Registered: May 2009
02-27-12 12:28 AM
A couple of problems here. Equation 2.1 here is correct for determining an optimal fraction, but on the top of page 3, he tries to express it in terms of the sum of natural logs -- the two are NOT equivalent except in what I call the "special case" which is frequently seen in gambling and rarely in trading (for example, a short position is never a candidate for the special case. Similarly, any forex transaction can never be a candidate for the special case, nor can any spread transaction. By extension, those which are members of the special case, actually are themselves members of the non-special case by virtue of the fact that every transaction is, in effect, a spread transaction). Thus, for the second form of this to yield and optimal "fraction" is virtually impossible, and it is the second form of this that is the expression of the Kelly Criterion. So once again there is the false presumption that the Kelly Criterion solution results in the expected geometric growth optimal fraction of ones capital to bet asymptotically. It simply is not true.
That aside, his conclusion is interesting and very interestingly developed. I would say though, that it, as with everything looking at optimal growth fractions, misses the mark in that it assumes one's criterion is to maximize asymptotic expected geometric growth. Knowing where the peak of the curve is, as well as the nature of the curve itself -- it's important geometrical nuances, and the acceptance of the inescapable fact that we are somewhere on this curve, and likely moving about it from holding period to holding period, allows us the luxury of now seeking out algorithmic paths along this curve to satisfy other criteria. -Ralph Vince