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.

https://www.cmegroup.com/trading/intere ... -fomc.html
**IF** the yield curve retains its shape and the whole curve shifts up by 50 bps go short term.

And this brings up the other thing I like about my model. With a couple of mouse clicks, I can change the assumption from a static yield curve to something else. This allows me to quickly see that it doesn't take a one-year increase of 50 bps to wipe out your excess expected 1-year return with the 7-year Treasury--an increase of as little as 10 bps will do the trick (incidentally, I've switched back to the zero-coupon model):

Now the 1-year return of the 7-year is only 2.40%, while the 1-year return of the 2-year is 2.63%--the 2-year in this scenario still has 10 bps of positive roll-down return, boosting it's return above the initial yield of 2.53%, while the roll return of the 7-year in this scenario is -39 bps (

negative 39 bps). The very flat yield curve in the 5-7 year region makes for very high risk relative to the expected excess return of the 7-year with the static-yield curve assumption, and that's risk I'm just not interested in taking, although I have no problem with you taking it.

And please don't tell us again you're going to sell the 7-year before you lose any money relative to the initial yield, and roll it into another 7-year. I've already challenged you on that strategy at least twice, and you haven't explained how that worked out for you over the last year.

Kevin