# Monte Carlo Simulations: A Sophisticated Way to Predict Your Chance of Financial Success

If you hear Monte Carlo simulation and think of luxurious casinos, the Mediterranean, high stakes poker, and extreme wealth, you aren’t necessarily wrong, but no, that is not what we are talking about here.

Monte Carlo simulations actually have nothing to do with gambling. Though, like their namesake, they are related to your possible wealth. Specifically, they are a useful tool for predicting the possibility that you will enjoy a financially secure future.

## What is a Monte Carlo Simulation?

A Monte Carlo simulation is a mathematical technique used to predict the probability of different outcomes. It enables you to account for unknowns.

It is a way of identifying a full range of possible futures.

## What Can a Monte Carlo Analysis Tell You About Your Retirement?

A Monte Carlo simulation can be an important analysis tool. It can tell you your “chance of success” for any desired outcome. In financial planning, it is most commonly used to predict investment outcomes.

However, with regards to retirement, it can tell you how likely are you to be able to fund your retirement through your longevity.

See your personalized Monte Carlo analysis – for the probability of having enough money for retirement – in the NewRetirement Planner.

## Why Are Monte Carlo Simulations Important for Retirement Planning?

Building a financial forecast requires you to make guesses about things you have little or no control over that may happen in the future. These guesses are called assumptions. Assumptions are unknown factors that will impact your finances.

Some of the assumptions that will impact your future retirement finances include:

• Rates of return on savings and investments
• Cost of living increases
• Housing appreciation
• Medical cost inflation
• How long you live
• Future tax rates and income thresholds
• Whether or not you’ll require long term care or suffer a major medical event
• Growth rates for work income
• And more…

Monte Carlo simulations are a way of predicting the range of possible outcomes for these types of unknowns or assumptions.

## How Does Monte Carlo Work?

When you run a Monte Carlo analysis, a computer is doing thousands of calculations to predict a range of outcomes and determine what is:

• A worst case scenario
• A best case outcome
• Everything in between

The analysis involves taking each assumption and applying a range of values to each assumption in every time period. It calculates results for every possible value, including the possible variation for the assumption over time.

## Comparing Monte Carlo to Linear Compounding Analysis

### Linear Analysis for Compounding Rate of Return

Let’s say you want to predict the future value of a stock investment with compounding returns.

In most simple financial calculations, you might enter your initial account value and the predicted rate of return. The system will apply that rate to every month or year and show you the results in a linear projection.

A simple way to think about linear calculations: (Today’s balance x rate of return) + (Next year’s balance x rate of return) + (Following year’s balance x rate of return) = Outcome or Final Amount

The official formula is:

But, come on. That is not how things work in real life. The investment you are trying to predict will go up. It will go down. Sure, it is possible that it will grow at the same rate month over month and year over year, but that is highly unlikely. Spikes and dips in the stock price over time will impact your final outcome.

Simple compounding is not a terrible way of predicting the future. In fact, it can usually get you in the ballpark. But, it is a relatively simplistic way to determine outcomes.

### Monte Carlo Analysis for Compounding Rate of Return

With Monte Carlo analysis, instead of calculating a steady rate of return, the calculation takes a range of possible outcomes in every specified time period and runs every possible scenario.

The mathematical formulas are complex. However, here is a simple explanation of how a Monte Carlo calculation might be applied to determine a range of results for compounding rate of return:

• For the first time period, the analysis will return a range of results using 1) your starting balance, 2) a  range of rates of return (using your specified rate as a base) 3) a more discreet time period — months rather than years for example
• This calculation will return a relatively small range of possible outcomes. Let’s say there are 25 possibilities at the end of year one
• The formula is then applied to each of the 25 outcomes from year 1 for year 2, resulting in a greater range of possibilities that might happen in the second time period
• For every time period, the number of possible results continue to multiply
• A Monte Carlo simulation could involve thousands or tens of thousands of recalculations before it is complete

So, a Monte Carlo calculation predicting what will happen over 20 years will show a narrow range of results in the first year. However, as the calculation projects farther out, the range of results becomes greater. So, there is a far greater range of possibilities in year 20 than in year one.

## So, What Does the NewRetirement Monte Carlo Simulation Tell You About Your Future?

There are many different ways to define retirement success. And, the NewRetirement Planner offers many different analyses.

One measure is the probability that you have adequate savings to cover your expenses (beyond what is paid for with income from sources other than savings) through your (and your spouse’s) lifetime.

Here is the chart in the NewRetirement Planner that uses Monte Carlo simulations. It actually shows both linear and Monte Carlo projections:

In the chart, you can see your:

Linear Savings Projection (Projected Savings): The light green line at the top of the chart indicates your linear projection for your savings. It is based on your specified rates of return and your inflation projections. You generate the chart using your optimistic, pessimistic or an average of those rates. (Use the toggle under the “My Assumptions” dropdown found on the right hand side of the top navigation.)

Using a linear projection, the person represented in the chart above will have \$1.2 million in 2061 and adequate savings to fund retirement through their expected lifetime.

Downside risk (Poor Outcome): The dark line on the chart is generated with Monte Carlo simulations. We run multiple projections, randomly varying asset returns and inflation rates based on historical data and a normal distribution. We run 1,000 of these simulations and use the results to generate the probability of plan success.

The ‘Poor Outcome’ is indicated by the dark green line in chart. It represents the 10th percentile of these simulations. In other words, 90% of the simulations did as well or better.

Using Monte Carlo projections, the person represented in the chart above is at risk of running out of savings in 2061. If this happens, they will not be able to cover their expenses through their longevity.

Seeing success? If your plan consistently results in success, even across the varied Monte Carlo simulations, that’s great. You can rest easy. You may even be free to spend more money – just make sure your plan is set up correctly.

At risk of running out of money? If you find yourself with perhaps 20% or more of your Monte Carlo simulations resulting in running out of money prior to your longevity age, then explore ways to increase income, save more, or spend less. Evaluating debt and tapping your home equity are some of the other ways to bridge the gap. Get additional recommendations in the “Coach” and “Strengthen Your Plan” sections of the Planner.