# Multiple futures

The cool part about historical backtesting is that there is less to argue about. The data is what it is. Everyone agrees about the returns of the S&P 500 in 2007.

*(Of course, it isn’t **quite** this simple and I plan on writing a future article on the many problems with historical data.)*

But until we all have time machines, the historical behaviour of the market is of limited concern. What we all care about is what the future is going to look like. Here’s where Monte Carlo simulations have some value: by using different parameters, different assumptions about the future, we can get a feel for the possibilities in the future.

The problem is that there are so many possibilities, everyone can find room for the pet vision of the future.

Of course, Monte Carlo simulations have their own large number of caveats. So all of this needs to be taken with a big grain of salt. Still, it is interesting to look at the variations.

## Base Case: 100% Equities, US historical returns, 0% bequest

Let’s start simple. What if the future is exactly like the US past. And you don’t plan on leaving anything behind for your heirs.

*(I had the wrong chart here before; thanks to Stefan for pointing it out!)*

As expected, the longer the retirement (the x-axis) the lower our withdrawal rate needs to be. And the more certainty we want (the different colored areas) the lower our rate needs to be.

- The blue line means, “only one time in 200 should this withdrawal rate fail”; that is, once every two centuries.
- The red line means “only one time in 100 should this withdrawal rate fail”; that is, once every century. This is the 1st percentile.
- The orange line means “95 times out of 100, this withdrawal rate will succeed”. This is the 5th percentile.
- The green line means “90 times out of 100, this withdrawal rate will succeed”. This is the 10th percentile.
- The last line, the purple one, is the 50th percentile. Half of the time this will work and half of the time you’ll need to cut your spending.

The first four lines (1-in-200, 1st percentile, 5th percentile, 10th percentile) tell you about worst case scenarios. You can decide which one counts as the worst case you want to plan for. If you’re super-paranoid, then maybe you’re focused on the 1-in-200 number. If you’re more happy-go-lucky then maybe you’re looking at the 10th percentile.

The 50th percentile, the purple line, tells us something about the average case. The other lines tell us about tail risk and worst case scenarios. This tells us about the “average case”.

**50% of the time, for a 60-year retirement, you could withdraw 5.83%.**

## Adding bonds

Going from 100% equities to only 60% equities reduces our average income but increases our worst case scenarios slightly.

## Maintaining Your Portfolios

What if you don’t want to end up with $0. You want to leave some to charity? This doesn’t affect withdrawal rates very much because of the effects of compounding really stack up. In general reducing your withdrawals by 0.5% (i.e. from 3% to 2.5%) is the difference between spending your entire portfolio and having 100% of it left.

Our base case: a 60/40 portfolio for a 60-year retirement and we want to maintain 50% of the portfolio at the end for our heirs.

## The end of American exceptionalism

What if we think that using American historical values from the 20th century is overly optimistic. We think world historical averages are more likely. This results in about a 0.5% reduction. The average case (the 50th percentile) sees the biggest drop.

## Pessimistic about valuations

What if you are worried about the current low yields and high valuations? We can build a model that autoregresses from the current values to historical values. Now we have a spectrum of models that are increasingly pessimistic.

- The US historical results
- Research Associates’ prediction for the next 10 years
- The World historical results
- An model for low yields and high valuations

## All the futures

With enough models, we can always find something to support our claim about the future.

The worst worst case scenario, “Conservative 100”, has us with a negative withdrawal rate. That is, there is withdrawing any money at all means we have a greater than 0.5% of failure. The most optimistic worst case scenario scenario, “Low Yields 60/40”, only allows 2.12% withdrawals in order to keep the failure rate under 0.5%.

When we look at 50th percentile results, the average case, things look different.

Both of these show what we already know: having lots of stocks is better on average but worse in the worst case.

But between these two charts we can see how wide retirement outcomes can vary depending on the assumptions about the future (and your portfolio in response to it).

The 5th percentile withdrawal rate can vary from 1.73% to 2.51%. All of those assumptions are defensible. Valuations are high. World historical returns cover nearly two dozen countries across more than a century. Research Associates has really smart people who spend a lot of time thinking about this. The US is still the financial powerhouse of the world.

Is 10th percentile safe? Or should it be 5th? Or 1st? Would you get on a plane that only has a 1% chance of crashing? Should it be 0%? How low do we have to go to get to a 0% chance of failure for a 60-year retirement and a 50% bequest?

The numbers are so low they aren’t even worth considering. 0.99%, 0.40%, 0.32%, 0.21%, “impossible”. Though I have a feeling that in these cases, you’d eventually give up on the idea of leaving a bequest.