Sharp, Sortino, Jensen's Alpha, M Squared

I know what the book says: I’m trying to go beyond the book here. Beta is the risk of a stock V/S the market. Sigma is the standard deviation of the returns. Why would SOR and JEN which are based on Beta be accounting for systematic risk only? Since Beta is the total risk of the stock shouldn’t SOR & JEN be accounting for total risk. Why is it that only a ratio based on s.d. accounts for total risk (systematic & unsystematic). Why is s.d. better than Beta?

beta is systematic risk measure… you need unsystematic risk added to that for TOTAL risk…

also, I assume by SOR you mean Sortino ratio which actually uses downside deviation not beta.