise in the price/SEC-yield relationship.
Ah, I'd glossed over the "trading" part. Yes, you want the same interval.

Conclusions? Mine is still that SEC yield is the gospel when it comes to making a decision. That's really what I'm buying.
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Re: So do we care more about change in bond price or bond yi

Post by abyan »

So here's a crazy question. Why do they call it interest rate risk if we actually want the interest rates to go up, so that our yield goes up? If you're buying bonds to hold for the long-term, say 10+ years, is there any interest rate "risk" that's really a risk at all? Rates go up and you earn more money while the nav goes down and you don't care because you've got 10 years for them to come back. And if rates go down, nav goes up so you still have more money. I'm just trying to understand, other than needing to withdraw money at an inopportune time that your nav goes down, if there's any real interest rate risk with intermediate or short term bonds?

And to put this in more practical terms, I'm now handling my parents' portfolio, and obviously have them heavily invested in bonds (they had none before) and a decent chunk of equity. And I'm still not sure how to tell my mom how her account is doing in a year from now, or in five years from now, when half the portfolio is in fixed income, a good chunk bonds and a good chunk money market and ibonds. What do I compare the portfolio to in order to show her how she's doing? How I did? I get with 100% equity you can just compare to the S&p 500. But with half fixed income, and then some of the fixed income is bonds, where you dont necessarily want the nav to go up, I'm still trying to understand how you judge how your portfolio is doing, and how you explain to someone else how it's doing? Just overall market value (including dividends, which we'll be reinvesting anyway)? Though if bonds dropped but now have a higher yield, even market value of the portfolio will understate how well it's really doing, right?

God I hate bonds :-)
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Re: So do we care more about change in bond price or bond yi

Post by ogd »

The short standardized answer is that other things equal, something that drops in the intervening time before rebounding is less preferable than something that stays constant. Higher volatility is something you demand payment for. That which you get paid for, in this particular decision, is interest rate risk.

The more long-winded answer in the case of bonds is that even if rates going up is in the long term preferable, your choice of bonds can still hurt you long term. Consider the position of someone holding cash vs you holding 10 year bonds. Now suppose 10 year yields move up to 5%; you are essentially stuck making the present 3% for 10 years (whichever way you account for it) while the guy holding cash can buy 10 year bonds making 5% and make 20% more money. Clearly there was a difference between your position and that of the cash holder, and we call that difference interest rate risk. That 20% extra return will extend into the long term and you will never make it back; it's not a short term thing.

Or if you think the cash guy was an unrealistic example of a lucky market timer, imagine that rates go up to 5% across the board, i.e. flat yield curve, which is not at all unusual. Then the cash holder will outperform you without even doing anything. In other words, your investment can underperform cash by the time 10 years is up. Whenever something has a chance of underperforming cash, I'd say we need to call that a risk.

Now before you go and put everything in cash, remember that something with the interest rate non-risk of cash only pays between 0 and 1% depending on how good of a deal you're getting. No free lunch. Until any interest rate increases actually materialize (if ever), you are building up a buffer against the cash guy outpacing you. That too will get reflected in long-term returns.

I think a good way to explain a rate increase to your parent is that the market value of the investment has dropped but it's now making more money going forward, which in the long run is better. Not much else; if the bonds are safe, the question of "how the bond portfolio is doing" doesn't really have illuminating answers: they're as safe as they've always been. The question makes more sense for the portfolio as a whole but even then I'm not sure there's a lot of value in finding a precise benchmark (e.g. balanced fund) and comparing to it; there will inevitably be small accidental differences but so what. The important thing is whether it's meeting your parents' needs and risk tolerance.
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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

ogd wrote: Conclusions? Mine is still that SEC yield is the gospel when it comes to making a decision. That's really what I'm buying.
Nope, I think "gospel" is too strong. I don't think we've seen anything here that indicates that distribution yield should be ignored. The price/SEC-yield relationship is interesting to explore, and it's nice to see that we can do some rational tweaks so that it looks less noisy (but still noisy compared to an individual bond). But the fact remains that the distribution yield has been more predictive of earnings over the last four years or so for the funds I've looked at. Here's the 17-month chart for VG Int-Term Inv. Grade (Admiral shares) (18 monthly distributions); here I've adjusted price for capital gain distributions, and divided by 3 for ease of comparison with yields.

Image

Say I based my decision to sell VFIDX at $9.95 on 5/31/2013 ($10.07 price adjusted for $0.12 of cap gain distributions) on the SEC yield of 2.22% to buy a CD at 2.25% (or 2% or whatever), while the distribution yield was 3.14%. The fund continued to pay distributions of about $0.03/share (distribution yields over 3%) each month. On 8/29/2014 (about 15 months later), price was $9.98, distribution yield was 3.16%, and SEC yield was 2.59%. So I would have ended up better off sticking with the fund; even though the SEC yield increased by almost 40 basis points, the adjusted price at the end of the period actually was a little higher!

Prior to doing this kind of analysis (first time 2.5 years ago), I would have expected price to fall, and to see more convergence of distribution yield and SEC yield as SEC yield increased, but instead, over this 15-month holding period, distribution yield and price started and ended at about the same values while SEC yield increased by almost 40 basis points.

This is not some new or particularly recent phenomenon. As I said, when I looked at this about 2.5 years ago I saw the same thing (so looking at yields and prices between 2.5 and 4 years ago. I expect that when we eventually have a sustained, multi-year increase in yields (hopefully in my lifetime), we will see price decrease (it must), and SEC yield converge with distribution yield. The point here is that distribution yield can be an important consideration when looking at periods of up to at least a couple of years for an intermediate-term fund, even with a moderate change in SEC yield.

I'll try to get around to doing the analysis on a fund where distribution yield and SEC yield are close, like Int-Term Treasury, but I'm not very interested in that fund since I don't own it.

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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

abyan wrote:Why do they call it interest rate risk if we actually want the interest rates to go up, so that our yield goes up? If you're buying bonds to hold for the long-term, say 10+ years, is there any interest rate "risk" that's really a risk at all? Rates go up and you earn more money while the nav goes down and you don't care because you've got 10 years for them to come back.
Yes, the risk is real. Here is a simple example, contrived to get the concept across. To keep it simple, I'll use the duration approximation rather than actual bond math.

You own $100 worth of an intermediate-term bond fund with a YTM of 2% with a duration of 5. I own $100 of a direct CD earning 2% with an early-withdrawal penalty (EWP) of six months of interest (1%). Tomorrow something crazy happens and the YTM on your bond fund increases to 4%. The duration rule of thumb says that the value of your fund will fall by about 10% (5 x 2%). I do an early withdrawal from my CD, losing 1% to the EWP, and reinvest it in the bond fund.

After this we're both earning the 4% yield, but you are earning it on $90 while I am earning it on $99. We both benefit from the higher yield, and you will eventually recover your loss, but you will never catch up with me. So we both benefit long term if rates go up, but I benefit more.

Of course it can go the other way, which is one reason I still own some bond funds. But the closer rates get to 0%, the more I'll shift into direct CDs, as long as the CD earns as much or more than the bond fund. The closer rates get to 0%, the more lopsided the interest-rate risk (more limited upside, but no less limited downside).

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Re: So do we care more about change in bond price or bond yi

Post by ogd »

Kevin M wrote:Prior to doing this kind of analysis (first time 2.5 years ago), I would have expected price to fall, and to see more convergence of distribution yield and SEC yield as SEC yield increased, but instead, over this 15-month holding period, distribution yield and price started and ended at about the same values while SEC yield increased by almost 40 basis points.
I still believe you're getting tricked by the up-and-down move in muni yields which makes it seem like the smoothing / slowness in distribution yields is an advantage, whereas that's only a peculiarity of the 2013-2014 muni season. As you argued to me successfully long ago, SEC yield is incredibly predictive over time. Time will tell.
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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

ogd wrote: I still believe you're getting tricked by the up-and-down move in muni yields which makes it seem like the smoothing / slowness in distribution yields is an advantage, whereas that's only a peculiarity of the 2013-2014 muni season.
The most recent chart above is not muni; it's Int-Term Inv-Grade, so nothing to do with munis. I'm not getting tricked by anything; I've been pocketing more than 3% month after month while SEC yields were predicting closer to 2% many months ago, and fund value hasn't gone down correspondingly.

I've done the analysis for Int-Term Treasury now. Since it's hard to see the details on the chart, for now just check out these numbers for VFITX:

Code: Select all

Date      Dist  SEC   Price (adjusted)
--------- ----- ----- ----------------
6/28/2013 1.40%  1.07%  11.25
9/30/2014 1.69%  1.65%  11.25
So a 15-month period with same price (adjusted for cap gain distributions) at beginning and end, but SEC yield increased by almost 60 basis points. Over this period average distribution yield was about 1.6% and average SEC yield about 1.5%, so again, dist. yield was more predictive of return over this period.
ogd wrote:As you argued to me successfully long ago, SEC yield is incredibly predictive over time. Time will tell.
Hmm, I don't think I argued that--at least not based on any analysis of data; again, I've been pondering this puzzle for at least 2.5 years. As I recall, I was challenging the notion that SEC yield systematically understated expected earnings due to the roll yield effect. I think I've come more around to the point of view that you and the others on the other side of the debate were arguing.

I still don't think we can depend on roll-yield (although we may benefit from it), but I have come around to the belief that given the current shape of the yield curve, SEC yield may understate expected earnings because bonds aren't held to maturity.

I agree that longer-term we'll be able to look back and see holding periods for which SEC yield was more predictive, especially of total return. That's one of the reasons we both like CDs, but in the meantime, we've been lucky and have been rewarded nicely by continuing to hold our bond funds. If paying some attention to distribution yields is a mistake, then it has been a lucky mistake that has helped persuade me to continue to hold 30% of fixed income in bond funds. When things eventually turn the other way, I'll be glad I have only 30% of fixed income in bond funds.

(Incidentally, my limit order to sell CMF was executed on Friday--I just noticed today--so more cash looking for a great CD deal, and a little less in muni bond funds).

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Re: So do we care more about change in bond price or bond yi

Post by jstrange1970 »

In response to the OP's original question, the answer is simple. YES

Whichever is impacting my bottom line the most at any point in time.
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Re: So do we care more about change in bond price or bond yi

Post by abyan »

"Yes" -- now there's an unequivocal answer :)

This has been really fascinating. And I brushed up on some of the old bond threads, which involve many of the same players in this thread, from earlier this year and last year. What a complicated business.
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Re: So do we care more about change in bond price or bond yi

Post by YDNAL »

abyan [OP] » Wed Oct 01, 2014 3:09 pm wrote:I get bonds, basically. I've done a lot of reading the past few months, while preparing to help my parents with their retirement accounts. And I understand that bond yields are inversely related to bond prices. And I understand the kind of things that affect the desirability of bonds.

I guess the thing I'm confused about is, I understand how to feel about stocks going up or down. I don't understand whether I should be happy or sad that Treasury prices are going up today while yield is going down....
It depends why (and timeframe) you invested in "Treasuries."
  • • If you need the money today, you should be happy.
    • If you need the money corresponding with duration, it doesn't matter, what matters is total return over time.
    • If you invested to mitigate Equity risk, the Treasury price that matters is when Equities dive 50% (or whatever).
ps. Sorry I didn't read 2 pages of responses (above is addressed?), but this is a bump to your thread nonetheless.
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Re: So do we care more about change in bond price or bond yi

Post by Trader Joe »

We care about both bond price and bond yield.
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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

Kevin M wrote: Here is a simple example, contrived to get the concept across. To keep it simple, I'll use the duration approximation rather than actual bond math.
I thought it would be useful to show this graphically. The setup is similar, except that we'll assume the one-time rate increase from 2% to 4% occurs at the end of year 1 (and rates remain unchanged thereafter). Here is the setup (the CD is a 5-year CD with an early withdrawal penalty (EWP) of six months of interest, which comes out to 1% for a 2% rate):

Code: Select all

              Bond  CD
              ----  ---
Year 1 yield    2%  2%
Year 2+ yield   4%  4%
Duration        5   n/a
EWP           n/a   1%
And here is the result:

Image

This shows the important points.
  • Bond fund owner is happy beyond about 6.5 years, since higher rate has compensated for the 10% loss in value, and return will continue to pull ahead of what it would have been without the rate increase.
  • CD owner is even happier, since by the end of year 2 the value of the new CD (or bond fund) has more than recovered from the 1% EWP, and pulled ahead relative to no rate change; and the CD owner's lead over bond owner continues to increase each year.
  • The concept of bond fund duration as the point of indifference applies approximately, since it took about 5.5 years for the bond fund to reach the point of indifference to the rate change.
(Note that the duration formula approximation for bond price change is not too far off from actual bond math for this scenario, and doesn't change the appearance of the graph much (I tried it). A bond with a coupon of 2% and modified duration of 5 will decrease in value by about 9.7% (vs. our estimate of 10%) if YTM increases from 2% to 4%.)

What if there is a one-time rate decrease instead? Let's assume that instead of rates doubling they fell by half, from 2% to 1%:

Image
  • Both bond fund and CD owner are unhappy, since their returns after 6 years are lower than if there had been no rate change.
  • Bond fund owner does a little better than CD owner, but the gap is not near as wide as if rates increased.
  • (Note that CD return is the same as if rates had not changed until end of year 5, at which point CD matures and proceeds are reinvested at the lower rate).
Does this help?

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Re: So do we care more about change in bond price or bond yi

Post by stlutz »

Thanks for the interesting back-and-forth ogd & Kevin!

A couple of things I would add:

My understanding is that:
--The SEC yield is of course based upon the yield-to-maturity/call of the bonds *currently*
--The distribution yield is based on the yield to maturity/call of the bonds *at the time that the fund purchased them*.

For a low-turnover fund, this can cause the distribution yield to diverge significantly from the SEC Yield. A good example here is VG Intermediate Term Tax Exempt. That fund has a very low turnover rate (a little over 10%), which suggests that they buy bonds and hold them often until maturity--just like an individual rolling her own bond ladder.

In contrast, VG Int. Term Treasury turns over its entire portfolio every year. As a result, the distribution yield will tend to track the SEC yield more closely.

In another thread a while back I used the examples of the Stlutz Intermediate Term Treasury Fund which buys a 5 year treasury bond, held for a year, sold it, and then did the same thing the following year. The Stlutz Intermediate Treasury Fund #2 instead maintains a rolling 10 year ladder, holding all bonds until maturity.

So, let me take these in order (Note: I'm approximating the numbers here and I'm assuming that the yield curve that existed on 1/1/2014 basically never changes just to make things simpler):

My fund #1: The 5 Year bond it bought on 1/1 yielded 1.7%. Because of the roll yield, the total return for the year would be about 3%. The SEC yield at the start would be 1.7%, and that would end up being my distribution yield. The fund price would increase from $100 to $101.3.

My fund #2: Every year it buys a new bond yielding 3%. The average YTM of it's portfolio is about 1.7%. So, the SEC Yield of this fund is 1.7%, but the distribution yield would be 3%, because it has to distribute income based on what securities were yielding when they were purchased. The NAV would be unchanged over the course of the year.

So, for comparison purposes, the total return of each of these two funds would be the same. In a taxable account, I'd prefer fund #1 as that provides more capital gains return and less income return.

As such, I'd come to the following conclusions:

a) For comparing fund A to fund B, SEC yield is the way to go.
b) Distribution yield gives a good indication of the payouts you should expect to receive, but it will not be a good estimate of total return.
c) Both SEC and distribution yield will be off when it comes to estimating the total return I should expect. The way I would do it (again, avoiding doing a bunch of Excel) is to simply look at the shape of the yield curve outside of the first couple of years. The steeper the curve is, the more SEC yield will underestimate the return I would expect to receive. On the other hand, if the curve is inverted, I would say just the opposite--SEC yield is overestimating. And if it was completely flat, the SEC Yield would be spot-on. Normally, where there is a slight slope beyond year 2, you can expect about .2% per year of return over the SEC yield.

Thoughts?
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Re: So do we care more about change in bond price or bond yi

Post by Naismith »

Just wanted to say how much I was enjoying this discussion....lots to think about....please continue with your graph slinging....
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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

stlutz wrote: My understanding is that:
--The SEC yield is of course based upon the yield-to-maturity/call of the bonds *currently*
--The distribution yield is based on the yield to maturity/call of the bonds *at the time that the fund purchased them*.
I'd like to focus on one thing at a time. My understanding is that Vanguard bond fund "dividend" distributions are just the monthly income from the coupon payments. The distribution yield is simply the distribution amount divided by the average price over previous month (annualized). So I don't see how it has anything to do with when they purchased the bonds or YTM. Do you have a reference that indicates otherwise?

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Re: So do we care more about change in bond price or bond yi

Post by stlutz »

My understanding is that Vanguard bond fund "dividend" distributions are just the monthly income from the coupon payments. The distribution yield is simply the distribution amount divided by the average price over previous month (annualized). So I don't see how it has anything to do with when they purchased the bonds or YTM. Do you have a reference that indicates otherwise?
My understanding has always been that mutual funds have to distribute income a way that matches what would occur if it was an individual's portfolio. So, for example, when a stock fund sells a security at a gain, it has to make a capital gain distribution and I pay taxes on that distribution at the long-term rate.

If I purchase an individual bond at a premium, I would amortize the bond premium so I'm only paying taxes based on the YTM and not on the [higher] coupon payments. If I bought a market discount bond, again, I would pay taxes based on the YTM and not just the coupon (although I can defer the market discount income until it matures). A fund would do the same in calculating distributions.

Consider a TIPS bond. When the principal amount adjusts each year for inflation, I have to pay taxes on that adjustment. If I own a TIPS fund, that amount is distributed to me as income because I have to pay taxes on it.

In short, distributions are based on what shareholders have to pay taxes on, which is not necessarily the same as cash flow for the fund.

Again, that's my understanding. Am definitely looking for confirmation/refutation from an expert on mutual fund accounting. :happy
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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

stlutz wrote: Again, that's my understanding. Am definitely looking for confirmation/refutation from an expert on mutual fund accounting. :happy
Yes, that's why I was asking for a reference; I've seen your thinking on this before, and I have never found anything verifying it in looking through prospectuses, annual reports, SAIs, etc.

Currently VWITX shows:

Unrealized appreciation/depreciation $0.83
Unrealized appreciation/depreciation as a % of NAV 5.82%

The latest semi-annual report shows:

Image

Note that distributions consist only of net investment income, and that unrealized capital gains are reflected in the NAV. This is what I expect, and why I think we see changes in individual bond prices reflected in change in fund NAV, not in distributions.

The question is is the gain/loss attributable to amortization of premium/discount included in net investment income, and only gain/loss due to change in bond price/yield due to market factors included in unrealized cap gain? I actually just spent some time looking through SEC regs and CFRs, and although I can find requirements to report "net investment income", I haven't yet found an actual definition specific to mutual funds.

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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

stlutz wrote: For a low-turnover fund, this can cause the distribution yield to diverge significantly from the SEC Yield. A good example here is VG Intermediate Term Tax Exempt. That fund has a very low turnover rate (a little over 10%), which suggests that they buy bonds and hold them often until maturity--just like an individual rolling her own bond ladder.

In contrast, VG Int. Term Treasury turns over its entire portfolio every year. As a result, the distribution yield will tend to track the SEC yield more closely.
At first, when I looked at the distributions by maturity for VWITX and VFITX, as shown in this reply in this thread it did not appear to me that VWITX holds bonds to maturity. However, I neglected to notice that the apparent concentration is due to the much broader ranges shown in the intermediate-to-long-term maturities. So I calculated percent of each maturity per year to see it more clearly:

Code: Select all

Matrty range  prcnt  years percent/year
------------  ----- ----- ------------
Under 1 Year  12.9%    1    12.90%
1 - 3 Years    9.6%    2     4.80%
3 - 5 Years    9.1%    2     4.55%
5 - 10 Years  26.5%    5     5.30%
10 -20 Years  41.0%   10     4.10%
Of course we can't see from this the actual distribution by year, but it does appear that there's a fairly even distribution by year, except for the high concentration under 1 year.

In terms of how this may or may not affect relationship between SEC yield and distribution yield, we can look at the two charts comparing them over the 17-month period for which Vanguard shows distributions.

First is VFITX (int-term treasury). Price is adjusted for cap gain distributions and scaled by subtracting 11, so 1.25 on the chart represents an adjusted price of 11.25.

Image

So here we see an initial wide gap between the yields, then a convergence of SEC yield toward distribution yield as yields have risen. But at I pointed out in an earlier reply, we also see that price on 9/13/2014 of $11.25 is exactly the same as adjusted price on 6/28/2013 (15 months earlier), despite an increase in SEC yield of about 60 basis points. I guess the fund managers are earning their pay by generating alpha.

Here's the updated chart for VWITX (int-term tax-exempt), in which price is scaled by subtracting 12 (so $1.80 on chart represents price of $13.80):

Image

Here we see convergence of SEC yield toward distribution yield as yields increased, then divergence as they decreased. For this fund the price/yield relationship looks more like what we'd expect, although there still are a few month-to-month changes where we see price and yield moving in the same direction instead of in opposite directions (no price averaging done here).

Some replies have provided explanations of why SEC yield is more volatile than distribution yield. That reasoning seems consistent with what we're seeing here in terms of the convergence and divergence of SEC yield and distribution yield.

Back to one of my main points--both charts show that distribution yield for one month has been much more predictive of earnings (fund net income distributions) for the next month (or two or three or fifteen), so distribution yield should not be ignored when making decisions relative to a holding period of up to a year or even more for an intermediate-term fund.

The common saying that distribution yield is backward looking and SEC yield is forward looking simply is not supported by the data (again, using Vanguard's definition of distribution yield). Both yield figures are calculated using averages over the previous month. Distribution yield seems to be more predictive of earnings over holding periods of up to one year or more. In theory, SEC yield should be more predictive of total return over a holding period equal to the fund's average maturity or duration. However, in another post I'll show an example of a short-term bond fund for which this does not appear to be the case.

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Re: So do we care more about change in bond price or bond yi

Post by ogd »

Kevin M wrote:The common saying that distribution yield is backward looking and SEC yield is forward looking simply is not supported by the data (again, using Vanguard's definition of distribution yield). Both yield figures are calculated using averages over the previous month. Distribution yield seems to be more predictive of earnings over holding periods of up to one year or more. In theory, SEC yield should be more predictive of total return over a holding period equal to the fund's average maturity or duration. However, in another post I'll show an example of a short-term bond fund for which this does not appear to be the case.
Kevin -- I strongly disagree with this paragraph and I also think it's actively harmful to people if we start espousing this view. The distribution yield is something that managers can manipulate, tricking investors into paying higher ERs or too many taxes only to see NAV declines bringing their total return behind the funds they were alternatively considering. This is the very reason for the creation of the standardized SEC yield figure. I am sorry to say that no amount of short-term analysis of a few funds will convince me otherwise, although I appreciate the exploratory nature of what you're doing.

Now, having gotten the negativity out of the way :beer , here are some things I can agree with:
1) Distribution yield is predictive of future distributions in the short and medium term. But not total return. So when you say "has been much more predictive of earnings (fund net income distributions) ... so distribution yield should not be ignored when making decisions" I agree, inasmuch as those decisions have to do with spending or tax savings that depend on distribution return specifically.
2) It's quite possible that well-behaved funds like Vanguard's distribute an approximation of SEC yield + roll yield. This could be because of the manager's desire to keep price stable and/or show sustainable, honest distributions, or perhaps because the IRS pushes them in that direction. The IRS has a lot to say about distribution vs capital gain returns, obviously, in both directions (taxable vs tax-exempt funds). Taxation rules, like stlutz says, are a big unknown for us amateurs in this picture.
3) It's also possible, if a lot more speculative, that well-behaved funds distributions express the managers' views on the amount of roll yield they'll be able to realize in the future, also for the purposes of keeping distributions honest. Their views might be a lot more informed than ours, which would suggest putting more weight on distribution yields like you are.

Note that (2) and (3) hinge on well-behaved. You'd have to trust the funds before taking these positions. This point, trust, will be hard to make to posters looking for help, if you are otherwise telling them to invest based on distribution yields.

Note also that most of this hinges on roll yield. I think it's telling that the behaviours vary between maturity-focused funds with a lot of turnover and the wide-maturity muni funds that have much longer holding periods because of liquidity, and thus are slower to adapt to the yield environment. As I was saying repeatedly, roll yield is not something you can count on and should be treated with cautious optimism at best.
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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

I'm not recommending that people compare mutual funds based on distribution yield. The SEC mandates 30-day SEC yield for a reason.

ogd, I'm puzzled that you react so strongly to the statement you quoted. Let's look at each individual statement.

"The common saying that distribution yield is backward looking and SEC yield is forward looking simply is not supported by the data (again, using Vanguard's definition of distribution yield)." This is just a fact. Look at the data. I'll explicitly add that I'm making this statement with respect to the Vanguard funds I've analyzed, so to be more clear, I'm saying that the quoted statement is not necessarily true; it is too much of a generalization.

"Both yield figures are calculated using averages over the previous month". This is just a fact.

"Distribution yield seems to be more predictive of earnings over holding periods of up to one year or more". OK, I should have said "seems to have been ... for the funds I've analyzed", but that should be clear from the context.

"In theory, SEC yield should be more predictive of total return over a holding period equal to the fund's average maturity or duration". I assume we agree on this.

"However, in another post I'll show an example of a short-term bond fund for which this does not appear to be the case". I haven't shown you the data yet, so I don't see how you can be concerned about this statement.

Rather than castigate me for propagating harmful views, why don't you look more closely at some of the anomalies that appear, and see if you can help explain them? Or take a particular factual statement I've made and tell me what's incorrect about it. Let's get back to a civil dialog about what the data shows. I enjoy the dialog, but not the lecture mode.

A personal example of what I'm saying is that I've found that in making decisions about selling Vanguard bond funds to buy CDs, distribution yield has been a relevant factor. Since I'm such a CD fan, I feel obligated to note that distribution yields of some Vanguard bond funds (like all the ones I still own) can make the trade-off less favorable to CDs; at least that has consistently been the case for the last few years. So I think it would be disingenuous of me not to note this--at least now and then if not every time I do a bond fund vs. CD comparison.

When both SEC yield and distribution yield of a fund are less than the rate I can get on a direct CD with less risk, the decision is easy, and I generally sell all of that fund and buy a CD. Examples of this have been Short-Term Investment-Grade and Limited-Term Tax-Exempt.

When the SEC yield is lower but the distribution yield is significantly higher, I'm more cautious, and move more gradually from the bond fund to CDs. An example of this has been Intermediate-Term Investment-Grade in IRAs.

Currently the SEC/Dist spreads on the int-term tax-exempt funds are quite large, both national and CA. When you factor in the tax exemption, the trade-off is less clear, especially for the CA funds. My toe in the water here has been cashing out CMF and CXA instead of swapping back into VCADX and VCLAX, but with CA tax-exempt distribution yields of 3.00% and 3.68%, I'm more willing to take the term and credit risk instead of moving into a taxable 2.3% 5-year CD, even though the SEC yields of 1.63% and 2.26% would seem to make it a more reasonable tradeoff. If a 3% 5-year CD comes along, I'll probably trim some more from these funds in favor of the CD.

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Re: So do we care more about change in bond price or bond yi

Post by ogd »

Kevin M wrote:I'm not recommending that people compare mutual funds based on distribution yield. The SEC mandates 30-day SEC yield for a reason.

ogd, I'm puzzled that you react so strongly to the statement you quoted.
Kevin: I used strong italicized words to emphasize that we were moving into territory that matters for people's portfolio choices and doing so under the wrong banner. I apologize if the change of tone offended you, but this is important.

It's impossible for me to see how your conclusions about dist. yields predicting returns would not be used for comparing funds, despite you saying so. The conclusion will just inevitably extend in that direction, with a simple "what about this fund which has much higher distribution yield". For example, take your determinations on what to do when SEC yield and dist yield compare in certain ways with a CD. Suppose they are both lower for a particular fund you like, but a poster has a fund XYZYX which is doing that thing we don't like wrt emphasizing distribution yield at the cost of NAV and the poster is ready to pay 1% ER for the privilege of having their capital returned to them. What then? How are you going to convince the poster that the high distributions are an illusion, having just talked about the predictive power of distribution yield? Arguments that this only applies to Vanguard funds will ring hollow.

Or when you talk about how "month in, month out, earning about 3% or more" and delaying selling accordingly, how is that different from buying XYZYX to grab that distribution yield for a few months?

Fundamentally, you can't say that your method of comparison can be used for comparing A to C, or B to C, without inevitably facing the comparison of A to B, even as you acknowledge it's invalid.
Kevin M wrote:"The common saying that distribution yield is backward looking and SEC yield is forward looking simply is not supported by the data (again, using Vanguard's definition of distribution yield)." This is just a fact. Look at the data. I'll explicitly add that I'm making this statement with respect to the Vanguard funds I've analyzed, so to be more clear, I'm saying that the quoted statement is not necessarily true; it is too much of a generalization.
It's backward looking data from one unusual period, when:
1) the funds were coming off higher yields in the past, 2012 and earlier
2) the yield curve was unusually steep and remained so longer than we expected (and it predicted.
3) the yields had a "hump" in the middle, for two rather unrelated reasons (interest risk off, credit risk on), meaning the funds spent a good portion of the period (eyeballing to more than half of the time x yield integrated area) at yields considerably higher than either endpoint (consider this point one explanation of the anomalies).
The apparent conclusions from this interval contradict the definitions. It isn't "theory" that SEC yields and bond YtMs are forward looking wrt return, it's by design and definition. There simply isn't anything in the distribution yield that captures the known future changes in bond values which are an integral part of bond return.

Or here's another way (pretty much the opposite angle) in which paying attention to distribution yields is harmful: if you remember last year during the bond ponic, a common theme was "my fund lost X% value, yet its distributions are unchanged or even declining month to month. I was told that yields would increase in compensation, but this isn't happening. Bond funds are bogus!" It took a lot of explaining about SEC yields and bonds returning to par value inside the fund to sway posters that were even listening. We need to be on solid ground when it comes to dissuading people from panic sales, as opposed to having to explain why this time the distribution yield is misleading.

Now I would agree that it isn't easy incorporating roll yield into comparisons of fund vs CDs or even individual bonds. My way (e.g. in the "rolling the yield curve" thread and references to it) is to point out that funds can do this, if the planets align, but it's by no means guaranteed. I definitely think that distribution yield is the wrong way to go about it.
Kevin M wrote:"Distribution yield seems to be more predictive of earnings over holding periods of up to one year or more". OK, I should have said "seems to have been ... for the funds I've analyzed", but that should be clear from the context.
You need to define "earnings" here, btw. My gut feeling is that you sort of mean returns, but I'm not sure. If you mean distributions, that's probably true but not meaningful after large changes in market yields where capital returns, the other component, gain outsized importance.

Also, I was willing to concede above that distributions might have more meaning from a tax perspective, for tax-exempt funds; e.g. in a very high tax bracket you might derive more benefit from the tax exemption while distributions are high than SEC yield alone would indicate. However, the muni market is subtly sensitive to the breakdown between tax-exempt and capital returns when it prices any given bonds so it's probably less than it looks. Like all arguments about implied tax discounts to yield, this is a rather long and complicated discussion.
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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

ogd wrote:
Kevin M wrote:"Distribution yield seems to be more predictive of earnings over holding periods of up to one year or more". OK, I should have said "seems to have been ... for the funds I've analyzed", but that should be clear from the context.
You need to define "earnings" here, btw. My gut feeling is that you sort of mean returns, but I'm not sure. If you mean distributions, that's probably true but not meaningful after large changes in market yields where capital returns, the other component, gain outsized importance.
In this context I'm using "earnings" to mean net income distributed by the fund; i.e., what Vanguard calls "dividends".

However, what we saw for the int-term TREASURY fund also showed an example that the same applied to total return over a 15-month period, along with the puzzling fact that adjusted price was the same at start and end of period despite yield increasing significantly. Not a muni fund, so no credit issues that you keep referring to. I haven't seen an explanation for that one yet. My hypothesis was that the fund managers generated alpha; after all, it is an actively managed fund.

This example is particularly interesting to me because of course I agree that capital gain/loss can overwhelm income return if there are big moves in interest rates relevant to the fund (which is one reason I prefer direct CDs), but that's not what we saw in this case. I'm not arguing anything here--just making an observation and soliciting input on what explains it.

For fun, I did a regression analysis of VFITX for this period using PortfolioVisualizer with the bond factors. Funny thing is that it shows negative alpha. However, this is not statistically significant (t-stat -0.93). The only statistically significant loading is on term risk (0.29, t-stat 2.4), which we'd expect. The next most-significant loading was on (stock) market risk at 0.19 with a t-stat of 2.2.

I'll just view your posts as cautions to unwary investors not to interpret anything I'm saying as justification to compare mutual funds using distribution yield.

I actually found a paper that found that neither SEC yield nor distribution yield was correlated with subsequent muni bond fund returns (they use Morningstar definition of distribution yield, which is trailing 12-month divided by current price adjusted for capital gain distributions). www.bnet.fordham.edu/finance_research_c ... aper_3.pdf. Note that they were looking at a a broad universe of funds, including those with loads. I read some of it, but got bored because it has minimal relevance to anything I do. What I was actually searching for was a reference on the requirements mutual funds must follow in distributing net investment income (again, what Vanguard refers to as dividends). They discuss the definitions of distribution yield (Morningstar version) and SEC yield, and they talk a little bit about the differences between muni bond funds and taxable bond funds, but I didn't find what I was looking for.

So, the data I'm presenting and making observations about should be viewed strictly as an investigation of the specific Vanguard bond funds I'm looking at. I think I'm mostly just making observations based on the data. Conjectures about why the data is what it is are interesting, but it's even more interesting to try and explain the data with other data or actual facts.

For example, it's a fact that the bond funds I've looked at with higher distribution yields have higher average coupons, which makes sense. Higher coupon means higher current yield for a bond, which translates to higher distributions for a bond fund. I actually did a bit of analysis on this last night. I'll probably present some of this in another post, but I've been thinking this discussion deserves its own thread. Based on OP's own admission, we've gone way over OP's head with all of this.

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Re: So do we care more about change in bond price or bond yi

Post by ogd »

Kevin M wrote:In this context I'm using "earnings" to mean net income distributed by the fund; i.e., what Vanguard calls "dividends".
Cool. As long as this is about "dividends" I don't have a problem with it. With the gotcha that "dividends without changes in price" is total return by any other name and claiming dist. yields as an indication of such would be problematic.
Kevin M wrote:However, what we saw for the int-term TREASURY fund also showed an example that the same applied to total return over a 15-month period, along with the puzzling fact that adjusted price was the same at start and end of period despite yield increasing significantly. Not a muni fund, so no credit issues that you keep referring to. I haven't seen an explanation for that one yet. My hypothesis was that the fund managers generated alpha; after all, it is an actively managed fund.

This example is particularly interesting to me because of course I agree that capital gain/loss can overwhelm income return if there are big moves in interest rates relevant to the fund (which is one reason I prefer direct CDs), but that's not what we saw in this case. I'm not arguing anything here--just making an observation and soliciting input on what explains it.
I'm glad you focused on this example. This is a fund I covered in "Riding the yield curve, in action" and it's a much cleaner example than the other two.

1) The credit risk downward trend of 2013-2014 that affects the muni and corp funds is not present here.
2) The performance of the indexed ETF iShares 3-7 year Treasury bond (IEI) is pretty much identical. So manager alpha can't be the explanation.
3) Without running the numbers, I'm pretty sure stlutz's method in this old thread would have generated the same numbers. If the ETF can do it, so can stlutz :mrgreen:

So I'm pretty sure this is entirely about roll yield. Since oversized returns can occur without oversized dist. yields, it supports the conclusion that those are probably coincidental in the other funds too.
I'll just view your posts as cautions to unwary investors not to interpret anything I'm saying as justification to compare mutual funds using distribution yield.
As per my message above I want to extend this to CDs as well, while allowing for roll yield to boost returns of mutual fund in a hard-to-predict way. And don't forget my other point, about the misinterpretation of distribution yields that don't increase with market yields. I really think it's best if we simply don't assign much meaning to them. Other than for taxes.
Kevin M wrote:For example, it's a fact that the bond funds I've looked at with higher distribution yields have higher average coupons, which makes sense. Higher coupon means higher current yield for a bond, which translates to higher distributions for a bond fund. I actually did a bit of analysis on this last night. I'll probably present some of this in another post, but I've been thinking this discussion deserves its own thread. Based on OP's own admission, we've gone way over OP's head with all of this.
A separate thread is probably a good idea. I might not get to participate in depth for a while because of sudden demands in real life (in a good way).
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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

ogd wrote:
Kevin M wrote:However, what we saw for the int-term TREASURY fund also showed an example that the same applied to total return over a 15-month period, along with the puzzling fact that adjusted price was the same at start and end of period despite yield increasing significantly. <snip>
<snip>
3) Without running the numbers, I'm pretty sure stlutz's method in this old thread would have generated the same numbers. If the ETF can do it, so can stlutz :mrgreen:

So I'm pretty sure this is entirely about roll yield.<snip>
It would be nice to try and actually explain this using numbers reported by the fund, changes in yield curve, etc. I'll have to review the old stlutz thread in detail later, but looking at the OP in that thread, the stlutz fund assumed a static yield curve. The yield curve was not static over the 15-month holding period in question, so we have to consider the effect of yield-curve changes as well.

Let me try to work through the thinking. First the facts:
  • Holding period was 6/28/2013 through 9/30/2014.
  • Price, adjusted for capital gains distributions was exactly the same at start and end of holding period.
  • There were two capital gain distributions totaling $0.073/share, without which price would have been higher by the amount of these distributions, about $0.073/share.
  • All other return came from dividend distributions (net investment income) of about $0.24 (which are used in the distribution yield calculations).
  • SEC yield was 1.07% at beginning of holding period and 1.65% at end of holding period, so 58 basis points higher.
  • As a point of comparison, nominal treasury yields for the 3, 5, 7 and 10-year treasuries increased by 0.41, 0.37, 0.26 and 0.00 percentage points respectively during the holding period.
So how might "roll yield" explain these facts?

(First a quick note on terminology. When I Google "roll yield", I get mostly links to articles about futures contracts. However, one hit led to an article on what we're talking about here, but used the term "roll return" to describe it. To make matters more confusing, apparently the terms "roll yield" and "roll return" are used interchangeably to describe the return related to convergence/divergence of futures and spot price of the underlying asset. We seem to be misusing the term, but the important thing is that we understand what we mean by it.)

The term "roll yield" is being used to describe the increase in a bond's price as it moves toward maturity, "rolling down" certain portions of the yield curve. This will be offset by the amount by which the YTM increases over the holding period at the point on the yield curve where we're measuring the "roll yield".

I've started doing some analysis of the relevant yield numbers, but don't have time to finish it now. Quick summary: 3-year to 10-year treasury yields (that make up the vast majority of the fund) increased during the holding period as noted above, but not enough to completely offset the "roll yield".

For example, at beginning of holding period (HP) 7-year yield was 1.96%, and at end of HP 5-year yield was 1.78%. So during the HP, as a bond decreased in maturity by 15 months in the 5-year to 7-year portion of the yield curve, the YTM of the bond decreased on average by (1.96 - 1.78)/2 = 0.09 percentage points (9 basis points) per yield-curve-year. If I'm thinking about this correctly, we multiply by about 15/12 to get the average decrease in yield over the 15-month HP in this portion of the yield curve, which gives us about 11 basis point decrease in YTM over the HP.

The YTM-HP decrease in the 7-10 year range was similar, at about 13 basis points. For the 3-5 year range it was higher at about 21 basis points.

This decrease in YTM would translate directly into an increase in price for an individual bond.

So the roll-yield theory is that adjusted price of the fund did not decrease as 3-year to 10-year portion of the yield curve moved up over the HP because of the roll yield effect working in the opposite direction. Also implied is that since the adjusted price of the fund was the same at start and end of HP, any realized roll-yield must have been delivered to shareholders either through capital gain or dividend distributions.

It's also noteworthy that the 10-year yield was the same at start and end of HP. So on the last day of the HP, proceeds from a 3-year bond sold at a profit could be used to reinvest in a 10-year bond for the same price as the first day of the HP. Of course we can't just look at begin and end of HP, since bonds must be sold throughout the period to maintain average maturity in the target range, so to better understand this we need to look at how the yield curve changed during the HP.

Question to the group ... again: can we find a reference that tells us if roll yield might be distributed as dividends (the stlutz understanding; i.e., SEC, IRS, or other accounting rules require it), capital gains (from selling bonds), or both? My working assumption is that dividends (net investment income) represents only coupon payments minus fund expenses, and that any bond price increase is only distributed to shareholders as capital gain distributions when bonds are sold at a net profit. It would be nice to see a reference to resolve this, since then one unknown could be removed from the analyses.

Kevin
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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

Kevin M wrote:I'll have to review the old stlutz thread in detail later, but looking at the OP in that thread, the stlutz fund assumed a static yield curve.
OK, reviewed the thread, and have to give stlutz credit for providing a reasonable explanation of roll yield offsetting increase in yield-curve yields to explain net gain/loss. First, here's a link to a post of mine in that thread in which I made the point that you can't depend on roll yield to make a profit (the fund had a loss during the holding period):

Treasuries, CDs, and Munis reconsidered (my post)

And then stlutz explained in the following post how the roll yield partially offset the loss from the increase in yield curve rates:

Treasuries, CDs, and Munis reconsidered (stlutz response to my reply)

That was a good example, and helps consolidate the notion of bond price increasing due to rolling down the yield curve working in the opposite direction of bond price decreasing due to increasing yield curve rates. That was basically the kind of calculation I was thinking of doing with the data from the example I presented for VFITX, and may still do.

Ironic--I just happened to notice this reply from ogd in that thread a little below stlutz's reply:
ogd wrote: In all seriousness, this will make a huge difference for me if I convince myself to move some cash that I [mis]allocated last year based on comparing FDIC-insured yields with SEC yields. This is non-emergency cash that should have normally gone into Treasuries. Particularly after this interest rate rise. This isn't just academic.
There's actually quite a bit of irony if you compare what we was said by certain people (including me) in that thread vs. this thread.

At any rate, I'm now starting to visualize an "equilibrium" scenario in which the yield curve moves higher over a given holding period by an amount at which resulting the bond price decreases are just offset by the bond price increases due to rolling down the yield curve. This assumes that the fund holds only (or mostly) bonds along the portion of the yield curve for which bond price would increase over time if the yield curve remained static. This provides an intuitive understanding of how the average maturity or SEC yield of a fund could gradually increase without a corresponding decrease in NAV.

I think some graphic illustrations would help, and want to work on that next (or soon at least).

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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

Kevin M wrote: Question to the group ... again: can we find a reference that tells us if roll yield might be distributed as dividends (the stlutz understanding; i.e., SEC, IRS, or other accounting rules require it), capital gains (from selling bonds), or both? My working assumption is that dividends (net investment income) represents only coupon payments minus fund expenses, and that any bond price increase is only distributed to shareholders as capital gain distributions when bonds are sold at a net profit. It would be nice to see a reference to resolve this, since then one unknown could be removed from the analyses.
After reading a bit about corporate bond accounting, here are my latest thoughts on this.

Amortization only relates to whether a bond was purchased at a premium or discount to par (face value). There are well-defined accounting methods for doing the amortization, and the methods have nothing to do with the increase or decrease in market value of the bond (e.g., from a combination of changing market rates and rolling down the yield curve).

If a fund is amortizing the bond premiums and discounts and passing the net on to shareholders, then amortization of premium bonds (purchased above par) will be passed on as expenses (since the book value of the bond is decreasing toward par), and amortization of discount bonds will be passed on as income (since the book value of the bond is increasing toward par). As stlutz has indicated, or at least implied (IIRC), the amortization schedule would be established when the bond is purchased; it would not be changed due to any change in market value of the bond.

I could see the net premium/discount amortization being included in "net investment income", which is passed onto shareholders in the form of "dividends".

Since the funds with distributions yields that are high relative to SEC yields (roughly average YTM) also have average coupons that are high relative to average maturity, the implication is that there is a net bond premium to par for the fund. Therefore, if funds are passing this on to shareholders, it will be a net expense, and reduce net investment income, and thus reduce distribution yield.

If the fund is not passing the net amortization onto the shareholders, then I'd expect it to be reflected in NAV, and in the case of funds with high average coupon, to put a downward pressure on NAV as the premium is amortized.

Conclusion: roll yield does not appear in dividend distributions (or the resulting distribution yield), and has nothing to do with dividend distributions being higher than SEC yield. Roll yield appears either as an increase in NAV (based on increase in price of underlying bonds), or in capital gain distributions (based on realized capital gains from bond sales). I'm assuming that unrealized capital gains are reflected in NAV (where else would they show up?). So we should be able to focus analysis of roll-yield effect on NAV change and capital gain distributions.

Of course it would still be nice to find an understandable summary of the accounting practices of bond mutual funds, but the tutorial I found on corporate bond accounting is the closest I could find: Accounting Topics - Bonds Payable - Explanation

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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

Kevin M wrote: Of course it would still be nice to find an understandable summary of the accounting practices of bond mutual funds ...
Found it in the annual report:

In the Statement of Operations (in annual report), there is one item listed as (gross) income: Interest. The expenses subtracted to get net investment income are what you'd expect: advisory fees, custodian fees, marketing and and distribution costs, etc.

In the "Notes to Financial Statements", here is the relevant note:
6. Other: Interest income includes distributions received from Vanguard Market Liquidity Fund and is accrued daily. Premiums and discounts on debt securities purchased are amortized and accreted, respectively, to interest income over the lives of the respective securities. Security transactions are accounted for on the date securities are bought or sold. Costs used to determine realized gains (losses) on the sale of investment securities are those of the specific securities sold.
So discounts and premiums are amortized and the result is included in interest income (and if I understand the meaning of "accreted" correctly, the net result is included in net investment income, which is distributed to shareholders as "dividends"). So dividend distributions consist of bond coupon payments and net amortized bond premiums and discounts.

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Chart visualizing "roll yield"

Post by Kevin M »

Below is a chart that attempts to graphically show what's being referred to as "roll yield" over a one-year period during which the yield curve changed. I switched from the 15-month holding period to a 12-month holding period to facilitate showing the change in bond yield as it moved one year toward maturity. I selected a 12-month period that has similar characteristics; i.e., yields generally increased, yet adjusted fund price was higher at end of holding period.

I used the treasury.gov yield curves for start and end of the one-year holding period, and used linear interpolation to estimate yields for the years they don't show (i.e., 4, 6, 8, and 9 years), which is good enough for my purpose here. I'm showing years 3 through 10 since this is the maturity range for the Int-Term Treasury bond fund.

Image

As indicated in the legend, the long blue line is the yield curve for 6/30/2014, and the long red line is the yield curve for 6/28/2013. Similar to the 15-month holding period I discussed before, we see that during this 12-month period the yield curve generally moved up, but anchored at the 10-year maturity which barely changed.

As an example of the yield-curve roll gain, look at the short line labeled "5 to 4" that connects the yield curves between years 4 and 5, which represents a bond that rolled down from 5-year to 4-year maturity. The YTM for this bond decreased from 1.41% to 1.25%, and the price increased accordingly. Note that this was a smaller change than if the yield curve had remained static, in which case the YTM would have decreased to 1.04% and experienced a larger price increase.

So here we graphically see the effect of increasing yields pushing bond price one way and the effect of rolling down the yield curve pushing it the other way.

We also see that there were larger YTM decreases (and larger price increases) in the 3-year to 5-year portion of the yield curve than for longer maturities. If 3-yr to 4-yr rates had increased by a little more (about 16 basis points), either through yield-curve flattening or more up-shifting, it would have wiped-out any yield-curve roll benefit.

It appears that the yield-curve roll gain was delivered to shareholders in the form of an increase in NAV of $0.05 and two capital gain distributions totaling $0.073 (not that roll-gain explains all of it, but it certainly seems reasonable that it's at least part of it).

Hope this helps.

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Re: So do we care more about change in bond price or bond yi

Post by ogd »

Fun stuff, Kevin! Like I said, I can't participate in depth, but I have a few observations.
Kevin M wrote: In the "Notes to Financial Statements", here is the relevant note:

6. Other: Interest income includes distributions received from Vanguard Market Liquidity Fund and is accrued daily. Premiums and discounts on debt securities purchased are amortized and accreted, respectively, to interest income over the lives of the respective securities. Security transactions are accounted for on the date securities are bought or sold. Costs used to determine realized gains (losses) on the sale of investment securities are those of the specific securities sold.
This is a great find! I've always wondered how the funds decide how to deliver gains. It appears that the observation that Vanguard funds tend to revert to a constant price is not accidental.
Kevin M wrote:It appears that the yield-curve roll gain was delivered to shareholders in the form of an increase in NAV of $0.05 and two capital gain distributions totaling $0.073 (not that roll-gain explains all of it, but it certainly seems reasonable that it's at least part of it).
The other thing that it did is it countered price declines that would have otherwise occured in a fund like VFITX, whose yields mainly went up. Speaking of price:
Kevin M wrote:Holding period was 6/28/2013 through 9/30/2014.
Price, adjusted for capital gains distributions was exactly the same at start and end of holding period.
There were two capital gain distributions totaling $0.073/share, without which price would have been higher by the amount of these distributions, about $0.073/share.
All other return came from dividend distributions (net investment income) of about $0.24 (which are used in the distribution yield calculations).
SEC yield was 1.07% at beginning of holding period and 1.65% at end of holding period, so 58 basis points higher.
During June 2013, SEC yield was going up fairly quickly. Since it's an average, the instantaneous value (if one was available) would probably be 10-20 bp higher. Or, what you can do is average the price as above for the preceding 30 days.
Kevin M wrote:
ogd wrote:In all seriousness, this will make a huge difference for me if I convince myself to move some cash that I [mis]allocated last year based on comparing FDIC-insured yields with SEC yields. This is non-emergency cash that should have normally gone into Treasuries. Particularly after this interest rate rise. This isn't just academic.
Yup, it's fun reading this. It was in fact precisely what I did and it was very rewarding. Right now with the yield curve flatter and CDs quite a bit better, I'm moving in the opposite direction, but so far the Treasuries have mostly stayed untouched, as rebalancing ammo for moves like last week. The main flow into CDs is from new money and even more so, munis, which after an extremely good year are not as competitive with the ever-weird CD market and in any event needed rebalancing.

I don't feel sorry for being convinced of anything in that thread, because it was in fact very good and even prescient. Compare: stlutz predicted 2.80% if the yield curve stayed constant. We in fact got 2.63% total return with the yield curve inching up slightly. Now that's what I call a useful thread :sharebeer More of those, please!

However, as I was hinting towards the end of that thread and as I am determined now, the party is not guaranteed or even likely to last. Our fellow bond investors make for some irritable neighbors, with their general insistence on such trite things as correcting mispricings between maturities.
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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

ogd wrote:
Kevin M wrote:It appears that the yield-curve roll gain was delivered to shareholders in the form of an increase in NAV of $0.05 and two capital gain distributions totaling $0.073 (not that roll-gain explains all of it, but it certainly seems reasonable that it's at least part of it).
The other thing that it did is it countered price declines that would have otherwise occured in a fund like VFITX, whose yields mainly went up.
Possibly. This is kind of what I showed in the most recent chart above, and one of the things I explained in that reply. However, there I just looked at the net decrease in YTM (up because of up-shift in yield curve, down because of declining maturity). The unknown that affects the actual price change of a given bond is the coupon rate. As I showed in a chart up-thread, price may increase or decrease as maturity decreases, depending on the coupon as well as the shape of the relevant portion of the yield curve.

For example, if we assume that a 5-year bond had the current average coupon of the fund, 1.8%, at the beginning of holding period (HP), then when YTM decreased from 1.41% at start of HP to 1.25% at end of HP, price would have increased by 25 basis points. However, for a bond coupon rate of 2.1%, bond price would have decreased by 2 basis points.

If I get motivated enough, I may be able to actually get more of a clue about this by looking at the actual holdings in the quarterly SEC filings close to start and end of HP. Since the fund has less than 100 bonds, something like this would be more feasible than for some of the other bond funds.

However, since we know NAV was higher at end of HP, and we know the yield curve shifted up across the entire range of maturities held by the fund, it seems reasonable to assume that average coupon rate of the bonds that were sold was generally high enough to produce a net positive price change. Whether the realized capital gains (that were distributed) were partly or entirely generated during the HP is another unknown; if we could view unrealized cap gains in an annual or semi-annual report from shortly before the start of HP, it would give us a clue. I couldn't find anything but the most recent reports on the VG site, which don't go back far enough. Again, maybe a clue in SEC filings.

We could actually probably learn a lot about how the fund is managed by looking at the change in holdings over time; e.g., are they mainly selling bonds as they hit the lower end of their target maturity range (3 years), or are they doing more active management trying to optimize things around the yield curve?

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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

ogd wrote: However, as I was hinting towards the end of that thread and as I am determined now, the party is not guaranteed or even likely to last.
You mean like I flat out stated toward the beginning of that thread()?
Kevin M wrote: With respect to munis and treasuries, I trust that the bond market is quite efficient, so I don't think there's generally a free lunch with either. Munis clearly have more credit risk than treasuries; the market prices this risk accordingly. There may be some inefficiencies from time to time, such as the muni bond fund scare a couple of years ago, and the muni bond ETF market price discount to NAV recently. Calm, rational investors may be able to take advantage of these inefficiencies, but nothing is certain.
And that goes for riding the yield curve, SEC yield, and yes, distribution yield as well!

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Re: So do we care more about change in bond price or bond yi

Post by Doc »

Kevin M wrote: Found it in the annual report:
6. Other: Interest income includes distributions received from Vanguard Market Liquidity Fund and is accrued daily. Premiums and discounts on debt securities purchased are amortized and accreted, respectively, to interest income over the lives of the respective securities. Security transactions are accounted for on the date securities are bought or sold. Costs used to determine realized gains (losses) on the sale of investment securities are those of the specific securities sold.
So discounts and premiums are amortized and the result is included in interest income (and if I understand the meaning of "accreted" correctly, the net result is included in net investment income, which is distributed to shareholders as "dividends"). So dividend distributions consist of bond coupon payments and net amortized bond premiums and discounts.

Kevin
Note on accretion of market discounts:

It is my understanding that the tax payer has the option of delaying the taxable income associated with market discounts until the bond matures or is sold. This is advantageous to the tax payer as it delays payment of the tax. At at least one brokerage firm I am aware of it is this option that is the default for the new FI cost basis reporting that went into effect this year. (Original issue discount including TIPS inflation adjustment is another matter and has to be accreted annually.)

I bring this up only because someone posted that bond fund distributions were related/equal to the taxable income of the fund. I don't know if the postponement of tax on the market discount is an option for funds . None of this probably has any relevance to the main topic of the thread.
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Re: So do we care more about change in bond price or bond yi

Post by ogd »

Kevin M wrote:You mean like I flat out stated toward the beginning of that thread()?
Kevin M wrote: With respect to munis and treasuries, I trust that the bond market is quite efficient, so I don't think there's generally a free lunch with either. Munis clearly have more credit risk than treasuries; the market prices this risk accordingly. There may be some inefficiencies from time to time, such as the muni bond fund scare a couple of years ago, and the muni bond ETF market price discount to NAV recently. Calm, rational investors may be able to take advantage of these inefficiencies, but nothing is certain.
And that goes for riding the yield curve, SEC yield, and yes, distribution yield as well!

Kevin
Yup, I found that Kevin to be very convincing, together with some of my own research :sharebeer
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Re: So do we care more about change in bond price or bond yi

Post by stlutz »

Nothing particular to add here, but just want to say thanks again to Kevin and ogd for doing all of the analysis and legwork on this!

Although with all of the attention that the stultz family of mutual funds received in this thread, I think I see an ER increase the funds' future! :wink: :moneybag
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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

Kevin M wrote: We could actually probably learn a lot about how the fund is managed by looking at the change in holdings over time; e.g., are they mainly selling bonds as they hit the lower end of their target maturity range (3 years), or are they doing more active management trying to optimize things around the yield curve?

Kevin
I did some work on this today. I copied/pasted the holdings from the latest annual and semi-annual reports into a spreadsheet, and did my own calculations of average maturity, average coupon, etc. Came out the same or close to the values stated in the report (more on the details later perhaps). This is the setup to do some more detailed analysis of changes in fund holdings over time, etc., but for now, here's the actual distribution of holdings (% of total market value) by term to maturity for the int-term treasury fund as of 7/31/2014:

Image

This is a finer-grained breakdown of this:

Code: Select all

Distribution by Effective Maturity
(% of portfolio)
1 - 3   Years   0.7%
3 - 5   Years  45.3
5 - 7   Years  29.0
7 - 10  Years  24.9
10 - 20 Years   0.1
While pulling the holdings from the reports, I reviewed the Chairman's Letter and the Advisors' Report, and found these comments enlightening:

From letter to shareholders:
Falling bond prices clipped the performances of the Short-Term and Intermediate-Term Treasury Funds, given that yields rose at the shorter end of the yield curve. The slim cushion provided from income earned over the six months, however, kept these funds in positive territory.
The three short- and intermediate-term funds’ allocations to shorter maturities contributed to their lagging their peer groups’ average returns, while the three funds’ performances versus their benchmarks were mixed.
From Advisors Report:
All four funds had durations shorter than those of their benchmark indexes. That stance, which can act as a buffer against rising interest rates, proved to be a drag on performance this time for the Intermediate- Term Treasury Fund in particular. Its average duration at the end of the period was 5.1 years, compared with 6.5 years for its benchmark.
On the positive side, some active yield curve management strategies added a little incremental return.
With rising rates in the offing, we are entering the second half of the funds’ fiscal year with durations still shorter than those of their benchmarks.
So clearly active management going on. Positive returns are explained by income offsetting price declines due to rate increases at shorter end of curve, and some positive impact from "active yield curve management strategies. No explicit reference to any contribution to returns from maturity decline, but perhaps they're lumping that in with active yield curve management.

And with respect to this:
Kevin M wrote:I couldn't find anything but the most recent reports on the VG site, which don't go back far enough. Again, maybe a clue in SEC filings.
I figured out how to use EDGAR to get a couple of the older reports, and loaded the data for a few prior periods into the analysis spreadsheet for further analysis.

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Re: So do we care more about change in bond price or bond yi

Post by ogd »

Kevin M wrote:So clearly active management going on. Positive returns are explained by income offsetting price declines due to rate increases at shorter end of curve, and some positive impact from "active yield curve management strategies. No explicit reference to any contribution to returns from maturity decline, but perhaps they're lumping that in with active yield curve management.
Well, the passive ETF IEI behaved about the same (with slightly smaller duration/volatility), so clearly management wasn't necessary for this level of returns. Or the entirely passive stlutz strategy, for that matter, which has no "if interest rates do this" decision points. What we got the market giveth, through its lack of decisiveness about the future of rates.

In a recent exchange with Doc who was fund-shopping I declared myself somewhat wary of the active management in VFIUX, to the degree it occurs. I would prefer it didn't try to guess anything. But given the low expenses and the small magnitude of the moves, it's mostly a shrug.

What's your remaining source of puzzlement? The breakdown between income and capital returns? There is I think a good example above for why we mostly don't care:
Kevin M wrote:For example, if we assume that a 5-year bond had the current average coupon of the fund, 1.8%, at the beginning of holding period (HP), then when YTM decreased from 1.41% at start of HP to 1.25% at end of HP, price would have increased by 25 basis points. However, for a bond coupon rate of 2.1%, bond price would have decreased by 2 basis points.
The second bond had a premium, which decreased like all premiums do approaching maturity as some of it was paid out; in this case, more than the yield changes could offset. However, without even bothering to verify the numbers: bond A (1.8%) and bond B (2.1%) had the same total return in the period and they have the same total return prospects going forward. So why would we care?
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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

For my next trick ... here is a chart that shows the change in VG int-term treasury holdings by maturity between Jan 31, 2014 and Jul 31, 2014:

Image

To calibrate, for a rolling bond ladder, we would have sold bonds as they reached 3-year maturity and bought 10-year bonds to refill the ladder. In the chart that would appear as negative bars in the maturity range of 1/31/2017 to 7/31/2017 and offsetting positive bars in the maturity range between 1/31/2024 and 7/31/2024. This assumes no net ladder/fund inflows or outflows.

Indeed, most of the bonds in the that reached 3-year maturity were liquidated, with a couple of large sales of bonds with maturities of 1-3 months beyond 3-years (as of 7/31/14--net -$687M). But although there were three new bonds purchased maturing in 2024 (+$183.5M), most of the buying occurred in the 4.5-year to 5.5-year term range (+$487M net, bonds maturing in 2019), with some additional concentration in the 6.5-year to 7-year range (+$100M).

Next, I thought it would be interesting to superimpose the actual yield curves for the fund on this chart, to see if this gives some insight into what the managers were thinking. Here's a clue. YTM changes between these dates for 3,5,7,10-year maturities were +0.33, +0.27, +0.11, -0.09 respectively.

So, although there were price declines due to rising rates at the shorter maturities, the price of the 10-year actually was higher at the end of the holding period. So perhaps the managers preferred to focus their buying in the ranges that also had experienced price declines due to rising rates. According to the semiannual report they also are anticipating rising rates, so are keeping fund duration significantly shorter than their benchmark, which also was accomplished by buying shorter-maturity bonds.

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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

ogd wrote: The second bond had a premium, which decreased like all premiums do approaching maturity as some of it was paid out; in this case, more than the yield changes could offset. However, without even bothering to verify the numbers: bond A (1.8%) and bond B (2.1%) had the same total return in the period and they have the same total return prospects going forward. So why would we care?
Because I am investigating the effect you refer to as "roll yield". Things make more sense when you keep them in context. My statement that your quote above responds to was in turn a response to this comment by you:
The other thing that it did is it countered price declines that would have otherwise occured in a fund like VFITX, whose yields mainly went up.
The "it" in your statement is referring to "yield-curve roll-gain" in my statement that you were responding to.

You have mentioned this "roll yield" as the explanation to return patterns that at first glance appear puzzling (at least to me). I think that's something that's worthwhile investigating, along with other factors that may also have as much or more impact. I'm certainly learning a lot in doing this research. Hope others are benefiting from it as well.

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Re: So do we care more about change in bond price or bond yi

Post by Doc »

Kevin and ogd,

I'm trying to follow this discussion as best I can. It appears that "roll yield" is an equivalent term to "rolling the yield" curve. Is my interpretation anywhere near correct?
Riding and Rolling the Yield Curve in Government Securities
An investment strategy that you may want to consider is Riding and Rolling the Yield Curve. Using $1.5 million, for example, purchase $500,000 each of the 4-year, 3-year, and 2-year Treasury Notes. (Or 12-month, 9-month, and 6-month bills; any term structure of maturities is possible.) Each year as the notes age, the 4-year note will become a 3-year note, the 3-year note will become a 2-year note, and the 2-year note will become a 1-year note.
...
In addition to these capital gains, the portfolio continuously earns income at approximately the 3-year note rate.
http://www.alistertalksbonds.com/invest ... ecurities/
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Re: So do we care more about change in bond price or bond yi

Post by ogd »

Doc wrote:Kevin and ogd,

I'm trying to follow this discussion as best I can. It appears that "roll yield" is an equivalent term to "rolling the yield" curve. Is my interpretation anywhere near correct?
Riding and Rolling the Yield Curve in Government Securities
An investment strategy that you may want to consider is Riding and Rolling the Yield Curve. Using $1.5 million, for example, purchase $500,000 each of the 4-year, 3-year, and 2-year Treasury Notes. (Or 12-month, 9-month, and 6-month bills; any term structure of maturities is possible.) Each year as the notes age, the 4-year note will become a 3-year note, the 3-year note will become a 2-year note, and the 2-year note will become a 1-year note.
...
In addition to these capital gains, the portfolio continuously earns income at approximately the 3-year note rate.
http://www.alistertalksbonds.com/invest ... ecurities/
Yes.

Perhaps "roll yield" is not a legitimate shortcut, given its use in futures and options elsewhere, as Kevin notes above. The shortest phrase I can find that's unambiguously about the yield curve is "roll-down return". Doesn't roll off the tongue as nicely, but we can start using that.
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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

Kevin M wrote: Next, I thought it would be interesting to superimpose the actual yield curves for the fund on this chart, to see if this gives some insight into what the managers were thinking. Here's a clue. YTM changes between these dates for 3,5,7,10-year maturities were +0.33, +0.27, +0.11, -0.09 respectively.
Ta-da! Here it is (kind of). Instead of showing the yield curves based on fund holdings for the two dates, I just show the change in YTM for the bonds held by the fund, which provides more insight anyway.

Image

The red line is the change in YTM, so absent any effect from declining maturity, bond price will be inversely related to the red line, so I visualize the bond price-change curve as roughly the reflection of the YTM-change curve about/across the horizontal (0%) axis.

As we've been discussing, there will be some offset in price movement due to the declining maturity effect (aka, "roll yield), but that's not reflected here. Come to think of it, I can actually just add a curve showing change in bond price--next task. But tack to this chart ...

Note that the largest increases in YTM were for bonds maturing in 2018, so those bonds also would have experienced the largest price declines. Conversely, the largest decreases in YTM were for bonds maturing in late 2022 through 2023, so these bonds would have had the largest price increases.

Note that purchases were concentrated in the in the middle range with YTM increase and price decrease. They had to buy some bonds of longer maturity to keep their average target maturity and duration, but note the cluster of purchases of bonds maturing in 2021, which had only moderate price increase (YTM decrease) compared to longer maturities.

It would be very interesting to be a fly on the wall where the bond managers are making their buy/sell decisions.

Kevin
If I make a calculation error, #Cruncher probably will let me know.
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Kevin M
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Re: So do we care more about change in bond price or bond yi

Post by Kevin M »

And here is the chart showing percent change in price along with change in YTM. To better see the inverse relationship, I multiplied change in YTM by the modified duration of the bonds (average of MD at start and end of period); so dP/P and DYxD should be approximately a reflection about the 0% axis.

Image

This shows pretty conclusively that for this six-month period, yield curve moves dominated price change in the range most bonds were sold (roughly 3-year maturity); any benefit from decreasing maturity (aka, "roll yield") was not enough to offset the losses. It also verifies that bond purchases were concentrated in ranges at which bond prices were at or below (or slightly above) what they were six month earlier.

Kevin
If I make a calculation error, #Cruncher probably will let me know.
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