motivated by e-mail

Here's what we want to do:
  1. Download ten years worth of daily prices for some stock, say GE.
  2. Generate a distribution of daily returns, like Figure 1.
  3. Apply this distribution of returns to a fictitious stock whose current price is, say $10.
        This fictitious stock has nothing to do with GE stock.
        Its evolution in time just uses the GE return distribution.
  4. Pick a number of days into the future, say 30.
  5. Select 30 returns at random, from the return distribution (as in Fig. 1).
  6. See what happens to your $10 stock, after 30 days.
  7. Repeat steps 5 and 6 a jillion times and generate a probability distribution of prices, 30 days in the future.

Figure 1
>And that's exact?
Are you kidding? To be exact you'd need this.

It's an estimate of a future stock price assuming the historical return distribution of GE stock is relevant. Now that you have an estimate ...

>Is there a spreadsheet?
Yes. Patience!
Having an estimate of a future price such as Figure 2, you might use it to estimate the value of a stock option, for example. In Fig. 2, the red dot is the current price that you've entered.

Black-Scholes says:
Call Premium = S*NORMSDIST((LN(S/K)+(R+V^2/2)*T)/(V*SQRT(T)))
- K*EXP(-R*T)*NORMSDIST((LN(S/K)+(R+V^2/2)*T)/(V*SQRT(T))-V*SQRT(T))

Figure 2
The various parameters involved are explained here and ...

>And the spreadsheet?

>That's so confusing that ...
There's an Explain sheet which looks like this.
>What about that option stuff?
Yeah, it's there, too ... and looks like this:
You stick in the Strike Price etc. and it calculates the option premium (a la Black-Scholes).
You also get the probability of achieving some Wished-for Stock Price.

In Fig. 3, that's the Break-even stock price, namely Strike + Premium
... and the probability of achieving this in 30 days is 34.7%.

>And that's exact?
Of course! Would I lie to you?

Figure 3

for Part II