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Monday, May 21, 2012

Monte Carlo Analyses - Useful or Not?

Financial planning is challenging because of the number of unknowns.  We reach a point where we aren't generating a career-type paycheck, from which date we need to generate an income.  We don't know how long we need to generate an income, the rate of inflation, or what market performance will be.

We can start by making point assumptions on the unknowns.  We can assume we'll live to be 100, inflation will average 3%, and our investments will earn 7%.  Then, given the desired income and our income sources, we can see whether our plan will succeed.  As we think about this, we realize that it is way too simplistic.  One important observation is that sequence of market returns and inflation are important.

An "elegant" way around this problem is to carry out a Monte Carlo analysis where many paths are generated for inflation and market returns.  Then, of the paths generated, we can get a percent of success determination (I hesitate to use the term "probability" because we are using a sampling technique - it is not exactly like flipping a coin which is, in fact, a probability).

I put elegant in quotations because, like many things mathematical, a Monte Carlo analysis can project a greater degree of determination than is actually obtained.  As such, it has the potential to be abused by  practitioners to present an aura of expertise.
Suppose 80% of the paths succeed?  What does this tell us?  Is it good practice to report to a client that his plan will "fail" 20% of the time?  Does it require more elaboration?  To put it bluntly - does a Monte Carlo analysis with an 80% success ratio mean that 20% of the time the client will end up eating dog food?  Is the client hearing what we are trying to convey?

This issue has been examined by Michael Kitces in Do Our Brains Really Even Know How To Evaluate A Monte Carlo Analysis? on his blog Nerd's Eye View.  Michael is perhaps the brightest young financial planner in the country, and his blog is a must-read for those interested in the cutting edge of financial planning research.

My own take is that Monte Carlo analysis is valuable at higher rates of failure.  For example, if the failure rate is 60%, you probably need to work longer, save at a greater rate, or draw down a smaller income stream.  On the other hand, if the failure rate is 20%, then examining flexibility issues comes into play.  Can the client cut down on spending for a few years to get back on a successful path?

The good part of all this, I think, is that it gets the planner and the client to focus on the dynamic nature of the process.  Financial plans need to be revisited.

I think we may even have to take a step back and reconsider what we mean by "success."  "Success" is defined as "not eating dog food" in the Monte Carlo results.  Many clients, however, define
success as dying broke.  The client who ends up with $4 million in the analysis is a "success" but not so according to his or her goals.  The real success metric may be the percentage of paths leaving a client with $100,000 or less.

For those interested in an easy-to-use program based on  Monte Carlo simulations, I recommend the T. Rowe Price Retirement Calculator.  It is free and straightforward.  Use it at least annually.


  1. Well, first of all there has been very few examples where investment reached 7% a year during last 20 years.
    Inflation has been raging as well well above 3%.

    But the article your quoted is definitely worth reading. I think the Monte Carlo analysis is indicative and as such is a good tool.

    However, the reality is that for the most of us retirement is a gamble, as we still counting on return and low inflation...

    1. Actually a well diversified portfolio returned approximately 9%/year over the past 20 years. Look at this link:
      Note that 13 of the 20 years were above 7%. This covers through 2010. Diversified portfolio was up last year and is up this year as well.
      I think 7% is conservative. Furthermore I'm not sure what the alternative is. CDs are around 1-2% and money markets are practically zero.
      I have to disagree with you on this one. I don't see investing in the global markets as a gamble. I'm typing his on a product that the whole world wants to own and wasn't available at the start of the 20 year period we're talking about! I want to participate in that kind of innovation.

  2. S&P 500 in 1991 was about 336 in 2011 it was about 1300.
    So the annual increase is about 7%.

    However in 2001 is was about 1000, while not it is 1300, so 300 is up. Or 30%, with inflation of 3% a year ...people actually actually lost money if not for dividends.

    And this is just a begging. With current monetary policies we will see inflation raging from next year. It will help the government to pay of the debt but it will wash out a lot of people hard work..

    1. If you are saying that stocks are headed lower and inflation higher over the near term then there are actually investments you can make that will make a killing in a scenario like that!
      Check out QID and TBT. I don't recommend them because I'm not sure what will happen next year. Still...I'm just saying.