Question re: statistics and financial modelling

March 2, 2006 6:19 PM

Question about semi-sophisticated statistics and financial modeling - lets say you have N asset classes - each class has a mean rate of return and a standard deviation of returns. Also, assume you hold a portfolio comprised entirely of these N asset-classes, in certain proportions. How do you determine the probability that the portfolio might produce the a certain rate of return over P periods?
posted by stuehler to Work & Money (9 answers total)

I don't really know the answer, but I can tell you that you'll need to know more than the mean and standard deviation to get that kind of result. You'll need to decide more exactly what shape you want the distribution of returns to have, which if you're going for realism, may not be easy.

But assuming you have a way around that, you could just run a simulation. That'd be the easy way.
posted by sfenders at 6:58 PM on March 2, 2006

As sfenders says, you'll need to make some assumptions on the distribution of the data. If they're normal then it's easy - add up the means and add the variances. Then just use standard statistical theory and your normal tables to work out the probability that a certain return is produced. (Similar formulae for different distributions.)

If not then trickier. Simulation might be best.
posted by TrashyRambo at 7:41 PM on March 2, 2006

This would be complicated because the processes would probably be serially-correlated. You'd expect the return on asset class A in 2005 to be correlated with its return in 2004. So each year isn't independent, which will nuke most of the naive methods.

My first reaction, which probably isn't helpful, is just to simulate the living shit out of it to create a probability density of collective rates of return.
posted by ROU_Xenophobe at 8:06 PM on March 2, 2006

Or, if I could read the English language, what TrashyRambo said.
posted by ROU_Xenophobe at 8:06 PM on March 2, 2006

year over year returns should not be serially correlated. That said the right way to answer this question is using a Monte Carlo simulation.
posted by JPD at 8:50 PM on March 2, 2006

That's surprising. I would have guessed that good and bad years come in streaks. I'm not saying you're wrong, just that it's surprising.
posted by ROU_Xenophobe at 9:41 PM on March 2, 2006

You'll also probably want to model some correllation-- a program like CrystalBall can handle this.

ROU-- I think that good and bad years have come in streaks (moreso than would be expected by chance), but the EMH says that these streaks are just noise.
posted by Kwantsar at 3:48 AM on March 3, 2006

Of course, for your sim, you'd need (N^2-N)/2 pairs of correlations.
posted by Kwantsar at 3:49 AM on March 3, 2006

Many people think that good and bad years typically come in cycles of one kind or another.
posted by sfenders at 5:59 AM on March 3, 2006