Will Trice said:

You're right, I didn't mean to imply that Mandelbrot is the only one

saying this.

Oh okay; I figured this was just a post-O, but I wanted to double-check.

He just seems to be jumping up and down about it at the

moment. The interesting thing for me is that if the market is

sufficiently fat-tailed, then the variance of market prices cannot be

You mean variance of market price _changes_, right? For the newbies...

calculated, and thus correlations cannot be calculated. Since

mathematical approaches to asset allocation revolve around the

correlation between assets, this has interesting ramifications for

financial planning.

But, as you know, not all mathematical approaches use a Gaussian model. The

Trinity study, for example, argues for diversity using the simple facts of

actual bond and stock returns of the last 50 years or so. Its conclusion:

Have X% in stocks, Y% in bonds, and you'll do better than having all of one

or the other. That is, assuming the future somewhat resembles the past,

anyway. The study is not about explicit mathematical correlation (or lack

thereof), yet it nonetheless supports the notion that an investor should

seek a balance of seemingly uncorrelated vehicles for investing, to optimize

return.

I was trying to get a better grip on the underlying assumptions of some of

the free online portfolio allocators I have been exploring. Some definitely,

simply rely on actual historical returns, albeit sampled over different

periods. Some, like T Rowe Price's, appear to be using at least in part

Gaussian models.

Indeed, even GARCH is sensitive to big events.

Robert Engle said that the inclusion (or not) of the 1987 crash makes a

huge difference in the choice of model parameters.

Two points occur to me that I think are important, both academically and

practically:

1.

Every site I've seen that discusses how a Gaussian distribution does not

reasonably foresee a crash like 1987's also insists that, therefore, insofar

as being able to plan financially, the sky is falling. They do not appear to

discuss the effect of the market circuit breakers put into place after and

because of 1987's crash. IMO, if the academic discussion is to have any real

value, then this is no small oversight. I presume the design of these market

"circuit breakers" was not undertaken lightly. Some serious financial and

mathematical (and probably psychological) thought must have went into them.

(Maybe I'm wrong and they were simple though; someone can google.) Other

steps are always being taken (e.g. laws have been passed, or lawsuits

brought) that have increased the pressure on markets and the companies who

make them up that go towards minimizing wild fluctuations. With some

exceptions, I would wager this is the general trend, anyway. The Enron

debacle, for example, has led to new measures. It seems to me that it's

really outrageous (and maybe even embarrassing) that Mandelbrot adherents

use the one-day 1987 crash to bolster their argument against ever using

(log-)normal distributions to model stock market price changes. I'd still be

interested in a measure of how likely the market weeks after 9/11/2001 were,

according to a Gaussian distribution analysis.

2.

The above realities remind me of what Skip posted (again?) recently about

the difficulty of predicting regulatory changes and their impact on

investing and so financial planning.

An interesting question in and of itself is the choice of data one uses.

Other than availability of more data points, why would one choose

daily over monthly? If daily is better than monthly, is hourly better

than daily? Is minutely better than hourly?

I agree these are good questions.

I am a little bothered by the fact that, the longer the interval, the more

important from _where_ within each interval one starts measuring return. I'm

sure there's a simple answer to this. And it's model specific...

I am also leery about getting sucked into the numerology of some of this.

How valid is it to assume any particular pattern of stock price changes in

the past will continue into the future? Stock price changes are not a result

of, say, biological phenomenon, where AFAIC it is more reasonable to assume

certain patterns will re-occur. Stock price changes are a result of economic

"principles," which so often do not rely on science per se but rather on

human and sociological behavior.

Thanks to all for the discussion so far, it has been interesting (for me

at least)

Likewise, though I realize you've been looking at these models longer than I

have.