# More Galton Goofiness

Look familiar? The decision tree above yields the distribution below. The distribution is a population of results but the destination of any individual ball is particular. If success is ending up on the right it is the result of enough rightward decisions and the sequence of rightward decisions to get you there. In the above there are 12 decisions applied to each ball before it reaches the mouth of its final bin. If the first 6 decisions are leftward it becomes increasingly unlikely you will wind up on the right. If the first 6 decisions are rightward it becomes increasingly unlikely you will end up left aka fail. This is the essential definition of sequence of return and the essential display of conditional or Bayesian probability. In your retirement spend down getting through the first half rightward has a big effect on eventual success.

Here is the Galton board taking a nap. In this case success is winding up on top.

This is a Monte Carlo of a 60 year 4% withdrawal on a 60/40 portfolio. It is basically a statistical creation of the Galton board placed on its side. Instead of the whole board being represented only the success is represented at the top of the graph, the “right” cohort of balls. After failure there isn’t much point in gilding the lily about how bad the failure is so instead the bottom graph represents how soon failure occurs. In the above 7869/10000 simulations succeeded, meaning about 25% of these retirements failed by the 60th year. I’ve come to believe this is the proper way to view retirement, not some rearward looking analysis. The rearward analysis says nothing about the future it only rehashes the past. I stopped by FIREcalc yesterday and ran my numbers, and I think the projections are optimistic. I was reading a forum discussing how closely FIREcalc can predict and what percent failure is a reasonable percentage of failure, in other words using FIREcalc as the mechanism to understand what is enough. That’s the real rub. Enough is based on what you will actually need from the start of portfolio deflation (retirement) until the end and that number, the most important number, is a single data point the projected WR based only on what would have worked in the past dating back to 1870 or something. Lincoln was shot in 1865 and I’m not sure 1870 data is relevant to the analysis.

The above analysis tells you likelihood of failure and when that is likely to occur. The probabilities are conditional. Here are the probabilities based on the first 3 years of return being the worst

Pretty stark only 2173 out of 10,000 simulations succeed. Here is the super safe 3% WR success rate on a 60 year portfolio with the worst SOR first.

Better, only about half fail instead of 78% but hardly super safe. In the Galton board example it took about half the choices (6/12) before the likelihood of failure to dramatically start to recede and the likelihood of success to overwhelm. 30 years is a long time to live on pins and needles. It’s actually not quite as gloomy as that but what’s the point of blogging if you can’t create a bit of dramatic tension. It’s during those initial 30 years however you have the best chance of affecting where your ball will reside at the end, that’s when the conditional probability is most active on the outcome. It definitely colors the perception of how much is enough.

The above discussion shows the risk involved in leveraging your future. The 4% portfolio is more leveraged than the 3% portfolio Here is 2%

9234/10,000 succeed after 60 years using a 2% leverage. Probably why Bernstein uses 2% as super safe. I get a lot of pushback on this stuff but knowledge of how to adjust the odds is power.

## 3 Replies to “More Galton Goofiness”

1. LearningToFish says:

Gasem,

This is the best explanation of sequence of return risk I have ever come.

Who would have thought a Galton board can crystalize the concept of sequence of return risk so well.

Thanks for the enlightening.

1. LearningToFish says:

?