Does finding Optimal-Kelly for a portfolio (irregardless of the any leverage considerations) also give you the best Sharpe Ratio?

So this is actually trivial and does not require calculus although one could do it with calculus, no doubt.

Kelly attempts to maximize growth which is given by:

g = risk free rate + (Sharpe ratio ^2)/2

When you succeed in finding optimal Kelly then you maximize g. Because of this simple formula it is obvious you are maximizing the Sharpe ratio when you maximize g (both being positive numbers and monotonically increasing).

This seems conclusive but troubling. All those years where Markowitz and Thorp debated the value (or lack of value) of the Kelly- criterion this connection was missed?

Oh well, ChatGPT 4 finally got it. I don’t see how it could be wrong within the relatively simple assumptions of the derivation of g in this formula (the usual Gaussian distribution etc)

This is not just an academic exercise for me. Portfolio Visualizer has some limitations in building a portfolio. I think there are some better ways that are not that hard mathematically, it seems. Several ways it seems now. That would be for another post, I think.

Jim