### Monte Carlo Simulations: An Overview

I have pieced together what I think is an overview of what to know about a Monte Carlo simulation. These have become quite a popular tool for financial planners to gauge how well your portfolio and your financial decisions will do over time. One of the best things about the Monte Carlo Simulation is that it does not take the market average and assume, let's say, an 8% return over time. Instead, it tests your portfolio and financial decisions against a 1,000 or more hypothetical returns on what the market has historically done. Therefore, in the simulation you may see years of downturn in your return with the upside prevalent as well. This helps an investor to stay focused and understand that the market is not always going up, but you can plan your decisions and portfolio so that over the long run your returns will be just fine.

To be more in depth, most people when they estimate what their portfolio will do over time build an Excel spreadsheet to project the results and make assumptions about how each part of the portfolio will perform.

For example, let's say there is $100,000 to invest and the assumption that the asset classes will produce the following annualized returns:

Stocks 9%

Bonds 5%

Cash Equivalents 2%

Now let's assume that the allocation is:

Stocks 70%

Bonds 20%

Cash Equivalents 10%

If all the investments follow exactly this pattern for ten years, the portfolio would then be worth $213,722, for an annualized return of 7.89%.

This sounds realistic. But for in-depth planning purposes is really only one of a wide range of possibilities. In real life, stocks often return much more or much less than 9% a year. Bonds and cash equivalents also fluctuate, however they are usually less dramatic.

So there could be wide variations around this deceptively specific estimate. But how wide? How good, or bad, could it reasonably get?

Imagine a bad, but by no means impossible, scenario: over those ten years, stocks lose 5% a year, bonds lose 2% a year, and cash equivalents are flat. Then the $100,000 stake would be down to $68,253, for an annualized return of -3.75%.

In a good, but not extreme scenario, stocks gain 12% a year, bonds gain 6% a year, and cash equivalents gain 3% a year. The $100,000 would have grown to $266,665, for an annualized 10.31%.

Reality will probably be somewhere in between, but this is not a given. And how can you quantify the chance that your stake will reach a point that will get you to your investment goals?

A Monte Carlo simulation provides the answer. This estimation technique allows for the wide range of possible percentage changes in each asset classâ€”and, therefore, the even wider range of possible portfolio values over your time horizon. Using thousands of scenarios, Monte Carlo simulation charts the relative likelihood of portfolio values. This enables a person to estimate the probability of reaching their goals. It should not be the only piece of financial planning, but is an important part of the overall picture.

To be more in depth, most people when they estimate what their portfolio will do over time build an Excel spreadsheet to project the results and make assumptions about how each part of the portfolio will perform.

For example, let's say there is $100,000 to invest and the assumption that the asset classes will produce the following annualized returns:

Stocks 9%

Bonds 5%

Cash Equivalents 2%

Now let's assume that the allocation is:

Stocks 70%

Bonds 20%

Cash Equivalents 10%

If all the investments follow exactly this pattern for ten years, the portfolio would then be worth $213,722, for an annualized return of 7.89%.

This sounds realistic. But for in-depth planning purposes is really only one of a wide range of possibilities. In real life, stocks often return much more or much less than 9% a year. Bonds and cash equivalents also fluctuate, however they are usually less dramatic.

So there could be wide variations around this deceptively specific estimate. But how wide? How good, or bad, could it reasonably get?

Imagine a bad, but by no means impossible, scenario: over those ten years, stocks lose 5% a year, bonds lose 2% a year, and cash equivalents are flat. Then the $100,000 stake would be down to $68,253, for an annualized return of -3.75%.

In a good, but not extreme scenario, stocks gain 12% a year, bonds gain 6% a year, and cash equivalents gain 3% a year. The $100,000 would have grown to $266,665, for an annualized 10.31%.

Reality will probably be somewhere in between, but this is not a given. And how can you quantify the chance that your stake will reach a point that will get you to your investment goals?

A Monte Carlo simulation provides the answer. This estimation technique allows for the wide range of possible percentage changes in each asset classâ€”and, therefore, the even wider range of possible portfolio values over your time horizon. Using thousands of scenarios, Monte Carlo simulation charts the relative likelihood of portfolio values. This enables a person to estimate the probability of reaching their goals. It should not be the only piece of financial planning, but is an important part of the overall picture.

## 6 Comments:

Concise and understandable enough to help me take my spreadsheet to the next level. Thanks.

So it seems Monte Carlo simulations apply statistics to an excel-based portfolio estimation?

Any good sites that offer online Monte Carlo portfolio analysis?

-Ken

So the next question is, how do we perform Monte Carlo simulations on our own porfolios?

banking guy and anon 2, I will get back to you on that. When I was originally writing this post, I did not find anything, but will do some more digging. I know there is a way to build this into an excel sheet and will definitely be exploring this option more in depth. On another note, a lot of investment firms are providing this for free (trying to generate accounts by offering this service).

Typically monte carlo simulations use a random process to select data from a probability distribution (for example portfolio returns) to build a series of probabilistic outcomes. Lots of assumptions are involved (for instance the assumption that stock returns have normal distributions). Still useful in financial planning if you understand the limitations, but typically NOT based on actual historical return patterns (for example in a recession, or in an economic expansion).

I ran across this discussion. My firm provides a Monte Carlo tool for personal portfolio management that is based in EXCEL. We have a bunch of papers on this topic at www.quantext.com. Financial Engines.com is a Monte Carlo tool online but it is not a full Monte Carlo--it assigns funds to specific asset classes and just simulates a few classes.

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