Maximizing Compound Rate of Return vs Maximizing Sharpe ratio

A reader, Mr. A. Goldstein, made a very useful observation about my article "Maximizing Compound Rate of Return". In that article I argued that if your goal is to maximize the compound rate of return, you should maximize the quantity m – s²/2, where m is the short-term (1-period) rate of return, and s is its standard deviation. In general, this is not the same as maximizing the Sharpe ratio of a strategy. However, Mr. Goldstein pointed out that, if you also optimize the leverage of your strategy using Kelly's criterion, then maximizing Sharpe ratio does in fact maximize the compound rate of return also. This follows from a calculation in section 7 of Dr. Edward Thorpe's paper www.bjmath.com/bjmath/thorp/paper.htm.

Mr. Goldstein also suggested a beta arbitrage strategy which he has allowed me to share with my readers in a future post.