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Riding the yield curve, in action

Posted: Sat Feb 08, 2014 5:22 pm
by ogd
Hi guys,

We live in interesting times in bond land, as if that needs repeating on this forum. The yield curve is relatively steep and it hasn't changed much overall since the bloodletting last summer, which seldom if ever happens. This has provided us a live experiment showing how bond funds (or narrow ladders) can get additional returns from the steepness of the yield curve.

Back in July, stlutz started this thread "Treasuries, CDs, and Munis reconsidered", which was to me very instructive. It was about a thought experiment on how much extra return you can get by rolling bonds before maturity and how this can be significantly higher than the SEC yield, or the alternate instruments available at the time.

Well, the market has given us the action needed to back up this thought experiment. Today the 5 year Treasury yield is 1.47%. The first time it reached that figure was June 24, 2013, when it ended at 1.48%. Furthermore, the yield curve has remained steep since, in fact slightly steeper:

Code: Select all

              3Yr    5Yr    10Yr
06/24/2013    0.73   1.48   2.57
02/07/2014    0.66   1.47   2.71
So what happened in this interval? VFIUX (Interm-term Treasuries, 3-10 years) has returned 1.82% in 7.5 months, corresponding to an annual return of 2.93%. I chose Treasuries because they are simpler and unaffected by credit risk changes meanwhile.

This is much more than the fund's SEC yield, either now or then, which is in the neighborhood of 1.4% - 1.6% depending on how you choose to read the 30 day smoothing. It's also much more than the CDs available at the time, and after state taxes it probably beats the fabled PenFed CD as well. VFIUX had no right to earn this much, except by the curve riding effect.

Lest you think that the managers of VFIUX did something funny and simply got lucky, take a look at:
VGIT (indexed, Treasuries + Agency MBS, slightly shorter): 1.72%, annualized 2.77%
IEI (Barclay's 3-7 Treasury index, shorter): 1.65%, annualized 2.65%

So everyone riding the curve in the intermediate range made quite a bit more than they were supposed to. Say what you will about uncertain bond times, but I like making 60% more than what I was promised, while the prospects going forward (yields) have stayed the same, i.e. no "bond bull market".

Disclaimer: because yields were so incredibly volatile in June 2013, these numbers change if going back and forward even a few days; for example, it's possible that the snapshots of morningstar and treasury.gov from the same date reflect different intraday numbers. I would have liked to have more stable numbers at that end, but it's a luxury that the bond market has not given us yet for a start - end interval that I'd consider long enough. We might get better comparisons in the future. The other disclaimer is that I still hold the belief I stated in that thread, which is that the yield curve cannot be expected to stay steep. But when it does, we profit.

Anyway, I think it's hard to dispute that real life returns have validated the curve riding bonus. Thanks again stlutz for drawing our attention to it on the theoretical level before the returns started coming in.

Re: Riding the yield curve, in action

Posted: Sat Feb 08, 2014 5:30 pm
by billyt
odg:
No one wants to hear this. It would shake their obsession with bondmageddon and 100% stock portfolios!

Re: Riding the yield curve, in action

Posted: Sat Feb 08, 2014 7:08 pm
by billyt
It's so ridiculous really. No one wants to hear the truth, do the math, or accept factual information.

Sadly, this post will sink like a stone.

While "Why own bonds at all?" will be around for days.

Re: Riding the yield curve, in action

Posted: Sat Feb 08, 2014 8:42 pm
by livesoft
Yep, and look at all the people trashing GNMAs. What is the YTD return of Vanguard GNMA fund? Why it is 2.31%! What is up with that?

Re: Riding the yield curve, in action

Posted: Sat Feb 08, 2014 8:56 pm
by ogd
livesoft: yes, some bond funds have recovered well this month, but what I'm talking about is a little different. The GNMA fund earned this much because of lower yields in that space; to a large degree it did so at the expense of future returns.

However, over the timespan that I mention, VFIUX (and maybe GNMA too, haven't checked) earned a great return without any significant moves in the yield curve. It did not have borrow from the future, so to speak. We are being rewarded handsomely for the uncertainties in the bond market. The rose is not all thorns!

Re: Riding the yield curve, in action

Posted: Sat Feb 08, 2014 9:04 pm
by Clive
Grabbing the Treasury yield curve values as of June 2013, plotting with X-axis time scaled indicates that the peak of the steepest part of the yield curve back then was around the 2019 period (casual glance by eye).

Looking up the price for a 2019 Treasury bond back in June 2013 indicates the 1% 6/30/2019 bond had a ask price of 95.7422

As of more recent the bid price of that bond was 96.7031

So over 228 days, (0.625 of a year) the capital gain = 1.003% assuming sold (including buy/sell spread)
1% Coupon yield / 0.957422 price = 1.0445% yearly yield x 0.625 years held = 0.653% income over holding period.
Combined = 1.656% over 0.625 of a year = 2.66% annualised

Image

Re: Riding the yield curve, in action

Posted: Sat Feb 08, 2014 9:06 pm
by weltschmerz
deleted

Re: Riding the yield curve, in action

Posted: Sat Feb 08, 2014 10:09 pm
by Clive
So in summary there are 3 ways to make money with bonds:

1) Interest payments
2) Capital gains from "riding the yield curve" when interest rates are stable
3) Capital gains from increased bond prices when interest rates are falling

If folks are worried about losing money in bonds due to rising interest rates...
Applying riding the yield curve to TIPS can help reduce rising interest rate risks should rising interest rates go hand in hand with rising inflation

Image

Re: Riding the yield curve, in action

Posted: Sat Feb 08, 2014 10:41 pm
by stlutz
Obviously, the "riding the yield curve" benefit comes from selling bonds before maturity. If you hold to maturity, you don't get the capital gains benefit. I wonder then, for the small-time investor, if it makes more sense to use bond funds instead of individual bonds. The professional bond fund managers are probably better able to follow the price movements of the bonds, and are probably able to get better execution prices than I would, thus maximizing the effects of the ride on the yield curve. I had been eschewing the bond funds recently in favor of doing it myself with individual bonds, so as to save the 0.1% expense ratio on the fund, but this may be foolish.
One of the conclusions we came to in the original thread that I didn't understand when I made the first post in it was that a bond ladder and a "bullet" strategy with the same duration will perform approximately the same. With a ladder, your return is determined by the yield is on bonds when you buy them. The 2.8% return that ogd illustrated is about what the yield was on an 11 year bond.

So, with the ladder, all of your return over time is from interest; with the "bullet" approach, it will come from a mix of interest + capital gains.

Re: Riding the yield curve, in action

Posted: Sun Feb 09, 2014 11:50 am
by billyt
That's right The Dan. Rolling your own bond ladder and holding to maturity reduces your returns. You are better off with a low cost fund.

Re: Riding the yield curve, in action

Posted: Sun Feb 09, 2014 12:16 pm
by stlutz
Rolling your own bond ladder and holding to maturity reduces your returns.
How so? Treasury Bonds can be bought and sold with no commission and with spreads of a few pennies on $100 at multiple brokers. If one wants to buy and hold a ladder to duration--that's fine; a ladder and a bullet strategy with the same overall duration will produce very similar returns with very similar risk.

I'm not looking to start a big fight here. There are a lot of posts on this forum arguing that rolling a ladder and holding to maturity has some magical power vs. buying a fund, when they are in fact pretty much the same thing. If there is no magical power of a ladder to reduce risk/add returns, it is also conversely true that there is no magic that a fund has that individual bonds do not. The individual Treasuries vs. treasury fund question should be a big yawner in terms of which is "better".

If one wants to take credit risk (i.e. corporate bonds, non-top-rated muni bonds), then a fund is definitely a much preferred option.

Re: Riding the yield curve, in action

Posted: Sun Feb 09, 2014 12:32 pm
by billyt
In a positive yield curve environment, your returns are reduced if you hold to maturity. Why hold a Treasury for those last 2 or 3 years earning next to nothing when you can sell at a premium and reinvest at higher rates in longer treasurys or CDs? Bond fund mangers (and the indexes that follow their aggregate decisions) know this and sell before maturity. If holding to maturity was the best way to generate a return from bonds, all the managed funds would be doing it.

Do you know more than all the other professional bond traders? If not, stick to a low cost bond fund.

Re: Riding the yield curve, in action

Posted: Sun Feb 09, 2014 12:35 pm
by ogd
billyt: I agree with stlutz that this doesn't make the ladder worse. Remember that a ladder of the same duration as VFIUX goes out to 10-11 years maturities, which are pretty high yielding. It's not a guarantee, but in general the yield curve even when steep tends to be linear enough that riding even the best point on the curve is not much better than extending the maturities out twice that much.

The one free lunch right now, from using a fund vs a ladder, is to use a savings account on the short end which lets you push the fund duration higher. Savings accounts beat Treasuries below 3 years handily, which is what makes it a free lunch. Such deadbeat Treasuries would be 25% - 30% of a ladder of the same duration as VFIUX.

My main point with this thread is that the funds are doing much better than their SEC yield, as a direct consequence of the bond market's uncertainty about where the yields are going. The same uncertainty that is making many apprehensive about bonds is making some of us quite a bit of money.

Re: Riding the yield curve, in action

Posted: Sun Feb 09, 2014 12:37 pm
by billyt
Holding to maturity clearly makes the case of the ladder worse.

Re: Riding the yield curve, in action

Posted: Sun Feb 09, 2014 12:56 pm
by Clive
Yahoo finance data ^TNX (10 year Treasury Yield). Year end values filtered out.

Assume a rolled 10 year ladder where each year the maturing bond (that had been held for 10 years) was rolled into another 10 year that had a coupon yield = 10 year market yield (i.e. bought at par value). For simplicity - as each bond was being held to maturity and assumed to have been bought at par value, the 10 year ladder data for each year is the average of the current and past nine years 10-year-yield's

Compared to a constant rolled 10 year (buy 10 year with a coupon yield = 10 year market yield, hold for a year, sell and buy another 10 year.....etc.)

For the constant rolled I assumed the 9 year yield after having held for a year was the same as the 10 year yield at that time. More likely the 9 yield yield would be less than the 10 year yield (positive sloping yield curve), so I also included a constant rolled series were it was assumed the 9 year yield was 0.25% less than the 10 year yield.

Image

Yahoo's ^TNX data extends back to 1962, but as a ten year ladder needs 9 prior years of data values the start year for the comparison was 1971 (note chart Title incorrectly states 1972 as I only noticed that after I'd posted the chart) . All gains shown are total gains (accumulation).

Broadly looks to me that the 10 year ladder was similar to constantly rolling a 10 year, assuming that generally the yield curve between 9 and 10 years was/averaged flat. If the yield curve between 9 and 10 years was positive and averaged 0.25% then the constant rolled 10 year was more rewarding.

Re: Riding the yield curve, in action

Posted: Sun Feb 09, 2014 1:07 pm
by Doc
ogd wrote: Disclaimer: because yields were so incredibly volatile in June 2013, these numbers change if going back and forward even a few days; for example, it's possible that the snapshots of morningstar and treasury.gov from the same date reflect different intraday numbers.
I think the Treasuries numbers are from their constant maturity series. IIRC they use a five (?) point spline fit and force it to match the closest actual security. This methodology would make the number slightly different from actual quotes.

There is a nice yield curve chart from the Treasury here:
http://www.treasury.gov/resource-center ... ation.aspx

(You need to add in the 2013/06/24 date to see the comparison. Note the x-axis is not linear.)

Re: Riding the yield curve, in action

Posted: Sun Feb 09, 2014 1:58 pm
by linuxizer
ogd- Another advantage of using a savings account for the short end is that it increases convexity for the same duration.

One way to view riding the yield curve is to calculate the implied interest rates on a single bond that you buy at maturity. It turns out if you go through the exercise and properly take into account opportunity costs by marking to market, with a postitively-sloping yield curve the first few years return more than the last few years, even though the coupon payments are the same. This happens due to capital appreciation that ostrich bond investors (those who don't mark-to-market) don't appreciate.

Consider a static (doesn't change over the time period considered, to isolate the particular effect we're interested in) yield curve that is positively sloped, say 5% for 20-year bonds, 3% for 10-year, and 1% for 1-year bonds.

You buy a 20-year bond for $1k at 5%. In the first 10 years you make:
[*]$50 per year (plus the interest on that--we'll assume it's short-term interest and ignore it but if you're more able to effectively roll this into a longer maturity you would make more)
[*]Plus the $171.69 in capital appreciation (remember, the interest rate did not change!).

In the next 9 years you make:
[*]$50 per year (again, plus the interest-on-interest)
[*]Minus the 1039.70-1171.69=-131.99 in capital depreciation.

Finally, that final year you make $50 in coupon payments (+i-on-i), minus the remainder of the capital depreciation as it is now worth par at maturity.

R code to reproduce:
library(maRketSim)
b <- bond( mkt=market(market.bond(i=.05),t=0), mat=20 )
summary( b, market(market.bond(i=.03),t=10) )
summary( b, market(market.bond(i=.01),t=19) )

Re: Riding the yield curve, in action

Posted: Sun Feb 09, 2014 4:03 pm
by Scooter57
VFIUX has only "returned 1.82% in 7.5 months" if you bought it in July when it hit a price low. If you had bought it instead, 2 months earlier, on April 30,l according to Morningstar you are still down 2.3% and that is total return, including dividends.

And the only reason that the fund is up YTD is that we are looking at only 5 weeks of performance. If you bought it in April or before, you are ahead of where you were Dec 31, 2013, but not where you were when you bought it.

So this argument appears to be a market timing argument. It proves only that you will get a nice return if you buy at a bottom and measure later during a temporary rise. However, for buy and hold investors what matters is long term gains, and with an intermediate fund that has a 5.24 duration and which Morningstar flags as "Highest risk", these seeming positive results can vanish very fast. And probably will.

The SEC yield of this fund is only 1.63, so my 3.05% CD is still a much better option and with no principal risk.

Re: Riding the yield curve, in action

Posted: Sun Feb 09, 2014 4:16 pm
by ogd
It's not a market timing argument, at least not a simple one. That's why I objected to livesoft's January GNMA numbers -- for my numbers I specifically chose a point where the state of the Treasury market was for all intents and purposes the same as today. I'm pointing out that despite this, VFIUX has returned far more than its SEC yield.

Furthermore, we have the theoretical arguments plain and clear and anyone can run their own simulation. The behavior of VFIUX is just real life confirmation.

Now you might argue that the fact that the yield curve has remained steep is itself an accident of market timing, it was not a priori expected to be so, and that would be a valid point. What I'm saying though is that we are as we speak extracting value from this steepness caused by the uncertainties about rates. So the risk that arguably exists in the market does no go uncompensated, above and beyond the SEC yield.

Re: Riding the yield curve, in action

Posted: Wed Mar 12, 2014 12:16 pm
by ogd
Thought I'd post a yield curve update, since we can now find Treasury yields back in August that are close to identical to today's. Moreover, these yield levels are relatively stable both today and in August, which is nicer than the June timeframe that I used previously.

Code: Select all

Date       3 Yr	5 Yr	7 Yr	10 Yr
03/11/14	0.79	1.62	2.25	2.77
08/28/13	0.79	1.62	2.22	2.78
Returns:
VFIUX (IT Treasury): 1.66%, annualizes to 3.13%
VBTLX (Total Bond Market): 2.45%, annualizes to 4.63%

Once again, this is without any material changes in market yields over the period. I'd call that pretty nice. The SEC yields of the funds are 1.58% and 2.23% respectively, so they're making close to double what they're supposed to. The SEC yields back in August were also pretty much at the current levels, although the 30 day smoothing makes it harder to pinpoint them.

For kicks, I also plugged in VCADX (CA IT munis), as per the original thread that was comparing all three, and I got such a huge number that it made me realize the yields in the muni space have behaved quite differently; they've gone down a lot since August. Back then VCADX was hovering in the 2.6% range SEC, whereas now it's 2.04%. There must have been major changes in credit quality perception or something of the sorts, since interest rates haven't budged. I can't find a stable plateau for VCADX close to current levels, so I'll withhold judgment on how well it's riding the curve.

But just look at those Treasuries and TBM milking it for all it's worth.

Re: Riding the yield curve, in action

Posted: Fri Jun 27, 2014 1:56 pm
by ogd
An update on the one year anniversary of the original thread "Treasuries, CDs and munis". We can look at actual one year results now, yay.

First, the yield curve:

Code: Select all

Date            3yr     5yr     10yr    30yr
06/26/2013      0.69    1.45    2.55    3.58
06/26/2014      0.90    1.64    2.53    3.35
So it's quite flatter (as I was arguing was expected), but mostly a wash in the intermediate region, certainly no tailwind for the result below.

The one year total returns:
VFIUX (IT Treasury): 2.63%
VBTLX (Total Bond Market): 4.98%
VWIUX (IT munis, national): 7.5%

So munis won this comparison by a mile, coming close to 10% pre-tax equivalent in the higher brackets. In general, though, I'd say that the outsized returns of riskier bonds were in good part due to improving credit outlook and unlikely to be repeated.

IT Treasuries are the most "pure" component; even they handily beat CDs available at the time, but we can also see the bonus starting to subside from my earlier projections as the yield curve flattened (i.e. the market coming to its senses).

TBM surprises me here: I wouldn't call it "risky" by any means, yet it got a much, much higher return than Treasuries. Perhaps one explanation is its higher proportion of long-term bonds, which benefitted from the flattening. Duration is comparable, but it fails to capture uneven moves in yields.

All in all, it's been a good year :sharebeer

Re: Riding the yield curve, in action

Posted: Fri Jun 27, 2014 2:18 pm
by Longtimelurker
Ogd - bottom line this for me. Does TBM index benefit from this? What about Vanguard Intermediate term muni fund? You guys lost me in the detail....

Re: Riding the yield curve, in action

Posted: Fri Jun 27, 2014 2:24 pm
by ogd
Longtimelurker wrote:Ogd - bottom line this for me. Does TBM index benefit from this? What about Vanguard Intermediate term muni fund? You guys lost me in the detail....
Yes, both. There are other factors, which is why the IT Treasury fund is the purest expression of the roll yield bonus. Imagine that extra 1% or so that the Treasury fund got over its own SEC yield as being a factor in the performance of TBM and munis.

Bottom line is, "in this interest rate environment" bond funds are making close to 2x their stated yield, because of those very uncertainties. You are getting paid handsomely for your risk.

Re: Riding the yield curve, in action

Posted: Fri Jun 27, 2014 2:27 pm
by Longtimelurker
ogd wrote:
Longtimelurker wrote:Ogd - bottom line this for me. Does TBM index benefit from this? What about Vanguard Intermediate term muni fund? You guys lost me in the detail....
Yes, both. There are other factors, which is why the IT Treasury fund is the purest expression of the roll yield bonus. Imagine that extra 1% or so that the Treasury fund got over its own SEC yield as being a factor in the performance of TBM and munis.

Bottom line is, "in this interest rate environment" bond funds are making close to 2x their stated yield, because of those very uncertainties. You are getting paid handsomely for your risk.

Ok. Got the credit risk stuff. So flattening the yield curve would diminish this benefit, but as long as it is steep, there is a benefit. Got it. Makes me feel better about buying bonds. Thank you!

Re: Riding the yield curve, in action

Posted: Fri Jun 27, 2014 4:44 pm
by stlutz
Thanks for the update, ogd--that's interesting. I didn't realize the curve had flattened that much over the past year

Re: Riding the yield curve, in action

Posted: Mon Jun 30, 2014 2:54 am
by bnes
ogd wrote:However, over the timespan that I mention, VFIUX (and maybe GNMA too, haven't checked) earned a great return without any significant moves in the yield curve. It did not have borrow from the future, so to speak. We are being rewarded handsomely for the uncertainties in the bond market. The rose is not all thorns!
But don't you have to realize those gains? If you're talking about price appreciation, that can evaporate.

Re: Riding the yield curve, in action

Posted: Mon Jun 30, 2014 3:19 am
by alexfrey
Interesting thread. I don't disagree with many of the comments, just wanted to point out that ex-ante (looking-forward) expected roll-yield can be quite different from ex-post calculated roll yield.

In particular, you can always calculate a roll yield for a past period, which could be positive or negative. But it isn't strictly clear that you should expect roll yield to be positive in the future, even if the yield curve is positively sloped. A positively sloped yield curve can indicate the expectation that rates will increase in the future. If the "expectations theory" of the yield curve is correct, then there is actually a (loose) no-arbitrage condition in which, for instance, buying a ten year bond should return the same as buying a five year bond and then rolling it over at the expected five-year rate five years from now.

Anyway, if everything is priced totally rationally then the negative impact of rates increasing can offset the positive impact of the roll yield. To the point of the thread, that hasn't happened the last year.

Now I suspect that right now that you are absolutely right and that the expected roll yield is slightly positive, but just wanted to point out that it is not accurate to assume that this is ordinarily true.

Re: Riding the yield curve, in action

Posted: Mon Jun 30, 2014 10:05 am
by Doc
alexfrey wrote:In particular, you can always calculate a roll yield for a past period, which could be positive or negative. But it isn't strictly clear that you should expect roll yield to be positive in the future, even if the yield curve is positively sloped.
1) Without testing I believe that there is always a roll yield if the slope of the yield curve is positive.

2) You might not realize that roll yield because of transactions costs.

Perhaps an interesting example of the cost/roll yield idea is some of the short duration TIPS ETFs. Vanguard and IShares use the 0-5 index while Pimco uses the 1-5. Does Pimco's use of derivatives and/or high volume reduce their transaction costs enough to make a roll yield strategy productive?

Re: Riding the yield curve, in action

Posted: Mon Jun 30, 2014 10:22 am
by ogd
bnes wrote:
ogd wrote:However, over the timespan that I mention, VFIUX (and maybe GNMA too, haven't checked) earned a great return without any significant moves in the yield curve. It did not have borrow from the future, so to speak. We are being rewarded handsomely for the uncertainties in the bond market. The rose is not all thorns!
But don't you have to realize those gains? If you're talking about price appreciation, that can evaporate.
Bond funds have high turnover, because of this curve riding a.k.a. maintenance of the maturity curve against the passage of time. Those mentioned have already "realized" many of the gains and the result is that they have roughly the same type of bonds as last year, only a few percent more of them.

Also, it's generally not useful to read too much into the division between coupon and capital gain when it comes to bonds. As long as the roll yield exists, you can take it in either form; for example, if you were expecting one over last year you could have bought a higher coupon bond at a premium and got more coupons, with the price appreciation cancelled out by the depreciation of the premium bond approaching maturity (and par value). Since some of my bonds are taxable, I'm a fan of capital gains, myself, as much as allowed by regulations.

Re: Riding the yield curve, in action

Posted: Mon Jun 30, 2014 10:31 am
by ogd
alexfrey wrote:In particular, you can always calculate a roll yield for a past period, which could be positive or negative. But it isn't strictly clear that you should expect roll yield to be positive in the future, even if the yield curve is positively sloped. A positively sloped yield curve can indicate the expectation that rates will increase in the future. If the "expectations theory" of the yield curve is correct, then there is actually a (loose) no-arbitrage condition in which, for instance, buying a ten year bond should return the same as buying a five year bond and then rolling it over at the expected five-year rate five years from now.
I fully agree with this. I don't expect roll yield to persist even starting from a steep yield curve, because if it flattens on schedule you will never get a value gain when you roll over a bond. I was pointing out in my latest update that the curve has been flattening, although behind schedule.

What I'm saying is, if you feel tempted to avoid bonds or go short because times are uncertain in bond land, it's worth understanding that you're getting paid quite a bit more for holding them now. Risk -- reward. By the time the future looks stable the yield curve will be flattish and the bonus gone.

Re: Riding the yield curve, in action

Posted: Mon Jun 30, 2014 2:15 pm
by alexfrey
ogd - think we are on the same page!

doc - I don't think I agree with: "I believe that there is always a roll yield if the slope of the yield curve is positive." There will always be a roll yield, but I don't find it accurate to say that you can expect it to be positive just based on slope of the current yield curve. "Riding the yield curve" could produce a negative or positive result, even with a positive yield curve. It's not as a result of transactions costs, but rather of the expectations about future interest rates that are embedded in today's yield curve.

To make this tangible, imagine an intermediate-term bond fund plans to buy a 10 year Treasury today and sell it five years from now. Today the 10 yr is at 2.54% and the 5 yr at 1.64%. But what matters to the fund is not the five year rate today, but the five year rate five years from now when they go to flip their bond. We can calculate more or less what the market expects the five year rate might be five years from now using the expectations theory of interest rates -- and it's about 3.44%. (See: http://en.wikipedia.org/wiki/Expectation_hypothesis). So a fund that buys a 10 yr at 2.54% and then sells it 5 years later at 3.44% would actually see a realized negative roll yield. Sure, if today's interest rates persisted for the next five years, they'd get a positive roll return, but the point is that the market is not expecting that to happen. If it were -- the yield curve would not be so positively sloped!

What I think is dangerous is assumming that you can boost your bond returns from riding the yield curve whenever there is a positive slope. Yes, this has happened the last year, but you should not expect that it will happen in the future.

Re: Riding the yield curve, in action

Posted: Mon Jun 30, 2014 2:40 pm
by ogd
alexfrey wrote:Today the 10 yr is at 2.54% and the 5 yr at 1.64%. But what matters to the fund is not the five year rate today, but the five year rate five years from now when they go to flip their bond. We can calculate more or less what the market expects the five year rate might be five years from now using the expectations theory of interest rates -- and it's about 3.44%. (See: http://en.wikipedia.org/wiki/Expectation_hypothesis). So a fund that buys a 10 yr at 2.54% and then sells it 5 years later at 3.44% would actually see a realized negative roll yield.
Hmmm. While we are on the same page, I think you have this detail wrong. The expectation for the 5 year 5 years from now is about 2.54% (minus a risk premium), i.e. little no gain but no loss either.

In general, it's very hard for the roll yield to be persistently negative, as it would require a persistent inverted yield curve, which doesn't happen.

I should also say that the roll yield is not an objective in itself for these funds, but a mere consequence of holding maturity constant vs the passage of time. The bonus is a reward for continuing to assume the same level of interest rate risk, rather than letting it taper down to zero.

Re: Riding the yield curve, in action

Posted: Mon Jun 30, 2014 3:29 pm
by Doc
alexfrey wrote:doc - I don't think I agree with: "I believe that there is always a roll yield if the slope of the yield curve is positive." There will always be a roll yield, but I don't find it accurate to say that you can expect it to be positive just based on slope of the current yield curve. "Riding the yield curve" could produce a negative or positive result, even with a positive yield curve. It's not as a result of transactions costs, but rather of the expectations about future interest rates that are embedded in today's yield curve
OK I forgot the caveat "if the yield curve remains unchanged" and since today's yield curve is "supposed" to be the best predictor of the future curve albeit not a good one I "expect" to remain "almost" correct. Even then the transaction cost can eat up any gains.

But is it not correct that in the absence of transaction costs you can't lose because you simply don't sell and let the bond mature if the curve has a positive slope at the start?

Re: Riding the yield curve, in action

Posted: Mon Jun 30, 2014 4:04 pm
by alexfrey
ogd wrote:
alexfrey wrote: The expectation for the 5 year 5 years from now is about 2.54% (minus a risk premium), i.e. little no gain but no loss either.
I get 3.45% if I actually run the calc in absence of a risk premium. My calculation is: =(1.0254 ^ 10 / 1.0164^5)^ (1/5)-1. This is solving for the five year rate five years from now that would make an investor indifferent between buying a ten year today and buying a five year with the expectation of rolling it over five years from now. 2.54% is the current 10 yr rate, 1.64% is the current five-year rate.

Re: Riding the yield curve, in action

Posted: Mon Jun 30, 2014 4:15 pm
by alexfrey
Doc wrote:
alexfrey wrote:doc - I don't think I agree with: "I believe that there is always a roll yield if the slope of the yield curve is positive." There will always be a roll yield, but I don't find it accurate to say that you can expect it to be positive just based on slope of the current yield curve. "Riding the yield curve" could produce a negative or positive result, even with a positive yield curve. It's not as a result of transactions costs, but rather of the expectations about future interest rates that are embedded in today's yield curve
OK I forgot the caveat "if the yield curve remains unchanged" and since today's yield curve is "supposed" to be the best predictor of the future curve albeit not a good one I "expect" to remain "almost" correct. Even then the transaction cost can eat up any gains.

But is it not correct that in the absence of transaction costs you can't lose because you simply don't sell and let the bond mature if the curve has a positive slope at the start?
Definitely agree with last part. If you're willing to own whatever bond you buy to maturity, you're guaranteed an IRR = to the yield to maturity, so I agree you always have that option so long as you don't need the money five years from now (or you're a mutually fund obligated by your prospectus to dump anything with a short maturity!).

I think the only area we might disagree slightly is that I think you are saying that the best (albeit imperfect) expectation one can have is that the yield curve doesn't change. My point is that the yield curve in itself embeds expectations about its future changes, and if you account for those expectations than the "riding the yield curve" effect may largely disappear.

Re: Riding the yield curve, in action

Posted: Mon Jun 30, 2014 4:41 pm
by Doc
alexfrey wrote:I think the only area we might disagree slightly is that I think you are saying that the best (albeit imperfect) expectation one can have is that the yield curve doesn't change.
I think that idea came from Larry Swedroe. IIRC his comment was something like "the current yield curve is the best predictor of the future curve but not a good one."

I'll let you and ogd debate whether the shape of the curve has some future predictions baked into it.

However I do prefer a 1-5 fund rather than a 0-5 because of the riding the yield curve effect but it's not a major factor.

Re: Riding the yield curve, in action

Posted: Mon Jun 30, 2014 5:33 pm
by Kevin M
Vanguard shows one-year return for int-term treasury admiral, VFIUX, as 0.65% as of 5/31. Not sure what the celebration is about.

Distribution yield for dividends has ranged between 1.5% and 1.73% during the last year, and the price is virtually unchanged since 6/28/13 (11.32 on 6/28/13 and 11.33 on 5/30/14). Any additional return came from the two long-term capital gain distributions during that period. Did the CG distributions come from riding the yield curve? Maybe. Seems like you have to know that to attribute return beyond dividends and price change to riding the yield curve.

At any rate, six months or one year is way too short of a time to evaluate actual yield vs. SEC yield for a fund with a duration of five years or more.

One thing that hasn't been mentioned is distribution yield, and although it hasn't been a huge factor for int-term treasury over the last year, the distribution yield of some bond funds still is much higher than SEC yield. For int-term tax-exempt distribution yield is 3.21% vs. SEC yield of 1.86%. For total bond dist. yield is 2.6% vs. SEC yield of 2.12%. Assuming no big price change, this will result in six-month and one-year returns that are much higher than indicated by SEC yield. But in theory, SEC yield should provide a better estimate of return over a period equal to the duration, although I looked at the history of a short-term bond fund awhile back, and distribution yield seemed to hold up better than expected.

Maybe SEC yield is understating expected yield somewhat (as long as the yield curve is positive at the lower end) since bonds aren't held to maturity. So bump up your yield estimate appropriately in comparing to other estimates if you believe that's the case. But don't confuse strategy with outcome, and pick a period of good bond returns to justify selecting bonds over direct CDs ex-post. At least also look at 2013, where term-risk showed up a bit, VFIUX return was -3%, TBM return was -2.15%, and the int-term TIPS fund return was -8.9%, while direct CDs earned exactly what we knew they'd earn (2%-3%).

As an owner of both bond funds and direct CDs, I know I'm giving up any upside in the CDs, but I'm also putting a hard limit on the downside, and that's one of the main objectives.

Kevin

Re: Riding the yield curve, in action

Posted: Mon Jun 30, 2014 6:31 pm
by acegolfer
This is an interesting topic and a lot of great discussions going on. If anyone doesn't mind the trouble, can you summarize the debate? If too busy to summarize, it's fine.

Re: Riding the yield curve, in action

Posted: Mon Jun 30, 2014 7:01 pm
by stlutz
If anyone doesn't mind the trouble, can you summarize the debate?
I don't know that there is really a debate as much as an exploration of how the math of a bond portfolio works. The original post where I started the discussion simply pointed out that absent any changes in interest rates, there are *two* sources of bond returns: a) interest b) capital appreciation that results from the fact that the bond I bought last year has gone up in price because it is now a lower-yielding, shorter term bond. This second part of the return equation has been an unsually large part of bond returns the past several years. My original example was:
To simplify things, let's take the Stlutz Intermediate Term Treasury Fund. Its strategy is to buy a T-note of just over 5 years in maturity, hold it for 1 year and then replace it with a new bond. Right now, this fund holds the 9/30/2018 bond yielding 1.54% and priced at 99.188. It has a coupon rate of 1.375% The common assumption is that the "expected" return on this fund is therefore 1.54%. However, funds like mine and VG Intermediate Term Treasury don't do this. They buy bonds, hold them for a while, and then sell them well before maturity (VG IT Treasury basically turns over its entire portfolio each year). Thus, if one assumes that the yield curve remains the same for the next year, my bond will then be a 4 year bond yielding 1.23%. That would mean the price would have gone up to 100.590. Thus, my return would be as follows:

the coupon 1.375% / 99.188 (the bond price) = 1.39%
capital appreciation from 99.188 to 100.592 = 1.42%
Total expected return for the next year = 2.80%
Another way to think about it is that the return of a bond fund is ultimately determined by the yield of the bonds *at the time you purchase them*. So, if you have a rolling 10 year ladder, your return is determined by the yields on the bonds when you buy them new--i.e. when they have 10 years to maturity. So, at the end of a day, one should expect a Treasury fund with an average duration of ~ 5 years to return what a 10 year bond is yielding.

Re: Riding the yield curve, in action

Posted: Mon Jun 30, 2014 7:25 pm
by acegolfer
Stulz,

Thanks for the summary. If you don't mind, here is my comment.

Even if the upward sloped yield curve doesn't change, bond price doesn't always increase next year. One reason why your bond price increased is because you used a discount bond (coupon < ytm) as an example. Everyone knows that the bond price must converge to par value at maturity so it can explain the price appreciation.

Here's a counter example using a 5-yr 3% bond,

Price of 5yr 3% bond today = -PV(1.54%, 5, 3, 100) = $106.97
Price of this bond next year (assuming same yield curve) = -PV(1.23%, 4, 3, 100) = $106.87 (price decrease and hence a negative capital gain)

So to claim that capital appreciation is a large part of bond return using a discount bond as an example is not a general statement.

Re: Riding the yield curve, in action

Posted: Mon Jun 30, 2014 7:34 pm
by HomerJ
ogd wrote:The one year total returns:
VFIUX (IT Treasury): 2.63%
VBTLX (Total Bond Market): 4.98%
VWIUX (IT munis, national): 7.5%
The above is impossible. One year ago, bonds had nowhere to go but down. Don't you read these boards? :)

Re: Riding the yield curve, in action

Posted: Thu Dec 18, 2014 6:18 pm
by ogd
Just wanted to post a small update in response to this thread being quoted elsewhere. What has happened since is that the yield curve has flattened quite a bit. Compare vs the beginning of the thread:

Code: Select all

              3Yr    5Yr    10Yr
02/07/2014    0.66   1.47   2.71
12/18/2014    1.10   1.68   2.22
This is also why I haven't posted more updates to the thread with total return, because my M.O. had been to find a similar curve some time in the past and compute total return between the two points, to isolate from the effects of yield changes, and that became impossible because the past is always much steeper.

The flat yield curve means that the roll bonuses available from riding it are quite a bit smaller. After running some quick numbers:

[Theoretical] total return from rolling 5 years to 4 years with the current yield curve is down to 2.5%. It used to be about 3% back in February.

More dramatically, in the 10 year range the theoretical roll return went down from about 3.8% (edit: corrected from 4.7%) in February to about 2.8% right now. That part is much flatter than the 5 year range.

So we can't expect to see returns that are nearly as big going forward. Coincidentally, you also hear less noise / worries about the interest rates going up dramatically Any Day Now, everyone seems to have calmed down. This reinforces in my mind two things I was saying back then: 1) you can think of the roll return as a nice reward for the market's worries about interest rate risk, and 2) we should generally expect it to go away going forward as the yield curve flattens.

Re: Riding the yield curve, in action

Posted: Thu Dec 18, 2014 8:10 pm
by weltschmerz
deleted

Re: Riding the yield curve, in action

Posted: Thu Dec 18, 2014 9:07 pm
by Johno
The Dan wrote:Thanks for this update, ogd. Even though the roll bonus has gotten smaller, it is still pretty good. The 2.5% total return from rolling from 5 to 4 years still beats most bank CDs, and the treasury interest is exempt from state taxes to boot. I have been buying treasuries this year in the 3- and 5-year area of the curve, where it has been steepest. As long as the extremely short-term securities (i.e. 1-month) are still yielding near 0%, there will be a roll bonus, even if the magnitude and the exact position along the yield curve changes. Worst-case scenario, if the short-term rates start to rise rapidly and the roll bonus completely disappears, I will have to re-evaluate the strategy.
It's important to be aware of roll yield effect, but I don't agree with comparing it to CD's as if there's no analogous effect there. It's kind of like when people say 'if rates go down 100bps you get a gain on a treasury but not a CD'. Not exactly. You don't get an immediately marketable capital gain in CD as you do with the treasury, but you do get the same opportunity cost advantage if you continue to hold either the CD or treasury, to hold something that yields 100bp more than what you could now replace it with.

Similarly with roll. The shape of the curve has changed somewhat in the last year but the 5yr treasury is close to the same, in 1.60's. Also best 5 yr CD's are generally the same (omitting the exceptional deal of 3% 5yr CD by PenFed last year) around 2.4. So, if you'd purchased a 5yr CD last year at 2.4 and another of equal size now, you have a 4.5 yr portfolio that yields 2.4; if for some reason yields are still the same in another year it will be a 4yr portfolio with a 2.4% yield when interpolated 4yr CD (and treasury) rate is much lower. It's the same effect as rolling around treasuries, or being in a bond fund, or rolling treasury note futures*, but in a different form.

Whether it's really equivalent depends in part on what you are trying to do. Buying a 5yr CD and holding to maturity is not doing the same thing as buying a 5yr note and then selling it and buying a new 5yr note every 6 months, that's apples and oranges, though you might prefer one or the other for good reason. Whereas if you buy a 5yr note to hold to maturity, it's equivalent to buying and holding the CD, in terms of duration over time, but there's no roll advantage to the treasury in that case...because you're not rolling it. It's just 1.66 yield when you could get 2.4 on the CD. Roll yield pick up is not intrinsic to the instrument IOW, but depends what you do with it. But OTOH the cheap put embedded in the CD is a real inherent difference between the instruments.

*Look into this if it's possible in your set up, because it definitely beats buying cash treasury issues and rolling *them*, for a retail investor. Because, say if the investment is $100k, you can safely keep perhaps $95k in a money market account earning around 1%; actual margin requirement on one contract ($100k notional) will be around $1k and $4k extra left in the futures account (assume zero interest) is a huge cushion for a one day move in a 5yr note price. But the price of the treasury note futures contracts will reflect the market clearing financing rate of the cheapest to deliver note for that particular contract, either general collateral repo (below LIBOR, which is <~.25% in three months) or even 'special' repo rate down to zero if the CTD note is a hard to obtain issue. So you'll effectively earn 95%*1%-100%*repo, *plus* the 'roll effect' return on holding a say a ~4.5yr note (if it's the 5yr note contract) for three months and rolling out to the next note of around three months later maturity (with contracts 3 months apart, underlying CTD's are also around 3 months apart in maturity, though not exactly each time).

Re: Riding the yield curve, in action

Posted: Thu Dec 18, 2014 9:13 pm
by TheTimeLord
billyt wrote:It's so ridiculous really. No one wants to hear the truth, do the math, or accept factual information.

Sadly, this post will sink like a stone.

While "Why own bonds at all?" will be around for days.
Then go 100% Bonds. Me, I will stick to listening to Mr. Bogle.

Re: Riding the yield curve, in action

Posted: Thu Dec 18, 2014 9:47 pm
by weltschmerz
deleted

Re: Riding the yield curve, in action

Posted: Fri Dec 19, 2014 3:58 pm
by ogd
Johno wrote:It's important to be aware of roll yield effect, but I don't agree with comparing it to CD's as if there's no analogous effect there. It's kind of like when people say 'if rates go down 100bps you get a gain on a treasury but not a CD'. Not exactly. You don't get an immediately marketable capital gain in CD as you do with the treasury, but you do get the same opportunity cost advantage if you continue to hold either the CD or treasury, to hold something that yields 100bp more than what you could now replace it with.
...
Roll yield pick up is not intrinsic to the instrument IOW, but depends what you do with it.
Don't necessarily agree with the main thrust of this argument. Being able to pick up roll yield does require the capability to sell an instrument for a price that reflects market yields at its remaining maturity. One can't do that with direct CDs, I can't ask my bank to redeem for more because this is a four year at X% and their fresh four year CDs are only Y%. I understand what you're saying about the opportunity cost, if I were actually interested in holding another four year instrument, but I am in fact willing to bring it back up to five years and the market is willing to repay me.

To make this work with CDs, you'd have to arbitrage the difference yourself. You could short Treasuries against a CD ladder, emulating every year an appreciated sale of the CD you continue holding, but nobody actually does that I think. It sounds particularly scary if you consider the possibility of Treasuries appreciating a great deal during a market crash (when pressure on your margin is already high), while you're still unable to extract the full value in your CDs for another four or nine years.

You could also make this into a risk story and say that I am making the extra money because I am taking more risk. The sum (or "integral") of the interest rate risk I take over 5 years is about double that of a 5 year ladder and more like a 10 year ladder. However, not all duration is rewarded the same and presently rolling five years to four makes more money than a 10 year Treasury ladder at steady state; CDs can still beat that but if we look back at the February yield curve and its reward of about 3.8% for rolling ten year Treasuries after one year, there's no safe fixed instrument that can beat that, period. I think it's undeniable that a steep yield curve provides a lot of potential energy that can be harnessed, and it's not just a mind trick.

The real ding against the curve riding story is that the yield curve steepness can't be expected to persist; at the very least, it's unreliable. Which is why I would not trade the "bird in the hand" of higher CD yields for projected rewards that might get diminished in short order, like they have been last year, and I do prefer CDs at the moment. And then there's the put option, which although balanced partially by the ability to sell appreciated Treasuries to buy stocks in a crisis, is still a net positive.

My intention with this thread was not really to show that funds are preferable to CDs, like the original post of stlutz, but really to show that the effect is real in practice, and to make the argument that an uncertain "interest rate environment" also makes us quite a bit money and should not be treated as pure risk. The rewards are quite real.

Re: Riding the yield curve, in action

Posted: Fri Dec 19, 2014 7:27 pm
by Kevin M
This thread might as well be titled "Bond math in action". All bond return comes from two sources: interest payments and price change. Neglecting default, which we can safely do for Treasuries, coupon payments are known in advance. So the only unknown is price change, and that depends purely on the prices at the beginning and end of the holding period.

A steep yield curve tells you nothing about the price of a particular bond at the end of the holding period, unless you can predict the shape of the yield curve at the end of the holding period--or more precisely, that you can predict the price/yield of your particular bond. Speaking in the present tense about rolling down the yield curve propagates the illusion that there is "a yield curve" that remains constant over time.

I think misusing the term "roll yield", which is commonly used for futures but not for bonds, does more to obfuscate the understanding of bond returns than to clarify it.

The one noteworthy understanding that the original stlutz thread highlighted was that the Int-Term Treasury bond fund does not hold bonds to maturity, but holds bonds in the range of 3-year to 10-year terms to maturity. Therefore, SEC yield may understate expected returns for a bond fund that does not hold bonds to maturity, since it is based on yield to maturity.

So what if the yield curve happens to cooperate and give you two snapshots in time where you can apply bond math and show some effect based on the assumption of a static yield curve? And so what now that the yield curve is not cooperating and you can't do so. Bond math still applies.

Kevin

Re: Riding the yield curve, in action

Posted: Fri Dec 19, 2014 8:10 pm
by ogd
Kevin: with all due respect, your message does not offer any clarifications. It seems to be along the lines "it's complicated" and "it's based on price changes". Well yes to the latter, and we're just attempting to shed some light on the former.

Here is a takeaway from the last 1.5 years: there is another source of returns for bond funds or similarly shaped portfolios, alongside the simplified bond math that we normally talk about in bond threads. We all know about the coupons, and we often talk about how when yield changes, bond values go up or down. But in the last period, we saw clear contraditions to the simplified bond math:

1) Yields have gone up steeply and are still up, yet bond funds have recovered very well, despite outflows and fear.
2) The "point of indifference" based on duration is about four years ahead of schedule for intermediate bonds.

So it's bond math indeed, but it's at a more detailed level and we can go ahead and explain how it is that bond funds did so well and even (to your point) why this is not necessarily expected performance that you should count on to lift your bonds going forward.

The behaviors that result from price changes are indeed complicated, much like a superposition of related frequencies results in a weird pattern of peaks and nulls, but when we do a Fourier transform we see that it's really just two simple notes. What I'm doing with the yield curve snapshots is attempting to separate the effect of curve shifts and curve steepness, so we can highlight that the steepness is important too (if it doubles your returns it's important by any definition), not just the shifts or "interest rate increases" that we normally talk about.

Re: Riding the yield curve, in action

Posted: Fri Dec 19, 2014 9:48 pm
by Johno
ogd wrote:
Johno wrote:It's important to be aware of roll yield effect, but I don't agree with comparing it to CD's as if there's no analogous effect there. It's kind of like when people say 'if rates go down 100bps you get a gain on a treasury but not a CD'. Not exactly. You don't get an immediately marketable capital gain in CD as you do with the treasury, but you do get the same opportunity cost advantage if you continue to hold either the CD or treasury, to hold something that yields 100bp more than what you could now replace it with.
...
Roll yield pick up is not intrinsic to the instrument IOW, but depends what you do with it.
1. Don't necessarily agree with the main thrust of this argument. Being able to pick up roll yield does require the capability to sell an instrument for a price that reflects market yields at its remaining maturity. One can't do that with direct CDs,

2. You could also make this into a risk story and say that I am making the extra money because I am taking more risk.
1. My point was not that you could or would do exactly the same thing but that any fixed income instruments on roughly parallel curves give an *analogous* effect. So, assuming for a moment 5yr is the max for CD's you obviously can't produce a ladder with a mid point at 5 yrs. But say for argument's sake the yield curve remained relatively stationary for 5yrs (which it largely has last 5, though it's of course a heroic assumption that it would for another 5, or any given 5). Buying a 2.4% CD every year you eventually get a steady state of approx 2.5yr avg life yielding 2.4%, way above the 2.5 yr CD rate let alone treasury rate (~1.5 and .8 respectively now). That's the same effect as 'roll yield', but realized a different way. It's not as if it simply doesn't exist in any form with a CD, just like it's wrong to say the benefit of falling rates doesn't exist in any form with a CD. It does exist, but plays out in slower motion, so to speak.

2. That wouldn't be 'making it' into a risk story, it *is* a risk story, :D . Rolling 5-ish year instrument every few months is much more duration risk than steady state ladder of 5 yr CD's. The duration risk equivalent trade is rolling 2.5-ish yr treasuries. But this isn't to say one can't do a duration riskier trade, or do a variety of trades opportunistically over time rather than methodically building a steady state CD ladder over time. The point is just that the end product effect of a stationary steep curve is the same, dealing apples/apples with the same maturities, if it persists long enough. It doesn't mean the CD is always best or it has to be all one or the other.

However again, as long as FDIC insurance has anywhere near the same/similar market effect as now, rolling treasury futures with most of the notional amount in highest yielding saving account is going to handily beat rolling cash treasuries for a retail investor. It's the same roll effect of one quarterly contract's underlying to the next (if you rolled the same t-notes in succession) plus the spread of 1% on almost all the notional minus the repo rate on 100% of the notional. There's not much real risk trade off there, it's just better (as long as the futures fit in IRA). CD v rolling futures has the real trade offs discussed (limited practical maturity of CD *ladder* especially, 'slow motion' roll harvest, but put option of CD)