Monte Carlo Simulation

CFA Level I
#1

Can someone explain the Monte Carlo Simulation

#2

A Monte Carlo simulation gives you the expected outcome of a situation. For example, let’s say we want to know the expected (average) value of a dice roll. Assuming that we have no knowledge of statistics, we could just roll the dice 10000 times, record each outcome, and take the average value of each outcome. A Monte Carlo simulation carries out this procedure through a computer program. This method is regularly applied in finance to calculate expected returns, probabilities of default, and other scenario outcomes.

#3

Just out of curiosity, Monte Carlo is just a term right? We can write any computer program that satisfy the purpose of Monte Carlo Simulation and call it a Monte Carlo Simulator? Thanks.

#4

Pretty much yes. I used this back during my internship at Morgan Stanley, and the massive number of trials was so PC intensive and would take so long that we could only run this overnight. We did this with portfolios of Mortgage Backed Securities and Emerging Market Bonds. Of course, this was back in 2006, so more often than not, our portfolios would generate a positive long-term return…

#5

OK thanks a lot …

#6

My current understanding of MCS is that you take a probability distribution, then sample it. But this should just get you approximately the exact same probability distribution as the one you originally had… so what’s the point of MCS?

From the example above, in order to roll a die 10000 times you would have to assume for example a uniform distribution, but then if you know the distribution, then you can easily calculate expectation?

I guess my question is kinda linked to historical simulation… I don’t see the difference between the two or why you even need either given that if you have a distribution, you can calculate the mean and the variance of them. So why bother sampling at all?

#7

It’s for modeling probability distributions that are difficult or impossible to describe analytically.

You’re correct: nobody would use Monte Carlo simulation to analyze the roll of a die.

But you might use Monte Carlo simulation to analyze the NPV of a project for which you are uncertain of many of the aspects:

  • What will demand for the product be in year 1, year 2, . . . year n?
  • What will the direct and indirect costs be in year 1, year 2, . . . year n?
  • What will the fixed and variable costs be in year 1, year 2, . . . year n?
  • What is the appropriate discount rate to use? Is it fixed or variable?
  • And so on

Unlike your die rolling example, here we’re not interested in the output for the specific probability distributions we choose for all of these random variables (except to the extent that we want to verify that we specified them correctly, and that the simulation is representing those distributions faithfully); we’re interested in the probability distribution of the output variable: the project’s NPV. We will then use that probability distribution to make a decision about whether to do the project or not.

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