Why gummy’s Sensible Withdrawals fail at HREFF

When I looked at HREFF with a variety of assumptions, gummy’s Sensible Withdrawals almost always did terribly. How poorly it did was a bit surprising to me. In McClung’s book Living Off Your Money, Sensible Withdrawal did okay with HREFF. What gives?

Sensible Withdrawals are a “common sense” scheme originally detailed by gummy on his webpage: http://www.gummy-stuff.org/sensible_withdrawals.htm.

decide upon some Minimum annual withdrawal rate … just enough to pay the bills (and live on bread and water) …then only withdraw beyond that if the market is good to us.

gummy suggests 3% as a minimum and then withdrawing 25% of any “extra monies” in years when the market is up, though he doesn’t appear to suggest these are based on any strong evidence. His page is a bit whimsical but he says

>How much more do we withdraw, after a good year?
 Oh, I don’t know. Maybe 25% of the extra monies.

In McClung’s book he uses different numbers than gummy: a minimum of 4% and then withdrawing 31% of any “extra monies”.

I’ll come back to McClung’s parameters later but for now let’s stick with gummy’s suggested parameters and try to understand why they seem to perform so poorly under HREFF.

In order to understand what’s happening with Sensible Withdrawals and HREFF we need to dive into a single simulated retirement to look at the decisions Sensible Withdrawals is making — and how HREFF scores those decisions.

The simulated returns that we’ll be using

On the surface, that sequence of returns doesn’t look especially noteworthy. It has one bear market of -20%. It has 9 years of negative returns out of 26.

A quick refresher on exactly what Sensible Withdrawals does:

  • If our portfolio didn’t grow last year (i.e. market returns were < 0%) then we take the minimum, which is defined as 3% of the original portfolio value. That means an inflation-adjusted $30,000.
  • If the portfolio did grow then we withdraw the minimum ($30,000) and 25% of the gains. Say the market goes up 8%. That means your portfolio goes from $950,000 to $987,221; that’s $37,221 of growth and we withdraw one-quarter of that.

For the sequence of returns above, here are the actual withdrawals that Sensible Withdrawals makes. I’ve compared it against McClung’s EM just for a point of reference.

With this set of withdrawals, Sensible Withdrawals has an HREFF-3 of 4.9%…which isn’t very good. EM has an HREFF-3 of 79.6%. A good HREFF is usually well above 60%. You can (very roughly) think of it like school grades: 90–100% is an A, 80–90% is a B, etc. So Sensible Withdrawals is “failing” according to HREFF-3.


Let’s go back to the definition of HREFF. For each withdrawal HREFF essentially gives you a score. McClung has a chart in his book to help visualise how this works:

The default is Epsilon 30

There are a couple of nuances to note:

  • If you only return the minimum, you don’t get any points. (In the chart above you can see this by noting that with an Annual Withdrawal of 3.0% the f(wi) is 0.0%. I suppose this is reasonable: if get exactly my “bare minimum withdrawal” I’m probably going be anxious and unhappy.
  • When you return more than the minimum you only get partial credit, on a sort of sliding scale. If the Annual Withdrawal is 3.5% then f(wi) is ~2.8%; only 80%. But if the Annual Withdrawal is 4.0% then f(wi) is 3.9%; about 98%. This also seems plausible: If I said I needed $30,000 as my minimum and I get $31,000 I’m not going to be thinking “okay, I’m totally safe now”; I’ll still be a bit stressed until my withdrawals are a bit above the minimum.

Armed with those observations, let’s go back to Sensible Withdrawals. If the portfolio didn’t see any annual growth then we only get the minimum: $30,000. Except that’s also the HREFF floor. Which means Sensible Withdrawals doesn’t get any points. 11 out of 27 years we withdrew $30,000, the minimum, meaning there are a lot of years where Sensible Withdrawals didn’t get any points from HREFF.

To add insult to injury, there are a few years when Sensible Withdrawals has some truly monster withdrawals: over $100,000 in two instances. Unfortunately, it doesn’t really get much credit for those. The HREFF formula assumes diminishing marginal returns on incomes.

At the end of this particular sequence, Sensible Withdrawals just leaves too much money on the table. At the end of 27 years of withdrawals the portfolio is still 79% of its original size.

Could you “fix” Sensible Withdrawals? Possibly. After all, gummy doesn’t seem to be suggesting that the 3% minimum or the “use 25% of excess monies” were optimal. You could raise the floor, though that increases your risk of running out of money. You could also take more of the excess monies. In his book, McClung actually takes 31% of the excess monies. (He says in his testing that was the optimal number.)

If I rerun things using McClung’s number (4% minimum, 31% of excess), Sensible Withdrawals does much better…but at that point you’ve set the floor so high it is the same as the 4% Safe Withdrawal Rate. The one that everyone is worried is too high for the current low yield environment.

I’m not thrilled about the idea that I need to figure out the best numbers to plug in, though.

My takeaways:

  • The minimum you set for Sensible Withdrawals is more important than in many other schemes. Even in good markets you’ll be spending a fair amount of time withdrawing the minimum. In the example above the Maximum Safe Withdrawal Rate was 6.2% but we still spent 40% of our retirement only withdrawing 3%. That means you probably want to set your minimum higher than your real minimum.
  • It is a very boom or bust withdrawal scheme. In one year it went from $30,000 to $118,000. And the next year it was back down to $30,000. That’s because it only looks at last year’s market when calculating how much “excess monies” you get.
  • The defaults gummy provided: 3% and 25% probably aren’t suitable. They’re likely to leave quite a lot of money on the table. Though that depends a bit on what future returns are like. That’s the same kind of weakness that the “4% Rule” has: you need to make guesses about the future at the beginning of your retirement. Is 3% too low? Or too high?


Let’s take a quick look at another strategy that always seems to do poorly under HREFF: Siegel & Waring’s “Annual Recalculated Virtual Annuity”.

ARVA is a PMT-based scheme. However it is fairly conservative with lifespan and extremely conservative with the discount rate used. Siegel & Waring suggest using the “risk-free” rate: a ladder of TIPS. Right now those are completely terrible, which means the calculations from PMT are very low.

At the end of this particular simulated retirement the portfolio has grown to 1.4-times its original size. 8 out of 27 withdrawals were under the floor of 3%. The largest single withdrawal was $49,563.

ARVA is extremely conservative. It is hard to shake the feeling that it is too conservative. Admittedly, you’re supposed to update the discount rate every year. Eventually (probably) TIPS will start yielding more. If that ever happens then ARVA will start looking better…but I don’t think it will ever be a top contender.

The Retrenchment Rule

Gordon Pye was (probably) the first person to suggest using actuarial methods (like PMT) to help create a withdrawal scheme. His first paper seems to have been in 1999, about 15 years before VPW was independently reinvented. He doesn’t use PMT directly, though. He has a few twists. And HREFF doesn’t like those twists.

In comparison to Sensible Withdrawals and ARVA, the Retrenchment Rule never does terrible. But it always kinda…so-so. In this particular case it has an HREFF-3 of 51.5%. (A reminder: EM had an HREFF-3 of 79.6%; ARVA 1.32%; Sensible Withdrawals 4.9%.)

In this particular case, the Retrenchment Rule actually did okay, it just got a bit unlucky. In the last two years it only withdrew $29,976, which is just below the HREFF floor. Nevertheless, it was below the floor and was punished.

This pattern repeats with the Retrenchment Rule: it is fairly common for the last 2 or 3 years of retirement to end up with withdrawals that are slightly under the HREFF floor of 3% (that is, $30,000). For instance, in another simulated retirement (not shown) the final three years are $27,981; $26,761; $26,761.

To an extent, this is simply an artifact of the floor we’ve chosen: if you rerun everything with a floor of 2.5 instead of 3, then the Retrenchment Rule fares better. For the simulation above, it has an HREFF-3 of 51.5% but and HREFF-2.5 of 78.9%. That’s very respectable.

But it is also partly because the underlying philosophy of the Retrenchment Rule conflicts a bit with how HREFF measures things.

early in retirement, retirees frequently have pent-up plans for activities such as travel. Once they have carried out those plans, however, additional spending on such activities provides less satisfaction. Later on, a more active and expensive standard of living gradually becomes less desirable as lifestyles necessarily slow with age even for those who remain in relatively good health. In view of this declining value for later withdrawals it is reasonable to discount their value relative to earlier withdrawals

HREFF, on the other hand, treats every year’s withdrawals as having equal value. Withdrawing $45,000 at age 67 is the same as withdrawing it at age 102. The Retrenchment Rule says, effectively, no I’d rather have that money at age 67, thank you very much.

So we frequently see Retrenchment Rule withdrawals reduce towards the end of your retirement. That’s not necessarily a bad thing: you got more money up front.

But the HREFF metric isn’t thrilled and docks a few points off of the Retrenchment Rule, resulting in its back-of-the-pack rankings.

To close things out, let’s take a look at all four systems charted against each other with this simulated year.

  • We can see the big spikes from Sensible Withdrawals (blue)
  • We can see the very low numbers from ARVA (red)
  • We can see that the Retrenchment Rule (green) gives you more money early in retirement
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