One would expect that holding all 2034s would be superior if yields climb to 4%. One would also expect that holding all 2040s would be superior if yields fell to -2%. Version 2 seems to predict that sort of behavior.
Rather than try to explain this, I'll just let it marinate and see if anyone notes any obvious explanations or glaring errors.
Remember that all I'm doing is plugging numbers into #Cruncher's simplified ladder spreadsheet, version 2, and sharing the results. I'm not recommending anything, or saying how well the model reflects reality.
The prediction from Version 2 that I wasn't expecting is that if the yield shifts to 0%, the net is exactly zero, independent of the multipliers of the bracket-year holdings. I guess that must be a feature that is a direct consequence of maintaining ARA = DARA under all conditions.
Perhaps it might be easier to understand that result if you could display the holdings of the 2025 - 2040 ladder years for that 0% yield/0.125% gap-year coupon case (as you did for the 2.00% gap-year coupon case previously). Like the two charts shown in this earlier post:
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.
Image may be NSFW.
Clik here to view.
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.
Image may be NSFW.
Clik here to view.
Things to note:<snip>
- 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.
Statistics: Posted by MtnBiker — Mon Jul 15, 2024 11:35 pm