FXP Stock Trading

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In these equations, the value SD A 2 can also be written as V or as (1.25 *M) "2.

This brings us to the point now where we can envision exactly what the relationships are. Notice that the last of these equations is the familiar Pythagorean Theorem: The hypotenuse of a right angle triangle squared equals the sum of the squares of its sides! But here the hypotenuse is A, and we want to maximize one of the legs, G.

In maximizing G, any increase in D (the dispersion leg, equal to SD or V A (1/2) or 1.25 * M) will require an increase in A to offset. When D equals zero, then A equals G, thus conforming to the misconstrued growth function TWR = (1 + R) A N. Actually when D equals zero, then A equals G per Equation (1.26).

So, in terms of their relative effect on G, we can state that an increase in A A 2 is equal to a decrease of the same amount in (1.25 * M) A 2.

To see this, consider when A goes from 1.1 to 1.2:

When A = 1.1, we are given an SD of .1. When A = 1.2, to get an equivalent G, SD must equal .4899 per Equation (1.27). Since M = .8 * SD, then M = .3919. If we square the values and take the difference, they are both equal to .23, as predicted by Equation (1.29). Consider the following:

Notice that in the previous example, where we started with lower dispersion values (SD or M), how much proportionally greater an increase was required to yield the same G. Thus we can state that the more you reduce your dispersion, the better, with each reduction providing greater and greater benefit. It is an exponential function, with a limit at the dispersion equal to zero, where G is then equal to A.

A trader who is trading on a fixed fractional basis wants to maximize G, not necessarily A. In maximizing G, the trader should realize that the standard deviation, SD, affects G in the same proportion as does A, per the Pythagorean Theorem! Thus, when the trader reduces the standard deviation (SD) of his or her trades, it is equivalent to an equal increase in the arithmetic average HPR (A), and vice versa!

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