Comments on: Question re: statistics and financial modelling

Question: Question re: statistics and financial modelling

stuehler — Thu, 02 Mar 2006 18:19:05 -0800

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?

By: sfenders

sfenders — Thu, 02 Mar 2006 18:58:44 -0800

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.

By: TrashyRambo

TrashyRambo — Thu, 02 Mar 2006 19:41:45 -0800

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.

By: ROU_Xenophobe

ROU_Xenophobe — Thu, 02 Mar 2006 20:06:25 -0800

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.

By: ROU_Xenophobe

ROU_Xenophobe — Thu, 02 Mar 2006 20:06:53 -0800

Or, if I could read the English language, what TrashyRambo said.

By: JPD

JPD — Thu, 02 Mar 2006 20:50:29 -0800

year over year returns should not be serially correlated. That said the right way to answer this question is using a Monte Carlo simulation.

By: ROU_Xenophobe

ROU_Xenophobe — Thu, 02 Mar 2006 21:41:13 -0800

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.

By: Kwantsar

Kwantsar — Fri, 03 Mar 2006 03:48:05 -0800

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.

By: Kwantsar

Kwantsar — Fri, 03 Mar 2006 03:49:15 -0800

Of course, for your sim, you'd need (N^2-N)/2 pairs of correlations.

By: sfenders

sfenders — Fri, 03 Mar 2006 05:59:44 -0800

Many people think that good and bad years typically come in cycles of one kind or another.