Why Monte Carlo Simulations Can Be Misleading

If you’ve even been given financial advice by someone at Wells Fargo or any number of other financial firms, the chances are high that the advisor you worked with used a Monte Carlo (MC) simulation in the sales process.

Because we believe that MC simulations are often used in a misleading manner, we wanted to put out a newsletter explaining how they work and why we think they are misused.

What is MC Simulating?
In layman’s terms, MC testing simulates the future investment return of the asset that is being tested. In the financial services industry, that is usually a stock or mutual fund, or an entire portfolio made up of multiple assets that an advisor is recommending to clients.

Advisors typically use software programs that will typically run at least 5,000 different simulations on the asset(s) being tested. If you plotted all 5,000 simulations, they might look something like the following:

monte-carlo-graph-lg2.png

After the simulations are completed, a software program creates one smooth looking line to illustrate what the “most likely outcome” would be for an investor based on the data from the 5,000 simulations. The smooth line in an MC simulation is typically called the “95% probability” line.

Why We Don't Like MC Simulations
Some advisors love to use the smooth looking MC simulated line and then tell clients it’s the “95% probability” line. What the smooth line ignores is that many of the 5,000 simulations had bad outcomes.

Example
For this example we used a software program that that not only calculates the 95% probability line, but it also has two additional lines in an attempt to show other potential outcomes. Assume the following:

  • Age: 40

  • Initial amount to invest: $10,000

  • Annual contributions to investment account: $10,000

  • Age to begin withdrawals: 65

  • Amount to withdraw annually: $75,000

We are not taking into account taxes (income or capital gain), money management fees, or just about any other variable you can think of. This is a simple example using a 60/40 mix of stocks and bonds for comparison.

Let’s first look at the classic smooth lines. The blue line is what most financial software programs would show and is what is considered the 95% probability line (most likely outcome).

60-40-mix-lg.png

The green line is the 75th percentile value (not likely to achieve this kind of return because it’s greater than the blue line which is the most likely outcome).

The red line is the 25th percentile value (more likely to achieve over the blue line this because it’s a lower rate of return).

The point of the green and red lines is to show people that you could get either of them instead of the blue line (even though the blue line is the “most likely” outcome).

The next chart not only has three different lines, but you’ll instantly notice that they are not smooth. Why not smooth? Because money does not grow or decline in smooth lines. Most investments don’t grow or decline at a linear rate of return. They go up and down in very unpredictable ways.

60-40-mixNo2-lg3.png

What do you think of the Squiggly Lines?
Most people would look at them and say…now that makes sense; that’s how money grows in the real world (i.e. it goes up and down over time, it does NOT grow in a smooth line).

Why do advisors give clients sales presentations that have one smooth line?

Well, our guess is that they like the one smooth line that has the label “95% probability.” If the line is to be believed (which it shouldn’t), it would arguably make sense that advisors can make more sales due to clients believing in and being comfortable with that smooth blue line.

Summary on Monte Carlo
Monte Carlo simulations can be a useful tool in the financial services industry. The problem is that the results may not always be used correctly by advisors. Selling off one smooth “95% probability” line may be the easiest way to make a sale, but is that the “right thing to do?”

As fiduciaries, it is our obligation to bring this potential misuse of MC simulations to the your attention and let you make up your own mind (and make up you minds about whether you are working with an advisor who is really using industry tools to help give the best/most suitable advice to clients or are using the tools simply to make sales).