A.I.M. Users Bulletin Board

[Qarel]

Hi Toofuzzy, no, Price/High = Cash is not equivalent to Low/Price = Stock. The easy way to show this is to refer you to your own High=10, Low=2, Price=3 example, but I am going to bore you:

We have
1) L/P = S (my rule of thumb)
2) P/H = C (your version)
With S and C as fractions (f.i. S=.7 and C=.3)
We also have
3) S+C = 1 (Stock+Cash is the whole of one investment)
Which is equivalent to
4) C = 1-S
We could plug this into 2) and get
5) P/H = 1-S
Now we add 1) and 5)
6) L/P + P/H = (S + 1 - S =) 1
The S's cancel out! Now let's give the fractions on the left the same denominator:
7) L*H/P*H + P*P/P*H = 1
Multiply with P*H to get rid of the stupid fractions
8) L*H + P*P = P*H
Bring P*H to the left side and write P*P as P^2
9) P^2 - H*P + L*H = 0

Now 9) looks an awful lot like the general quadratic equation:
10) a*x^2 + b*x + c = 0
with P for x, a = 1, H for b and L*H for c. Now 10) does have at most two solutions for x, for any a, b, and c, so 9) also has at most 2 solutions for Price, for any combination of Low and High. That means that 1) and 2) are only equivalent for a maximum of 2 prices given any combination of High and Low, and not for any price, which was what you supposed.

Toofuzzy?

Karel