Combining CAPE with PMT to tame retirement withdrawals, part 1

Valuations are one of the enduring will-o-wisps of investing. They seem too important to ignore…but almost impossible to use effectively. Perhaps most famously, Federal Reserve Chairman Alan Greenspan spoke of “irrational exuberance”. But he said that in December 1996. The S&P 500 stood at 743.25. Yet Greenspan was wrong. The stock market never went below that level again. Even during the depths of the dotcom crash it never went below 800. If you had got out of the market when Greenspan spoke about “irrational exuberance” you would have lost tons of money…and never gotten back in.

But is there way we can kinda use valuations? Like…just a little bit?

I think using a PMT calculation is The Best Way™ to handle retirement withdrawals. However, the PMT calculation has one number — the “rate” — that requires a bit of a judgment call.

Different sources use different numbers:

  • The Bogleheads VPW uses the global historical average for stocks and bonds.
  • Siegel & Waring tell you to use current TIPS rates (under 1% right now).
  • Gordon Pye uses 8%.
  • Ken Steiner uses 4.5%.

One good thing about a PMT calculation is the rate you pick doesn’t have to be perfect. The PMT calculation will (slowly) self-correct. However, that doesn’t mean the rate has no impact. Here’s the results for a 1950 retiree using two different rates, VPW and Gordon Pye. This shows the first 20 years of retirement. That is, ages 65–85, when you’re most likely to still actually be alive.

From age 65 to 76, using Pye’s 8% results in an average of $15,000 a year more compared to VPW. Eventually, of course, VPW catches up — and even surpasses Pye. But it takes over a decade to do it. And even then, it isn’t like using Pye’s 8% left you poor — your annual withdrawal is still more over $70,000 a year. (By contrast, using the 4% SWR would have meant only withdrawing $40,000 in this same scenario.)

It should be clear that picking a better “rate” for the PMT calculation can help optimise your retirement spending. But it also has the potential to help deal with sequence of returns risk. Of course, there is no way to perfectly immunise ourselves from sequence of returns risk. But we can use the rate in PMT to help.

The way it works is pretty simple: we want to take advantage of the market’s apparent tendency for mean reversion. If valuations are high, then use a low rate. If valuations are low, then use a high rate. We can use CAPE, or more accurately the inverse of CAPE. 1/CAPE. If CAPE is 22.5 then we’ll use a rate of 1/22.5 = 0.04444.

What do we want to get out of this? We want a smoother sequence of withdrawals. We don’t want to see huge cuts in our withdrawals. But we also want to tamp down on huge increases as well.

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When we look at a 1999-retirement, when CAPE was 44 and the dotcom crash was right around the corner, it seems to have done exactly what we would hope.

The “CAPE agnostic” version starts out higher ($44,500) but has a dramatic cut in withdrawals ($35,500; 20% lower)as the crash happens. The “CAPE aware” version starts out lower ($36,900) and sees a much, much milder cut in withdrawals ($35,200; 5% lower).

But before we go congratulating ourselves…is this really such a big win? Yes, we don’t have to cut spending. But it isn’t like we somehow “come out ahead”. Notice that the “CAPE aware” withdrawal line is lower at every point for the first decade. We gave up 3 years of higher spending at the beginning of our retirement…for what?

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We see a bit more “upside” in a 1929 scenario. But, honestly, even the “CAPE agnostic” isn’t doing that bad for most of this timeline.

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And during “worse case” scenarios…I guess it is a bit better, especially towards 9+ year mark. $33,000 vs. $24,000. $36,000 vs. $28,000.

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This is the best case study yet. It seems to be exactly what we’d like to see. Our initial returns start out higher (because CAPE was low) and then stays (relatively) flat.

1980 also looks like a perfect example:

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But it isn’t all good news…

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The “CAPE aware” version starts out very high and slides down over the 20 years. It starts out at $70,000 and bottoms out at $46,000. That’s a $26,000 cut in retirement withdrawals. Not exactly “smooth”. On the other hand, it isn’t like the “CAPE agnostic” line is clearly superior: it isn’t smooth and, at least for the first decade, results in lower withdrawals.

Just by looking at a random scattering of charts, we should feel some cautious optimism towards using valuations in our PMT calculation. We saw a few instances where it worked great, a few instances where it was a minor improvement, and no instances where it was clearly & obviously inferior.

Before we can make a firmer conclusion we need to figure out what kind of metrics would help convince us one way or another. We talked about “smoother withdrawals”, so standard deviation of the withdrawals seems like a good metric to look at. But is that enough? I’m not sure.

I think there are 2 or 3 things we’re trying to accomplish with this:

  1. If we retire during a bubble (whatever that means) we want to withdraw less that we normally would, assuming there will be probably be a crash in the next 3–4 years. This is partly about anchoring. If we retire withdrawing $55,000 then it just kinda sucks to have to cut that to $40,000 after just 24 months of retirement.
  2. If there are “flash crashes” or “flash bubbles” we don’t want to increase/decrease our spending only to revert it the following year.
  3. If there’s a crash, we want to withdraw more than we normally would, under some kind of assumptions about recoveries & returns to the mean.

And finally, we want to do all of that without reducing our average withdrawals “too much” (whatever that means).

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