The cost of volatility

Early Retirement Now has a long series on safe withdrawal rates for early retirees. You can get started with the introduction here. The focus is on early retirees, which is a nice change from the usual “assume you are 65 years old and have a 30-year planning horizon”. He has a few other twists that make the whole series interesting, so I recommend you give it a read.

In Part 7: A Google Sheets Toolbox he provides a Google Sheet that let’s you play around with some of it yourself. It is pretty nifty and I wish more people would make their spreadsheets/software available like that.

One problem with trying to figure out things for early retirees is there just isn’t very much data for how a 60-year retirement might work. If you only rely on historical data then then the last year of retirement in your data would be 1956, which would give you a 1956–2016 retirement. Not many people are going to find that a particular compelling exercise.

The only way to compensate for that is to extend your data somehow. You have three basic choices:

• Wrap around. That is, after 2016 go back and reuse the 1926 data again. This is the approach that McClung takes in his book Living Off Your Money. It has some advantages (you get the Great Depression all over again, making it hard for people to say you’re being too optimistic).
• Do some kind of Monte Carlo simulation to generate random fake data.
• Assume fixed returns going forward. For instance, stocks will return 6% every year from now until 2075.

All of them have pros and cons but the last choice, assuming fixed returns, is probably the worst choice. Unfortunately, it is also the choice made by Early Retirement Now.

The problem is that static returns every year mean you are ignoring volatility. Because of the effects of compounding on stocks and bonds there is a difference between their arithmetic average return and their geometric average return.

Imagine that a stock had the following returns:

• -5%
• 5%
• 15%

The arithmetic average is the number you’re used to: ((-5) + 5 + 15) / 3 = 5. 5% average return.

So if you started out with \$100 you’d have:

• \$100 + 5% return = \$105 after 1 year.
• \$105 + 5% return = \$110.25 after 2 years.
• \$110.25 + 5% return = \$115.7625 after 3 years.

Right?

Wrong.

• \$100 and lose 5% = \$95
• \$95 + 5% = \$99.75
• \$99.75 + 15% = \$114.7125

You actually end up with \$1 less. That \$1 is the difference between the arithmetic and the geometric average. It is a “tax” caused by volatility. And the more volatility, the bigger the tax.

Here’s another example that still has an arithmetic average of 5% but has much more volatility:

• \$100 and lose 20% = \$80
• \$80 + 20% = \$96
• \$96 + 5% = \$100.80

Now you’ve lost nearly \$15 dollars to the volatility tax.

The Early Retirement Now spreadsheet defaults to assuming constant 5% returns on equities from 2017 to 2076.

That gives a safe withdrawal rate (the 1% part of the distribution) of 3.46%.

Let’s replace those constant returns with some random returns. These will have an arithmetic average of 5% but a standard deviation of 20%.

Now the safe withdrawal rate has dropped to 2.96%! That’s substantially lower than we originally thought.

Now, this is just one particular set of random future data. This isn’t an attempt to predict the future: this is just trying to show the effect that volatility can have. And when we’re relying on a lot of data (as the Early Retirement Now spreadsheet does by having 60 years of future data), ignoring all that volatility can skew our results.

What does the use of constant returns look like in practice? In other words, what’s an example of how constant returns might skew results?

Imagine that you’re a simulated retiree. You’re a few decades into your retirement but you still have 20 years of retirement left. You started out with \$1,000,000 but that’s been whittled down to \$460,000. You are withdrawing \$35,000 a year (3.5% of your original portfolio).

But \$35,000 from a \$460,000 portfolio is a 7.6% withdrawal rate for the next 20 years. Is that safe? Would you feel comfortable withdrawing 7.6% of your portfolio starting today for the next 20 years?

If you assume constant returns, then the situation looks fine. But if you assume volatility, then you’d say the retiree is in a precarious position and has been withdrawing too much. You’d probably end up deciding that their original withdrawal rate of 3.5% was too high and should have been lower.

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