If you’re like most planners, at one time or another you’ve found it difficult to explain Monte Carlo Simulation in a way that a client can understand and accept. Monte Carlo has become mainstream, clients are asking questions, and it’s great to have good answers. I’ll try to clearly and simply explain what it is, its purpose, why it’s useful, and how Money Tree’s Monte Carlo simulations really work.
 
Monte Carlo Simulation is a way to model and emulate future behavior of a complex system under variable conditions we cannot accurately predict. That is to say, it’s a whole series of experiments trying to find out what might happen in the future under conditions that mimic the real world. We don’t know what the future will really be like, but if we try enough ‘realistic’ experiments, we can understand how a financial plan will work in a whole range of potential futures. This is a really great way to test plans, and a very clear means of explaining that the future is unpredictable and quite variable.

In one of Money Tree’s normal retirement projections, rates of return are assumed to be stable year by year. Maybe the rates change at retirement, to recognize the change of investor behavior at the end of the working years. These average rates of return are used to grow the various accounts, assuming investments perform at their averages each year. This normal retirement projection uses annual estimated portfolio rates of return and inflation rates to project asset growth and use.

This traditional technique to create financial projections is an excellent procedure to make smooth, easy to explain examples of what a family’s financial future might look like. As long as everyone understands that it shows the average, or middle case, then it’s a great projection and a solid basis for good planning and decision-making. But it’s simplicity fails to show clients the whole range of what really might happen, and doesn’t do an adequate job of helping clients understand the upside and downside of the variability in financial markets. Using probability and random numbers, Monte Carlo Simulation shows a bigger picture.
 
Monte Carlo introduces random volatility into the annual rate of return assumptions within each retirement projection. The projection is run over and over again, ten thousand times. In all the projection’s calculations, the return for each year is changed, so the results are all different, while the rates of return average out right.

The whole collection of results from these computations is used to illustrate the trends and potential range of future outcomes. This allows you to discuss a percentage of success for the individual’s retirement plan, in the form of a probability percentage. For example, the Monte Carlo simulation may show that your client has a 62% probability of having money at their life expectancy under one plan, and 78% under another.
 
Money Tree Software’s Monte Carlo process takes into consideration all the investments, distributions, expenses, and taxes of the individual client’s normal projection while running the Simulation. The complete richness of our full financial planning model is incorporated into the Monte Carlo process.
 
A standard deviation value is used to control the magnitude of the random changes in each projection’s annual rate as it is varied each year above or below the average rate of return for the client’s investments.

If your client’s estimated standard deviation is 5 and his estimated rate of return is expected to be 7%, then 95% of the random rates of return will fall within 7% plus or minus two standard deviations (10%), a range of -3% to 17%. Most of the results fall close to the average, 67% will be within 2% to 12%. Some returns will be outside two standard deviations, returns worse than –3% and greater than 17% can and will occur in the model as well as real life, but are infrequent. Upside and downside is limited to five standard deviations, in this case limited to a very infrequent –18% and an equally infrequent 32%.
 
These statistics and technical explanations can be confusing and a little intimidating to a client that doesn’t really understand or care about statistical analysis. For most people, it’s far easier to explain Monte Carlo as a series of tests for the financial plan, to see how it performs in various potential financial futures. We don’t know what the future will bring, so we make a thousand reasonably calculated guesses, and try out their plan in each one. This gives us a good picture of what the overall range and scope is likely to be.
 
If they have ever seen a weather forecast, then they can understand the Monte Carlo results. If there were an 80% chance of sunshine for the weekend, you would feel pretty comfortable in planning a picnic at the local park. However, if the weatherman were predicting a 40% chance of sunshine over the weekend, then you would probably be better off spending the weekend reading a book or playing monopoly with the family.
 
The same holds true for Monte Carlo probability projections. If the results show an 80% success ratio for having enough money to make it to the end of life expectancy, then your client can feel pretty comfortable with the financial plan you have provided him. If there is only a 40% success rate of making it to the end of life expectancy with their current financial plan, then your client is going to need to make some changes in their retirement strategy.

If someone’s plan attains a 65% success ratio under their current assumption, 76% success if they retire two years later, and 82% success if they save an additional $3,000 per year, then you and your client can evaluate the plans’ relative performance and value using terms and examples that are consistent and understandable.
 
Ultimately, Monte Carlo is not predicting the future, but is a good way to understand a projection’s behavior and evaluate financial plans under the real world stresses of volatile financial conditions. More importantly, it is a very powerful way of comparing and discussing modifications of individual financial plans.