# Using Monte Carlo Simulations in Financial Plans

As part of our financial planning process, we like to “stress test” a client's plan. One of the tools we use is a Monte Carlo simulation. When coordinated with traditional straight-line financial planning projections, thoughtful tax planning and our “hurdle rate” calculations, Monte Carlo simulations help us compare different retirement planning options or scenarios to help project and illustrate which alternatives will have the highest probability of success (as defined as our client’s reaching financial goals). The Monte Carlo is a tool that can help us help our clients make better and more informed retirement and investment planning decisions.

## Estimating Investment Returns

All financial forecasts must account for variables like inflation rates, market volatility and investment returns. The “catch” is that these variables have to be estimated and the estimate used is key to a forecast's results. For example, a forecast that assumes stocks will earn an average of 4% each year for the next 20 years will differ significantly from a forecast that assumes an average annual return of 8% over the same period. (For more, see: Monte Carlo Simulation: The Basics.)

Estimating investment returns is particularly tricky. For example, the volatility of stock returns can make short-term projections almost meaningless. Multiple factors influence investment returns, including unpredictable events such as natural disasters, global political events and terrorist attacks. So, it's important to understand how different forecasting handle uncertainty.

## Basic Forecasting Methods

Straight-line forecasting methods assume a constant value for the projection period. For example, a straight-line forecast might show that a portfolio worth \$125,000 today would have a future value of approximately \$250,000 if the portfolio grows by an annual compounded return of 8% for the next nine years (a doubling per the rule of 72).

This projection is helpful but it has a flaw. In the real world, returns aren't typically that consistent from year to year. One example of this is that your retirement results may turn out very different if your retirement starts out in a bear market (like in 2000 or 2008). This is the “sequence of returns risk” that I discussed in an article called Afraid of Retiring into a Bear Market? Tips to Hedge Bets.

Forecasting methods that utilize scenarios provide a range of possible outcomes. Continuing with the nine year example above, a "best-case scenario" might assume that your portfolio will grow by an average 10% annual return and reach almost \$210,000. The "most-likely scenario" might assume an 6% return (for a \$250,000 value) and the "worst-case scenario" might use 4%, resulting in roughly \$177,000. Scenarios give you a better idea of the range of possible outcomes. However, they aren't precise in estimating the likelihood of any specific result.

Forecasts that use Monte Carlo analysis are based on computer-generated simulations that try to replicate the behavior of economic variables, financial markets and different portfolio allocations.

## Why Is a Monte Carlo Simulation Useful?

In contrast to straight-line projections discussed above, a Monte Carlo simulation is designed to account for volatility, especially the volatility of investment returns. It enables you to see a series of thousands of possible outcomes, taking into account not only the many variables involved, but also the range of potential values for each of those variables.

By attempting to replicate the uncertainty of the real world, a Monte Carlo simulation can provide a detailed illustration of how likely it is that a given investment strategy might meet your needs. For example, when it comes to retirement planning, a Monte Carlo simulation can help you answer specific questions, such as:

• Given a certain set of assumptions, what is the probability that you will run out of funds before life expectancy (longevity risk)?
• If that probability is unacceptably high, how much additional money would you need to invest each year to decrease the probability to 10%?
• Given my resources and hurdle rate, will I be better off if I have a more aggressive portfolio allocation versus a more conservative portfolio allocation?

## The Mechanics of a Monte Carlo Simulation

A Monte Carlo simulation typically involves hundreds or thousands of individual forecasts or "iterations" based on data that you provide (e.g., your portfolio, time frames and financial goals). Each result is based on the historical performance of each investment class included in the simulation. (For more from this author, see: Planning for Retirement the R.I.T.E. Way.)

Each investment in your portfolio tends to have a return for a given period. Standard deviation measures the volatility of the returns of that asset class around its average for that period. As an example, the returns for stocks have a higher standard deviation than the returns for U.S. Treasury bonds in most timeframes.

There are various types of Monte Carlo methods, but each generates a forecast that reflects varying patterns of returns. For example, the modeling of stock returns could produce a series of annual returns such as: year one: -10%; year two: -5%; year three: +16%, and so on.

For projections to life expectancy, a Monte Carlo simulation will produce a series of randomly generated returns to produce each series represented in each forecast. A separate series of random returns is generated for each iteration in the simulation and multiple combined iterations are considered a simulation. Many times, Monte Carlo results are shown as a graph over the time period of your life expectancy shown as a series of statistical "bands" around a calculated average or from higher to lower probabilities or even as just a “percentage success” number (such as 90% success rate).

## Pros and Cons of Monte Carlo

A Monte Carlo simulation illustrates how your future finances might look based on the assumptions you provide. Though a projection might show a very high probability that you may reach your financial goals, it can't guarantee that outcome. However, a Monte Carlo simulation can illustrate how changes to your plan could affect your odds of achieving your goals.

In my opinion, the probability of success number (say 90% success) in an individual outcome is not what is overly important, but rather you should focus on whether one scenario has a higher probability of success than another alternative. That is the true value of a Monte Carlo analysis. When combined with periodic progress reviews and plan updates, a Monte Carlo forecast is a great tool that helps financial planners guide clients into making better and more informed financial planning decisions. (For more from this author, see: Avoid Money Worries With Proper Planning - Part 1.)