Roll Breakeven Yield

[Admin/YBB]

What is the tradeoff between buying x-yr now and roll vs buying 2x-yr now?

Yield for x-yr now = ix%
Yield for 2x-yr now = i2x%
Roll Breakeven Yield for x-yr in x years = iroll%

The Roll Breakeven formula is:

iroll = 2*i2x - ix

This is an approximate formula. The exact formula is:

iroll = 100*[{(1 + 0.01*i2x)^2}/(1 + 0.01*ix)} -1]

So, if YOU think that x-yr yield will be higher than iroll in x years, buy x-yr now and then roll; if YOU think that x-yr yield will be lower than iroll in x years, buy 2x-yr now. YOU don't have to look for what the others in the media are saying.

The idea will work for, say x-yr and 5x-yr too, but will require more rate scenario assumptions. The cleanest application is for x and 2x.


For examples on 6/11/23, see  big-bang-investors.proboards.com/post/37954/thread

T-Bill 6-mo vs 1-yr
6-mo 5.39%
1-yr 5.17%
Roll Breakeven 4.95%
So, if YOU think that 6-mo will be higher than 4.95% in 6 months, buy 6-mo T-Bill now and then roll; if YOU think that 6-mo will be lower than 4.95% in 6 months, buy 1-yr T-Bill now. So, YOU don't have to look for what the others in the media are saying.

T-Bill 1-yr vs T-Note 2-yr
Roll Breakeven 4.01%

T-Note 5-yr vs 10-yr
Roll Breakeven 3.58%

The idea will work for, say x-yr and 5-yr too but will require more rate scenario assumptions. The cleanest application if for x and 2x.

home.treasury.gov/resource-center/data-chart-center/interest-rates/TextView?type=daily_treasury_yield_curve&field_tdr_date_value_month=202306

[Admin/YBB]

A simple EXTENSION is to periods (z) that can be split into 2 UNEQUAL periods (x, y; z = x + y) & when Treasury auctions are available for both periods, or are bought in the secondary market.

For T-Bill Auctions, 1+2=3; 1+3=4; 2+4=6; possible months for x+y=z.
For T-Bills/Notes/Bonds Auctions, 1+2=3; 2+3=5; 2+5=7; 10+20=30; possible years for x+y=z.
For the secondary market, any x, y are possible.

The TRADEOFF is between buying x-yr now & then roll into y-yr vs buying z-yr now.

Yield for x-yr now = ix%
Yield for y-yr now = iy% (not needed, but may be useful for iyest)
Yield for y-yr in x years = iyest% (your estimate)
Yield for z-yr now = iz%
Roll Breakeven Yield for y-yr in x years = iroll%

The Roll Breakeven formula (approximate) is found from:

z*iz = x*ix + y*iroll.

Two rearrangements are:

iroll = (1 + x/y)*iz - (x/y)*ix,
or
iroll = iz + (x/y)*(iz-ix).

So, if you expect iyest > iroll in x years, buy x-yr now & then roll into y-yr,
or, if you expect iyest < iroll in x years, buy z-yr now.

EXAMPLE: 1-yr T-Bill vs 3-yr T-Note, 6/12/23
x = 1, y = 2, z = 3
1-yr 5.18%
2-yr 4.55% (not needed)
3-yr 4.16%
Roll Breakeven iroll = (1 + 1/2)*4.16 - (1/2)*5.18 = 3.65%

If your estimate of 2-yr in 1 year is higher than 3.65%, buy 1-yr now & then roll into 2-yr (likely based on iy now & the Fed talk),
or, if your estimate of 2-yr in 1 year is lower than 3.65%, then buy 3-yr now (unlikely based on iy now & the Fed talk).

If z has to be broken into more than two periods, then more assumptions for rate scenarios must be made.