motivated by a discussion on xltraders
Suppose we have some stock or option or mutual fund and we want to see how quickly it achieves some target price.
Assume the current price of the asset is Po. Example: Po = $57.60
We'd like to (eventually) reach a target price of TP. Example: TP = $60.00
The price would then have to travel a distance of TP - Po. Example: TP - Po = $2.40
Suppose that, after t days, the price is P(t). Example: P(3) = 58.45
Then the price has travelled a distance of P(t) - Po. Example: P(3) - Po = $0.85
As a fraction of the distance required to achieve our target price, that's X(t) = (P(t) -Po) / (TP-Po)
Example: X(3) = (0.85) / (2.40) = 0.35 or 35%
Now, we'd like to see how rapidly our asset price is moving, in the direction of the target price, so ...
>So that's the velocity: V = dX/dt, right?
Well, our t-values don't change continously. They're t = 0, 1, 2, etc., so we consider:
V(t) = (X(t) - X(t-1) ) / (t - (t-1)) = X(t) - X(t-1).
Now the graph of X(t) = (P(t) -Po) / (TP-Po) looks just like the price graph P(t)
(except for some rescaling) as shown in Figure 1.
So V(t) = X(t) - X(t-1) is just (P(t) -P(t-1)) / (TP-Po) is just the velocity associated with the price-graph
(except for some rescaling).
That's shown in Figure 2.
>Upper velocity and lower velocity?
Them's just some level lines to see how you're doin'.
>So how come that velocity is sometimes negative, sometimes positive?
When the price increases the velocity is positive and when it decreases the velocity is negative.
There's a spreadsheet to play with ... just click on the picture;
Here's some more pretty pictures:
>So we're talkin' stock prices, eh?
Well, if we were talking options, then this "velocity" would be related to
>And it's useful?
Useful to whom?