How Many Trials?

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The number of trials you should run in Monte Carlo simulations is related to the number of variables and the number of occurrences per trial.

Let’s look at an example. Assume you’re trying to determine the future value of a portfolio you will hold for five years. Assume also that there are no cash inflows or outflows to consider. Furthermore, assume the only variable in the analysis is the return on the portfolio. In this case the number of variables = 1 (the return), and the number of occurrences per trial = 5 (1 variable x 5 years). If you ran 100 trials you would have 500 total occurrences (1 variable x 5 years x 100 trials). Each time a trial is run the variable changes (randomly), not just in the first year but in each year it occurs. Since MCS selects numbers at random, it may select bad returns in the early years and good returns later, or the reverse may be true. In any event, each time a trial is run the ending portfolio value is changed. You’ll need to run a sufficient number of trials to assure you are modeling as many outcomes as possible. There is a point of diminishing returns, however. You’ll know you’ve reached this point whenever the additional numbers of trials yields little or no effect on the outcome (probabilities). In the above example, 250 to 500 trials may suffice.

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In the retirement example used earlier, let’s assume we identified 20 variables. If the time horizon we’re modeling is 30 years and we ran 1,000 trials, then there would be 600 occurrences per trial (20 variables x 30 years) and 600,000 total occurrences (600 occurrences per trial x 1,000 trials).

So how many trials should we run? Let’s say we increased our trials from 1,000 to 3,000 and the probabilities changed significantly, but at 5,000 trials there was little or no change. In this case, then, the ideal number of trials is probably somewhere between 3,000 and 5,000. It’s difficult to say with any certainty how many trials should be run. You’ll have to experiment with this on a case-by-case basis. A simple rule of thumb is that the more variables you include, the more trials you should run.

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