# The Shockingly Simple Maths – Anecdotal Evidence

The thing that started my journey to financial freedom was reading the post the shockingly simple maths behind retiring early from Mr Money Mustache. When I read that somehow everything seemed to click for me. It all just boils down to your savings rate.

The actual numbers are less important compared to the rate at which you save. Rather- its the ratio between what you spend and what you save. Spend it all (0% saving rate), and you will never be able to retire. Save it all (100% saving rate) and you can retire- but will probably starve. And in the happy middle ground, a savings rate which will allow you to retire.

The larger your savings rate, the shorter the period will be before you can retire.

Savings Rate (%)Working Years Until Retirement (yr)
0Never
1051
2037
3028
4022
5017
6012.5
708.5
805.5

Once you hit that magical number you will start to draw down on your savings at a safe rate of 4% per year. And the only assumptions is that you can gain an investment return of more than 5% before inflation.

## Is It Really That Simple?

However, lately, I have been reading some post stating that in reality, it’s not as simple as what Mr MMM lays out. And it’s true. There are many simplifications made with this model. But isn’t that the same with any model?

Even when you build a model to simulate the interaction of radiation with matter- which is an example of a true stochastic (random) phenomenon, you will need to make simplifications.

Oh, but you might say that you could use a Monte Carlo model to simulate the randomness. Even if you did this- there are still simplifications made in how electrons, protons, and photons interact with matter.

And if you could get rid of all the simplifications in your model- you wouldn’t have enough computer power to run the simulation.

So a model is inherently a simplified version of reality. That doesn’t mean it’s an inferior model. Models are made to simplify complex systems into something that we can uses. Where we can easily manipulate variables and make predictions on how the system will behave. We can gather insight into the very thing that we are modelling.

## The Reasons Why

There are two reasons that I often read as to why this retirement model does not work. The first is that the market doesn’t give you smooth steady returns and instead gives you different returns every year, some good years and some bad years.

The second reason is that what you are withdrawing each year will vary depending on the amount you have invested. Some years it will be more than you need, and other years it will be less. The wild swings in withdraws, which is your income, make it highly unrealistic for anyone to be able to support their lives day to day.

It’s not that I don’t understand the reasons why people think the model won’t work. They are perfectly legitimate reasons. And at firsts, I was a sceptic too. It’s can’t really be that easy, can it? And if it is that easy- why isn’t everyone on the road to FI.

So, instead of dismissing the model based on these above reasons- I did some simulations- more on that later.

## Anecdotal Reasoning

Let’s address the second reason first. That is the model won’t work because the 4% you withdraw each year will vary. Some years it will be more than you need, and other years it will be less.

So, of course, there are going to be good investment years and bad investment years. Some years withdrawing 4% is going to be greater than what you need to spend, and some years it’ll be less than what you need.

My solution to this is to simply not spend that extra money on good investment years. You don’t have to spend all the 4% and let lifestyle inflation set in. You can either withdraw the extra money and keep it in cash to cover the shortfall for the bad investment years, or you can just leave it invested, in which case it will help grow your equity for next year.

Think about it- If you received a bonus from work or some other windfall, would you spend it all right now? Or would you save it and add it to your growing investment portfolio? Considering that you are probably aiming towards FI you are going to do the latter.

So the varying withdraw amount is a non-issue. And if it is such an issue for you, you might just have to work another year or two so that you have a buffer already build up.

#### Varying Withdrawal Rate

Now, Let’s address the first reason. That is the model won’t work because the market doesn’t give you smooth returns over your investment lifetime.

For me, this reason isn’t too hard to anecdotally prove to be a non-issue. This is because if you average the returns over a long period of time for major stock markets, the averages are well above the 5% needed for the model to work. The NZX50 has had an average of 7.8% return over the last 69 years. And the S&P 500 has had an even better return of 9.8%. (table of past returns for the NZX50 here)

Even if you did manage to be the worst investor in the world you will still be growing your investment portfolio. Not convinced? Check out my calculations on what would happen if you invested before all the major stock market crashes for the NZX50.

The only real downside to not hitting the average 5% over your investment time frame is that it might take you a few more years before you hit your FI goal. Big deal- your still miles ahead compared to if you hadn’t started.

## Verdict

In my opinion, the 4% retirement rule is a robust model. I think it’s probably the best model to plan with. The 4% withdrawal will consistently be a really safe figure to aim for. It might be a perfect model, but it’s a model.

In the next post, I will show you the results of some simulations using the S&P 500 and NZX50 data. Since I have only shown you some anecdotal evidence here. So join my mailing list so you don’t miss out on that!

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