The Math of Early Retirement

Why work when you can retire?

The biggest challenge with early retirement is knowing that you have enough money, because life is sometimes capricious and work skills atrophy. It would be horrible to retire in your fifties from a high-paying job only to run of money when you’re 80 and can only be employed as a Walmart greeter.

But we live in a world where stock market crashes happen and inflation rises and falls. How the heck can you know how much a loaf of bread will cost in 30 years? Or 50 years?

Forecasting the future

There’s no way to be completely certain. It’s possible that the politicians and bankers will mess up the country so badly that hyperinflation will destroy the savings of everyone, and it’s hard to guard against that without going to extremes that are completely horrible in any scenario except a complete failure of the country’s financial system. International diversification can help you a bit, but only a bit.

Thus, you have to accept that early retirement does come with some small chance of a terrible outcome– say 1%–that you cannot avoid.

But it’s a bad strategy to optimize your life for extremely low probability outcomes. Instead, you want to optimize for the most likely outcomes in a way that is reasonably robust against extreme outcomes.

The basic idea

Applying this strategy to retirement, we want to determine how much money we need now to live for the rest of our lives without working, with a reasonable margin of safety for extreme events. The easiest way to figure this out is by inverting the question. Instead ask, what percentage of my portfolio can I withdraw each year (adjusted upwards for inflation), without worrying too much about running out of money?

One way to start answering this question is by taking a reasonably diversified portfolio, and seeing how it would have performed during various time periods and various withdrawal rates. For instance, how would the portfolio have done if you retired in 1970? 1952? 1929? (Gulp!) How long would it have lasted if I took out 3% every year? How about 5%?

If you do this a bit, you’ll figure out quickly that the order of the good years and bad years matters. If you lose 30% in the first year, you have a much worse outcome than if you lose 30% in the 15th year. This means that simple models like “a portfolio averaging 7% per year” don’t represent reality well at all.

When you start running the numbers, you find that historically, if you withdrew 4% a year (adjusted for inflation) from a 75% stock/25% bond portfolio, you would never have run out of money after 30 years, regardless of when in the last century you retired. What’s more, you’ll find that 30 years is almost the same as infinite–if the portfolio still has money left after 30 years, it is almost equally likely to have money left at 50 years.

Increasing robustness

So that takes care of the most likely outcomes. But I’d also like it to be robust against many extreme outcomes. Perhaps in the future there will be something that rarely has happened in the past, like stocks and bonds both falling dramatically at the same time for a decade. To take care of this sort of scenario, I’d like to add an extra margin of safety by using 2.5-3.5% withdrawal rates instead.

The most likely outcome of using these lower withdrawal rates is that I get rich, generating far more cash than I’ll ever spend. In some sense, this is a loss. If you equate spending with happiness (which I wouldn’t recommend), it means that I will be less happy in my early retirement than I could have been. On the other hand, it also means that in later retirement, I will be able to increase my spending without running into problems and still leave a healthy inheritance.

What’s the number?

Suppose you decide to be very conservative, and only spend 2.5% each year. Then, if you know your spending, you now know exactly how much money you need to save for early retirement. Want to spend $40,000 a year? Well, you’ll need 40 times that–$1.6 million.

And this is where it gets interesting, because the less you spend a year, the less money you need before you can retire. But it’s also true that the less you spend a year, the more you can save.

Suppose you net $50,000 a year and are saving $10,000 a year, and want to live off $40,000 per year. If, while you’re working, you’re making 7% off your investments, then it will take approximately 37 years to save $1.6 million for retirement.

But suppose instead, you can live off $20,000 a year, and are happy to continue doing that in retirement. Well, then you only need $800,000 retire, and can do that in 16 years, saving $30,000 a year. In a way, by reducing your expenses, you get a double hit–you save more each month and need less money in the end.

The bottom line

What this means is if you really care about early retirement, the way to do it is to cut your expenses and be happy with less. That might seem ridiculous, but there are some people with high-paying jobs who take this to the extreme, and are able to retire in under a decade. Like, in their early thirties. And the math all works.

This isn’t for everyone. But it might be for you. It’s a question of what you value the most. Would you rather have a Starbucks coffee every day, a nice car, and designer clothes for the next 30 years? Or would you rather pick up 50 extra hours of free time every week for 20 years, to use as you wish?

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