The Sharpe ratio is defined as return/risk, generally as mean(ret)/sd(ret), where ret represents the data set of returns of an investment. However, I have seen other ratios that I also like. What I tend to do is filter stocks by Sharpe ratio, and then filter the top 100 stocks through another filter for the sortino ratio, or the omega ratio. This seems to prefer one ratio over another though.
What if I mixed the Sharpe ratio and the Sortino ratio together? Why not maximize the Sharpe(ret)*Sortino(ret)? What does this mean?
If the answer is yes, then why not just take a bunch of ways of understanding return, such as mean, an average growth factor, and multiply them. Then risk could be the multiplication of standard deviation, maximum drawdown, average drawdown, downside deviation, etc? It seems like maximizing (ABCD)/(EF*G) is a method of optimizing a portfolio while attending to many ratios and factors instead of one at a time.