Playing the odds - Monte Carlo Simulation

Monte Carlo simulation was original a pathetical theory used to predict the probability of random movement of molecules. The theory was simply that if you knew the standard deviation from an outcome of an event, that you could properly calculate the probability of that outcome by repeatedly generating a result from a random number based on that standard deviation. In its most simplest term, the standard deviation (SD) defines the window of outcomes from which to generate the random number and the associated probability of each number.
For example when throwing a pair of dice you know the outcome is between 2-12 (the window of outcomes), you also know that there is no difference between throwing a 1 or a 6, so all you need to do is randomly generating numbers of 1 – 6 for each dice. Over a period of randomly generating throws, you will be able to determine the probability of getting a total of 2. We know mathematically the outcome is once every 36 times. By random generation however, it may take thousands of throws to get that average. For example if you got 2 twice in a 36 throws (one more than you should), you might think it’s 1 in 18. However over 360 throws you may get a number like 12 which is closer to the 1 in 36 you would expect. However after 3600 throws you may get closer to the 1 - 36 you expect because even if you are over or under by one or two throws, the sheer number will make that a small impact, for example 101 out of 3600 is very close to the real probability of 1 in 36. This same principle was applied to modern day investment vehicles with as it appears now poor results. This was almost predictable for many reasons. First the window of outcomes and the standard deviation.

Unlike a pair of dice which have defined outcomes, investment gains/loses are almost infinite and the SD can’t be accurate calculated because we have limited history on the probability of each of those returns since we have only 60 years of returns from mature investment markets. And an additional problem is if you would need 3600 throw to get a good idea of the out of something with only 36 possible outcomes, how many random generation would you need for something with many more times the possible outcome. With dice you know the chance of a 1 is 1 in 6. With an investment you cant accurate know the probability of a 5% return simply because we haven’t had enough years to determine the correct SD. And without an accurate SD, this exercise will generate a worthless number. If you ran a Monte Carlos simulation ten yars ago the chances of a negative return would be near 0 if not 0. However that is what we currently have, an S&P 500 having a negative return. So today if you run a Monte Carlos simulation you will get a measurable possibility of a negative return in the next 10 years. If the prediction 10 years ago was wrong, why would the prediction now be right.
Mainstream financial planning media from the Wall Street Journal to FinancialAdvisorMagazine.com are now picking up on the flaws. Here is hoping advisors return to the fundamental principles of financial planning and move past the need to give certainty to the uncertain.

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