kaesler wrote: Wed Feb 05, 2025 4:07 pm
MtnBiker wrote: Wed Feb 05, 2025 4:02 pm
What are your thoughts on this idea?
First problem to be solved would be: estimating the duration of a bond that does not yet exist.
The logical assumptions would be:
1) Each gap year is covered by a duration-matched mixture of bracket years, such as Jan 2035 and Feb 2040.
2) The yield of each gap year is assumed to be as linearly interpolated between the present day 2035 and 2040 yields.
3) Noting that the ladder computes the interest in years prior to 2035 based on the coupons from the bracket year mix, we then make the assumption that the coupon rate of each gap year is a linear interpolation between the 2035 and 2040 coupon rates.
4) Via a disclosure, we specify that if the coupon rate of the actual gap year, when issued, differs substantially from the assumed coupon rate, then bonds may need to be swapped between the pre-gap years and gap year to correct for any major changes in interest in the pre-gap years vs principal in the gap year (a process known as ARA (annual real amount) smoothing). ARA smoothing means that the income stream will be as calculated, assures that the average duration of the income stream will be as assumed, and the duration matching used to hedge against interest rate changes will not be degraded due to the difference between the assumed gap coupon rate and the actual, as realized, coupon rate.
I think these 4 assumptions are enough information to calculate the duration of the bonds that do not exist. I'm too lazy to do the calculations at the moment, but I would suggest that the resulting durations would likely be very close to what one would calculate by linear interpolation between the bracket year durations. Here is what we have today using linear interpolation:
Code: Select all
Year Duration
2040 12.81
2039 12.05
2038 11.29
2037 10.53
2036 9.77
2035 9.01
Using the ladder manual tool, if I try to build a 2035 to 2040 ladder with 20K of annual income, I find that I need 14 of the 2040 bonds to cover 2040 and 18 of the 2035 bonds to cover 2035. The number of bonds to cover the intervening gap years is basically a linear interpolation of the number of bonds to cover the bracket years:
Code: Select all
No. of Bonds
Year 2035 2040 Duration Income
2040 0 14 12.81 $20,654
2039 4 11 12.05 $20,661
2038 8 8 11.26 $20,576
2037 12 5 10.44 $20,397
2036 14 3 9.91 $19,601
2035 18 0 9.01 $19,862
Just as it isn't possible to hit the Income targets exactly, the duration targets can't be matched exactly either. Juggling the mixture of bracket years covering each gap year changes the duration and income slightly one way or the other. I hope this gives a general idea of how it could be done.
Note that I intentionally used income amount targets on the low side for 2035 and 2036, since the ladder tool underestimates (neglects) the interest payments received from reinvesting the 2035s to cover the gap years.