# MONTE CARLO SIMULATION

Can some please explain this model to me, am lost on the concept even after sevral readings on it, i want to know what the concept is all about and steps in constructing a monte carlo simulation. thanks

Let me give you an example of what we sometimes do at work that I believe would qualify as a Monte Carlo simulation: (I would assume this is a pretty common thing as it is not terribly complicated - keep in mind this is done in the context of evaluating a clients current asset allocation) We plug risk and return assumptions of various asset classes (US Equity, INTL Equity, High Yield, Hedge Funds, Fixed Income, etc) into the software, then input some ranges/restrictions for the allocation of each asset class, sample: US Equity 30-80% INTL Equity 10-30% Core Fixed 15-30% High Yield 0-10% Hedge 0-7% etc. The software runs a bunch of scenarios and the end result is what is called the efficient frontier where the model spits out say 5 potential asset class mixes that maximize your risk/reward profile. What we find is some clients can reduce risk, while maintaining the same expected return (say by adding hedge funds), or keep the same risk while increasing their expected return. Or, sometimes they are already on the efficient frontier and a change to the risk profile would not lead to a better portfolio. (i.e. increase risk, but expected return would fall) Now, whether or not this is particularly insightful is another question entirely as it is only as good as the assumptions (garbage in, garbage out), but I don’t want to drone on uneccessarily so I will stop here and if you have questions or want clarification, ask away.

Its always nice to read something smart. Good work Paul, that was insightful. Good way to refresh my memory.

Hmm. I dunno. If you are generating an efficient frontier from assumptions about the return distributions of each of those asset classes, there isn’t much reason to do a Monte Carlo simulation. Give me means and variances (and not even any more distributional assumptions than that) and I’ll give you every point on the efficient frontier analytically. Just because there is a randomness in a process doesn’t make it Monte Carlo. Monte Carlo usually means that we generate random paths for securities and then calculate something desired from the path. Usually this is something too complicated to solve analytically. For example, Monte Carlo VaR is often calculated by (say) modelling each security in a portfolio individually so that they each depend on 10 different factors. We have (say) 500 securities in the portfolio and since they are all dependent on some subset of these factors they are all correlated. Finding the return distribution analytically is just not tractable - in theory you might be able to do it, but it involves calculating each correlation, doing transformations, etc. Too much work. Instead, I just decide on distributions for each factor (e.g., they are each lognormal with 0 drift and variance given by the historical variance over the last 6 weeks and some correlations between the factors). Then I let my computer generate paths for each factor according to my distributions. I reprice each security according to the path. Then I reprice the entire portfolio. Then I do this 5 bazillion times. My 95% Monte Carlo Var will be some number so that 95% of the portfolios performed at least this well in my sample.

I agree with Joey on this one. We use MC extensively. We are into valuation and risk management. We use MC for example to generate paths when evaluating OAS for example. (Just think about the probability tree that is part of the curriculum someplace)

Thanks Emra, though my glory seems to have been short lived… Just when I thought I was actually adding something to the board! Upon re-reading the book and with Joey and Nodoubt’s explanation, I can see that what I described could fall outside the definition of a Monte Carlo simulation. So, what is the key disqualifier? Is it because a Monte Carlo sim must, by definition, do the random generation of variables (stock price, interest rates, etc) on its own, whereas in my example the user actually defines the risk and return factor and nothing is really left to randomness? Is that the key distinction that I missed? (Too bad I am going to be offline for the next several days and cannot continue this conversation.)

I use MC to simulate stock prices. just need a good vlookup and the countif and the rand function. what you describe is EF and optimal portfolio modeling, that is not MC per se. but good thread!!!

I think you have it now Chi Paul. You are definitely adding something to the board, even if I thought your response was a little off the mark. Everyone here (including me for sure) says off the mark stuff and then it gets corrected by the process. That’s good stuff and helps everyone learn things.