Edge cases with Pye’s Retrenchment Rule

Last time I wrote about Pye’s Retrenchment Rule I was trying to convince myself whether using an 8% discount rate made sense or not. Along the way, I realised I had misread his paper at first.

His use of PMT is fairly different from many others. It is a nuance I didn’t pick up when I first read his paper. For Pye, the PMT calculation provides a ceiling rather than a schedule of withdrawals. Every year, take last year’s withdrawal and adjust it for inflation. If it is less than the PMT calculation, use that. This is “less efficient” than using PMT directly; sometimes you will be withdrawing quite a bit less than PMT tells you to. But Pye is more concerned about smooth income (“avoiding painful retrenchment”) than about squeezing every last cent from the portfolio.

When you graph the Retrenchment Rule against raw PMT it looks like a staircase:

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randomly generated returns

This is clearly more conservative than raw PMT. It is possible that the “unused” income could help smooth out future withdrawals in bumpy markets, though I’m not sure how large that effect would be. (You can see this in action above, for instance around years 7–11 where skipping a “raise” also meant you were able to defer a cut.)But it also will lead to some situations that are decidedly conservative.

The Retrenchment Rule never adjusts income upwards, which means if you retire at the beginning of long bull market you’ll end up with a large portfolio that is “wasted”.

Here we can see that our withdrawals stay constant even though the market has been so good that we could double our withdrawals for most of our retirement.

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another set of random returns

For many of us, leaving a bunch of money on table might be undesirable but hardly the end of the world. If we were happy living on $75,000 a year, what are we really going to spend all that other money on anyway?

But the Retrenchment Rule is also susceptible to sudden market declines that are quickly reversed. In this case, you will aggressively retrench your spending. The market recovers quickly but you keep your spending very low.

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another set of random returns

In this case you’re living on $18,000 a year for 15 years of your retirement when raw PMT says you could be withdrawing $25,000 to $40,000. In this case it feels like the Retrenchment Rule has you living an unnecessarily parsimonious life.

I think there’s a lot of merit to Pye’s suggestion of leaving gains on the table. No matter what a spreadsheet tells you, no matter what backtesting says, I think most retirees would have trouble pulling an extra $10,000 or $20,000 out after a single good year in the market and spending it on vacations or home remodeling.

Maybe there’s an opportunity here for something like McClung’s Prime Harvesting? Where only part of the excess withdrawals go to lifestyle creep but the majority gets reinvested into bonds in order to smooth future withdrawals by giving you a less volatile portfolio?

I’ll have to think about that one more.

But it seems clear to me that Pye’s Retrenchment Rule needs some kind of adjustment upwards. His article was written for an audience of financial advisors who are having annual meetings with their clients. In that context, I think the financial advisor would use some “common sense” and adjust things upwards in the edge cases I showed earlier.

That’s mostly fine: we don’t need to over-engineer every single aspect of a withdrawal plan. But it does make it hard to do these kind of programmatic comparisons when there is a step of “and then the human advisor uses common sense” in the middle of a 10,000 iteration Monte Carlo analysis.

A bigger problem is that people will disagree on what counts as common sense. Should you wait 2 years before adjusting upwards? 5 years? How fast should you adjust upward? In his Extended Mortality Updating Failure Percentage, McClung introduces a “scaling function” to control the speed of upward and downward revisions in withdrawals. Maybe we could lift that concept and reuse it here? Maybe we find that the answers don’t matter much and any reasonable choices work well. Or maybe we find something else. Quite often we are led astray by our common sense intuitions.

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