Once upon a time I ran across a discussion, in
Randomness in the Stock Market. I got to thinking ...
... that, although the future evolution of the market (or a particular stock)
isn't predictable with any degree of accuracy, one doesn't expect every future is
equally likely. Some futures are more likely than others.
Exactly! Yet a weather prediction which is off by a few degrees is quite likely.
Anyway, I suspect it's reasonable to consider that markets have a certain degree of uncertainty which may be large ... or small. Just like the weather. A forecast which gives tomorrow's time of sunrise, say 5:24 AM, has little uncertainty. A forecast which says that tomorrow's DOW will increase by 200 points has a much larger uncertainty. Suppose we consider a stock which grows, monthly at a fixed, deterministic rate of 1.2% plus a random, hence unpredictable, rate. Is the future evolution random?
>Are you saying that the S&P 500 has a predictable component?
I'm saying that there's a degree of uncertainty associated with the S&P 500, but the past
fifteen years can be generated as a combination of a deterministic component
plus a random component. However ...
Good question. However, I can promise you that, whatever it is, it can be generated
as a combination of a deterministic component plus a random component.
No, but ...
No, I don't think so. It just has a certain degree of uncertainty. By deterministic, I
mean that we can determine this component, from historical precedent. It's like
predicting the weather next week. We look at historical weather patterns and make a
determination. Then we guesstimate the random component, trying to reduce the degree of uncertainty
associated with this component by looking at weather patterns elsewhere, prevailing winds, jet stream activity,
price/earnings ratios, if the Feds meet that week, quarterly earnings reports, etc..
Well, I have a better chance of estimating the random component in the short term.
Fifteen years is a long time and the best we can do is look at historical precedent
and use that to extrapolate. That'd give us a deterministic component. The random component
depends upon so many things that we cannot know. Besides, even
my deterministic component may not agree with yours, but I suspect we'll both make a
determination which involves a higher market value fifteen years from now.
Yes. That's the significance of the word deterministic, from the philisophical idea of
determinism, that man's
actions are determined by antecedent causes ...
I hold to the view that the principles which govern our behaviour, and, indeed, the behaviour of the physical world, are partly deterministic, partly random. Newton's Laws of Motion, for example, have a small random/unpredictable component. They've served us in good stead for hundreds of years, yet we cannot guarantee that they define the future evolution of the universe. Indeed, Einstein generated a different set of Laws. Each can be used as a deterministic component to predict the future ... and each has an associated unpredictable component. Each is based upon the observed, antecedent - or prior - behaviour of the world, and each is used to predict future events with, hopefully, a small random error.
Have you ever heard of
Heisenberg's Uncertainty Principle?
It doesn't matter. In any case it should not
deter us from trying to estimate the deterministic component. For example, if we knew the past
history of a comet, Sir Isaac Newton would have said that the entire future path of the
comet is deterministic. Heisenberg would disagree. There's always uncertainty.
A completely deterministic philosophy would say that man has no free will. All actions
have been programmed. All future events are pre-determined, by certain incontrovertible
Laws. However, if we accept the idea that the future is at least partly random
and is governed by Laws which are only partly deterministic, then we can choose to act
this way or that ...
Why do we think the sun will rise at, say, 5:24 AM?
But that doesn't guarantee that the prediction for tomorrow will be accurate. It just says
that it's been that way for eons, so we expect it to be that way tomorrow.
The degree of uncertainty is small. How do we know that? Because prior predictions have been
It's like the markets.
For years it's been growing, over the long term, so we have some confidence in saying it'll
grow in the future ...
Yes, long term. Of course, that's no guarantee that ...
Of course, but even the equations are based upon examining the past behaviour ... and they've
been accurate in the past, with a small error, so ...
Right, yet ...
Very little uncertainty there, because ...
Right, but that's no guarantee that ...
There's always uncertainty, but the degree of uncertainty is small, like tomorrow's sunrise.
>You said it's a real stock ...
Okay, here's the same scheme for "the market".
>Hmmm ... even the degree of uncertainty is ... uh ...
>How does the simulation compare to a deterministic evolution ...?
The deterministic graph uses a fixed annual return (based upon precedent) whereas the Monte Carlo simulations use a random selection of returns (selected from a log-Normal distribution), but ...
>Looks like the simulations sorta fluctuate about the deterministic.
Sure. Just Right-Click on the picture, above, then Save the file (not the picture!) to download a .ZIPd copy. Note: it has macros.