Investing - Theory, News & General • Re: Filling the TIPS gap years with bracket year duration matching

I think there are multiple goals in attempting to duration match a new issue TIPS with bracket year TIPS, which isn't the case when duration matching using all secondary market issues; i.e., using longer-term and shorter-term TIPS or TIPS funds to match the duration of an intermediate-term TIPS or fund. This complicates the mathematical analysis.

The goals that come to mind are:

1. Generate a known nominal amount for purchase of the gap year TIPS when issued. It's a nominal amount because one new-issue 10-year TIPS will cost close to $1,000, since unadjusted price will be close to 100, and index ratio will be close to 1. This isn't exact, because new issues aren't actual par bonds; the larger the difference between coupon and yield, the more deviation from a price of 100. The low and high prices for new-issue 10y TIPS auctioned to date are 98.881 and 100.447 respectively, so cost has ranged from $988.81 to 1,004.47, which is a delta of +0.45% to -1.12%. The average cost has been $994.25.
2. "Lock in" historically attractive longer-term real yields. We aren't exactly locking them in, since we'll be selling well before maturity, but this is where the duration matching theory comes into play, and needs to be mathematically analyzed for different yield-curve change scenarios, different coupon reinvestment rates, and different coupon reinvestment strategies. This may be of less interest when 10y yields are historically unattractive, as they were in recent years.
3. Hedge unexpected inflation risk from now until issuance of a gap-year TIPS. This point was emphasized by Mel wrt I bonds, but of course there there are different ways to do it with TIPS as well.

There may be more, but these come to mind immediately, and provide fodder for some discussion.

The safest way to achieve goal #1 would be with a STRIPS (zero-coupon nominal Treasury) maturing close to the gap year TIPS issue date, since it provides a known amount of nominal dollars at maturity. A low-coupon Treasury would be a reasonable alternative. Neither TIPS nor I bonds do this as reliably.

The way to achieve #2 is with longer-term TIPS. I bonds don't do this, and longer-term nominal Treasuries don't do this.

The most reliable way to achieve #3 with TIPS would be to buy TIPS maturing close to the gap-year issue date. This provides as much reliable inflation protection as I bonds, keeping in mind the different ways the inflation adjustments are done, and that both methods lag actual inflation. And of course using TIPS is a generalizable solution, unlike I bonds due to annual purchase limits.

So it seems the goal is to find a solution that optimizes achievement of the three subgoals, and to be able to use math to prove it.

It seems to me that most folks building (or maintaining) non-rolling ladders today for income flooring would have Goal #2 in mind. #1 and #3 are of no interest to me.

Although I'd want to get to the math, consider this thought experiment.

• Shortly after purchasing the bracket year TIPS at more than 2% yield, real yields drop back into negative territory, and inflation drops close to 0%, or perhaps below. The latter hasn't happened for an extended period in a long time, but it has happened, and we're looking for certainty in ARA regardless of economic conditions.
• We reinvest all of our coupons at negative real yields, and possibly negative nominal yields.
• Shortly before the issuance of the gap year TIPS of interest, yields shoot up to historical highs or higher. The 10y TIPS hit 4.40% on Jan 18, 2000. Of course this drives long term prices way down.
• The gap year TIPS is issued at a very attractive yield, but still at a cost of close to $1,000 per bond, and we now sell our bracket-year TIPS at extremely depressed prices, with no or negative earnings from the coupons already paid out.

How does duration matching work in this scenario?

Maybe I'm missing something, but, with respect to Goal #2, it seems to me that the roller-coaster real-yield trajectory proposed in your thought experiment wouldn't affect duration matching in any negative way.

• With respect to duration matching the swap, the only thing that matters are the conditions at the time of the swap. How would real yields dropping back into negative territory, and inflation dropping close to 0%, or perhaps below, change the effectiveness of duration-matching the swap at some later date?
• The pre-swap coupons are part of the DARA for those years. Why would they be reinvested?
• It doesn't matter if yields shoot up again or stay in a tailspin. Duration matching still works (assuming parallel yield shifts) when it comes time to make the swap.
• The pre-swap coupons already paid out are not a factor when making the swap. Those coupons were already spent as part of the income floor provided from the ladder inception to swap date. (The only coupons that I suggested might want to be optionally reinvested are any excess portion of coupons that are generated post-swap, in the case where the post-swap coupon contributions to DARA are higher than originally planned when the ladder was first set up.)

EDIT: I would like to add a note that the yields contained in my personal non-rolling TIPS ladder have already survived such a roller-coaster ride with no untoward effects. When purchased in 2018, the 10-year yield was around +1%. Subsequently yields plunged to less than -1% and then climbed to as high as +2.5%. The ladder has functioned as originally anticipated with respect to providing an income floor and covering the gap years with excess duration-matched holdings.

Statistics: Posted by Kevin M — Wed May 29, 2024 9:17 pm