Riding the Yield Curve

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bikenfool
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Riding the Yield Curve

Post by bikenfool » Wed Jan 22, 2014 1:44 pm

I've been pondering the technique of 'riding the yield curve'. It seems to me that it increases the returns of a bond portfolio by quite a bit (~1%) in a positive sloping yield curve like we have now. This leads me to a few questions.

It's been said here many times that the 30 day SEC yield is the best estimate for the future returns of a bond fund. If the fund manager uses the yield curve can't they do better than that? Even an index, if it's an intermediate term index will benefit.

For an index ETF such as TIP, which has significant percentage of holdings in short and long term, couldn't a person get a better return and the same duration/avg mat with individual holdings in the 5 - 10 yr maturity range. If the returns are greater, there must be some implicit increased risk. I guess the risk would be that the 5-10 yr rates increase more than the short or long term rate.

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Re: Riding the Yield Curve

Post by Doc » Wed Jan 22, 2014 2:07 pm

I think your are overestimating the effect. Without getting into the weeds too much, if you had a five year note that your could sell with one year remaining at a 1% premium your "bonus" for riding the curve is 1%/5 years or 0.2%. (Maybe it's 1%/4 years.) But in any case the bond traders are well aware of it and arbitrage most of it away which is probably why the the yield curve isn't a straight line. I'm well above my paygrade here. I think the only way we retail investors can take advantage of it is to choose a 1-5 fund instead of a 0-5. In the TIPS case this is the Pimco fund vs the Vanguard fund.
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Re: Riding the Yield Curve

Post by ogd » Wed Jan 22, 2014 2:11 pm

bikenfool: the problem is, the yield curve is not static -- in fact it's always expected to flatten. Longer points on the curve predict the future of the shorter points, all the way down to the Fed overnight rates. If all goes as expected, you will make about the SEC yield plus a little risk premium, but not substantially more.

Will everything go as expected? I don't know, but the bond's market track record is very, very good in that regard (I remember Jack saying 92% accurate somewhere, i.e. SEC yield matching future returns), and I'm too humble to think I can top it.

As for riding it, many funds naturally do it by their construction. You might choose one with a narrower maturity range if you want to pursue this, but it's unlikely that going all the way to individual bonds transacted frequently will buy you much.

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Re: Riding the Yield Curve

Post by richard » Wed Jan 22, 2014 2:54 pm

ogd wrote:bikenfool: the problem is, the yield curve is not static -- in fact it's always expected to flatten. Longer points on the curve predict the future of the shorter points, all the way down to the Fed overnight rates. If all goes as expected, you will make about the SEC yield plus a little risk premium, but not substantially more.
Yes, other than "expected to flatten". Putting this another way, the standard model is that longer rates reflect expectations of future short rates plus a term (risk) premium. If the yield curve is positive, it suggests an expectation that rates will rise (depending on the magnitude of the term premium), in which case a shorter bond won't increase in value as much as if short rates remain stable.

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Re: Riding the Yield Curve

Post by magician » Wed Jan 22, 2014 3:02 pm

ogd wrote:Longer points on the curve predict the future of the shorter points, all the way down to the Fed overnight rates.
You're citing the pure expectations theory of interest rates, which is only one theory which tries to explain the shape of the yield curve. Others include the liquidity premium theory and the preferred habitat theory. In neither of those do forward rates predict future spot rates.

Pure expectations may be true, and it may not; it's not remotely as certain as your sentence makes it sound.
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Re: Riding the Yield Curve

Post by ogd » Wed Jan 22, 2014 3:14 pm

magician: do those other theories predict flattening of the yield curve because of some other reason? In practice, it does seem to go flat after a period of steepness much more often than not. I am asking because I truly don't know this. If that expectation didn't exist, it would seem that SEC yield would underestimate actual future returns an awful lot.

richard: same question, sort of -- as long as expectations are a component, they would put flattening pressure on the curve, would they not? I understand that the risk component might move to counter that, but I'd also expect the moves in that risk component to be unpredictable, averaging to zero. Which leaves flattening as the only reasonable expectancy.

I'm quite curious about this. It has a lot of impact on my choice of fixed income and tax placement, right now I'm always working off of SEC yields.

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Re: Riding the Yield Curve

Post by richard » Wed Jan 22, 2014 3:29 pm

Conventional wisdom, so far as I can tell, is that a flattening or inverted yield curve is, in effect, a prediction that the economy will slow or enter a recession. A strongly rising yield curve is, in effect, a prediction of a strong economy.

I don't see why a risk premium would average zero. I'd expect it to always be positive. Unfortunately, there's no way to directly observe it.

Liquidity would seem a component of a risk premium.

I don't believe preferred habitat is anywhere close to being as popular as the expectations theory.

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Re: Riding the Yield Curve

Post by ogd » Wed Jan 22, 2014 3:39 pm

richard wrote:I don't see why a risk premium would average zero. I'd expect it to always be positive. Unfortunately, there's no way to directly observe it.
I was saying that the delta in risk premiums would average zero, you can't predict anything about it. Meaning that if the delta from expectations is positive (on the short end), the combined expectation is also positive, i.e. towards flattening.
richard wrote:Conventional wisdom, so far as I can tell, is that a flattening or inverted yield curve is, in effect, a prediction that the economy will slow or enter a recession. A strongly rising yield curve is, in effect, a prediction of a strong economy.
I'm with you on inverted, but you could have a strong economy at a steady state with a flat curve, i.e. rates can't be expected to rise forever. Maybe "strong and steady" is irrelevant because it never happens. :D

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Re: Riding the Yield Curve

Post by magician » Wed Jan 22, 2014 4:19 pm

ogd wrote:magician: do those other theories predict flattening of the yield curve because of some other reason?
The liquidity premium theory can explain a normal yield curve, but not a flat or inverted yield curve. It's basis is that . . . well . . . there's a liquidity premium: higher rates for less liquidity (i.e., longer time to maturity).

The preferred habitat theory can explain any shape for the yield curve. It's basis is that investors have maturities that they want, and will accept lower yields to get them. If they have to take other maturities (shorter or longer), they'll require a premium to do so. It's nothing more than supply and demand: at maturities that have high demand, the price is higher (yields are lower); at maturities that have low demand, the price is lower (yields are higher).

Frankly, I suspect that the real explanation is a combination of liquidity premium and preferred habitat; there may be some pure expectations in there, but I'd be surprised if that's the dominant reason for the shape of the yield curve.
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Re: Riding the Yield Curve

Post by magician » Wed Jan 22, 2014 4:22 pm

richard wrote:I don't believe preferred habitat is anywhere close to being as popular as the expectations theory.
I don't know about its popularity, but it seems plausible. Insurance companies, for example (which are huge fixed income investors), like to match their assets and liabilities (maturity and duration, if possible); they would definitely have preferred maturities, and would demand extra yield for longer or shorter maturities than their preferred (because either of those will increase their risk).
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Re: Riding the Yield Curve

Post by bikenfool » Wed Jan 22, 2014 4:52 pm

Doc wrote:I think your are overestimating the effect. Without getting into the weeds too much, if you had a five year note that your could sell with one year remaining at a 1% premium your "bonus" for riding the curve is 1%/5 years or 0.2%. (Maybe it's 1%/4 years.) But in any case the bond traders are well aware of it and arbitrage most of it away which is probably why the the yield curve isn't a straight line. I'm well above my paygrade here. I think the only way we retail investors can take advantage of it is to choose a 1-5 fund instead of a 0-5. In the TIPS case this is the Pimco fund vs the Vanguard fund.
A 10 yr treasury yields about 2.8%. Price=100;
A 7 yr yields about 2%. Price=105.18. 5.2% in 3 yrs, on top of the coupon.

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Re: Riding the Yield Curve

Post by ogd » Wed Jan 22, 2014 5:29 pm

magician: the expectations theory just makes a lot of sense to me. Everyone knows that the 10 year bond will be a 7 year bond in three years, with just as good credit in the case of Treasuries. So it's just intuitive that they expect the 7 year yield to be around 2.8% by then, with some risk premium that it doesn't turn out this way -- less than you'd expect because there are risks in the other direction as well.

Otherwise, as birkenfoot says, the market would just be handing you a good chunk of money. If the discrepancies would be this large, the big market players (particularly insurance companies) have a lot of ways to hedge and profit.

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Re: Riding the Yield Curve

Post by richard » Wed Jan 22, 2014 5:36 pm

ogd wrote:
richard wrote:I don't see why a risk premium would average zero. I'd expect it to always be positive. Unfortunately, there's no way to directly observe it.
I was saying that the delta in risk premiums would average zero, you can't predict anything about it. Meaning that if the delta from expectations is positive (on the short end), the combined expectation is also positive, i.e. towards flattening.
Could you please say that another way and provide an example.
ogd wrote:
richard wrote:Conventional wisdom, so far as I can tell, is that a flattening or inverted yield curve is, in effect, a prediction that the economy will slow or enter a recession. A strongly rising yield curve is, in effect, a prediction of a strong economy.
I'm with you on inverted, but you could have a strong economy at a steady state with a flat curve, i.e. rates can't be expected to rise forever. Maybe "strong and steady" is irrelevant because it never happens. :D
Flat yield curves are highly unusual. Most of the time yield curves are positive, occasionally they invert, but I can't recall ever seeing a truly flat yield curve, even when switching from positive to inverted. When have you seen a flat yield curve?

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Re: Riding the Yield Curve

Post by richard » Wed Jan 22, 2014 5:48 pm

magician wrote:
richard wrote:I don't believe preferred habitat is anywhere close to being as popular as the expectations theory.
I don't know about its popularity, but it seems plausible. Insurance companies, for example (which are huge fixed income investors), like to match their assets and liabilities (maturity and duration, if possible); they would definitely have preferred maturities, and would demand extra yield for longer or shorter maturities than their preferred (because either of those will increase their risk).
Expectations is more popular because it is more general and explains things well.

The preferred habitat theory may be viewed as a part of the expectations theory. For example, "The preferred habitat theory is another guide of the liquidity premium theory, and states that in addition to interest rate expectations, investors have distinct investment horizons and require a meaningful premium to buy bonds with maturities outside their "preferred" maturity, or habitat." Also "The Liquidity Premium Theory is an offshoot of the Pure Expectations Theory."

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Re: Riding the Yield Curve

Post by ogd » Wed Jan 22, 2014 5:48 pm

richard wrote:
ogd wrote:
richard wrote:I don't see why a risk premium would average zero. I'd expect it to always be positive. Unfortunately, there's no way to directly observe it.
I was saying that the delta in risk premiums would average zero, you can't predict anything about it. Meaning that if the delta from expectations is positive (on the short end), the combined expectation is also positive, i.e. towards flattening.
Could you please say that another way and provide an example.
Actually, I can't :oops: You're right. What matters is the current difference in risk premium between, say, the 10 year and 5 year, going down to Fed funds rate where the risk is zero. I was thinking that we only care about the difference between the current 5 year risk premium and the future 5 year premium, but this is not so. The two time axes confused me, as they often do.
ogd wrote:
richard wrote:Conventional wisdom, so far as I can tell, is that a flattening or inverted yield curve is, in effect, a prediction that the economy will slow or enter a recession. A strongly rising yield curve is, in effect, a prediction of a strong economy.
I'm with you on inverted, but you could have a strong economy at a steady state with a flat curve, i.e. rates can't be expected to rise forever. Maybe "strong and steady" is irrelevant because it never happens. :D
richard wrote: Flat yield curves are highly unusual. Most of the time yield curves are positive, occasionally they invert, but I can't recall ever seeing a truly flat yield curve, even when switching from positive to inverted. When have you seen a flat yield curve?
By flat I mean flat-ish, with very small differences compared to the magnitude of the yield. I wish there were some nice software to visualize it, but most of the data points that I've eyeballed in http://research.stlouisfed.org/fred2/data/GS10.txt vs GS5 and GS3 have that feature. Certainly nothing that you can use to extract any significant curve riding bonus.

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Re: Riding the Yield Curve

Post by magician » Wed Jan 22, 2014 6:19 pm

richard wrote:
magician wrote:
richard wrote:I don't believe preferred habitat is anywhere close to being as popular as the expectations theory.
I don't know about its popularity, but it seems plausible. Insurance companies, for example (which are huge fixed income investors), like to match their assets and liabilities (maturity and duration, if possible); they would definitely have preferred maturities, and would demand extra yield for longer or shorter maturities than their preferred (because either of those will increase their risk).
Expectations is more popular because it is more general and explains things well.
I'm not sure that it is more general, but it does explain any yield curve shape.
richard wrote: The preferred habitat theory may be viewed as a part of the expectations theory. For example, "The preferred habitat theory is another guide of the liquidity premium theory, and states that in addition to interest rate expectations, investors have distinct investment horizons and require a meaningful premium to buy bonds with maturities outside their "preferred" maturity, or habitat." Also "The Liquidity Premium Theory is an offshoot of the Pure Expectations Theory."
What is the source of your quotes here?
Simplify the complicated side; don't complify the simplicated side.

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Re: Riding the Yield Curve

Post by stlutz » Wed Jan 22, 2014 9:29 pm

We discussed this issue in another thread several months back. The conclusion was that the best way to estimate expected return was to look at the yield of bonds with maturities at double the current duration. So, for treasuries, the combined 1 year return--coupon yield plus price cange--of a 5 year bond could be estimated by looking at the 10 year yield.

The large return effect of yield curve riding will continue until short rates are allowed to climb above zero or longer term rates become Japan-like.

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Re: Riding the Yield Curve

Post by richard » Wed Jan 22, 2014 9:35 pm

richard wrote: The preferred habitat theory may be viewed as a part of the expectations theory. For example, "The preferred habitat theory is another guide of the liquidity premium theory, and states that in addition to interest rate expectations, investors have distinct investment horizons and require a meaningful premium to buy bonds with maturities outside their "preferred" maturity, or habitat." Also "The Liquidity Premium Theory is an offshoot of the Pure Expectations Theory."
magician wrote:What is the source of your quotes here?
Wikipedia, source of all knowledge :)
http://en.wikipedia.org/wiki/Yield_curve

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Re: Riding the Yield Curve

Post by bikenfool » Wed Jan 22, 2014 10:05 pm

stlutz wrote:We discussed this issue in another thread several months back. ....
Can you point us to that thread?

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Re: Riding the Yield Curve

Post by stlutz » Wed Jan 22, 2014 10:08 pm

It was one I started--something like, "Treasuries and CDs reconsidered.". (I'm on my little tablet at the moment so copying a link in is kind of a pain. :happy )

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Re: Riding the Yield Curve

Post by #Cruncher » Wed Jan 22, 2014 10:45 pm

bikenfool in [url=http://www.bogleheads.org/forum/viewtopic.php?p=1933020#p1933020]the original post[/url] wrote:For an index ETF such as TIP, which has significant percentage of holdings in short and long term, couldn't a person get a better return and the same duration/avg mat with individual holdings in the 5 - 10 yr maturity range. If the returns are greater, there must be some implicit increased risk. I guess the risk would be that the 5-10 yr rates increase more than the short or long term rate.
Your question is similar to one asked in the thread, Why TIPS fund vs Individual TIPS of same maturity?, which I attempted to answer in this response. It showed that indeed one could get a better return from a single medium term TIPS than one could from three TIPS having an average maturity equal to that of the medium term one.

Here is a modification of that comparison where I choose the three TIPS such that the average duration, not the average maturity equals that of the medium term bond. I do this because duration is a better indicator of interest rate risk than is maturity. (Current yields-to-maturity (YTM) are from WSJ TIPS Quotes 1/22/2014.)

Code: Select all

                           Macaulay  ----- Current ----    YTM    ------ New ------   Price
  Maturity  Coupon   Life  Duration    YTM       Price     Incr      YTM     Price    Change
----------  ------  -----  --------  --------   -------   ------  --------  -------   ------
07/15/2016  2.500%   2.48     2.42   (1.345%)   109.72%   1.000%  (0.345%)  107.09%   (2.4%)
07/15/2021  0.625%   7.48     7.32    0.245%    102.81%   1.000%   1.245%    95.59%   (7.0%)
04/15/2029  3.875%  15.23    12.20    1.022%    140.14%   1.000%   2.022%   124.18%  (11.4%)
                    -----    -----   --------                                         ------
  Average            8.39     7.31   (0.026%)                                         (6.9%)
The 7.32 year duration of the July 2021 is almost identical to the 7.31 average duration of the three TIPS. Yet it has about a 0.27% point higher YTM (+0.245%) than the average YTM of the 3 bonds (-0.026%). And since its duration is the same as the average, one would expect it to have about the same interest rate risk assuming an equal rise in interest rates. The four columns on the right show this to be the case. If interest rates immediately rose 1% point for all three bonds, the average price fall of 6.9% would be about the same as the 7.0% price fall of the July 2021.

But maybe the market is telling us that it doesn't expect interest rates to rise equally for all maturities or durations. What if it expects the yield curve to become more horizontal? Were this to happen as interest rates rise, the medium term TIPS would fall more than the average. This is shown by the following table. It is the same as the one above, except instead of assuming an equal 1% point rise in yields, it assumes the rate for the long term TIPS is unchanged and the rates for the short and medium term rise to equal it (i.e., the yield curve becomes horizontal).

Code: Select all

                           Macaulay  ----- Current ----    YTM    ------ New ------   Price
  Maturity  Coupon   Life  Duration    YTM       Price     Incr      YTM     Price    Change
----------  ------  -----  --------  --------   -------   ------  --------  -------   ------
07/15/2016  2.500%   2.48     2.42   (1.345%)   109.72%   2.367%   1.022%   103.61%   (5.6%)
07/15/2021  0.625%   7.48     7.32    0.245%    102.81%   0.777%   1.022%    97.15%   (5.5%)
04/15/2029  3.875%  15.23    12.20    1.022%    140.14%   0.000%   1.022%   140.14%    0.0%
                    -----    -----   --------                                         ------
  Average            8.39     7.31   (0.026%)                                         (3.7%)
In this case the price of the July 2021 would fall 5.5% which is more than the 3.7% average price fall for all three TIPS. So maybe it is the risk of interest rates rising in this manner which accounts for the higher YTM of the single medium term TIPS.

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Re: Riding the Yield Curve

Post by bikenfool » Wed Jan 22, 2014 11:23 pm

stlutz wrote:It was one I started--something like, "Treasuries and CDs reconsidered.". (I'm on my little tablet at the moment so copying a link in is kind of a pain. :happy )
Must be this one:
http://www.bogleheads.org/forum/viewtop ... 0&t=118751

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Re: Riding the Yield Curve

Post by Clive » Thu Jan 23, 2014 5:15 am

Given a positive sloping yield curve then the best valued at any one time assuming no change in the yield curve is near the peak of the steepest part of the yield curve as that is where the yield falls off the fastest (price rises the quickest). i.e. if the 5 year is the peak yield and the 4 year yield is sizeably below that, then holding the 5-year for a year and the yield curve remaining the exact same would see a greater reward.

However yield curves don't tend to remain the same from year to year and the current yield instantaneous curve reflects a prediction of the forward yield curve (implied forward yield curve), that in this case might have the one year time 4-year yield relatively higher than other maturities (that potentially negates the benefit of having bought the 'better valued' 5-year).

A potential benefit of holding individual bonds rather than a fund of bonds is that of better liquidity options. You tend to hold bonds for stability and maintenance of purchase power reasons for money that you want to spend at a later date rather than today. Perhaps for instance to buy more stock should stock prices decline. If a year ago you bought say a third in each of 3, 10 and 16 year bonds such that you now held 2, 9 and 15 year maturity bonds and stocks had dived in price such that you were looking to liquidate some bonds in order to buy some more shares, then you can select which individual bond maturity to sell. If longer maturity bond prices had risen then that might be the 15 year, otherwise it might be the 2 year. If after having perhaps sold some 15 year to buy more stock some time later stock prices had rebounded back up again, then the price of those 15 year bonds might be down - such that you sell some stock to re-buy 15 year bonds with the proceeds. Over that cycle you had greater control of exactly which bonds were traded and less of a portfolio value loss when stocks declined due to the 'inverse correlations' between choice of bonds sold/bought.

For retail investors however 'playing' (trading) bonds can be relatively expensive (wider spreads than institutional investors etc.). For liquidity purposes I personally prefer what I call a rate-tart approach - looking to hold each rung of a 5 year ladder of bonds to maturity. When each bond is held to maturity you don't need to mark to market and the reward is the average of the current and past four years 5-year yields (assuming each rung is equally weighted). Portfolio reviewing at the time a bond matures (some cash in hand). Should liquidity be required before a bond had matured then marking to market is involved and might require either the longer or shorter end to be disposed of in order to buy more stock (decision made at the time). When rolling (or adding) I tart around for the best net-real rate available at the time for the replacement 5 year (inflation bond, conventional bond, cash deposit etc. that yields the best potential after inflation (real), after tax (net) reward). I also do trade the bonds before maturity and will switch out a holding should a better alternative become apparent. For instance if the current 2 year treasury bond would reward 1% if held to maturity, but a safe high street 2 year cash-bond is on offer that's paying 2% then providing the after taxes/costs also shows a benefit for switching then I'll rotate the 2 year holding into that alternative.

As a guide, if a current UK 5 year ladder were being bought more recently (start of 2014) then each of 1 through 5 year high street cash-bonds were rewarding more than each of 1 through 5 year Treasury bonds on a net (after taxes) basis by just shy of a 1% difference (1.5% gross difference). A problem however is that two of those bonds are with the same provider and there are limits as to how much can be safely deposited with any one provider (should the bank go broke).

By the way the choice of a 5 year ladder is purely down to potential tax efficiencies as in the UK you can buy and hold to maturity Gilts (treasury bonds) with at least 5 years to maturity at the time of purchase inside a ISA account (tax exempt). Its not permitted however to buy gilts with < 5 years inside a ISA. The comparison using net-real measure is purely to determine whether conventional or inflation bonds look to be the better choice at any one time - which involves some prediction. Junkier bonds can also be considered/included - generally where the higher yield reflects the default risk. Often defaults cluster, so you also have to predict whether defaults are likely to soar during the term when deciding whether the additional potential rewards are worth the risk.

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Re: Riding the Yield Curve

Post by richard » Thu Jan 23, 2014 7:23 am

If you assume the yield curve will not change, then why not buy the longest and highest yielding bond?

If your portfolio goes from "3, 10 and 16 year bonds such that you now held 2, 9 and 15" you've obviously shortened maturity. The best way to think of bond portfolios is portfolios with more or less constant maturity (funds, rolling ladders) and those with declining maturities (individual bonds not rolled). If you want flexibility with funds, hold funds with various maturities.
<snip>When each bond is held to maturity you don't need to mark to market<snip>
Prices of bonds and funds fluctuate whether or not you choose to mark to market. Stop looking at the price of a fund and you can pretend it's not marked to market. Sell longer funds and buy shorter and you can have simulate holding individual bonds to maturity. I'm not clear why a long-term investor would want a portfolio with declining maturities. If you roll (reinvest or otherwise hold maturity more or less constant), then you have a fund equivalent. If you don't, then after a while you don't hold any more bonds.

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Re: Riding the Yield Curve

Post by Epsilon Delta » Thu Jan 23, 2014 9:24 am

richard wrote:If you assume the yield curve will not change, then why not buy the longest and highest yielding bond?
Because the yield curve is yield to maturity and not the yield for the next year. So if you plan to sell next year it does not tell you what you want to know. The curve does not reflect the way the bond price will change as it moves down the yield curve.

Suppose the yield curve is
1 year - 0.1%
2 year - 2.0%
3 year - 2.1%

If you hold a 2 year bond for 1 year it becomes a 1 year bond, yielding 0.1% so you get 2% interest and 1.9% appreciation or 3.9% total return.

If you hold a 3 year bond for 1 year it becomes a 2 year bond yielding 2.0%, so you get 2.1% interest and about 0.2% appreciation for a total return of 2.3%.

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Re: Riding the Yield Curve

Post by Clive » Thu Jan 23, 2014 9:29 am

If you want flexibility with funds, hold funds with various maturities.
Using 2008 and 2009 data from Simba's spreadsheet, respective yearly total gains of :

VTSMX (Stocks) -37.04% +28.7%
VFSTX (Short dated bonds) -4.75% +14.03%
VBMFX (Total Bond) +5.05% +5.93%
VUSTX (Long dated) +22.52% -12.05%

Such that holding perhaps 50% stocks combined with 25% in each of short dated bonds and long dated bonds would have catered for selling long dated to buy stocks after 2008, selling stocks to buy long dated after 2009 as being the more productive choice. So yes holding funds with various maturities could be as viable as holding individual bonds. That however is subject to costs/taxes and accordingly one or the other (directly held bonds versus bond funds) could have one that is more cost/tax efficient than the other. As bond funds buy/hold bonds and charge you a management fee for doing so, generally its not unreasonable to anticipate that cutting out the middleman will be the more cost effective choice if your preference is for holding a range of separate/different maturities.

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Re: Riding the Yield Curve

Post by grayfox » Thu Jan 23, 2014 9:53 pm

bikenfool wrote:I've been pondering the technique of 'riding the yield curve'. It seems to me that it increases the returns of a bond portfolio by quite a bit (~1%) in a positive sloping yield curve like we have now. This leads me to a few questions.
I think you are on to something.

Suppose I bought a 5-year STRIP, held it for one year, and sold it as a 4-year strip. IF, (Big if) interest rates don't change, then the bond prices will be the same as today.

……………………………..bid/ask……….……YTM
5-year 2019-Feb-15 91.918/91.964….1.66%
4-year 2018-Feb-15 94.920/94.959.…1.28%
from WSJ STRIPS

The YTM = 1.66%. But if I paid 91.964 and sold it for 94.920, my return will be

(94.920 - 91.964)/91.964 = 0.032143 = 3.2%

Almost twice the YTM! The same as the 2025-May-15 which has YTM=3.2%

Meanwhile the actual 1-year T is only yielding 0.15%. So you can get a guaranteed 0.15%, Or try this trick and hope interest rates stay the same or go down. It's worth a try.

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ogd
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Re: Riding the Yield Curve

Post by ogd » Thu Jan 23, 2014 10:45 pm

grayfox: risk is risk. You have an exposure of 5 years regardless of whether you intend to sell after a year. So you can't compare to a 1 year Treasury.

The only answer to this riddle that makes sense to me is that the 4 year YtM will be much closer to 1.66% come next year. Otherwise it's too easy. It's not like the passage of 1 year is a surprise to anybody.

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Re: Riding the Yield Curve

Post by Clive » Fri Jan 24, 2014 2:55 am

grayfox wrote:Suppose I bought a 5-year STRIP, held it for one year, and sold it as a 4-year strip. IF, (Big if) interest rates don't change, then the bond prices will be the same as today.

……………………………..bid/ask……….……YTM
5-year 2019-Feb-15 91.918/91.964….1.66%
4-year 2018-Feb-15 94.920/94.959.…1.28%
from WSJ STRIPS

The YTM = 1.66%. But if I paid 91.964 and sold it for 94.920, my return will be

(94.920 - 91.964)/91.964 = 0.032143 = 3.2%
Riding the yield curve involves selecting the better valued at the time (perhaps on the assumption that today's yield curve is as good a predictor as any of tomorrows yields).

If you select where the yield curve declines the fastest (is the steepest) then the capital appreciation could be the fastest.

[?? Note : not sure as this is foreign to me (UK investor looking at US data/assets)] From that link you supplied Feb 2018 and Feb 2017 looks to me to be steeper than your choice and the Feb 2018/2017 is set to potentially total return 3.96%. Its also quite steep between Nov 2023 and Nov 2022 (7.3% Total Return). If the 3-year (or 8 year) yields are lower in a year time then that adds, if the yields are higher then that detracts. Whilst that applies across the entire yield curve and the implications are that yields will generally rise, those two examples are a indicator of possible better valued choices (or of anticipation that something around those dates is likely to see increases in yields around those dates).

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Re: Riding the Yield Curve

Post by linuxizer » Fri Jan 24, 2014 6:57 am

#Cruncher- The 3 bond portfolio has higher convexity so lower interest rate risk. Look up barbell vs bullet portfolios.

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grayfox
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Re: Riding the Yield Curve

Post by grayfox » Fri Jan 24, 2014 8:25 am

……………………………..bid/ask……….……YTM
5-year 2019-Feb-15 91.918/91.964….1.66%
4-year 2018-Feb-15 94.920/94.959.…1.28%
from WSJ STRIPS

(94.920 - 91.964)/91.964 = 0.032143 = 3.2%
That was quote from WSJ. Here is prices and yields from VBS. The bid/ask spread looks wider than reported on WSJ. There is no commission, but you buy at the ask and sell at the bid.

……………………….bid/ask……….……YTM
2/15/2019 92.170/92.358 1.621%/1.580%
2/15/2018 94.924/95.096 1.290%/1.245
from VBS bond desk

(94.924-92.358)/92.358 = 0.277832 = 2.7%

Lower potential return because more is given up to the middlemen via bid/ask spreads.

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Re: Riding the Yield Curve

Post by richard » Fri Jan 24, 2014 8:29 am

Epsilon Delta wrote:
richard wrote:If you assume the yield curve will not change, then why not buy the longest and highest yielding bond?
Because the yield curve is yield to maturity and not the yield for the next year. So if you plan to sell next year it does not tell you what you want to know. The curve does not reflect the way the bond price will change as it moves down the yield curve.
Agreed - that's the right thing to do if you plan to ride the yield curve. It's another example of how you can profit if you can accurately predict market prices. It's not the right thing if you plan to hold.

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Re: Riding the Yield Curve

Post by grayfox » Fri Jan 24, 2014 9:50 am

Assuming that I bought a 2/15/2019 STRIP at the VBS ASK price 92.358, I made this table in Excel showing what the profit would be for various 4-year interest rates a year from now. I showed from rates from 0% to 3%

Code: Select all

Settlement	Maturity	BID	COST	BID-YTM	Profit	Return
01/24/15	02/15/19	100.000	92.358	0.00%	7.642	8.27%
01/24/15	02/15/19	99.595	92.358	0.10%	7.237	7.84%
01/24/15	02/15/19	99.192	92.358	0.20%	6.834	7.40%
01/24/15	02/15/19	98.792	92.358	0.30%	6.434	6.97%
01/24/15	02/15/19	98.393	92.358	0.40%	6.035	6.53%
01/24/15	02/15/19	97.996	92.358	0.50%	5.638	6.10%
01/24/15	02/15/19	97.602	92.358	0.60%	5.244	5.68%
01/24/15	02/15/19	97.209	92.358	0.70%	4.851	5.25%
01/24/15	02/15/19	96.818	92.358	0.80%	4.460	4.83%
01/24/15	02/15/19	96.429	92.358	0.90%	4.071	4.41%
01/24/15	02/15/19	96.042	92.358	1.00%	3.684	3.99%
01/24/15	02/15/19	95.657	92.358	1.10%	3.299	3.57%
01/24/15	02/15/19	95.274	92.358	1.20%	2.916	3.16%
01/24/15	02/15/19	94.893	92.358	1.30%	2.535	2.74%
01/24/15	02/15/19	94.514	92.358	1.40%	2.156	2.33%
01/24/15	02/15/19	94.137	92.358	1.50%	1.779	1.93%
01/24/15	02/15/19	93.761	92.358	1.60%	1.403	1.52%
01/24/15	02/15/19	93.388	92.358	1.70%	1.030	1.11%
01/24/15	02/15/19	93.016	92.358	1.80%	0.658	0.71%
01/24/15	02/15/19	92.646	92.358	1.90%	0.288	0.31%
01/24/15	02/15/19	92.278	92.358	2.00%	-0.080	-0.09%
01/24/15	02/15/19	91.912	92.358	2.10%	-0.446	-0.48%
01/24/15	02/15/19	91.547	92.358	2.20%	-0.811	-0.88%
01/24/15	02/15/19	91.185	92.358	2.30%	-1.173	-1.27%
01/24/15	02/15/19	90.824	92.358	2.40%	-1.534	-1.66%
01/24/15	02/15/19	90.465	92.358	2.50%	-1.893	-2.05%
01/24/15	02/15/19	90.107	92.358	2.60%	-2.251	-2.44%
01/24/15	02/15/19	89.752	92.358	2.70%	-2.606	-2.82%
01/24/15	02/15/19	89.398	92.358	2.80%	-2.960	-3.20%
01/24/15	02/15/19	89.046	92.358	2.90%	-3.312	-3.59%
01/24/15	02/15/19	88.696	92.358	3.00%	-3.662	-3.97%
01/24/15	02/15/19	88.347	92.358	3.10%	-4.011	-4.34%
01/24/15	02/15/19	88.000	92.358	3.20%	-4.358	-4.72%
01/24/15	02/15/19	87.655	92.358	3.30%	-4.703	-5.09%
01/24/15	02/15/19	87.311	92.358	3.40%	-5.047	-5.46%
01/24/15	02/15/19	86.970	92.358	3.50%	-5.388	-5.83%
01/24/15	02/15/19	86.629	92.358	3.60%	-5.729	-6.20%
01/24/15	02/15/19	86.291	92.358	3.70%	-6.067	-6.57%
01/24/15	02/15/19	85.954	92.358	3.80%	-6.404	-6.93%
01/24/15	02/15/19	85.619	92.358	3.90%	-6.739	-7.30%
01/24/15	02/15/19	85.285	92.358	4.00%	-7.073	-7.66%
01/24/15	02/15/19	84.953	92.358	4.10%	-7.405	-8.02%
01/24/15	02/15/19	84.623	92.358	4.20%	-7.735	-8.38%
01/24/15	02/15/19	84.294	92.358	4.30%	-8.064	-8.73%
01/24/15	02/15/19	83.967	92.358	4.40%	-8.391	-9.09%

For a 1-year holding period, the return will depend on what future bid price I can sell the bond at in one year. In other words, what interest rates are a year from now. If rates stay the same, I'll do better than a 1-year Treasury. If rates fall I'll do better.

If rates rise, I'll do worse. Rates above about 2% (currently 1.29%), the price will be less than what I paid, a the investment will produce a loss over the 1-year holding period. :oops:

For the range of future interest rates shown, 0% to 3%, the range of outcomes is from -9% to 8% annual return.

:arrow: This table demonstrates that there is a distribution of possible outcomes using this strategy.

[Edited to correct an error in table.]
Last edited by grayfox on Sun Jan 26, 2014 8:42 am, edited 1 time in total.

linuxizer
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Re: Riding the Yield Curve

Post by linuxizer » Fri Jan 24, 2014 9:55 am

richard wrote:Because the yield curve is yield to maturity and not the yield for the next year. So if you plan to sell next year it does not tell you what you want to know. The curve does not reflect the way the bond price will change as it moves down the yield curve.
Agreed - that's the right thing to do if you plan to ride the yield curve. It's another example of how you can profit if you can accurately predict market prices. It's not the right thing if you plan to hold.[/quote]

The reason the riding the yield curve has an expected return is that it's risky. That doesn't mean you need to accurately predict market prices to make investing in it a perfectly reasonable thing to do, any more than you have to know what stock prices are going to be next year to make investing in the stock market a perfectly reasonable thing to do.

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Re: Riding the Yield Curve

Post by bikenfool » Fri Jan 24, 2014 10:34 am

bikenfool wrote:
stlutz wrote:It was one I started--something like, "Treasuries and CDs reconsidered.". (I'm on my little tablet at the moment so copying a link in is kind of a pain. :happy )
Must be this one:
http://www.bogleheads.org/forum/viewtop ... 0&t=118751
Thanks stlutx for pointing me to the other thread, that was very informative. Of particular interest was this:
http://www.bogleheads.org/forum/viewtop ... 0#p1757925
stlutz wrote:...This fund would have a duration of about 5.1. The YTM of the bonds in the fund are 1.37%. Yet when I ran the same calculation on all of the bonds in the portfolio, I ended up with a 1 year expected return of 2.44%--not very much different from the "bullet" strategy of holding a single bond with a duration of 5.1.

I was kind of confused at first of how I could end up with an expected return of 2.44% instead of 1.37% when I am holding the bonds to maturity. Then it clicked. The return of a bond held to maturity will always be the yield at the time you purchased the bond. A bond ladder is always rolling. So, when my fund is buying the bonds, it is buying 10 year bonds. Right now those yield 2.5%--pretty much right in line with my 2.44% calculation.

In short, in terms of expected return, there really isn't that much difference between 1 bond with a duration of X and a ladder of bond with a duration of X.
and ogd's followup
ogd wrote:Yes, the 10 year comparison clicked with me as well, in this post above http://www.bogleheads.org/forum/viewtop ... 0#p1741931 . It says that a "rolling" fund of duration x can make roughly as much as the YtM of a bond with duration 2x. Moreover, this is a relation that stays true when the yield curve flattens.
At 1st I thought this must be wrong, but it isn't. Let me simplify it for myself. Lets say we have an positive straight line yield curve, from 0 to 2% up to 10 yrs. The rates aren't changing. Consider a steady state bond ladder, 0 - 10 yrs. Each bond is purchased with a YTM of 2% and held to maturity so the cash flow or earnings or whatever you want to call it is 2%. But the average YTM is 1%. What was not obvious, to me anyway, is that this is only possible because the NAV of the ladder is higher than par since the bonds have ridden the yield curve down to 5 years (average). What does this mean? Does it mean that the NAV of the ladder, or a comparable bond fund will increase in a rising yield curve environment? If a 0-10 fund can make roughly the same as the YTM of a 10 yr bond, what if the fund has the same duration, but holds 4-6 yr maturities, the return would be the same as the 0-10 fund !? :confused
Like someone else said, it's amazing how something as simple as a bond can be so confusing.

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Re: Riding the Yield Curve

Post by Epsilon Delta » Fri Jan 24, 2014 12:10 pm

bikenfool wrote:Let me simplify it for myself. Lets say we have an positive straight line yield curve, from 0 to 2% up to 10 yrs. The rates aren't changing. ... If a 0-10 fund can make roughly the same as the YTM of a 10 yr bond, what if the fund has the same duration, but holds 4-6 yr maturities, the return would be the same as the 0-10 fund !? :confused
Yes, the 4-6 year latter gives the same result as the 0-10 year.
You buy the 6 year yielding 1.2%, collect 1.2% interest for two years and sell a 4 year yielding .8%. The price appreciation gives you the other .8% per year.

A rough look at the price appreciation:
A $100, 4 year bond at 0.8% will pay four payments of $0.8 and one payment of $100 (return of principle) for a total payment of $103.2.

A $100 nominal 6 year bond yielding 1.2% will pay $100 + 4 * $1.2 = $104.8 in its last 4 years. So at the start of the 4 years it will be worth roughly $1.6 more than the 4 year bond. That gives you $0.80 per year in capital gains which is the 0.8% needed above.

I have made some simplifying assumptions because the coupons are much smaller than the $100 principle so the duration of both bonds are close to 4 years. If the (collective) coupons are large the above argument isn't accurate.

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grayfox
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Re: Riding the Yield Curve

Post by grayfox » Fri Jan 24, 2014 4:18 pm

Clive wrote: If you select where the yield curve declines the fastest (is the steepest) then the capital appreciation could be the fastest.

[?? Note : not sure as this is foreign to me (UK investor looking at US data/assets)] From that link you supplied Feb 2018 and Feb 2017 looks to me to be steeper than your choice and the Feb 2018/2017 is set to potentially total return 3.96%. Its also quite steep between Nov 2023 and Nov 2022 (7.3% Total Return). If the 3-year (or 8 year) yields are lower in a year time then that adds, if the yields are higher then that detracts. Whilst that applies across the entire yield curve and the implications are that yields will generally rise, those two examples are a indicator of possible better valued choices (or of anticipation that something around those dates is likely to see increases in yields around those dates).
I think the WSJ are more reflective of wholesale prices, i.e. what some big bond trader would be able to buy and sell at. Retail investors get bigger spreads and worse prices.

So I looked at the prices of the 2/15/2018 and 2/15/2017 on VBS, which is what I could actually get.

Code: Select all

Settlement   Maturity   BID      ASK    BID-YTM   ASK-YTM   PROFIT   Return
01/24/14	02/15/17	97.469	97.563	0.842%	0.811%
01/24/14	02/15/18	95.000	95.172	1.271%	1.226%	2.297	2.41%
Basically what I would say is going on with Riding the Yield Curve:

Today the Feb-2018 is trading at about 95. In four years it will be exactly 100. But it doesn't go there at a constant growth rate. If the yield curve didn't change in the 4 years, it would follow the curve. The gains would be bigger when it's steep, and smaller gains when it's shallow. So the first year it goes from 95 -> 97.5 (halfway). After that it goes slower. The final year it only goes from 99.8 -> 100.

The only fly in the ointment is that the yield curve is not fixed, so you really can't count on the price be 97.5 in one year. In fact, the profit/loss depends only on what the price will one year hence, which you would have to say is a random variable.

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Re: Riding the Yield Curve

Post by ogd » Fri Jan 24, 2014 5:23 pm

bikenfool wrote:Like someone else said, it's amazing how something as simple as a bond can be so confusing.
bikenfool: the more I learn about bond pricing, the more I realize that it's in fact the simplest model in which obvious mispricings don't exist. For example, that bonds sold before maturity are not underpriced, or that riding the yield curve doesn't work for very long because the market is merely pricing the future and will continue to price it right as it materializes, if all goes as expected.

It's sort of like Einstein's General Relativity: fiendishly complicated math, often unsolvable, yet it's the simplest model satisfying some very very basic principles.

My own personal takeaway from this is, buy an IT fund with favorable tax and risk characteristics, and don't worry much about it otherwise.
bikenfool wrote:What was not obvious, to me anyway, is that this is only possible because the NAV of the ladder is higher than par since the bonds have ridden the yield curve down to 5 years (average). What does this mean? Does it mean that the NAV of the ladder, or a comparable bond fund will increase in a rising yield curve environment?
It means that if the yield curve stays the same, the NAV rises as it rides down the ladder, transforming those 2% initial yields into capital gains that you may or may not choose to take. But the yield curve is (at least in my opinion, see alternate theories above) always expected to go towards flat, at the level of its longer end. It's not expected to rise uniformly or to stay the same. If you are able to make more money than YtM / SEC yield by riding, it means that either the bond market was wrong or perhaps that you earned rewards from the increased risk that was initially priced in (which could have easily turned out otherwise). But no free lunch -- as in, you are not expected to make any more money than the risk you took.

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Re: Riding the Yield Curve

Post by #Cruncher » Sat Jan 25, 2014 7:21 am

linuxizer wrote:#Cruncher- The 3 bond portfolio has higher convexity so lower interest rate risk. Look up barbell vs bullet portfolios.
linuxizer, please explain how you measure "interest rate risk". I thought I was measuring it when I calculated how the prices of 3 TIPS responded, each and on average, to an instantanious across-the-board 1% point increase in yield. As this extract from the table in my post shows, the medium term bond's price fell almost exactly the same percent as the average of all 3 bonds. Therefore, I'd conclude the "3 bond portfolio" has the same, not lower, interest rate risk.

Code: Select all

                           Macaulay    Price
  Maturity  Coupon   Life  Duration    Change
----------  ------  -----  --------    ------
07/15/2016  2.500%   2.48     2.42     (2.4%)
07/15/2021  0.625%   7.48     7.32     (7.0%)
04/15/2029  3.875%  15.23    12.20    (11.4%)
                    -----    -----     ------
  Average            8.39     7.31     (6.9%)

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Re: Riding the Yield Curve

Post by Clive » Sat Jan 25, 2014 7:45 am

#Cruncher wrote:when I calculated how the prices of 3 TIPS responded, each and on average, to an instantanious across-the-board 1% point increase in yield. As this extract from the table in my post shows, the medium term bond's price fell almost exactly the same percent as the average of all 3 bonds. Therefore, I'd conclude the "3 bond portfolio" has the same, not lower, interest rate risk.

Code: Select all

                           Macaulay    Price
  Maturity  Coupon   Life  Duration    Change
----------  ------  -----  --------    ------
07/15/2016  2.500%   2.48     2.42     (2.4%)
07/15/2021  0.625%   7.48     7.32     (7.0%)
04/15/2029  3.875%  15.23    12.20    (11.4%)
                    -----    -----     ------
  Average            8.39     7.31     (6.9%)
As did the barbell (2016/2029 50/50 average = 6.9%) in your example. However academia suggest

The barbell has greater convexity than the bullet because duration increases linearly with maturity while convexity increases with the square of maturity. If a combination of short and long durations, essentially maturities, equals the duration of the bullet, that same combination of the two convexities, essentially maturities squared, must be greater than the convexity of the bullet https://www.inkling.com/read/fixed-inco ... ell-versus

Is it perhaps that the differences are so small to be mostly insignificant - assuming 0.1% to be 'noise' ?

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Re: Riding the Yield Curve

Post by linuxizer » Sat Jan 25, 2014 8:49 am

How did you calculate the price changes? Duration X rate change, or using the actual present value calculation?

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Re: Riding the Yield Curve

Post by #Cruncher » Sun Jan 26, 2014 7:18 am

linuxizer wrote:How did you calculate the price changes? Duration X rate change, or using the actual present value calculation?
The latter. You can check it yourself with a bond calculator like ficalc.com using a 1/22/2014 settlement date. Enter the yields from the tables in this post and you'll get prices within 0.01% point of what's shown.

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Re: Riding the Yield Curve

Post by linuxizer » Sun Jan 26, 2014 7:38 am

That's good. But if you then used that 1% change to select your bonds then you have selected your bonds to have a duration plus convexity (plus residual moments) change that is exactly equal. Should start to see differences again with a bigger/smaller rate change. Still, a 1% change is a pretty big one. A little surprising that the yield is still higher for the bullet. Maybe points to steepness of the yield curve on the short end.

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Re: Riding the Yield Curve

Post by grayfox » Sun Jan 26, 2014 8:51 am

What I especially like about this "Riding the Yield Curve" strategy is that it takes a guaranteed, default-free investment with a known outcome (U.S. Treasury), and turns it into a bet on future interest rates with a distribution of possible outcomes.

It's much more exciting to have a chance to get 3% or higher, with the possible of losing money, than to get a sure 1.6%.

:?: I wonder of there is a way to leverage it up so that the expected return is 12% or 30%? :moneybag How would that work?

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Re: Riding the Yield Curve

Post by linuxizer » Sun Jan 26, 2014 11:05 am

grayfox wrote:What I especially like about this "Riding the Yield Curve" strategy is that it takes a guaranteed, default-free investment with a known outcome (U.S. Treasury), and turns it into a bet on future interest rates with a distribution of possible outcomes.
If you're investing in nominal Treasuries, the real outcome is definitely not known. If you're rolling a ladder, the outcome is not known. If you're not rolling a ladder, the outcome is still somewhat unknown, because you don't know what rate you'll get on your coupon payments when they are reinvested.

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Re: Riding the Yield Curve

Post by grayfox » Mon Jan 27, 2014 7:50 am

You need to separate the wheat from the chaff.

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Re: Riding the Yield Curve

Post by linuxizer » Mon Jan 27, 2014 8:01 am

grayfox wrote:You need to separate the wheat from the chaff.
Always a good policy, when milling grain....

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Re: Riding the Yield Curve

Post by grayfox » Mon Jan 27, 2014 12:53 pm

I just noticed that we can get historical quotes on WSJ. So I don't have to wait a year to see how "riding the yield curve" works out. They have historical prices and yields for regular Treasuries and TIPS, but not for STRIPS.

Suppose that a year ago, on January 24, 2013 I bought a 2-15-2019 2.75% Treasury. That's about a six year bond. Then I sold it one year later when it is a 5-year bond.

Here are some prices and YTM's for Jan 24, 2013

Code: Select all

Settlement	Maturity	Coupon	BID	ASK	YTM	
01/24/13	02/15/18	3.50%	113.4453	113.4922	0.774%
01/24/13	02/15/19	2.75%	110.2656	110.3047	0.993%	
http://online.wsj.com/mdc/public/page/2 ... stcalendar

So I paid $110.3047, will collect $2.75 interest during the year, and then sell it on Jan 24, 2014, hopefully at a higher price. I'm not going to calculate the exact price I expect (maybe later), let's say it's about 111. The gain would be the 2.75 interest plus 0.695 capital gain = 3.445 total gain, which works out to about 3.12% expect total return.

Fast forward to January 24, 2014. Here is the actual result

Code: Select all

B/S	Settlement	Maturity	Coupon	BID	ASK	YTM	Interest	Cap Gain	Total Gain	Total Return
SOLD 01/24/14	02/15/19	2.75%	105.5781	105.6250	1.507%
BUY 01/24/13	02/15/19	2.75%	110.2656	110.3047	0.993%	2.750	-4.727	-1.977	-1.79%
I got the 2.75 interest as expected, but since interest rates went up, there was a capital loss. Total return was -1.79%.

I hope this is clear. Gotta run!

linuxizer
Posts: 1553
Joined: Wed Jan 02, 2008 7:55 am

Re: Riding the Yield Curve

Post by linuxizer » Mon Jan 27, 2014 1:03 pm

grayfox wrote:I hope this is clear.
What good is a single year of data for anything?
grayfox wrote:Gotta run!
Fox indeed!

User avatar
grayfox
Posts: 4933
Joined: Sat Sep 15, 2007 4:30 am

Re: Riding the Yield Curve

Post by grayfox » Mon Jan 27, 2014 2:41 pm

linuxizer wrote: What good is a single year of data for anything?
It shows that "riding the yield curve" strategy is a crapshoot. The OP thought that it increases the returns of a bond portfolio by quite a bit (~1%) in a positive sloping yield curve like we have now.

Well the expected return may have been higher, but the actual result was to reduce the actual return by about -2% when interest rates rose. It's just making a bet on future interest rates using the naive interest rate forecast, i.e. yield curve one year hence will be the same as today.

Now if someone wanted to speculate on future interest rates, I think they would want a better forecasting model than that. Maybe take into account some other variables or that interest rates were at ultra low rates and more likely to rise. No if there is no good forecast model, why bother?

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