Predicting the Future ... maybe
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Having gazed for some time at historical stock performance, what are the chances that you could use that info to predict the future evolution of your portfolio?

>I'd say zero. Am I right?
Yes, but you can guess ... and there are lots of way to do that:

  • Calculate the Mean and Standard Deviation of historical returns and, armed with those two numbers, construct a Normal Distribution.
  • Calculate the Mean and Standard Deviation of historical returns and, armed with those two numbers, construct a Logormal Distribution.
  • Calculate the Mean, Standard Deviation and perhaps other characteristics of historical returns and, armed with those numbers, construct some other sexy Distribution.
  • Use the actual historical returns and select them at random a la Monte Carlo (or some other sexy ritual).
  • Use Ito's Magic Formula and ...
>Ito's what?
If you assume a lognormal distribution (using historical Mean and Standard Deviation) you can try Ito's Formula:
The (lognormal) distribution of Prices P at time T years in the future is:

where
P is the price T years in the future
Po is the current price
r is Mean Return
s is Standard Deviation

Shape of the "density" distribution

>If I have that "density" distribution, how do I use it?
You'll probably want to generate the "cumulative" distribution which will give you the probablility that your stock will attain a certain price, T years from now.
It looks like this:
Of course, it'll change with T
... and r and s:
>Okay, start with Ito's Density and generate a Cumulative ... but how?
Read all about it.
>And that'll give me a peek into the future?
It'll give you some numbers. That should make you happy, but predicting the future? Don't count on it!

Of course, sticking a Mean and Standard Deviation into some formula will give a smooooth curve.
If you generate a Cumulative Distrubution from actual historical returns, it won't be quite as elegant.
For example, here's the cumulative distribution for monthly GE returns over a 10-year period:

It gives the probability that a future monthly return will be less than something.
In the chart, it suggests that there's a 60% probability that you'll get less than a 2% monthly return.

>And that's guaranteed?
Probabilities are always guaranteed.
If you don't get 2% I just say: "Too bad. You were in that other 40%".

 
 

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