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

Following on from my previous post, using #cruncher’s spreadsheet to adopt Plan 2, i.e., buy multiple amounts of the bond maturing in the year after the gap, with multipliers of 1 and 6 for 2034 and 2040 results in no bond purchase for 2034 and an income shortfall in 2033 (in other words, the bonds maturing in 2040 would have to be sold starting in 2033 rather than in 2034). In order to provide the required income in 2033, multipliers of 1.45 (2034) and 5.55 (2040) have been used instead. Assuming a required income of $40k per year and prices as of 1 July 2024, the outcomes are given below (note that using these multipliers, no bonds maturing in 2034 are bought – I’ve started the table at 2033).
Since no bonds maturing in 2034 were purchased, in 2034 the retiree will sell all bar 24 of the 148 bonds maturing in 2040 to provide income for 6 years, i.e., 2034, 2035, … 2039 (the 24 remaining bonds maturing in 2040 will, together with the coupons from later bonds, provide the income for 2040). I note that an alternative approach would be to sell enough of the 2040 bonds each year to provide the required income, although this comes with the risk that the income in the final year of the gap, 2039, might fall short.

The proceeds from the sale will depend on the number of bonds sold, n (in this example n=148-24=124 bonds), the yield to maturity (ytm), and therefore price, prevailing in 2034, and the CPI adjusted principal, CAP (1450.67 in July 2024 for the 2040 bond) such that

proceeds=n*CAP*price/100.

As mentioned above, the price will depend on the yield. For example, since the coupon for the bond maturing in 2040 is 2.125%, and the remaining term in 2034 is 6 years, the price will range from 142.01 (for a ytm of -4%) to 90.09 (for a ytm of +4%).

Of the proceeds from the sale, about $32.2k, i.e., required income of $40k, less the final coupon of the 2040 bonds being sold, $1911 and the coupons from the post-gap ladder, $5850, will be needed to provide income for 2034.

The following table then contains the price, the proceeds from the sale (before reducing the amount by $32.2k to provide for the 2034 income), the annual income derived from a five year ladder (i.e., for 2035, 2036, 2037, 2038, and 2039), the income from the remaining post gap coupons (PGC), the total income and the number of rungs, N that could be constructed to provide an income of $40k per year.
For a ytm of 4%, the total income of $33.7k is nearly 16% below the target of $40k. Historically, the highest yield observed for 5 year TIPS has been just over 4%, although this rate was observed only briefly towards the end of November 2008. The total income for the strategy of buying bonds at the end of the gap decreases with increasing yield which is the opposite behaviour to buying bonds at the beginning of the gap (see my previous post).

Combining the two plans in a 50/50 approach (i.e. averaging the results in the above table with the equivalent one in the previous post), leads to the following outcomes for income and number of rungs N.
Holding a fixed proportion of bonds pre- and post-gap, greatly improves the results even over this large range yields. For example, the total income only falls to about 3% below the $40k target at a yield of 4%. Of course, this is not duration matching since the proportion of before and post gap bonds is fixed at the start and does not respond to changes in yield, and hence duration, but does result in an income that may be close enough to that required.

Cheers
StillGoing

Statistics: Posted by StillGoing — Tue Jul 09, 2024 3:24 am — Replies 267 — Views 22574

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