Bonds: Rolling Down the Yield Curve

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Bonds: Rolling Down the Yield Curve

Post by Shakespeare » 15 Dec 2012 11:44

In drafting this draft article on finiki http://www.finiki.org/wiki/User:Shakesp ... ome_ladder

I ran into a problem: estimating the net yield on a bond ETF.

The common way to estimate that yield is to subtract the MER from the YTM. However, when you look at the index construction, you often find that the index does not hold bonds to maturity. Instead, the index is (say) 1-5 years for a short-term ETF which means the holdings are sold when the maturity is down to one year. This opens up a technical strategy called "rolling down the yield curve" which allows returns to be enhanced when there is a normal yield curve (i.e. upward sloping) by selling a bond early. If the steepest part of the yield curve is captured by the purchase and sale of the bond, returns are enhanced.

An RBC paper is here: http://funds.rbcgam.com/pdf/di/articles ... tegy_e.pdf

The problem is that I don't know how much the bond ETFs will benefit from this. My guess - and it's just a guess - is that the MER will roughly cancel out.

Can somebody with more knowledge shed more light on this?
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Re: Bonds: Rolling Down the Yield Curve

Post by like_to_retire » 15 Dec 2012 12:09

I remember at the start of this year, one of the sharper tools in our shed, adrian2, discussed the situation in this thread.

He explains it quite nicely. I admit I had never thought of it before reading that thread.

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Re: Bonds: Rolling Down the Yield Curve

Post by newguy » 15 Dec 2012 12:10

Without doing all the math my guess is that it would depend on how linear the yield curve slope is and what the average duration is. If your bond fund can benefit from being on a steep part of the yield curve then it helps. If the slope is linear then avg yield (keeping extra short and just buying longer than the avg) would be almost the same as rolling.

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Re: Bonds: Rolling Down the Yield Curve

Post by Shakespeare » 15 Dec 2012 12:23

Thanks for linking that thread. I had forgotten about it.

It still looks like (roughly speaking) the MER or more of an index ETF could be recovered. So the technique of subtracting the MER from the YTM is wrong.

Unfortunately, the amount recovered by the ETF is going to vary with bond curve shape. I don't know if there is an easy way to estimate this.

This may be one of the little extras available to professionals (with institutional pricing) that makes James Hymas think most people should use bond ETFs rather than holding them directly.
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Re: Bonds: Rolling Down the Yield Curve

Post by like_to_retire » 15 Dec 2012 12:28

This may be one of the little extras available to professionals (with institutional pricing) that makes James Hymas think most people should use bond ETFs rather than holding them directly.
Yeah, and to take advantage of the concept with individual bonds, you have to sell them before maturity, and there's the rub. The spread is horrible for the small fry trying to sell a bond for a decent price.

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Re: Bonds: Rolling Down the Yield Curve

Post by newguy » 15 Dec 2012 12:45

I was looking for a graph or picture explaining this for people but this paper does a good job and it has some math examples if you want numbers.

http://www.insuranceam.db.com/insurance ... r_2010.pdf

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Re: Bonds: Rolling Down the Yield Curve

Post by Shakespeare » 15 Dec 2012 13:15

Thanks, I added that to the wiki writeup.

Makes bond ETFs look better as well as simpler than individual bonds, although GICs still have an advantage.
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Re: Bonds: Rolling Down the Yield Curve

Post by like_to_retire » 15 Dec 2012 13:45

Shakespeare wrote:Makes bond ETFs look better as well as simpler than individual bonds, although GICs still have an advantage.
ETF's do have a few other advantages than individual bonds.

1. They have the advantage of automatic reinvestment of distributions, freeing you from having to find a home for the coupons that are thrown off by real bonds.

2. Your hands aren't tied to waiting for a real bonds maturity date to get some quick cash.

3. ETF's have the advantage of offering the ability to sell small quantities to generate cash.

4. Short term ETF's have quick recovery from interest rate increases and they can give you that exposure to a collection of corporate bonds, since many short term funds use corporates to lift their yields.

5. Low price of admission for the small invester. Real bonds aren't really worth buying under $10K.

6. If you use ETF's for income, you don't care about the NAV as long as capital isn't required.

But, and here's a knock against the ETF, if there's a need to consume capital when the cash thrown off by the ETF isn't sufficient for your needs, then I feel it would be better to use a ladder. If rates are rising, the ladder avoids selling units with a depressed NAV, as capital can be withdrawn from the bonds maturing at 100 cents on the dollar.
I generally prefer the ladder myself as I can control the duration and any capital gain liabilities (those pesky ETF T3's at the end of the year), along with ensuring I keep the average weighted coupon rate near the average weighted YTM (using a minimum of premium bonds). I also get a defined rate of return and a know principle at maturity.

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Re: Bonds: Rolling Down the Yield Curve

Post by Insomniac » 15 Dec 2012 14:47

IMO, another advantage of is ETFs is that they make it easy to keep your asset allocation up to date; simply buy or sell units if and when necessary. For this reason, you probably shouldn't have all your FI in a GIC ladder.

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Re: Bonds: Rolling Down the Yield Curve

Post by Shakespeare » 15 Dec 2012 15:47

If rates are rising, the ladder avoids selling units with a depressed NAV, as capital can be withdrawn from the bonds maturing at 100 cents on the dollar.
That's mental accounting since the value of the bond ladder is similarly depressed to the ETF.
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Re: Bonds: Rolling Down the Yield Curve

Post by like_to_retire » 15 Dec 2012 16:00

Shakespeare wrote:
If rates are rising, the ladder avoids selling units with a depressed NAV, as capital can be withdrawn from the bonds maturing at 100 cents on the dollar.
That's mental accounting since the value of the bond ladder is similarly depressed to the ETF.
Yes, the entire ladder's value is depressed, just as the entire ETF's NAV is depressed, but with a ladder your income is drawn from the 20% that cashes out at maturity at 100 cents. You don't have access to that 20% with an ETF when you require income from capital.

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Re: Bonds: Rolling Down the Yield Curve

Post by jiHymas » 15 Dec 2012 16:05

Shakespeare wrote:
If rates are rising, the ladder avoids selling units with a depressed NAV, as capital can be withdrawn from the bonds maturing at 100 cents on the dollar.
That's mental accounting since the value of the bond ladder is similarly depressed to the ETF.
I would consider it to be a change of strategy - the withdrawal of capital from maturities necessarily implies that there will be less capital to be reinvested in the new rung of the ladder. To put it another way, the ladder operator in this instance is reducing duration in response to a recent - and not necessarily forecast - increase in yields. Fine, for those who wish to indulge in market timing!

I consider the 'ladder vs. ETF' argument to be largely a red herring. Yes, there are real differences, in terms of institutional pricing and MER, but questions of portfolio management (such as decreasing term in response to recent history) are not entirely relevant. You name the strategy, I can slap a wrapper on it and call it an ETF.

The real question is: what strategy is best aligned with your portfolio goals, particularly when taking costs, diversification and liquidity into account.

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Re: Bonds: Rolling Down the Yield Curve

Post by Shakespeare » 15 Dec 2012 16:15

Well, I can still see the advantage in GIC ladders - guarantee, probably better yield, at the expense of liquidity.

Bond ladders not so much.
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Re: Bonds: Rolling Down the Yield Curve

Post by like_to_retire » 15 Dec 2012 17:59

All these theories work great in theory, and are fine in the accumulation phase, but when the real world happens in the withdrawal phase and you require actual income, it's different.

If rates rise and the NAV of that ETF is depressed and I need to sell some units to pay for my groceries, I will wish I had listened, and had a GIC or bond ladder come due and take 100 cents on the dollar instead of some reduced percentage on the dollar with an ETF. Over the long run, of course there's no difference between the ETF and the ladder, but on the day you need food, there is a difference.

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Re: Bonds: Rolling Down the Yield Curve

Post by newguy » 15 Dec 2012 18:04

I made a spreadsheet, I think it's pretty accurate but you never know with my math (or excel's price formula). I think you may need to enable analysis tool pack.

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edit. Fix selling formula to reflect selling yield thx to JHymas.
Last edited by newguy on 15 Dec 2012 20:25, edited 2 times in total.

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Re: Bonds: Rolling Down the Yield Curve

Post by Shakespeare » 15 Dec 2012 18:11

That seems to show a miniscule yield improvement.
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Re: Bonds: Rolling Down the Yield Curve

Post by newguy » 15 Dec 2012 18:20

Shakespeare wrote:That seems to show a miniscule yield improvement.
Not a very steep curve, from 1% to 2.5%. It's not unusual to have more than a 1.5% change. I should have added something to easily change the yield curve but you can enter manually some numbers. Only the ones ending in 00YR are used for calcs and then only 2 of them at a time.

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Re: Bonds: Rolling Down the Yield Curve

Post by Shakespeare » 15 Dec 2012 18:25

Yes, but the references I checked suggested 0.5%. That's a lot different from 0.03%.
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Re: Bonds: Rolling Down the Yield Curve

Post by newguy » 15 Dec 2012 18:29

Shakespeare wrote:Yes, but the references I checked suggested 0.5%. That's a lot different from 0.03%.
You may want to check my math (or really my use of excels math). I'm not really sure how 'price()' works. I also invested the coupon and the end of each year, how is cdn bond interest paid? Semianually and a straight division like 3% = two 1.5% payments, or what? I doubted it would make a big difference.

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add: it's also called the zero cpn bond curve, but I assume that's just to make it easier to interpolate and other yields are very close.

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Re: Bonds: Rolling Down the Yield Curve

Post by Shakespeare » 15 Dec 2012 18:45

I dropped the estimated advantage from 0.5% to 0.3% because only half a broad ETF is corporate. It doesn't change the conclusion that XSB or similar is quite inferior in yield to a GIC ladder of selected highest-yielding GICs.

There is a moral hazard point in there somewhere, but I'm not going to get into that on finiki.
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Re: Bonds: Rolling Down the Yield Curve

Post by newguy » 15 Dec 2012 19:14

I just looked at the RBC doc and I don't get their math. Using their own numbers I get a difference of .22% which is pretty close to my spreadsheet if you put in a 4.72% coupon.

They say
21.11% holding for 7 years (2.77% / yr like they say)
19.38% holding for 6 years (3.00% / yr like they say)

They seem to be saying that 3-2.77 = 0.57 but we know from grade school that it's .22% (after rounding).
Their extra yield must come from selling a 1 year bond and buying a 7 year or longer bond. IOW changing the duration and cheating.

What they're really looking at is just buying a longer duration bond and calling it smart. Their starting conditions are different ie. a 7 yr. vs. a 6 yr. bond.

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Re: Bonds: Rolling Down the Yield Curve

Post by Shakespeare » 15 Dec 2012 19:24

My specific concern is XSB, which (like other short-term bond ETFs) is actually 1-5 vs a 0-5 GIC. So roll down is built into the index (and hence ETF) structure - probably deliberately.

This makes a comparison difficult, but there is no doubt that with a normal yield curve 1-5 is going to beat 0-5. The question is how much.
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Re: Bonds: Rolling Down the Yield Curve

Post by newguy » 15 Dec 2012 19:49

Shakespeare wrote:This makes a comparison difficult, but there is no doubt that with a normal yield curve 1-5 is going to beat 0-5. The question is how much.
But RBC is showing something like 1-6 to 0-5 (or 1-7,0-6 in their case), it beats from extending duration, not just the roll down.

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Re: Bonds: Rolling Down the Yield Curve

Post by Shakespeare » 15 Dec 2012 19:52

A GIC ladder with 1 year rungs varies from 1-5 to 0-4, so there is a duration difference if the bond ETF maintains 1-5 - which it can more easily do because it has more holdings.
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Re: Bonds: Rolling Down the Yield Curve

Post by jiHymas » 15 Dec 2012 19:53

newguy wrote:I made a spreadsheet, I think it's pretty accurate but you never know with my math (or excel's price formula). I think you may need to enable analysis tool pack.

newguy
Formula for sell price wrong, should reference cell B9, not B6 for yield. New result = Old result +57bp

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