J. Stevens

The Efficient Market, Debugged

I find the opening to your piece somewhat fanciful, however what really popped out at me is your description of the Kelly Criterion (i.e., Optimal-f). This is incorrect.

The Kelly formula is often expressed as: ((g+1)*p-1)/g

Where, g = the ratio of the amount gained when there is a gain, over the amount lost when there is a loss; and p = probability of a gain.

While I’ve never seen anyone else break this down before, this is simply the mathematical equivalent of: M/ag

Where M = the mean return; and ag = the average gain when there is a gain.

Your description on the other hand, (expected return - risk-free rate) / variance, sounds more like a description of the Sharpe Ratio, where variance would be the standard deviation of returns (not SD squared, which is how you have it illustrated in your formula (“s2”).