Kendrick Wakeman

Most financial planners will use “Monte Carlo Analysis” to build financial plans for their clients. Specifically, Monte Carlo Analysis projects a client’s financial picture into the future based upon the client’s portfolio and various savings, spending, and life goals/circumstances. The key point of the analysis is to see if the client can make it through life, achieve all their goals, and go to room temperature without becoming destitute. Many academics and professionals agree it is the most effective form of analysis for this task in production today. One of the big benefits of Monte Carlo Analysis is that it can be a flexible tool that produces output that clients can truly understand, even if they have no financial training whatsoever. This adds value, builds trust, and gives clients the clarity and confidence to move forward.

But Monte Carlo Analysis has a downside: while the output is simple and understandable, the mechanics of it are difficult to explain to people. Actually, it is probably more accurate to say that, while the concept of Monte Carlo Analysis is simple enough, most rational people will see it as an overly complex and illogical solution to what seems like a fairly simple problem. Which, in turn, makes them think that they are misunderstanding you, or possibly that the industry at large has gone off its rocker. The elephant in the room seems to be: “You say my portfolio should average a 6% return over the next 20 years, so why don’t you just project out that my portfolio will gain 6% each year over the next 20 years?” It is a justified question as assuming our portfolio balance goes up 6% each year would seem to fit the “average of 6%” comment and it is simple math.

Speaking to the Elephant

So, before we get into the mechanics of Monte Carlo, let me speak to the elephant: some years you will win and some you will lose, and the order of when you lose and when you win determines where you end up. This is because you are contributing and withdrawing money from your portfolio over the course of your life. Consider the two examples below where one portfolio goes down 50% in the first year and then up 50% in the next year, and the other vice-versa. In each, we contribute $10 at the end of the first year:

As you can see, in one case the result is $90 and in the other case the result is $80, all because of the sequence of returns. Now, those are some big movements chosen for shock effect and easy math, but the same holds true if you went up 6% in one year and down 6% in the next. So, what we need is a way to take into account all possible sequences of wins/losses in the future, along with all our desired contributions and withdrawals.

Monte Carlo simulation is a powerful and flexible framework that allows us to take into account (1) all the possible sequences of returns in the future and (2) any sort of cash contribution/withdrawal pattern we choose. This gives us an understanding of how our plan might turn out and make decisions that are at least statistically informed. As you see, the answer is not as simple as “my portfolio will grow at an average of 6% per year.” Now that you know that there is actually a reason to run a complex calculation like Monte Carlo, let’s touch upon how it works.

The Heart of Monte Carlo

At the heart of Monte Carlo is a statistical engine that randomly moves your portfolio up or down each day in the future. When you string all the days together, it becomes one possible version of the future. Sometimes people say that the random movement is like “flipping a coin many times.” But, in reality, it is not, and I wish they would stop saying that. Flipping a coin is a completely random 50/50 event representing only two outcomes. The statistical engine that randomly moves the portfolio up and down is much more sophisticated. It chooses from many different potential returns. It could choose -0.15%, +1.02%, +2.44%, or some other number. But overall, the numbers it chooses conform to the expected return and expected volatility of the portfolio (think bell curve). That is to say that it will probably choose a smaller movement more often than a larger movement – depending on the volatility of the portfolio – and a positive return more often than a negative return – depending on the expected return of the portfolio.

Since we are moving the portfolio up and down each day, we can insert the cash contributions and withdrawals whenever we like. We can increase or decrease them as well. We can even simulate complex behavior, like contributing more in down markets and less in up markets, or panic selling if the market declines enough. In short, using this approach to constructing a possible future is extremely flexible. And, as an added benefit, the output is something that is intuitive and easy for people to understand: how much money the simulation predicts they might have at any given time in the future. You don’t need a lot of financial training to understand that.

Wash, Rinse, Repeat

But, as flexible as this simulation method might be, a single random potential future is completely useless since it is highly unlikely that that particular version of the future is what will happen. So, we save that version and repeat the process again. In fact, we repeat the process 10,000 times. Now we have 10,000 possible futures and there is a good chance that one of them will be close to the one that actually happens. And, by examining all of them, we can get a reasonably good idea of where we might end up, including what an “average” outcome looks like, as well as what a “bad” or “good” outcome might look like. That is a valuable set of data that can help guide our decision-making.

The glaring point of the above is that the number of times you simulate a possible future is extremely important. Unfortunately, running 10,000 simulations is computationally intense, so some people are tempted to run just a few hundred or even a few thousand simulations. However, with so few simulations, you may not have enough potential futures to make a reasonable estimate. In fact, you probably won’t even get the same answer each time you run your analysis because the simulations are random and you won’t have the Law of Large Numbers on your side.

For example, we ran three different Monte Carlo analyses, one with 250 simulated futures, one with 1,000, and one with 10,000.  We then re-ran the same analyses another 99 times to see if the values would change. The portfolio was a simple $100,000 portfolio of the S&P 500. For each analysis, we posed a simple question: “what is the percent likelihood that I will not outlive my assets.” In other words, what is the percent likelihood of not becoming destitute. For the 250-simulations group, the answer ranged from 65% to 86%, even though each analysis was using the exact same inputs. This inconsistency would be very difficult to explain to a client, in our opinion. At 1,000 simulations, the results were better, but the results still varied from 69% to 80% between runs. For many advisors, that is the difference between a failed plan and a successful one. Only at 10,000 simulations did we see the spread drop down to 2%, with re-runs coming in between 75% and 77%.

Performed correctly, Monte Carlo Analysis gives an advisor a powerful tool to forecast future savings into the future no matter what the sequence of returns, savings patterns, spending patterns, and goals. Possibly even more importantly, it gives advisors a way to show the trade-offs of different planning choices to clients in a way that they can understand: future savings balances. As the advisor/client conversation moves away from “just trust me” and toward collaboration, understanding, and validation, Monte Carlo analysis becomes an increasingly powerful tool in the advisor toolbox.