# Adding a floor to variable withdrawals.

Variable withdrawal schemes can often see us cut our withdrawals dramatically in retirement. It is tempting to add some kind of floor — a minimum withdrawal that we won’t go below. “Sure, the algorithm says to withdraw $27,500 this year. But that would represent an unacceptable reduction in my standard of living. It would mean giving up my mobile phone or cancelling internet or selling my house and moving to an apartment. Instead I will withdraw $32,000. After all, the market will probably bounce back next year, anyway.”

But how can we pick a floor that is “right”? What does “right” even mean? What tradeoffs are we making? Money doesn’t come from nowhere, so we *must* be increasing some kind of risk somewhere, right?

As soon as we add a minimum, we re-introduce the risk of total portfolio depletion. What’s more, by combining the minimum floor with variable withdrawals on the upside we are guaranteed to have worse failure scenarios than the floor alone.

*(Unless otherwise specified all simulations assume a 60/40 portfolio over a 30 year horizon.)*

To make this clear, let’s look at an extreme example. Let’s set the floor at 4% and retire in 1969. Normally 4% withdrawals run out of money after 28 years. By adding variable withdrawals on the upside, we run out of money after 26 years.

Now, that might actually be a tradeoff you’re willing to make. Maybe a 4% floor is fine? After all, in all the other scenarios you’re getting much higher withdrawals, on average. We’re trying to balance increased risk of shortfalls in worst case scenarios versus increased spending in all other scenarios.

First let’s quantify how much we’re actually increasing the risk of shortfalls. We simulate 118 retirements and each one is 30 years long. That’s 3,540 “retirement-years” in total.

Using normal 4% withdrawals we have a total of 12 shortfall years out of those 3,540. A 0.33% shortfall rate.

If we use floor+variable, with a floor of 4%, then we have a total of 30 shortfall years out of those 3,540. A 0.84% shortfall rate.

- 1906 went from sustaining all 30 years of retirement to having a shortfall in the 28th year.
- 1962 went from lasting all 30 years to a shortfall in the 27th year.
- 1964 went from lasting all 30 years to a shortfall in the 27th year.
- 1965 went from a shortfall in the 28th year to a shortfall in the 27th year.
- 1966 went from a shortfall in the 26th year to a shortfall in the 24th year.
- 1967 went from lasting all 30 years to a shortfall in the 28th year.
- 1968 went from a shortfall in the 27th year to a shortfall in the 25th year.
- 1969 went from a shortfall in the 27th year to a shortfall in the 26th year.

We can see that even in failure, the portfolios lasted nearly the full length of retirement. The increased shortfall was generally about 2 years.

It is tempting to call that “good enough”, honestly. The soonest a failure occurs is at the 25th year of retirement. That’s age 90, assuming the standard “retire at age 65” scenario. There’s about a 50% chance that *both* people in the couple are dead by then, making withdrawals moot. There’s a 90% chance that at least one of them is dead, possibly reducing retirement expenses.

But maybe you think having *any shortfall* at all is unacceptable. What floor should you use? We can chart the total number of shortfall years versus various floors. With a 3.5% floor there is only a single year of shortfall in all of (US, so far) history. With a 3.4% floor there are none.

So let’s tentatively say that combining a variable withdrawal scheme and a 3.4% floor is “safe”.

Of course, using a floor of 3.4% means we are drawing down our portfolio substantially. In some cases very close to $0. So we run into the usual problem with any kind of fixed withdrawal amount. At some point the portfolio values get so low that it is implausible to assume actual human beings wouldn’t change their strategy. Just look at the portfolio values at the 20th year (i.e. a retiree can reasonably assume 5–10 more years of withdrawals)

There are several instances where the portfolio is down to 30% or less of its original value. That, in turn, means we are withdrawing a huge percentage of our remaining portfolio every year.

Would you really withdraw over 10% of your current portfolio just because that is your “floor”? On the other hand, raw variable withdrawals alone (at least if you’re following VPW) will have you withdrawing around 8% of your portfolio in Year 20 already. Still, some of the spikes are not just “a little bit higher than 8%”. They are *way* higher than VPW’s 8%.

Still, let’s stick with our floor of 3.4% for a minute and see where it gets us. Let’s look at the canonical 1969 Worst Case Scenario.

Unsurprisingly, it falls somewhere between ConstantDollar (traditional 4% withdrawals) and VPW (variable withdrawals). It does worse than 4% withdrawals for 20+ years. But it doesn’t run out of money. It does better than VPW for about 10 years in early retirement but then does worse than VPW for 10 years in late retirement. That might be a reasonable tradeoff for many.

Also notice that you spend most of your retirement only withdrawing the floor of 3.4%. This calls into question what this floor actually represents. Is your floor a retirement that you’d truly be happy with? Or does it mean a beans & rice and never seeing the grandkids kind of retirement? Are you left wishing you had worked just a few more years rather than spend two decades only withdrawing 3.4%?

We still have unresolved the perennial question of how much risk we’ve introduced. We know that at some points our portfolio drops substantially. That’s just the nature of market crashes. And things don’t always get back in track in just a year or two.

The blue hump is the “extra risk” we take by using the floor. We can see it is neither small nor brief. We’ve eliminated shortfall risk — but shortfall risk assumes we’re sitting at the end of our retirement with perfect knowledge of how it all played out. We’ve introduced “along the way” risk — retirees never know, at the time, how long it will take markets to recover and they suffer from anxiety until they do.

How can we decide whether that “along the way risk” is “too much”? I mean…that blue hump *looks* big. But what does that even mean? Here we can turn to Moshe Milevsky’s “risk quotient”. Without going into details, let’s assume it is a proxy for an average person’s feeling about the chances of their portfolio running out at some point, given their current age and withdrawal rate. It is (one way) to calculate a retiree’s current “sleep well at night” rating.

The risk quotient spikes up substantially when using the 3.4% floor. There’s a period of 7 or 8 years where it is above 0.30. In other words a retiree is sitting there thinking, “the way things are going there’s *at least* a 1-in-3 chance of my retirement going up in flames”. And for one terrible year it approaches 0.50. “Welp, it is a coin-flip whether my retirement works out or not.”

As we use a lower and lower floor, this risk quotient is going to go down. So we can try different floors and see what the worst (i.e. biggest) risk quotient is for each.

Remember, we can think of pure variable withdrawals as “the safest we can get” (at least in terms of portfolio depletion). And in the previous chart we saw that VPW never really gets above a risk quotient of 0.20 (at least not until very late in retirement; let’s set that aside for now). So if we think of 0.20 as our “maximum tolerable risk quotient”, we need to set the floor at 2.4% to hit that target. That is quite a bit lower than the 3.4% we started with.

But maybe we’re willing to tolerate a little bit more worry about (eventually) running out of money in order to increase our standard of living *right now*. It isn’t clear that there’s one, single, obvious answer. That slope seems pretty linear, suggesting where you choose along that slope is going to be down to some personal preferences that are harder for me to quantify.

There’s actually another factor to consider up until now. The lower the floor is, the less actual, practical use it is. Consider the 2.4% floor we mentioned above. What’s the actual difference between a 2.4% floor…and just not bothering to have a floor at all?

If you look *really* closely you can see there’s a single year — somewhere around Year 13 — where the floor gets you a few extra hundred dollars. Why even bother having a floor under those circumstances?

We can look at the various floors — ranging from 2.5% up to 3.0% and see how big of a difference they actually make.

It isn’t until the floor gets up to 2.9% that it appears to make any real difference. Even with a floor of 2.8%, it rarely comes into effect and when it does the amounts are usually trivial. There is a single year where you get 20% extra income ($28,000 instead of $23,259). That is nice but it is only a single year. The *next best* year you only get 6% extra income by using the floor ($28,000 instead of $26,383). Again, an extra $1,600 is nice. An extra $130 a month. But I’m not convinced it is *enough* nicer to be worth the hassle of using a floor at all. If you’re going to pick a floor that low…why even bother?

With a floor of 2.9% things are *bit *better. But still not amazing:

`6 1.072845`

10 1.050801

11 1.099193

12 1.061807

13 1.246786

14 1.060445

This can be read as “in the 6th year of retirement, using a floor gives you 1.072845 the income of not using a floor”. That is, a 7.2% improvement. We can see there are six years where it improves the results and the improvement is at least 5% in each case.

With a floor of 3.0% we finally see some substantial improvements:

`6 1.109841`

9 1.013685

10 1.087035

11 1.137058

12 1.098458

13 1.289823

14 1.096976

15 1.011634

16 1.013856

9 years where we saw an improvement. 3 of them over 10%. 6 of them over 8%.

But also note that using a floor means you do *worse* once the recovery kicks in. In the 14th year of your retirement, using a floor means you withdraw $30,000 instead of $27,347. But it *also* means that in the 18th year of your retirement you withdraw $36,634 instead of $39,685.

Okay, that was pretty long. How would I sum all of that up?

*(Reminder: this only ever considered 30-year retirement lengths and is based on historical backtesting using only US data. For early retirees considering a longer retirement…I have no idea yet how applicable it is.)*

- First, I’m still pretty dubious about the whole concept of a floor. I don’t think it is remotely obvious that, on the whole, they are useful. They only come into play during the biggest crises…and that’s exactly when relying on historical backtesting is more dubious. What if things really
*are*different in this crash? - For the very risk-tolerant, I don’t think it is
*totally*insane to pair a high floor (e.g. 4%) with variable withdrawals. But you’d better have some Plan Bs in your back pocket: home equity, willing to live only on Social Security payments, inheritance when your Boomer parents die, etc. - A floor between 2.4% — 3.4% can all be plausibly argued for.
- However, a floor above 3% means a retiree is willing to tolerate (at least for a year or two; and remember in the real world that can feel like a very, very, very long time!) a 1-in-3 chance of their portfolio running out of money before they die.
- If you just want someone to tell you a number: use 3% as your floor. It is a nice, round number. There is no shortfall risk. The risk quotient, your “sleep well at night” number will spike to up to 0.33 for a single year in worst case scenarios. But you can live with that. It provides a meaningful enough improvement, compared to not using a floor, for a few years in the depths of a crash.