# Perfect Withdrawal Amount and Modifying the Initial Rate

In McClung’s book *Living Off Your Money* in the chapter “Putting It All Together” he shows how to, well, put together all of the bits and pieces in to a complete systematic withdrawal plan. He includes a table summarising the recommendations.

For the majority of the book he focuses on a 30-year retirement span (since that’s what most other people use, he is trying to make apples-to-apples comparisons). But in the table he provides suggestions for 15-, 20-, 30-, and 40- year retirements. Each of which includes an adjustment to the initial withdrawal rate. This initial withdrawal rate is further adjusted depending on whether you’re using the aggressive, primary, more conservative, or most conservative recommendations.

Given how detailed the rest of the book was, this table always seemed weird to me. I could never figure out where the initial withdrawal rate changes came from. Why +10% for a 20-year retirement and not +5% or +15%? Or, for that matter, +7% or +12%.

## The Perfect Withdrawal Amount

Suarez, Suarez, and Walz have a relatively recent (2014) paper, “The Perfect Withdrawal Amount” that provides a way to get some perspective on this. For now, I’m not going to do a full-dive into it (maybe at another time) but it does provide a way to generate lots of nice tables.

This is showing us withdrawal amounts for various lengths of retirement and probability of them succeeding. For instance, go to row “15” for a 15-year retirement. Then go to column “30th” for the 30th percentile withdrawal. 7.62%. This is telling us that for a 15-year retirement, if you withdrew 7.62% there was only a 30% chance you would ever need to reduce your withdrawals.

The full tables can be found on Google Drive here.

Now that we’re armed with lots and lots of withdrawal rates we can investigate the relationship between length of retirement and the withdrawal rate.

- 30 years ⇨ 40 years. Using the primary recommendation, McClung suggests cutting the initial withdrawal by 5%.
- 30 years ⇨ 20 years. McClung suggests increasing the initial withdrawal by 10%.
- 30 years ⇨ 15 years. McClung suggests increasing the initial withdrawal by 20%.

## 15-year retirement

Which percentile do we use for comparisons? Due to a quirk of the data, the less certainty you want the *less* you should increase. At the 10th percentile, going from a 30-year retirement to a 15-year retirement results in a 67% increase in the withdrawal rate. But at the 50th percentile, it only results in a 50% increase in the withdrawal rate. That seems backwards, right? Surely if I want to be *more* certain of my outcome, I should increase the withdrawal rate *less* not more.

This counterintuitive result is because we are comparing a 15-year retirement and a 30-year retirement. The longer the retirement the steeper the drop-off needs to be to increase certainty.

You can see that a 30-year retirement needs to reduce the withdrawal rate by 37% to go from 50th percentile to 10th percentile. A 15-year retirement only needs to reduce the withdrawal rate by 30%.

In any case, we have a pretty good case for increasing the withdrawal rate by 50% — not the 20% McClung suggested.

## 20-year and 40-year retirements

When we do the same comparison for a 20-year retirement the result is: a 24% increase.

When we do it for a 40-year retirement it says we need an 11% decrease.

Here are the differences, side-by-side, along with an example of how they might work out in practice if the “default” withdrawal rate were 4.5%

Overall they are much more aggressive on the short side and more conservative on the long side. Roughly, the numbers are about double what McClung suggests in each case.

If you plot withdrawals rates against length of retirement it looks like this.

The curve flattens out such that the difference between a 40-year retirement and a 60-year retirement is less than the difference between a 10-year retirement and an 11-year retirement. That’s why you can’t apply a simple linear adjustment like “-5% for 10 years over the baseline length and +5% for 10 years under the baseline length”. McClung’s recommendation aren’t linear but it appears they may not be non-linear enough.

## Why the difference?

The results in the Perfect Withdrawal Amount tables are based on a Monte Carlo analysis which means you need to provide some market assumptions. My calculations above are based on a 50/50 portfolio where the mean return has been reduced from its American historical average to one closer to the world historical average.

If I use different assumptions do I get different results?

Sure. But the outcome doesn’t vary as much as I expected.

The most optimistic scenario is if you use 100% equities. The least optimistic scenario is if you use 100% bonds. Here’s how those look (along with some other scenarios).

The closest we come to a match is McClung suggests -15% for a “most conservative” 40-year retirement. With 100% bonds and 40-years we see -16%.

But what does McClung mean by aggressive, primary, more conservative, and most conservative? That isn’t crystal clear but we can make an inference from the asset allocation he recommends at each step:

- Aggressive: 60/40
- Primary: 50/50
- More conservative: 40/60
- Most conservative: 30/70

Overall, I’m not seeing a lot of support (at least with this methodology) for McClung’s suggestions for making adjustments to the initial withdrawal rate.