The two charts in this post show the Version 2 spreadsheet for 2% yield (yield unchanged) and multipliers M equal to 3.43 and 3.57 for 2040 and 2034, respectively. One can compare the principal and cost of the 2034 and 2040 rungs before and after the swaps. The Delta-principal and Delta-cost for these rungs shows the amount of excess holdings sold to make the swaps.Kevin M wrote: ↑Wed Jul 10, 2024 5:28 pm So we now have two tracks going to evaluate the results of different gap coverage methods. I'll continue a bit on the track I've been on, but now using #Cruncher's version 2 of the simplified ladder spreadsheet, which ensures that total ARA equals total DARA, regardless of whether or not any gap years are filled.

The current model has these features:

In this post I'll only cover the bracket year method, using initial multipliers for 2040 and 2034 based on duration matching as discussed in the first few posts of this thread.

- Assumes all gap years are filled in 2029, with the 2025-2029 proceeds used for expenses.
- So the ladder now is a 25-year ladder instead of a 30y ladder, with terms to maturity reduced by 5 years each.

First, here is the ladder before any gaps are filled, with the rows for 2041-2054 hidden since they aren't of particular interest, other than providing "Interest later bonds" for the maturities that are shown.

Things to note:Here's the way it looks after filling the five gap years, assuming gap year cost and yield of 2%:

- The total proceeds (aka total ARA), in cell J32 with the cursor focus, now equals total DARA of 2.5M for the 25y ladder. Recall that previously this was greater than total DARA; this is the result of the change for version 2.
- The multipliers for the 2040 and 2034 of 3.43 and 3.57 are based on duration matching at 2% yields.
- The terms to maturity, in column C, are all reduced by five years, so, for example, the 2034 now is a 5y bond and the 2040 is an 11y bond.
- The multipliers for the 2025-2029 are all 0, since these are assumed to have been consumed. The only impact on the analysis is that these are not involved in any sales or purchases necessary to match ARA to DARA for the pre-2034 maturities.
- The gap year coupons are irrelevant with no gaps yet filled.

Things to note:

- The only relevant cost column for this scenario, one of the three covered here, is Cost at 2%, since I'm assuming all yields are 2% from 2030-2040; I've highlighted the relevant cost cells, which include the gap years since we're buying them, the bracket years since we're selling them, and the 2030-2033 since we will buy or sell them so that ARA = DARA.
- Total proceeds still equals 2.5M, as it should.

Delta-principal for 2040 is 238,351

Delta-principal for 2034 is 159,099

2040/2034 excess holdings ratio is 1.498:1 (based on principal)

Delta-cost for 2040 is 241,267

Delta-cost for 2034 is 157,224

2040/2034 excess holdings ratio is 1.535:1 (based on cost)

The excess holdings at 2% yield for 2040 are about 50% higher than for 2034 even though the multipliers are about equal (2040/2034 = 0.961:1). This shows why I am thinking that using multipliers fails to achieve the desired ratio of excess holdings.

EDIT: Another observation from the first chart above is that for a fixed pair of multipliers, the ratio of excess holdings costs seems to vary depending on the prevailing yield at the time. This implies that if the original ladder with excess bracket-year holdings is created at low yield (say 0%) using a certain set of bracket-year multipliers (say 3.5/3.5), the mix of 2040/2034 excess bracket holdings based on cost would be different than if the ladder was created at higher yield (say 4%). If the duration-matching goal is to create the ladder with a set of bracket year holdings with costs in a certain ratio (say 50/50) at any given starting yield, using a fixed pair of multipliers doesn't seem to be the way to do that. (The multipliers that provide best duration matching would differ somewhat depending on the initial level of interest rates.)

While multipliers of 3.88 and 3.12 for 2034 and 2040 are predicted to give an excellent duration match using #Cruncher's TIPS ladder building spreadsheet, my intuition says that these values may not be universal. These multiplier values apply for a ladder constructed at a yield level of 2% and using January 2034 and February 2040 for the excess bracket year holdings, and with the five swaps completed simultaneously in 2029 after all gap-year issues become available. Somewhat different multipliers may apply when using different TIPS for the bracket year holdings and/or when yields deviate away from 2% when the ladder is constructed. Any difference in ideal multipliers if the swaps are made annually between now and 2029 remains to be determined.

If the goal of duration matching is for the

*of the excess bracket-year holdings to track the*

**cost****of the hypothetical gap-year holdings as yields change, shouldn't the relative**

*cost***of the excess holdings of the two bracket-years be what is initially set to the desired ratio (say 50/50)?**

*costs*