motivated by a conversation on Morningstar
So the suggestion (after looking carefully at data over the last umpteen years) is that the probability that a stock price will decrease after T years is roughly 1/T.
After 5 years, the probability that the stock price will decrease is (about) 20% ... and that's 1/5, expressed as a percentage.
After 10 years, the probability is (about) 10% and after ...
>Yeah, so is it true?
The calculations were based upon historical data, but I thought it'd be neat to see if good ol' Ito agreed.
>And what's the answer?
He's got this neat formula for the distribution of stock prices after T years, starting at a price Po,
assuming a Mean Return = r and Standard Deviation = s. See ?
Note that P(T) is the price at time T so the question is:
"What's the probability that P / Po < 1?"
'course, it'll depend upon our choice of r and s, but it's quite neat and ...
>A picture is worth a thousand ...
Here's a picture:
Here are some more pretty pics:
Note that, as T increases, one would expect the distribution of prices to be more widespread, more smeared,
more spread out, more ...
>More smeared? Is that a technical term?
It's sorta like this
For the chosen parameters, the Expected price gets bigger and the percentage of prices that lie below the starting price ... that gets smaller.
>And all this is guaranteed ... by the Math, right?
Guaranteed? Nothing is guaranteed!
>What about death and taxes?
Uh ... well, almost nothing is guaranteed.
>Okay, it's interesting to know what Ito says about losing money, but what about making money?
Good idea. Let's do that.
for Part II