Optimalf 119
FIGURE 4.2 Asymmetrical leverage
A 20% loss requires a 25% gain afterwards to recoup. A 30% loss requires
a 42% gain afterwards to recoup. This is asymmetrical leverage. In fixed
fractional trading we have seen that the trader will tend to have on more
contracts when she takes a loss than when she has a win. This is what
amplifies the asymmetrical leverage. It is also what curves theffunction,
since the peak of theffunction represents that point where the trader has
the right amount of contracts on to go into the losses and come out of the
losses (with asymmetrical leverage) and achieve the maximum growth on
her money at the end of a sequence of trades (see Figure 4.2). Thefvalue
(X axis) that corresponds to the peak of thisfcurve will be known as the
optimalf(fis always in lowercase).
Sofis a curved-line function, and this is due, in part, to the fact that
asymmetrical leverage is amplified when reinvesting profits.
And how do we find this optimalf? Much work has been done in recent
decades on this topic in the gambling community, the most famous and
accurate of which is known as the Kelly Betting System. This is actually
an application of a mathematical idea developed in early 1956 by John L.
Kelly, Jr., and published in the July 1956Bell System Technical Journal.^3
(^3) Kelly, J. L., Jr., “A New Interpretation of Information Rate,”Bell System Technical
Journal, pp. 917–926, July 1956.