Putting Out a FIRE Part I: The Numbers Don’t Add Up

Noah doesn’t enjoy life. Not at the moment, anyway. And he doesn’t anticipate much enjoyment in any of the next 5 years, either.

But that’s ok. Noah has a plan.

Noah is frugal. He lives in a small 2-bedroom flat on the outskirts of London. He doesn’t go on holiday. He hasn’t purchased a new item of clothing since 2018. He would never, gun-to-his-head-never, purchase barista-made coffee or other caffeinated beverages. Not even from the 1-little-old-lady stall at the end of his road. Why do that when it’s cheaper to make coffee at home?

He lives like this because he’s trying to save. If he saves enough, he can live off the income generated from the return on investing the (huge) pile of savings. So Noah lives cheap and works for a company he deep-down kind of loathes doing a job he deep-down kind of hates in order to maximise his income.

Because he wants to retire early. He has seen on Reddit that as soon as he hits some accumulation milestone – £1M, 30x annual expenses, livable income of 4% of pot value, etc. – he can ride off into the sunset, never to work again.

What Noah doesn’t realise, however, is that the return assumptions used to generate these required milestones might not be as robust as he originally thought.

Just like the simulation

Assume Noah and his wife have managed to save £1M by age 35. The “4% Rule” is often touted amongst the FIRE community so let’s use that. Noah withdraws 4% of £1M which is, let me run the numbers, oh yes – £40,000 a year. We assume Noah withdraws this amount each year, rather than a % of his portfolio. Let’s assume that Noah and his wife wish to live happily ever after on this amount until they are 100, 65 years into the future.

Now, obviously, the ability of Noah et al. to stay retired and not return to work is dependent on the returns Noah et al. can generate from their respective mountains of squirrelled-away GBP. Return is kind of important.

First we consider the scenario in which Noah relieves a constant rate of return each year every year:

Return (%)-5-3-1135
Terminal Wealth (£M)000004.5
Noah terminal wealth with annual return constant.

return < withdrawal amount = back to work

So all we need to do is determine what rate of return we are likely to receive, then we can work out if our savings will run out (or not). But unfortunately us and Noah and his wife and the rest of the FIRE community, the market doesn’t (1) kindly provide us with a constant rate of return each year, (2) tell us what that return will be, and (3) choose returns from a uniform distribution. In reality, our annual returns should look a little more like this:

Percentage annual price return of the FTSE 100. Source: Yahoo Finance. Also used in: Does the Stock Market Always Go Up?

Let’s try the normal distribution, with mean 0.05 and standard deviation 0.1:

30 observations drawn randomly from N~(0.05, 0.1).

Note that the expected return here is greater than Noah’s initial rate of withdrawal. So in each period, his pot is expected to increase. To see if it does, we allocate a rate of return drawn randomly from this normal distribution for each year and look at his wealth path for 100 trials:

100 trials of Noah’s wealth path with returns drawn from ~N(0.05, 0.1).

Sure, in some scenarios Noah gets depressingly rich. But please ladies and gentlemen direct your attention to the bottom of the chart – there are many scenarios in which he runs out of money and is forced to return to work.

What about when returns are drawn from a different distribution? Let’s use one with more weight around the mean and longer tails, which is a better reflection of actual returns. This time we draw from a Laplace distribution with location parameter 0.05 and scaling parameter 0.075. Note again that the expected return here is greater than the initial rate of withdrawal. But again we see that in many trials poor Noah runs out of money (ignore the fact that we arrive at negative terminal wealth – in reality, 0 is an absorbing barrier):

100 trials of Noah’s terminal wealth with returns drawn from ~Laplace(0.05, 0.075).
So what?

These are just simulations. They may not reflect reality: returns may not look like this over the next 65 years. This is because it’s very difficult to simulate complex environments, as I’ve touched on multiple times before.

There are other nuances, too. Some may argue that we should be withdrawing a % of our portfolio, rather than a set amount. Some may say we should withdraw more in ‘up’ years and less in ‘down’ years. Some would argue Noah should retire later or save more or live on less.

Practicalities are also ignored. What if Noah and his wife want to buy a house? This would reduce their pot size but give them a usable asset. How realistic is saving £1M by age 35? Not very, unless your stock options at Amazon vest or the particular niche that your hedge fund specialises in just so happens to experience a bull-run. How much will £40,000 a year buy you in 30 years’ time with inflation at 5%? Not much.

But these are footnotes. They don’t affect our conclusion: FIRE doesn’t work if you get unlucky. “I’ll risk it.” Noah says. No. Don’t. Remember – we are trying to minimise the probability of an unacceptable outcome. FIRE fails to do this.

What do you think?

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