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Monte Carlo Analysis

December 03, 2012

When you sit down with a financial professional toupdate your retirement plan, you're likely to encountera Monte Carlo simulation, a financial forecastingmethod that has become popular in the last fewyears. Monte Carlo financial simulations project andillustrate the probability that you'll reach your financialgoals, and can help you make better-informedinvestment decisions.

Estimating investment returnsAll financial forecasts must account for variables likeinflation rates and investment returns. The catch isthat these variables have to be estimated, and theestimate used is critical to a forecast's results. Forexample, a forecast that assumes stocks will earn anaverage of 4% each year for the next 20 years willdiffer significantly from a forecast that assumes anaverage annual return of 8% over the same period.

Estimating investment returns is particularly difficult.For example, the volatility of stock returns makesshort-term projections almost meaningless. Multiplefactors influence investment returns, including eventssuch as natural disasters and terrorist attacks, whichare unpredictable. So, it's important to understandhow different forecasting methods handle thisinherent uncertainty.

Basic forecasting methodsStraight-line forecasting methods assume a constantvalue for the projection period. For example, astraight-line forecast might show that a portfolio worth$116,000 today would have a future value ofapproximately $250,000 if the portfolio grows by anannual compounded return of 8% for the next 10years. This projection is helpful, but it has a flaw: Inthe real world, returns aren't typically that consistentfrom year to year.

Forecasting methods that utilize "scenarios" provide arange of possible outcomes. Continuing with the10-year example above, a "best-case scenario" mightassume that your portfolio will grow by an average12% annual return and reach $360,000. The

"most-likely scenario" might assume an 8% return (fora $250,000 value), and the "worst-case scenario"might use 4%, resulting in a final value of roughly$171,000. Scenarios give you a better idea of therange of possible outcomes. However, they aren'tvery precise in estimating the likelihood of anyspecific result.

Forecasts that use Monte Carlo analysis are basedon computer-generated simulations. You may befamiliar with simulations in other areas; for example,local weather forecasts are typically based on acomputer analysis of national and regional weatherdata. Similarly, Monte Carlo financial simulations relyon computer models to replicate the behavior ofeconomic variables, financial markets, and differentinvestment asset classes.

Why is a Monte Carlo simulationuseful?In contrast to more basic forecasting methods, aMonte Carlo simulation explicitly accounts forvolatility, especially the volatility of investment returns.It enables you to see the spectrum of thousands ofpossible outcomes, taking into account not only themany variables involved, but also the range ofpotential values for each of those variables.

By attempting to replicate the uncertainty of the realworld, a Monte Carlo simulation can actually providea detailed illustration of how likely it is that a giveninvestment strategy will meet your needs. Forexample, when it comes to retirement planning, aMonte Carlo simulation can help you answer specificquestions, such as:

• Given a certain set of assumptions, what is theprobability that you will run out of funds before age85?

• If that probability is unacceptably high, how muchadditional money would you need to invest eachyear to decrease the probability to 10%?

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Prepared by Broadridge Investor Communication Solutions, Inc. Copyright 2012

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The mechanics of a Monte CarlosimulationA Monte Carlo simulation typically involves hundredsor thousands of individual forecasts or "iterations,"based on data that you provide (e.g., your portfolio,timeframes, and financial goals). Each iteration drawsa result based on the historical performance of eachinvestment class included in the simulation.

Each asset class--small-cap stocks, corporate bonds,etc.--has an average (or mean) return for a givenperiod. Standard deviation measures the statisticalvariation of the returns of that asset class around itsaverage for that period. A higher standard deviationimplies greater volatility. The returns for stocks have ahigher standard deviation than the returns for U.S.Treasury bonds, for instance.

There are various types of Monte Carlo methods, buteach generates a forecast that reflects varyingpatterns of returns. Software modeling stock returns,for example, might produce a series of annual returnssuch as the following: Year 1: -7%; Year 2: -9%; Year3: +16%, and so on. For a 10-year projection, aMonte Carlo simulation will produce a series of 10randomly generated returns--one for each year in theforecast. A separate series of random returns isgenerated for each iteration in the simulation andmultiple combined iterations are considered asimulation. A graph of a Monte Carlo simulation mightappear as a series of statistical "bands" around acalculated average.

Example: Let's say a Monte Carlo simulationperforms 1,000 iterations using your currentretirement assumptions and investment strategy. Ofthose 1,000 iterations, 600 indicate that yourassumptions will result in a successful outcome; 400iterations indicate you will fall short of your goal. Thesimulation suggests you have a 60% chance ofmeeting your goal.

Pros and cons of Monte CarloA Monte Carlo simulation illustrates how your futurefinances might look based on the assumptions youprovide. Though a projection might show a very highprobability that you'll achieve your financial goals, itcan't guarantee that outcome. However, a MonteCarlo simulation can illustrate how changes to yourplan can affect your odds of achieving your goals.Combined with periodic progress reviews and planupdates, Monte Carlo forecasts can help you makebetter-informed investment decisions.

Important: The projections or other informationgenerated by Monte Carlo analysis tools regardingthe likelihood of various investment outcomes arehypothetical in nature, do not reflect actual investmentresults, and are not guarantees of future results.Results may vary with each use and over time.

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