How Flipping Coins Helps You Make Better Financial Decisions

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A Monte Carlo is a method used to simulate possible outcomes given a set of parameters or assumptions. In a comprehensive financial plan, Monte Carlo can be used to test the strength of your financial plan against adverse market conditions.

Monte Carlo analysis is an improvement over the prior method of just using a constant portfolio return for each year in your financial plan. While using a constant return can simplify the charts and give you a basic understanding of what is happening in your plan, it fails to account for a basic fact that returns each year are not constant. Every year they vary from the average – some years by quite a lot.

In fact, from 1926 to 2022, the average annual return for the S&P 500 was around 12%. However, out of the 97 years this represents, only 8 years fell withing a 2% range of this average (10% to 14%).

To illustrate what Monte Carlo is, let’s imagine that you are given a regular coin and asked to play a game. The purpose of the game is to generate a hypothetical rate of return for a portfolio.

Here are the game rules:

Start with $100.
Flip the coin 10 times and write whether it was heads or tails.
For each head that you get, you win $10.
For each tail that you get, you lose $5.
At the end of the 10 flips, calculate the return for your portfolio!

Grab a coin and check out the Coin Flip Game at the end of the post!

Let’s think about what can happen in this game

Range of Outcomes: The best possible ending value after 10 flips is $200 (10 x $10), which is obtained by flipping all heads. The worst possible ending value after 10 flips is $50, which is obtained by flipping all tails. Every other outcome will fall between these two values. If you and I play at the same time, we will most likely not get the same result.

Probability: When you flip your coin, you have a 50% probability of heads and a 50% probability of tails. In a game where you can flip a coin 10 times, there are 1,024 possible combinations of coin flips, but only 11 possible ending outcomes are shown here:

$200

$185

$170

$155

$140

$125

$110

$95

$80

$65

$50

Pathing: While there are only 11 possible ending values, the path to those ending values is different. For example, five heads then five tails feels different than five tails followed by five heads.

Expected Payout: The expected payout represents how much we can expect to earn while playing this game. To calculate this, you sum up the probability of each outcome multiplied by the expected payout of that outcome. So, the expected payout of playing this game is $2.50 per flip which is calculated by multiplying the probability of heads (50% of the time) by its payout ($10) and the probability of tails (50% of the time) by it’s payout (-$5). After 10 flips, your average total payout is $125.

As a result of this, the following two outcomes are equally likely and possible:

If you only play the game once, you might come out ahead or you might come out behind. It is impossible to know beforehand which outcome you experience.

However, as you play the game more and more, you’ll begin to see that different outcomes are more likely than others. For example, earning $125 is significantly more likely to obtain than earning $200. There is only 1 way to achieve $200 (10 heads in a row) whereas $125 can be achieved 252 different ways.

If you played the game hundreds or thousands of times, your outcomes will begin to resemble the below chart which is called a distribution chart.

What does Monte Carlo Mean for Your Financial Plan

In financial planning, we use Monte Carlo to simulate different market returns which in turn results in different portfolio results. To make the analysis more market like, we exchange fixed returns in dollar value like +$10 of -$5 as in the flip game for percentage returns like +10%, -5%, +18%, -7.2%, or any number of different projected returns. The probability of each return is usually based off of historic asset returns, but can be based off a number of increasingly complex factors or methods to generate a more robust analysis.

Using those simulated returns, we project your future financial plan factoring in your income, savings, expenses, and assets to come up with a reasonable estimate of how well you are able to sustain your goals in future. Monte Carlo analysis helps to come up with a good estimate of the possible outcomes as well as identify what areas of concern there might be in your plan.

Unfortunately, unlike a game where you can plan play multiple times, you only get one set of future market returns to work with. You cannot choose which you get; you cannot rearrange them; and you cannot go back to capture more of them if they’ve already passed.

For example, if you have a really great set of market returns, your retirement portfolio could end up with $6,000,000. Or, given a poor set of return, you could run out around age 90.

Monte Carlo analysis can help you assess a number of different risks and strategies like Sequence of Return Risk, Retirement Longevity Risk, Guaranteed Income Options, and more.

Finally, it is important to understand that Monte Carlo is just one tool in a comprehensive financial planner’s toolbelt and not the be-all, end-all. Many assumptions go into generating a Monte Carlo analysis, many of which will prove to be off from what actually happens. The point is to provide a more robust analysis of your plan so that we can review and assess strategies to help you achieve your financial goals.

For a more detailed conversation on how financial planners use Monte Carlo analysis, check out my article: From Risk to Resilience: How to Build a Strong Plan for an Uncertain Future – Gilbert Wealth