## Monte Carlo Simulation – why do we use it?

Investments and financial planning must deal with an uncertain and unknowable future; therefore it frequently involves efforts to “model” the future. Given certain investment decisions, how likely is it that a particular investment strategy will succeed in reaching the goals set for that portfolio?  For example, will a portfolio provide enough retirement income to last a lifetime?  Or will expected investment results pay for a grandchild’s education?

What is a Monte Carlo Simulation?

One way to analyze these issues is by using a Monte Carlo simulation. From a theoretical perspective, a Monte Carlo simulation is a method of estimating the probable outcome of an event in which one or more of the variables affecting the outcome are chosen randomly.  The heart of the Monte Carlo process is to simulate an event many times.  During each simulation the variables are allowed to fluctuate according to a pre-selected range for the variable.  The outcome of each simulation is then ranked according to the likelihood of its occurrence.

As a very simple example, how often would an individual player win at the card game Solitaire…..the Monte Carlo approach would have the player play 100 times, or more, and then record the results. The number of successful plays becomes the probability of winning.

Monte Carlo applied to Financial Planning and Investments

In the investment world, a Monte Carlo simulation is helpful to an investor in understanding the role risk plays in portfolio selection and design. Investing does involve risk, including the possible loss of principal.

For example, rates of return for stocks, bonds, and other investments will vary from year to year. Depending on the historical time frame chosen, a particular investment will have good years and bad years.  From this historical data it is possible to calculate the highs, lows, and average returns for the investment.  The analysis will also determine how widely the annual rates of return varied from the average, resulting in a distribution of probable rates of return around the average.

To estimate the return that a particular investment or portfolio could achieve over a future time period, a Monte Carlo simulation randomly generates a rate of return for each year in the analysis, based on the historical distribution of probable rates of return. More complex simulations will include inflation on spending, distributions, and income tax rates.  This process is repeated numerous times, sometimes thousands of times, until complete.  The result of each simulation is ranked by percentiles.  In the case of a retirement analysis, success would be measured by having enough money to last until the expected mortality.  Failure would be running out of money early too many times in the simulation.

The Monte Carlo can be helpful in portfolio design in that several scenarios can be run comparing outcomes using different risk levels associated with different portfolio mixes. It should lend some perspective to what risk could be posed by various investment strategies.  At Washington Trust Bank we strive to put this analysis to use for our Wealth Management & Advisory Services clientele.

Limitations of Monte Carlo

All hypothetical projections of future investment results should be regarded as only approximations or a best guess as to what the future might bring. Although a carefully constructed Monte Carlo simulation can compare one risk level to another and show potential risks and rewards, it should not be regarded as predictive or a guarantee of the future by any means.  When addressing any investment or financial planning question the guidance of a trained and experienced professional is strongly recommended.

Footnote: The name “Monte Carlo” derives from a code name given to this type of analysis by scientists working on nuclear weapons projects in the 1940’s.