## In defense of short-term treasuries

Discuss all general (i.e. non-personal) investing questions and issues, investing news, and theory.
danielc
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### Re: In defense of short-term treasuries

Doc wrote:
Mon Jul 16, 2018 2:41 pm
I don't understand exactly what "Term Premia" means. But I think the general gist is the premium you get from rolling a one to buying a ten and holding to maturity.
I thought that the link you posted did a good job at explaining it. So if today the rate on 1-year treasuries is 2% and you think that next year they'll be 2.4%, then a sequense of 1-year treasuries for 2 years will yield around 2.2% net. If you accept a 2-year treasury for 2.3% you have accepted a 0.1% term premium for the extra year... At least that's how I understand it. So in my example, if you accepted a 2-year treasury for 2.05%, you would be accepting a negative term premium of -0.15%. The page that Kevin linked calculates the current term premia at:

Code: Select all

``````Maturity    Term Premium
1 Year     -0.19 %
2 Years    -0.28 %
3 Years    -0.34 %
4 Years    -0.38 %
5 Years    -0.42 %
6 Years    -0.45 %
7 Years    -0.47 %
8 Years    -0.49 %
9 Years    -0.51 %
10 Years    -0.52 %
``````
So it looks to me like your best bet right now is to hold the shortest term thing you can get.

tigerdoc93
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### Re: In defense of short-term treasuries

I’m confused. Should I buy short term or intermediate term treasuries? My portfolio is 65% stocks 25% bonds 10% cash/I bonds. My bonds are 80% total bond market and 20% short term corporate. Thanks.

danielc
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### Re: In defense of short-term treasuries

tigerdoc93 wrote:
Mon Jul 16, 2018 4:10 pm
I’m confused. Should I buy short term or intermediate term treasuries? My portfolio is 65% stocks 25% bonds 10% cash/I bonds. My bonds are 80% total bond market and 20% short term corporate. Thanks.
That's what we are debating. But don't worry, the difference won't be important. By far the most important thing that determines your risk and return is your stock vs bond allocation, followed by expense ratios and taxes.

Your bonds look fine to me.

Doc
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### Re: In defense of short-term treasuries

danielc wrote:
Mon Jul 16, 2018 3:41 pm
So it looks to me like your best bet right now is to hold the shortest term thing you can get.
But I don't have to hold that 2 year note for an extra year. I can sell it after one year.

I don't have to hold that intermediate term note to maturity. At the time that the current yield on a new note that matches the remaining time on my original note I just sell my original note and have lost nothing. In the meantime I have been getting a higher coupon.

As I said I don't understand the purpose of "term premia" but I don't think its significance is being interpreted properly.
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.

jalbert
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### Re: In defense of short-term treasuries

That is not what a Monte Carlo simulation is. It assumes a probability distribution and uses a random number generator and the distribution to generate a time series of simulated outcomes. The value Monte Carlo simulations is limited for investment outcome simulations because we don’t actually know the probability distribution of returns.
Risk is not a guarantor of return.

danielc
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### Re: In defense of short-term treasuries

Doc wrote:
Mon Jul 16, 2018 4:35 pm
But I don't have to hold that 2 year note for an extra year. I can sell it after one year.
That wouldn't achieve anything. The price of the 2-year note will adjust so that 1 year later investors are indifferent between buying your 2-year note with 1 year left in it, or just buying a regular 1-year bill that just came out.
Doc wrote:
Mon Jul 16, 2018 4:35 pm
At the time that the current yield on a new note that matches the remaining time on my original note I just sell my original note and have lost nothing.
That is not true. The market value of a treasury can go down. This is precisely what the term risk is about. If you buy a 2-year note at 2% and next year the 1-year bills are returning 5%, the market value of your 2-year note will be less than the price you paid for it.
Doc wrote:
Mon Jul 16, 2018 4:35 pm
As I said I don't understand the purpose of "term premia" but I don't think its significance is being interpreted properly.
I see that. I hope that my comment above clarifies this a bit.

danielc
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### Re: In defense of short-term treasuries

jalbert wrote:
Mon Jul 16, 2018 4:40 pm
That is not what a Monte Carlo simulation is. It assumes a probability distribution and uses a random number generator and the distribution to generate a time series of simulated outcomes.
Drawing randomly from a list of values is equivalent to assuming that that list of values represents the probability distribution. There is no rule that says that a Monte Carlo simulation is required to use a parametric distribution with a simple algebraic form. There is a whole universe of MC methods that are used to explore non-parametric, highly dimensional, or otherwise complex probability distributions. You see this being used, for example, in MCMC problems, bootstrapping, etc. Furthermore, I would argue that drawing from historical values is superior to, for example, fitting a Gaussian, because forcing a Gaussian distribution makes an additional, unwarranted assumption (e.g. it forces thin tails).

jalbert
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### Re: In defense of short-term treasuries

If you do want to use historical data, we can calculate the historical efficient frontier using portfoliovisuslizer going back to 1977 (the limit of the data) for a high equity allocation and either ST or IT treasuries. Setting the min for stocks at 79% and max for stocks at 80% but leaving ST and IT treasuries unconstrained so that the optimizer can choose whatever mix is best results in:

https://www.portfoliovisualizer.com/eff ... rtTreasury

Note that if you have a low equity allocation, then IT treasuries are enough riskier stand-alone to find a shorter duration:

https://www.portfoliovisualizer.com/eff ... rtTreasury
Risk is not a guarantor of return.

jalbert
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### Re: In defense of short-term treasuries

danielc wrote:
Mon Jul 16, 2018 4:51 pm
jalbert wrote:
Mon Jul 16, 2018 4:40 pm
That is not what a Monte Carlo simulation is. It assumes a probability distribution and uses a random number generator and the distribution to generate a time series of simulated outcomes.
Drawing randomly from a list of values is equivalent to assuming that that list of values represents the probability distribution. There is no rule that says that a Monte Carlo simulation is required to use a parametric distribution with a simple algebraic form. There is a whole universe of MC methods that are used to explore non-parametric, highly dimensional, or otherwise complex probability distributions. You see this being used, for example, in MCMC problems, bootstrapping, etc. Furthermore, I would argue that drawing from historical values is superior to, for example, fitting a Gaussian, because forcing a Gaussian distribution makes an additional, unwarranted assumption (e.g. it forces thin tails).
A histogram of historical values is still simulating a probability distribution that may not be the accurate distribution of future returns.
Risk is not a guarantor of return.

danielc
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### Re: In defense of short-term treasuries

jalbert wrote:
Mon Jul 16, 2018 5:10 pm
A histogram of historical values is still simulating a probability distribution that may not be the accurate distribution of future returns.
I know.

Side-note: Nit-pick on the definition of "histogram". A table of values is not a histogram. (but that doesn't change the validity of what you said).

danielc
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### Re: In defense of short-term treasuries

jalbert wrote:
Mon Jul 16, 2018 4:54 pm
If you do want to use historical data, we can calculate the historical efficient frontier using portfoliovisuslizer going back to 1977 (the limit of the data) for a high equity allocation and either ST or IT treasuries. Setting the min for stocks at 79% and max for stocks at 80% but leaving ST and IT treasuries unconstrained so that the optimizer can choose whatever mix is best results in:

https://www.portfoliovisualizer.com/eff ... rtTreasury
I think a better way to make your point is to look at all 20-year intervals from 1977 to the present day. There are 20 such periods, and out of those (and fixing stocks at 60%) only the first three had a tangency portfolio dominated by ST treasuries. I think this is a good argument against my original post, because the tangency portfolio gives you a way to balance volatility and return.

Doc
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### Re: In defense of short-term treasuries

danielc wrote:
Mon Jul 16, 2018 4:41 pm
Doc wrote:
Mon Jul 16, 2018 4:35 pm
But I don't have to hold that 2 year note for an extra year. I can sell it after one year.
That wouldn't achieve anything. The price of the 2-year note will adjust so that 1 year later investors are indifferent between buying your 2-year note with 1 year left in it, or just buying a regular 1-year bill that just came out.
Doc wrote:
Mon Jul 16, 2018 4:35 pm
At the time that the current yield on a new note that matches the remaining time on my original note I just sell my original note and have lost nothing.
That is not true. The market value of a treasury can go down. This is precisely what the term risk is about. If you buy a 2-year note at 2% and next year the 1-year bills are returning 5%, the market value of your 2-year note will be less than the price you paid for it.
Doc wrote:
Mon Jul 16, 2018 4:35 pm
As I said I don't understand the purpose of "term premia" but I don't think its significance is being interpreted properly.
I see that. I hope that my comment above clarifies this a bit.
No it doesn't help at all.
That wouldn't achieve anything. The price of the 2-year note will adjust so that 1 year later investors are indifferent between buying your 2-year note with 1 year left in it, or just buying a regular 1-year bill that just came out.
Exactly.

You apparently didn't understand what I was trying to illustrate. Let me try an example. I buy a 5 year note with a 3% coupon. At that time a 4 year note has a 2% coupon. Six months later the coupon on a new 4.5 year note is 2.5%. I'm still ahead. My note is above par. Another six months go buy and the coupon on a new 4 year note has risen to 3% which is the same as the note I already own. Therefore the price of my note is now back to par and I can sell it and get back all my principle and reinvest it. In the one year I have owned it I have earned 3%. Unless the one year note was earning 3% when I bought my five I come out ahead. The problem I see with "term premium" calculation It assume that I hold my original five to maturity and compare that with rolling a one year note five times.

I'm sure that the "roll premia" has some use somewhere but not in the case I am interested in.
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.

danielc
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### Re: In defense of short-term treasuries

Doc wrote:
Mon Jul 16, 2018 5:46 pm
No it doesn't help at all. ... Let me try an example.
Let's try my example instead because the whole point of my example was to make a negative term premium. Clearly, if you pick a different example you will get a different answer. My example was:
danielc wrote:If you buy a 2-year note at 2% and next year the 1-year bills are returning 5%, the market value of your 2-year note will be less than the price you paid for it.
Let's unpack that: Today you pay \$1000 to buy a bond that will pay you \$20 next year and \$1020 the year after. This is a 2% nominal return. In contrast, your arch-nemesis takes the short-term route. He buys 1-year bills for two years. Suppose that this year the 1-year bill has a return of only 1% and next year they jump to 5%, as in my example. So your arch-nemesis will pay \$1000 today. In 1 year he gets \$1010 which he reinvests at 5% and the year after he gets \$1060.50 back.

NOW let's consider your plan of exchanging your 2-year note next year:

1) Today you buy a note for \$1000.

2) Next year you get a \$20 coupon and you still have a year to go on your note.

3) But today the interest rates for 1-year bills have gone up to 5%. If you want to sell your note, you need to sell it at a value that will give 5% return to whoever buys it from you.

\$1020 / 1.05 = \$971.43

That's the price at which you have to sell your note. If you sell it, you can reinvest those \$971.43 into a 1-year bill returning 5%, and that's just going to give you the same \$1020 that you were originally going to get. In other words, selling your 2-year note to buy a 1-year note at 5% did absolutely nothing for you. You still finish the second year with \$1040 in your pocket. All you did was move pieces of paper around. Meanwhile, your arch-nemesis is sitting on his \$1060.50 fortune laughing at you because he made \$20.50 more than you.

This is what a negative term premium does. In your example you chose a positive term premium, so of course that's the answer that it gave.
Doc wrote:
Mon Jul 16, 2018 5:46 pm
The problem I see with "term premium" calculation It assume that I hold my original five to maturity and compare that with rolling a one year note five times.
As my example shows, there is no such assumption. The problem is that you have explicitly chosen an example that had a positive term premium and then you wondered why it didn't show a negative term premium.

jalbert
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### Re: In defense of short-term treasuries

You can try different historical periods to come to whatever conclusion you want.

I believe that for low equity allocations, a shorter duration is preferred due to the inflation risk of IT treasuries. I believe that at high equity allocations, IT treasuries and equities have historically shown enough diversification benefit for an intermediate duration to be preferred.

It is not an all-or-nothing thing. If you start at a very low stock allocation, you will want a short duration. As stock allocation increases there is benefit to increasing duration until it is an intermediate duration of treasuries when the stock allocation is high.

At low stock allocations, TIPS are even better than ST treasuries.

I consider trying to analyze the term premium and/or risk-adjusted returns of different subclasses of nominal bonds as standalone investments to be a waste of time. Their benefit is for diversification of equity risk, and the combined portfolios are what should be considered.

Others may have a different view of this and manage their portfolios accordingly.
Risk is not a guarantor of return.

Kevin M
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### Re: In defense of short-term treasuries

danielc wrote:
Mon Jul 16, 2018 5:19 pm
I think a better way to make your point is to look at all 20-year intervals from 1977 to the present day. There are 20 such periods, and out of those (and fixing stocks at 60%) only the first three had a tangency portfolio dominated by ST treasuries. I think this is a good argument against my original post, because the tangency portfolio gives you a way to balance volatility and return.
It probably is not coincidental that portfolios dominated by short-term Treasuries did better only for the first three periods, when yields were generally increasing in the early years of those periods, but generally decreasing since the end of 1981.

I just don't think a period of mostly decreasing yields, falling from historically high yields, is a good data set on which to base probabilities going forward, starting from historically low yields.

Kevin
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Kevin M
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### Re: In defense of short-term treasuries

Doc wrote:
Mon Jul 16, 2018 5:46 pm
You apparently didn't understand what I was trying to illustrate. Let me try an example. I buy a 5 year note with a 3% coupon. At that time a 4 year note has a 2% coupon.
Let's stop right there. You're positing a yield curve with a slope of 100 basis points per year between 4-year and 5-year maturities, while the current yield curve has a slope of only 4 bps/year in that region.
Six months later the coupon on a new 4.5 year note is 2.5%. I'm still ahead. My note is above par. Another six months go buy and the coupon on a new 4 year note has risen to 3% which is the same as the note I already own. Therefore the price of my note is now back to par and I can sell it and get back all my principle and reinvest it.

Sounds great, but with the current yield curve, the 4-year yield only has to increase by 5 basis points in a year before the 1-year return on your 5-year note is below the initial yield of the 4-year note.

And you might lose 3-4 basis points on the bid/ask spread, taking you most of the way to wiping out your strategy without any change at all in yields. I just don't see how this is a feasible strategy, especially with the yield curve as flat as it is.

In this scenario, with a mild increase of only 5 bps in a year for all yields, the 2-year note does well, because the slope of the yield curve is 20 bps/year between 1-year and 2-year maturities.

Let's look at what actually happened over the last year, when of course yields increased much more than 5 basis points.

Are you telling us that you were able to continue to sell every one of your Treasuries with no loss and continue to roll them over in the face of these rising yields over the last year??? I don't think so.

Kevin
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Doc
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### Re: In defense of short-term treasuries

Kevin M wrote:
Mon Jul 16, 2018 7:48 pm
Let's stop right there. You're positing a yield curve with a slope of 100 basis points per year between 4-year and 5-year maturities, while the current yield curve has a slope of only 4 bps/year in that region
I made up numbers to try to illustrate to danielc what rolling the yield curve means. Comparing a ten year projected average of a one year rolled again and again to a ten held to maturity bogles my mind. I just don't get the point.
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.

nisiprius
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### Re: In defense of short-term treasuries

Kevin M wrote:
Sun Jul 15, 2018 8:37 pm
nisiprius wrote:
Sun Jul 15, 2018 6:14 pm
[*]The extra return of intermediate-term bonds, compared to short-term bonds (or cash!) is large enough to care about.
Really? Don't you mean "has been" instead of "is"? And doesn't it depend on the period we look at? How do you know what the returns will be going forward over any particular time period?
Shame on me. I try to review my postings for verb-tense problems before posting. But it is a terrible, terrible mental trap that requires constant vigilance.
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danielc
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### Re: In defense of short-term treasuries

Doc wrote:
Tue Jul 17, 2018 7:42 am
I made up numbers to try to illustrate to danielc what rolling the yield curve means. Comparing a ten year projected average of a one year rolled again and again to a ten held to maturity bogles my mind. I just don't get the point.
"Rolling down the yield curve" is a thing you can do when the term premium is positive (and ideally large). If you look up an article about it, the article will tell you that this plan will lose money if interest rates rise too fast. Furthermore, the longer the maturity the less they need to rise to make you lose money. A negative term premium means that the expected future changes in interest rates are high enough that you are better off holding the shorter term securities instead.

Doc
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### Re: In defense of short-term treasuries

danielc wrote:
Tue Jul 17, 2018 1:15 pm
"Rolling down the yield curve" is a thing you can do when the term premium is positive (and ideally large).
I don't get this "term premia" concept. The Fed has some "analysis is based on a five-factor, no-arbitrage term structure model." It seem they take the estimate for a 1 year note and in this case roll it ten time to get a comparison with a ten year note held to maturity. Maybe their model is great but I would never buy a ten year note and hold it to maturity so the model is worthless to me.

To get a positive roll down yield effect all you need is a positively sloped yield curve. In order to calculate the amount of the roll down yield you have to assume a constant yield curve. OK as of today we don't expect a constant yield curve so we can't calculate the roll down yield but as long as the curve is positive the roll down yield is there.

As of early this month both Kevin and I were calculating a positive roll down yield. (We use different methods so get slight different values.) But you are saying that the term premia is negative so there is no roll down yield. I do not understand.
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.

danielc
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### Re: In defense of short-term treasuries

Doc wrote:
Tue Jul 17, 2018 2:11 pm
I don't get this "term premia" concept. The Fed has some "analysis is based on a five-factor, no-arbitrage term structure model." It seem they take the estimate for a 1 year note and in this case roll it ten time to get a comparison with a ten year note held to maturity.
Did you see my example? I tried to explain it there. A positive term premium is the extra money you get for buying a longer term bond instead of a series of shorter term ones. If the yield curve is static (a risky assumption) then yes, the comparison would just be between (for example) holding a 5-year bond or buying a 1-year bond every year five times. If the yield curve is static and has a positive slope, you are better off with the 5-year bond. In this case you can also apply the "rolling down the yield curve" strategy. Kevin wrote about that two weeks ago. But now imagine that the yield curve is not static. Specificaly, imagine that interest rates are rising. Rising interest rates can reduce the premium, and can even make it negative. I gave the example that if this year the 1-year bonds return 1% and the 2-year bonds return 2%, but next year the 1-year bonds will return 5%, you are better off buying buying a 1-year bond each year. My example was an example of a negative term premium.

Doc wrote:
Tue Jul 17, 2018 2:11 pm
To get a positive roll down yield effect all you need is a positively sloped yield curve.
That is not correct. You ALSO need the yield curve to be static, or at least not increase too rapidly. If interest rates are increasing, that means that the yield curve is shifting upward.
Doc wrote:
Tue Jul 17, 2018 2:11 pm
In order to calculate the amount of the roll down yield you have to assume a constant yield curve. OK as of today we don't expect a constant yield curve so we can't calculate the roll down yield but as long as the curve is positive the roll down yield is there.
This is where you're going wrong. It is not enough that the yield curve retain a positive slope. You need the yield curve to not shift upward too rapidly. If today the 1-year and 2-year bonds return 1% and 2% and next year they return 5% and 6%, the yield curve has retained the positive slope, but locking the 2% today would be the wrong choice.

Doc wrote:
Tue Jul 17, 2018 2:11 pm
As of early this month both Kevin and I were calculating a positive roll down yield. (We use different methods so get slight different values.)
That must be the same thread I linked to. I've only read the first couple of posts, but I see your name further down.
Doc wrote:
Tue Jul 17, 2018 2:11 pm
But you are saying that the term premia is negative so there is no roll down yield. I do not understand.
Specifically, I'm saying that the roll down yield is negative. Hopefully my example and my other comments helped.

Doc
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### Re: In defense of short-term treasuries

danielc wrote:
Tue Jul 17, 2018 2:57 pm
I gave the example that if this year the 1-year bonds return 1% and the 2-year bonds return 2%, but next year the 1-year bonds will return 5%, you are better off buying buying a 1-year bond each year. My example was an example of a negative term premium.
No argument except "but next year ... will return 5%". Hindsight is 20-20 but foresight is not.
danielc wrote:
Tue Jul 17, 2018 2:57 pm
That is not correct. You ALSO need the yield curve to be static, or at least not increase too rapidly. If interest rates are increasing, that means that the yield curve shifting upward.
Agreed but you do not have to keep holding your original note. If the yield shifts up enough so that your note is no longer carrying a premium you just sell it. You do not achieve the capital gain part of the roll down yield but for that period of time you are getting a higher coupon. If the curve shifts up very rapidly so that you essentially don't have any time to sell before the price of your note goes below 100 you are correct. But again that's foresight.
danielc wrote:
Tue Jul 17, 2018 2:57 pm
Specifically, I'm saying that the roll down yield is negative. Hopefully my example and my other comments helped.
But it's not. Maybe you should define what you mean by roll down yield.
Rolling Down The Curve
If you buy a longer-term bond and the yield curve has a normal slope, the market price of a bond naturally increases as the bond rolls down the yield curve. For example, say you buy a five-year bond, paying a 5 percent coupon with a 5 percent yield -- the bond is priced at face value. After two years, you own a three-year bond. If rates have not changed, the market yield on the now three-year bond should be lower, because it is a shorter-term bond. However, your bond pays a 5 percent interest rate, so the bond's market value must be higher. An investor buying the bond to now earn the 4 percent yield that three-year bonds are paying would pay 103.5 percent of the bond's face value. Your bond has gained value as it rolled down the yield curve.
https://finance.zacks.com/rolldown-return-10616.html
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Kevin M
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### Re: In defense of short-term treasuries

danielc wrote:
Tue Jul 17, 2018 2:57 pm
Doc wrote:
Tue Jul 17, 2018 2:11 pm
In order to calculate the amount of the roll down yield you have to assume a constant yield curve. OK as of today we don't expect a constant yield curve so we can't calculate the roll down yield but as long as the curve is positive the roll down yield is there.
This is where you're going wrong. It is not enough that the yield curve retain a positive slope. You need the yield curve to not shift upward too rapidly.
I don't know if people understand the charts I posted yesterday, but both of them illustrate this exact point.

The first chart showed a hypothetical increase of 5 basis points for all yields over a 1-year period, so the hypothetical yield curve one year from now (Yield 1, red) is positively sloped, with exactly the same slope between each maturity that it has today (Yield 0, blue). This results in hypothetical 1-year returns (yellow/orange) that are lower than the initial yields for all original maturities great than three years.

I define "roll-down return" as the difference between the return and the initial yield, so in this hypothetical case, the realized 1-year roll-down return is negative for all maturities greater than three years. I generally assume a 1-year holding period because it's easy to model, but the roll-down return could be calculated for some other holding period. I probably would annualize the return regardless.

I think it's worthwhile to clarify whether we're discussing the expected roll-down return assuming a static yield curve, which is what Doc typically is referring to, or the realized roll-down return based on what actually happens with the yield curve. Of course one could also estimate expected roll-down return using a different assumption than a static yield curve.

The second chart showed the actual yield curves from 7/17/2017 (Yield 0, blue) and 7/16/2018 (Yield 1, red), along with the realized 1-year returns (yellow/orange). The yield curve was positive a year ago, as it is today, but it has flattened some, with shorter-term yields increasing more than longer-term yields. The relevant point here is that even though the slope of the yield curve at the end of the 1-year period was still positive, the realized roll-down return was hugely negative, not only falling well below the initial yields, but exceeding the initial yields in magnitude for maturities greater than two years, resulting in negative 1-year returns for those maturities.

The main point of the first chart was even though the expected roll-down return assuming a static yield curve is positive at all maturities, it doesn't take much of an increase in yields, only 5 basis points, for the realized 1-year roll-down returns to go negative for maturities of longer than three years.

For purposes of completeness, the chart below shows the expected 1-year returns assuming a static yield curve for the 7/16/2018 yields. The gap between the 1yr Rtn curve and the Yield 0 / Yield 1 curves (which are the same because of the static yield curve assumption) shows the expected 1-year roll-down returns assuming a static yield curve (SYC).

For example, the 5-year Treasury, used in the discussion yesterday, has an expected 1-year SYC roll-down return of 15 basis points, which added to the initial yield of 2.75%, gives an expected 1-year SYC total return of 2.90%. The first chart from yesterday shows that it only takes an increase of 5 basis points over one year to more than wipe out the expected roll-down return.

Kevin
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danielc
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### Re: In defense of short-term treasuries

Doc wrote:
Tue Jul 17, 2018 3:26 pm
No argument except "but next year ... will return 5%". Hindsight is 20-20 but foresight is not.
Of course. So the term premium is based on expectations about the future and those can be wrong.

Doc wrote:
Tue Jul 17, 2018 3:26 pm
Agreed but you do not have to keep holding your original note. If the yield shifts up enough so that your note is no longer carrying a premium you just sell it. You do not achieve the capital gain part of the roll down yield but for that period of time you are getting a higher coupon. If the curve shifts up very rapidly so that you essentially don't have any time to sell before the price of your note goes below 100 you are correct. But again that's foresight.
Yes. If the increase in interest rates is small enough that you merely lose the capital gain, then yes, you would have made money from the higher yield. If the increase in interest rates is higher than that, you would have a capital loss. If the capital loss is large enough, you can lose money.

Of course, we don't know the future. The term premium is based on expectations and those can be wrong.

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### Re: In defense of short-term treasuries

Kevin M wrote:
Tue Jul 17, 2018 3:55 pm
I define "roll-down return" as the difference between the return and the initial yield, so in this hypothetical case, the realized 1-year roll-down return is negative for all maturities greater than three years. I generally assume a 1-year holding period because it's easy to model, but the roll-down return could be calculated for some other holding period. I probably would annualize the return regardless.
I use a slightly different definition which leads to the same place but confuses the discussion. I define "roll-down return" as the annualized return between purchase and sale. I assume a holding period equal to the time between the points on the Treasury's Constant Maturity Curve instead of one year because it's easy to model. The latter may result in my getting a "smoother" curve than Kevin.
For example, the 5-year Treasury, used in the discussion yesterday, has an expected 1-year SYC roll-down return of 15 basis points, which added to the initial yield of 2.75%, gives an expected 1-year SYC total return of 2.90%. The first chart from yesterday shows that it only takes an increase of 5 basis points over one year to more than wipe out the expected roll-down return.
Even with our differences it still only takes a small increase in the flattening of the yield curve to wipe out the "roll-down return".

In the last couple of weeks the slope of the yield curve has increased at the short end but remained about the same from about 3 years out. Scary.
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### Re: In defense of short-term treasuries

danielc wrote:
Tue Jul 17, 2018 4:34 pm
Yes. If the increase in interest rates is small enough that you merely lose the capital gain, then yes, you would have made money from the higher yield. If the increase in interest rates is higher than that, you would have a capital loss. If the capital loss is large enough, you can lose money.
No. That's where our conflict comes from. I don't lose money because I sell the note when it drops to par. The "term premium" assumes that you keep the longer note until it matures.
Federal; Reserve Bank of San Francisco wrote:What is the term premium?

Briefly stated, the term premium is the excess yield that investors require to commit to holding a long-term bond instead of a series of shorter-term bonds. For example, suppose that the interest rate on the 10-year U.S. Treasury note is about 5.5%, and suppose that the interest rate on the 1-year U.S. Treasury bill is expected to average about 5% over the next 10 years (“note” and “bill” are the customary names for U.S. Treasury securities of these maturities). Then the term premium on the 10-year U.S. Treasury note would be about 0.5%, or 50 basis points.
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### Re: In defense of short-term treasuries

Doc wrote:
Tue Jul 17, 2018 5:01 pm
No. That's where our conflict comes from. I don't lose money because I sell the note when it drops to par. The "term premium" assumes that you keep the longer note until it matures.
There is no such assumption in either my example, or Kevin's example. The calculation of a 1-year return is for a 1-year holding period. Look again at my example and Kevin's plots. In my example, \$1000 invested invested on a 2-year bond was sold after 1 year for a capital loss of \$28.57 which was greater than the \$20 coupon. Kevin's plots show the same calculations for far more realistic examples than mine, and for several maturities. Still 1 year return though.

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### Re: In defense of short-term treasuries

danielc wrote:
Tue Jul 17, 2018 5:10 pm
Doc wrote: ↑Tue Jul 17, 2018 5:01 pm
No. That's where our conflict comes from. I don't lose money because I sell the note when it drops to par. The "term premium" assumes that you keep the longer note until it matures.
There is no such assumption in either my example, or Kevin's example.
Good. That's where I am getting confused. Your definition of Term Premium is apparently different from the San Francisco Fed's.
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### Re: In defense of short-term treasuries

Doc wrote:
Tue Jul 17, 2018 5:01 pm
No. That's where our conflict comes from. I don't lose money because I sell the note when it drops to par.
You keep saying this, but I challenged the feasibility of this strategy in my post yesterday, viewtopic.php?p=4024638#p4023488, and you did not answer the challenge:
Kevin M wrote:
Mon Jul 16, 2018 7:48 pm
Sounds great, but with the current yield curve, the 4-year yield only has to increase by 5 basis points in a year before the 1-year return on your 5-year note is below the initial yield of the 4-year note.

And you might lose 3-4 basis points on the bid/ask spread, taking you most of the way to wiping out your strategy without any change at all in yields. I just don't see how this is a feasible strategy, especially with the yield curve as flat as it is.

In this scenario, with a mild increase of only 5 bps in a year for all yields, the 2-year note does well, because the slope of the yield curve is 20 bps/year between 1-year and 2-year maturities.

Let's look at what actually happened over the last year, when of course yields increased much more than 5 basis points.

Are you telling us that you were able to continue to sell every one of your Treasuries with no loss and continue to roll them over in the face of these rising yields over the last year??? I don't think so.
What I really meant was with no loss relative to the initial yield.

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### Re: In defense of short-term treasuries

Doc wrote:
Tue Jul 17, 2018 4:53 pm
I define "roll-down return" as the annualized return between purchase and sale.
As I keep explaining, this is just annualized (total) return, so there is no need to call it something else. I've never seen anyone else define roll-down return this way, including in all the references you've linked to.
Doc wrote:
Tue Jul 17, 2018 4:53 pm
I assume a holding period equal to the time between the points on the Treasury's Constant Maturity Curve instead of one year because it's easy to model. The latter may result in my getting a "smoother" curve than Kevin.
It's fine to do it the way you do. It doesn't really matter that much. You actually introduce some error into your model by treating the CMT par yield curve as a zero-coupon yield curve--perhaps about as much as I do by interpolating to get the yields for the maturities not published by the Treasury.

As has been discussed elsewhere, one can get yield curves from the Federal Reserve Board that have both par yields and zero-coupon yields at every maturity from 1-year to 30-year if you want more precision, but as I've shown elsewhere, the differences are so small that it doesn't really matter.
Even with our differences it still only takes a small increase in the flattening of the yield curve to wipe out the "roll-down return".
Well, the yield curve could flatten by the longer-term yield falling or by the shorter-term yield increasing. We're both talking about the shorter-term yield increasing.

If you buy a 10-year note, it doesn't matter what happens to the 10-year yield if you're valuing the note at a later time; e.g., if valuing it one year after purchase, what matters is the 9-year yield at that time. It doesn't matter whether the 9-year yield increases because of flattening between 9-year and 10-year maturities, or because the entire yield curve shifts up.

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### Re: In defense of short-term treasuries

Maybe Kevin and Doc can comment on this:

I was reading Kevin's thread and this post explains how the 1-year return is affected by a shift in the yield curve. It appears that, to a good approximation, if the slope between the N-year yield and the (N-1)-year yield is X basis points, a "rolling down the yield curve" strategy that buys an N-year bond today and sells it next year is basically making a bet that in the next year the yields on (N-1)-year bonds will not increase by more than 2X bp.

Does that sound right?

If so, we can express the choice of maturity in terms of that bet. Right now the current yield curve is:

Code: Select all

``````Maturity    1 Yr    2 Yr    3 Yr    5 Yr    7 Yr    10 Yr   20 Yr   30 Yr
Yield       2.34    2.57    2.65    2.75    2.83    2.87    2.92    2.99
``````
For each pair of maturities I compute 2 x the yield difference divided by the number of years and I get the following "bets":

Code: Select all

``````Buy      Instead of    If you think that rates will increase less than
-----    ----------    -----------------------------------------------
2 Yr      1 Yr        46.00 bp         next year
3 Yr      2 Yr        16.00 bp         next year
5 Yr      3 Yr        10.00 bp / yr    for  2 years
7 Yr      5 Yr         8.00 bp / yr    for  2 years
10 Yr      7 Yr         2.67 bp / yr    for  3 years
20 Yr     10 Yr         1.00 bp / yr    for 10 years
30 Yr     20 Yr         1.40 bp / yr    for 10 years
``````
Expressed in this way, I think 2 Yr is the longest I'd be willing to buy. Even then, I'm not sure it's worth the risk.

---------------------------------------------
EDIT: If you add a 15bp transaction cost, all the bets look a lot worse. For 2 Yr you need rates to increase less than 31 bp. I don't think I want to take that bet.

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### Re: In defense of short-term treasuries

danielc wrote:
Wed Jul 18, 2018 2:16 am
Does that sound right?
No. I'm not really versed with the way Kevin does his calculations but when he's looking at points between the constant maturity points he divides by the difference in time which would not always be 2.
For each pair of maturities I compute 2 x the yield difference divided by the number of years and I get the following "bets":
There is other data on the the future shape of the yield curve at least at the low end. One is the CME Dot plot https://www.cmegroup.com/trading/intere ... -fomc.html Another is based on futures contracts. The point is that all this data is already baked into the curve by the bond pros and there is not much chance you or I or even Kevin can do better. It is a generally accepted principle that "the best estimate of the future yield curve is the current yield although not a very good one".
danielc wrote:
Wed Jul 18, 2018 2:16 am
If you add a 15bp transaction cost, all the bets look a lot worse. For 2 Yr you need rates to increase less than 31 bp. I don't think I want to take that bet.
The current bid/ask on the two for qty 10 is less than 2 bps (Schwab). Commission and markups are included in that spread.

If I had \$25k spare cash hanging around I would buy a six month T-bill. That would get me past the election, 2 FOMC meetings with rate hike likelihood and well into my familiarity with the new tax code and still allow me to buy longer T's at the January auctions.
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### Re: In defense of short-term treasuries

danielc wrote:
Wed Jul 18, 2018 2:16 am
Maybe Kevin and Doc can comment on this:

I was reading Kevin's thread and this post explains how the 1-year return is affected by a shift in the yield curve. It appears that, to a good approximation, if the slope between the N-year yield and the (N-1)-year yield is X basis points, a "rolling down the yield curve" strategy that buys an N-year bond today and sells it next year is basically making a bet that in the next year the yields on (N-1)-year bonds will not increase by more than 2X bp.

Does that sound right?
It depends what your criterion is, but regardless of what it is, I don't think this rule of thumb applies very well. Is your criterion that your 1-year return is at least the original yield of the N-year Treasury, or at least the original yield of the N-1 Treasury, or something else?

I can run a couple of tests to investigate. First, I'll use the CMT yields from 7/17/2018 for the Yield 0 curve (looks like you are using yields from 7/9/2018), then for the Yield 1 curve I'll apply your algorithm of increasing each N-1 yield by 2X the difference between the original N and N-1 yields. For example, for Yield 0 curve, 2-year is 2.62%, 3-year is 2.69%; difference is 7 basis points, so for Yield 1 curve, 2-year yield will be 14 basis points higher = 2.76%. Here's the result:

I don't see a regular pattern in the 1-year returns that consistently meets either of the criteria at all maturities.

As another check, I'll set the initial yield curve (Yield 0) to what I call the Doc 20 model, which is to anchor the curve at the current 7-year yield, then set all other yields so that the curve is linear with a slope of 20 bps/year. So the 7-year is 2.83%, the 6-year is 2.63%, and the 8-year is 3.03%, for example. I then set the 1-year later yield curve at 40 basis points higher for all yields. This is what we get:

Here we use the same 2X increase in all yields, but the resulting 1-year returns don't look like the first chart, but are relatively flat at all maturities.

Kevin
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### Re: In defense of short-term treasuries

stlutz wrote:
Sun Jul 15, 2018 6:01 pm

We've had a significant period where short-term bonds were the best. More recently we've had a significant period of time where long-term bonds were the best. One can try to guess which might work best in the future or one can try to split the difference in some way by, say, owning "intermediate" term bonds or bonds with a variety of maturities.
Or use the barbell approach.
I don't, but it seems sound.

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### Re: In defense of short-term treasuries

Doc wrote:
Wed Jul 18, 2018 10:49 am
It is a generally accepted principle that "the best estimate of the future yield curve is the current yield although not a very good one".
I don't think this is a generally accepted principle--it's a view propagated by Larry Swedroe and DFA, and supposedly based on some work by Fama, but it is far from a universally accepted theory on the term structure of interest rates.

Among central bankers and academics, a more common view is that the yield curve reflects both expectations of future rates and term premia. The static yield curve assumption implies that the expectation for future rates is no change, in which case the yield curve reflects only term premia.

Although term premia are not directly observable, many people have views about the path of future rates other than no changes (static yield curve), and there are models that are used to estimate the decomposition of the yield curve into expected future rates and term premia. It is one of the NY Fed models, discussed already in this thread, that currently estimates negative term premia at all maturities to 10 years.

Here is an article by Ben Bernanke that discusses this topic:

Why are interest rates so low, part 4: Term premiums. From that article:
Ben Bernanke wrote:Figure 4, provided by Tobias Adrian, takes a closer look at some components of Treasury yields since the beginning of 2013. The 10-year yield, in green, rose sharply during the taper tantrum of 2013, then fell through 2014. The dark blue line shows the estimated term premium. The difference between the yield and the term premium is the risk-neutral yield, plotted in light blue in Figure 4. The risk-neutral yield, an estimate of what the 10-year Treasury yield would be if investors were indifferent to risk, actually rose through 2014, implying that the recent decline in yields is entirely due to a falling term premium.
Here is the referenced Figure 4 from that article:

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### Re: In defense of short-term treasuries

Kevin M wrote:
Wed Jul 18, 2018 12:29 pm
danielc wrote:
Wed Jul 18, 2018 2:16 am
It appears that, to a good approximation, if the slope between the N-year yield and the (N-1)-year yield is X basis points, a "rolling down the yield curve" strategy that buys an N-year bond today and sells it next year is basically making a bet that in the next year the yields on (N-1)-year bonds will not increase by more than 2X bp.
It depends what your criterion is, but regardless of what it is, I don't think this rule of thumb applies very well. Is your criterion that your 1-year return is at least the original yield of the N-year Treasury, or at least the original yield of the N-1 Treasury, or something else?
Thanks for the help. The criterion was "N-year Treasury returns more than (N-1)-year Treasury". My understanding was that if yields go up by X bp that wipes out the "roll down return", but you still have the larger coupon from the N-year Treasury. But if yields go up another X bp, then the roll down return is negative and that wipes out the difference in the coupon between the N-year and N-1 year treasuries. At least that's how I interpreted the second and third plots in this post.

Kevin M wrote:
Wed Jul 18, 2018 12:29 pm
For example, for Yield 0 curve, 2-year is 2.62%, 3-year is 2.69%; difference is 7 basis points, so for Yield 1 curve, 2-year yield will be 14 basis points higher = 2.76%. Here's the result:

I don't see a regular pattern in the 1-year returns that consistently meets either of the criteria at all maturities.
Indeed. I was expecting to see a horizontal 1-yr return line between the 2-Year and 3-Year maturities. A flat 1-yr return line would have meant that you didn't lose any money by choosing the 3-Year maturity instead of the 2-Year one. I wonder why that didn't happen. How is this example different from the example in your other post where you increased the yields by 40 bp and the differences were all 20 bp?
Kevin M wrote:
Wed Jul 18, 2018 12:29 pm
As another check, I'll set the initial yield curve (Yield 0) to what I call the Doc 20 model, which is to anchor the curve at the current 7-year yield, then set all other yields so that the curve is linear with a slope of 20 bps/year.
I'm confused. How does forcing the yield like to be straight make sense except as a toy example?
Kevin M wrote:
Wed Jul 18, 2018 12:29 pm
So the 7-year is 2.83%, the 6-year is 2.63%, and the 8-year is 3.03%, for example. I then set the 1-year later yield curve at 40 basis points higher for all yields. This is what we get:

Here we use the same 2X increase in all yields, but the resulting 1-year returns don't look like the first chart, but are relatively flat at all maturities.
Yeah. So in that example if you choose the 8-Year instead of the 6-Year and rates go up 40 bp, at least you didn't lose any money for making that choice. Any increase larger than 40 bp means that you would have been better off with the 6-Year. I was expecting to see this working pairwise for a realistic yield curve. Back to your first example, where 2-year is 2.62%, 3-year is 2.69%, I was expecting that increasing yields by 14 bp would make the 1-yr return line flat between 2-Yr and 3-Yr. I don't understand why that didn't work.

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### Re: In defense of short-term treasuries

danielc wrote:
Wed Jul 18, 2018 3:44 pm
Thanks for the help. The criterion was "N-year Treasury returns more than (N-1)-year Treasury". My understanding was that if yields go up by X bp that wipes out the "roll down return", but you still have the larger coupon from the N-year Treasury. But if yields go up another X bp, then the roll down return is negative and that wipes out the difference in the coupon between the N-year and N-1 year treasuries. At least that's how I interpreted the second and third plots in this post.
It worked out that way because in that post I used what you call the "toy example" below, with the initial yield curve having a constant slope of 20 bps/year. The "toy example" in this more recent post is exactly the same as the third plot in the post you're referencing. It's not going to work out the same for different initial yield curves.
Indeed. I was expecting to see a horizontal 1-yr return line between the 2-Year and 3-Year maturities. A flat 1-yr return line would have meant that you didn't lose any money by choosing the 3-Year maturity instead of the 2-Year one. I wonder why that didn't happen.
But you didn't lose any money with the 3-year compared to the 2-year--the return is significantly higher for the 3-year given the initial yield curve and your 2X N-1 yield increase.

The return line is steeply upward sloping from 2-year to 3-year returns because the initial yield curve is much steeper between 1-year and 2-year (23 bps/year) than between 2-year and 3-year (7 bps/year), so the 2X increase in the 1-year yield (46 bps) had a proportionally larger impact than the 2X increase in the 2-year yield (14 bps), despite the shorter maturity of the 2-year security. In other words, the 3.3X larger yield increase of the 1-year compared to 2-year had a larger negative impact on the 2-year than the roughly 1/2 longer initial duration of the 3-year compared to 2-year had on the 3-year.
How is this example different from the example in your other post where you increased the yields by 40 bp and the differences were all 20 bp?
Which example was that? Differences between what and what?
I'm confused. How does forcing the yield like to be straight make sense except as a toy example?
Initially, for other posts, I thought a constant slope yield curve was a nice way to illustrate that if the N-1 yield increases by the magnitude of the initial slope between N-1 and N maturities, the return will equal the initial yield; i.e., the rolldown return will be 0% for all maturities. For the purposes of the post we're discussing here, it was just a convenient alternative yield curve to show that your thinking on the 2X increase in yields doesn't have a consistent result, but instead depends on the initial shape of the yield curve.
Yeah. So in that example if you choose the 8-Year instead of the 6-Year and rates go up 40 bp, at least you didn't lose any money for making that choice. Any increase larger than 40 bp means that you would have been better off with the 6-Year.

Again, this is just a result of the initial yield curve and the specified yield increases.

Take another look at the chart in this post earlier in this thread. The assumption there was a static yield curve, so yields didn't increase at all, yet the returns of all maturities greater than the 7-year had lower returns than the 7-year. In other words, you "lost money" by choosing the 10-year over the 7-year, even with no yield increases at all.
I was expecting to see this working pairwise for a realistic yield curve. Back to your first example, where 2-year is 2.62%, 3-year is 2.69%, I was expecting that increasing yields by 14 bp would make the 1-yr return line flat between 2-Yr and 3-Yr. I don't understand why that didn't work.
There's nothing particularly unrealistic about a yield curve with a fairly constant slope between 1-year and 10-year maturities. Go to this dynamic yield curve site, and drag the timeline in the right chart back and forth, watching the shape of the yield curve in the left chart. It's not hard to find such historical yield curves.

There's no reason to expect that a yield curve with a non-constant slope is going to respond to a specified yield curve change in the same way as one with a constant slope. Your 2X increase spec results in a parallel increase in the yield curve for the linear-slope case, but something radically different for the current yield curve.

Although I thought the linear yield curve was a convenient way to illustrate certain concepts, I think it might have misled you into thinking there's more regularity or predictability in returns and yield curve changes than there actually is.

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### Re: In defense of short-term treasuries

Kevin M wrote:
Wed Jul 18, 2018 10:56 pm
danielc wrote:Indeed. I was expecting to see a horizontal 1-yr return line between the 2-Year and 3-Year maturities. A flat 1-yr return line would have meant that you didn't lose any money by choosing the 3-Year maturity instead of the 2-Year one. I wonder why that didn't happen.
But you didn't lose any money with the 3-year compared to the 2-year--the return is significantly higher for the 3-year given the initial yield curve and your 2X N-1 yield increase.
Yeah. But I was expecting a flat 1-yr return line. My mistake. I just worked out the formula for the change in yields that would have made the 1-yr return line flat. It's an ugly formula that doesn't provide any useful intuition.

Kevin M wrote:
Wed Jul 18, 2018 10:56 pm
The return line is steeply upward sloping from 2-year to 3-year returns because the initial yield curve is much steeper between 1-year and 2-year (23 bps/year) than between 2-year and 3-year (7 bps/year), so the 2X increase in the 1-year yield (46 bps) had a proportionally larger impact than the 2X increase in the 2-year yield (14 bps), despite the shorter maturity of the 2-year security. In other words, the 3.3X larger yield increase of the 1-year compared to 2-year had a larger negative impact on the 2-year than the roughly 1/2 longer initial duration of the 3-year compared to 2-year had on the 3-year.
Oh! And that's another thing I forgot about entirely. I forgot that the 2-Yr treasury ALSO has its own roll down return. So even the unhelpfully complex formula I worked out is wrong because I was comparing the 3-Yr total return to just the coupon of the 2-Yr. Yeah... so... nevermind. Thanks for the explanation. At least now I know where I went wrong.

Kevin M wrote:
Wed Jul 18, 2018 10:56 pm
Take another look at the chart in this post earlier in this thread. The assumption there was a static yield curve, so yields didn't increase at all, yet the returns of all maturities greater than the 7-year had lower returns than the 7-year. In other words, you "lost money" by choosing the 10-year over the 7-year, even with no yield increases at all.
I see. I hadn't appreciated that point before. I can see how how the yield curve changes slope at 7-Yr and that seems to get... sort of "magnified" in the 1-yr return curve.

Kevin M wrote:
Wed Jul 18, 2018 10:56 pm
There's nothing particularly unrealistic about a yield curve with a fairly constant slope between 1-year and 10-year maturities. Go to this dynamic yield curve site, and drag the timeline in the right chart back and forth, watching the shape of the yield curve in the left chart. It's not hard to find such historical yield curves.
Oh, wow. I hadn't realized that either. Yeah, I can easily find near-constant-slope yield cuves. I can even easily find times when the yield curve has a negative slope. How's that possible? Why would anybody buy a 10-year Treasury that with a lower yield than a 7-year Treasury?
Kevin M wrote:
Wed Jul 18, 2018 10:56 pm
Although I thought the linear yield curve was a convenient way to illustrate certain concepts, I think it might have misled you into thinking there's more regularity or predictability in returns and yield curve changes than there actually is.
Yeah. But in the ended I ended up learning a lot from this, so that's a good thing.

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### Re: In defense of short-term treasuries

danielc wrote:
Sat Jul 14, 2018 11:36 pm
triceratop wrote:
Sat Jul 14, 2018 11:29 pm
Historical returns, from beginning of 2008 bear market (Oct 9 2007):

VFISX: ST Trs
VFITX: IT Trs
VUSTX: LT Trs
VTSAX: US TSM

The return spread demonstrated above is such that the max drawdown figures provided above are called into question.
Good graphic. Clearly shows the value of longer-term during a market crash. That said, most people do not advocate LT treasuries as their bond allocation, despite their superior performance during a crash. Do you agree with that advice?
I had an opportunity to ask Eugene Fama this question. He recommends using ST treasuries and taking risk on the equity side.

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### Re: In defense of short-term treasuries

unclescrooge wrote:
Thu Jul 19, 2018 12:59 am
I had an opportunity to ask Eugene Fama this question. He recommends using ST treasuries and taking risk on the equity side.
I'd love to hear more about that conversation. Any details? Reasons? Was he talking about the market right now or in general?

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### Re: In defense of short-term treasuries

An attempt to clarify a few misunderstandings or approach minutiae which confuse our discussion.

1) Yield curve
Kevin M wrote:
Wed Jul 18, 2018 2:58 pm
Doc wrote: ↑Wed Jul 18, 2018 10:49 am
It is a generally accepted principle that "the best estimate of the future yield curve is the current yield although not a very good one".
I don't think this is a generally accepted principle--it's a view propagated by Larry Swedroe and DFA, and supposedly based on some work by Fama, but it is far from a universally accepted theory on the term structure of interest rates.
My take is that there are many different theories/models/opinions on the future shape of the yield curve. The professional bond traders/investors are aware of these and they "vote" on which is one is most correct by trading/investing their money. The resulting money weighted average is the current yield curve. It may not be right but I certainly can't make any judgement on it that is better than theirs.

2) Our objective for investing in bonds:

Some of us look at bonds as that part of our portfolio that will never lose principal. It is cash that gives us some return. Primary concern is fixed price followed by maximizing return. Others think of the bond part of our portfolio as a way to dampen the variance of equities. Primary concern is low or even better, negative correlation with equities followed by liquidity. Return is not even a consideration or at least a minor one. These differences lead to confusion when two posters are addressing the problem from opposite ends of the spectrum.

3) Roll down yield defintion
Some people think of this as the capital gain that can be achieved by selling before maturity. Others think of it as both the capital gain plus the difference in coupon. The total return approach. Kevin uses the first idea and gets concerned with BEY or APY or whatever. I use the total return approach because I use a zero coupon coupon model and I can't even separate the two. The difference is negligible at least with coupons as low as they are now. Fuhgeddaboudit. (See my signature block.)

4) I forgot what this one was

Cheers,

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

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### Re: In defense of short-term treasuries

danielc wrote:
Thu Jul 19, 2018 12:02 am
Kevin M wrote:
Wed Jul 18, 2018 10:56 pm
The return line is steeply upward sloping from 2-year to 3-year returns because the initial yield curve is much steeper between 1-year and 2-year (23 bps/year) than between 2-year and 3-year (7 bps/year), so the 2X increase in the 1-year yield (46 bps) had a proportionally larger impact than the 2X increase in the 2-year yield (14 bps), despite the shorter maturity of the 2-year security. In other words, the 3.3X larger yield increase of the 1-year compared to 2-year had a larger negative impact on the 2-year than the roughly 1/2 longer initial duration of the 3-year compared to 2-year had on the 3-year.
Oh! And that's another thing I forgot about entirely. I forgot that the 2-Yr treasury ALSO has its own roll down return. So even the unhelpfully complex formula I worked out is wrong because I was comparing the 3-Yr total return to just the coupon of the 2-Yr. Yeah... so... nevermind. Thanks for the explanation. At least now I know where I went wrong.
I wanted to discuss the duration impact a bit more.

Just considering one particular maturity, the shape of the initial yield curve has nothing to do with the 1-year realized return. All that matters are the maturity/duration, initial yield, and final yield. In other words, the realized return of the N-year security has nothing to do with the initial yields of other maturities. Those only come into play if you're comparing realized returns to expected returns based on a static yield curve or some other estimated yield curve change, and that's what has been bogging us down, I think.

The concept of (modified) duration as an indicator of the sensitivity of bond price to change in yield is one of the more basic bond concepts, and is at least roughly understood by many if not most who read bond threads. The chart of the linear yield curve with a constant incremental increase in yields kind of illustrates this, as we see monotonically decreasing returns with increasing maturity.

The approximation for relating percentage price change to percentage point yield change (for relatively small changes in yield) is:

Code: Select all

``dP/P = -Dm * dY``
where dP/P = percentage price change, Dm = modified duration, and dY = percentage point change in yield.

For example with a modified duration of 2, and change in yield of +0.1 percentage points, we'd expect a -0.2% change in price.

At small yields, modified duration is only slightly less than duration, and for a zero-coupon bond, duration = maturity. For example, at a yield of 2%, a 5-year zero has a duration of 5 years and a modified duration of 4.9 years.

It turns out that the percentage point change in 1-year return of the N-year security is related to the duration of the N-1 year security, as shown in the chart below. This chart uses zero-coupon bonds, a flat initial yield curve with all yields = 2.00%, and a 0.1 percentage point increase in yields over one year.

We see that the 1-year return of the N-year security is the initial yield minus 0.10 percentage points times the duration of the N-1-year security. For example, the 1-year return of the 2-year security is 1.90% (2.00% - 0.1 pp), the 3-year security is 1.80% (2.00% - 0.2 pp), etc.

If we look at the third decimal point in percent point change of 1-year return, we start to see some small differences due to modified duration not being exactly equal to duration, and perhaps due to convexity, more so in the longer maturities. For example, the 1-year return of the 10-year security is 1.104%, so slightly higher than 2.00% - 0.9 pp.

Kevin
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### Re: In defense of short-term treasuries

Doc wrote:
Thu Jul 19, 2018 12:20 pm
<snip>
My take is that there are many different theories/models/opinions on the future shape of the yield curve. The professional bond traders/investors are aware of these and they "vote" on which is one is most correct by trading/investing their money. The resulting money weighted average is the current yield curve.<snip>
Exactly. And many of those votes include estimates of the future path of short-term yields that are not the same as today's short-term yields, resulting in a term premium that is not directly observable in today's yield curve.
3) Roll down yield defintion
Some people think of this as the capital gain that can be achieved by selling before maturity.
This model works only if considering par bonds, which is a convenient way to think about it, but not the only way.
Others think of it as both the capital gain plus the difference in coupon. The total return approach. <snip> I use the total return approach because I use a zero coupon coupon model and I can't even separate the two.
I've never seen anyone besides you define roll-down return as equal to total return. Please cite a reputable source that does so, if you can.

The way I define roll-down return applies to a zero-coupon model, a par bond model, or any other model.
Kevin uses the first idea and gets concerned with BEY or APY or whatever.
I used to use the first model with par bonds to explain it, because it is easy to conceptualize. The model I now use is independent of the coupon rate, whether it be equal to initial yield, 0%, or any other value. Bond-equivalent yield (BEY) and APY have nothing to do with the roll-down return discussion.

As I've said multiple times, I define roll-down return as the difference between the return (expected or realized) and the initial yield. There is an initial yield for zero-coupon bonds, just like there is for par bonds, so it's easy to "separate out" the roll-down return from the initial yield.

The initial yield is roughly the expected return for a bond held to maturity--for a zero-coupon bond it is exactly the expected return if held to maturity (well, maybe not exactly, since I think zero-coupon YTM is expressed as BEY, so maybe BEY and APY have a little bit to do with the roll-down discussion, but this is a distraction relative to the conceptual understanding, and I think it applies equally to zero-coupon or par bonds).

So you can think of the roll-down return as a bonus or a penalty relative to the return if you held the bond to maturity. It's really only a roll-down return if the yield when you sell (or evaluate the value of) the bond is less than or equal to the initial yield, otherwise it's actually a roll-up return, which is negative.
The difference is negligible at least with coupons as low as they are now. Fuhgeddaboudit. (See my signature block.)
No, the difference is huge. With your definition, roll-down return = total return, which for a static yield curve would be 2.92% (for par, 2.93% for a zero) for a 5-year note using 2/18/2018 CMT yields, and by my definition would be 0.15% (for par, 0.16% for a zero), with 2.77% coming from the initial yield.

Kevin
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### Re: In defense of short-term treasuries

Kevin, a zero coupon bond has no coupon so all of the return is the roll down return by both of our definitions.
Kevin M wrote:
Thu Jul 19, 2018 2:32 pm
No, the difference is huge. With your definition, roll-down return = total return, which for a static yield curve would be 2.92%
OK so you don't like my "total return" nomenclature. OK. My definition of roll down yield as "total return" is the capital gains plus the difference in coupon income. That's "total return". You want to use only the capital gain part.

It seems to me the way you want to describe "roll down return" is if the price after 1 year is back to 100 there is no roll yield. You are ignoring the higher original coupon that you got for the longer bond. So the difference in our calculations, what we put in our pocket, is only the difference in coupon for one year. And that's not a big deal unless you are trading millions of bond a year. It's not going to make enough of a difference to say that a 3-2 roll is significantly better than a 4-3 roll.
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### Re: In defense of short-term treasuries

Doc wrote:
Thu Jul 19, 2018 3:47 pm
Kevin, a zero coupon bond has no coupon so all of the return is the roll down return by both of our definitions.
Sorry to interject in your discussion with Kevin, but I think he has made it very clear that this is not the case. A zero coupon bond has a yield, just like a par bond. It makes perfect sense to define roll-down return as the return that you get on top of that initial yield. I don't know what else anyone can say to explain this more clearly. It is literally the extra return you get by the act of rolling down the yield curve.

Conversely, it makes no sense to define roll-down return = total return, because what the heck would be the point of inventing a new term? If you want to talk about "total return" then just call it "total return" and be done with it. Inventing new terms for familiar concepts achieves nothing and adds needless confusion. I'm sure you are a wonderful person, but let's not pretend that your definition makes any sense, or that Kevin's definition is somehow confusing.

Doc
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### Re: In defense of short-term treasuries

Here's my Roll down Yield chart from the beginning of the month:

The "best" return comes from buying a 7yr note and selling it a 5yrs: 2.97%
The shortest time I look at is buying a 2yr and holding to maturity: 2.53%

Is it worth the risk of buying a seven instead of a two for 40 bps a year?

The CME Fedwatch Tool (Dot Plot) is predicting a 54% probability of 50 bps increase in the Fed funds rate by the end of the year.

IF the yield curve retains its shape and the whole curve shifts up by 50 bps go short term.
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.

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### Re: In defense of short-term treasuries

danielc wrote:
Thu Jul 19, 2018 4:18 pm
Doc wrote:
Thu Jul 19, 2018 3:47 pm
Kevin, a zero coupon bond has no coupon so all of the return is the roll down return by both of our definitions.
Sorry to interject in your discussion with Kevin, but I think he has made it very clear that this is not the case. A zero coupon bond has a yield, just like a par bond. It makes perfect sense to define roll-down return as the return that you get on top of that initial yield. I don't know what else anyone can say to explain this more clearly. It is literally the extra return you get by the act of rolling down the yield curve.

Conversely, it makes no sense to define roll-down return = total return, because what the heck would be the point of inventing a new term? If you want to talk about "total return" then just call it "total return" and be done with it. Inventing new terms for familiar concepts achieves nothing and adds needless confusion. I'm sure you are a wonderful person, but let's not pretend that your definition makes any sense, or that Kevin's definition is somehow confusing.
Exactly. After all the discussions Doc and I have had about this, both on the forum and in PMs, I don't know why he can't understand the difference between total return and roll-down return, and that my definition of roll-down return works the same for zero-coupon and coupon bearing securities.

I think it stems from earlier discussions, in which I primarily discussed it in terms of the income return and capital return components of a par bond, in which case roll-down return is indeed the capital return component. As I've explained repeatedly, if you instead define it as the difference between the initial yield and the total return, there is no difference in the concept of roll-down return between a par bond (or any other coupon-bearing bond) and a zero-coupon bond.

Kevin
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CuriousTacos
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### Re: In defense of short-term treasuries

danielc wrote:
Sat Jul 14, 2018 4:28 pm
Hello,

Common wisdom is that Intermediate Term (IT) treasuries are better for diversifying stocks than Short Term (ST) treasuries. The resoning provided is that, when markets crash, the Fed lowers itnerest rates and ITs go up in value. However, I ran Monte Carlo simulations and it looks like (1) there isn't much of a difference, and (2) ST actually look better in most cases.
In these monte carlo simulations, the historical data used for ST Treasuries is from 1977-2017, while the data used for IT Treasuries is from 1972-2017, so this isn't a fair comparison.

If you re-do the simulations using 1977-2017 for both, the results for IT Treasuries look much better (link vs link).

However, 1972-1977 are important to include since it was a bad time for longer term bonds. Cash is the closest thing to ST Treasuries, and portoflio visualizer has data for cash for the full time period, so we could compare IT Treasuries to cash (link vs link). IT Treasuries still come out ahead in this comparison.

danielc
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### Re: In defense of short-term treasuries

CuriousTacos wrote:
Thu Jul 19, 2018 8:20 pm
However, 1972-1977 are important to include since it was a bad time for longer term bonds. Cash is the closest thing to ST Treasuries, and portoflio visualizer has data for cash for the full time period, so we could compare IT Treasuries to cash (link vs link). IT Treasuries still come out ahead in this comparison.
ST Treasuries are not the same as cash. Specifically, a 1-year Treasury has a higher return than cash.

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### Re: In defense of short-term treasuries

Doc wrote:
Thu Jul 19, 2018 4:30 pm
Here's my Roll down Yield chart from the beginning of the month:

There's nothing wrong with this chart, except calling it a "roll down yield" chart. What you're showing are the expected annualized (total) returns for zero-coupon bonds assuming a static yield curve using the CMT yields from 7/13/2018. You're not showing a separate expected roll-down return component, you're just showing expected total annualized return. (As I've explained, a minor technical point is that the CMT yields are par yields, not zero-coupon yields, but at current low yields, the differences are negligible.)

Let's focus on your 7->5 expected (total) return of 2.97%. That can be decomposed into the initial 7-year yield of 2.79% and a 2-year expected annualized roll-down return of 0.18%. You show the necessary numbers to calculate the roll-down return, you just don't calculate it and show it explicitly.

What I'm doing with my chart is very similar, and I can calculate your exact 7->5 expected return number from the data used to generate the chart (or I can calculate it directly, as you do). Where the CMT values are provided, such as for 3->2, I can read the exact same number off my chart as shown in your chart (if I click on the chart and hover my cursor over the data point, or I can just read the number directly from the spreadsheet data used to generate the chart).

Here's my chart showing something similar, also assuming zero-coupon notes, and using the same CMT data from 7/3/2018:

What you show as the 3->2, for example, I show as the (expected) 1yr rtn for the (initial) 3-year term to maturity. The number is exactly the same in both charts--2.83%. The yields you show in row 7 of your chart are shown in the Yield 0 curve of my chart (since the yield curve is assumed static, the Yield 0 and Yield 1 curves are the same, and appear as one red curve).

The expected 1-year roll-down return is shown visually as the gap between the Yield 0 curve and the 1yr rtn curve.

Your 7->5 return can be calculated exactly as the geometric average of my 7-Year and 6-year maturity 1-year returns, and approximately as the arithmetic average of these returns (in this particular case, equal to the 5th decimal place = 2.96521%).

So my model is essentially no different than yours, assuming zero-coupon notes and a static yield curve. Note that nowhere here have I mentioned coupon return (income return) or capital gain (capital return). I can work with zeros with this model as easily as I can work with par notes. My main motivation for building the model this way was so I could communicate on your terms, verify your numbers exactly for myself, and try to explain how the concept of roll-down return has nothing to do with the coupon rate of the security.

Now here's one cool thing about the model. With two mouse clicks, I can switch it from a zero-coupon curve model to a par curve model (which is what the CMT curve actually is), where coupon rate = initial yield (and initial price = 100). Here's the way the chart looks after this quick switch:

Although the numbers are slightly different, the difference in the return curves is barely noticeable. I'm hammering on this to try and help you understand that I'm not locked into the notion of coupon/income return and capital return at all to conceptualize roll-down return. It can be understood with either zero-coupon or coupon-bearing securities.
The "best" return comes from buying a 7yr note and selling it a 5yrs: 2.97%
The shortest time I look at is buying a 2yr and holding to maturity: 2.53%

Is it worth the risk of buying a seven instead of a two for 40 bps a year?

The CME Fedwatch Tool (Dot Plot) is predicting a 54% probability of 50 bps increase in the Fed funds rate by the end of the year.