Name of Portfolio that maximizes Sharpe?

The one which touches the tangent line.

An infinte number of portfolio’s touch the tangent line , because on the eff. frontier you can construct an infinite number of tangents, one at each unique point of the eff frontier. Be more specific. Which of the several portfolio’s that lie on tangentsl to the eff. frontier has maximum sharpe ?

tangent at the Market Portfolio.

right on. The Market Portfolio has the highest Sharpe ( for non-leveraged portfolios, i.e. all portfolios that lie on the eff. frontier )

Just putting the sequence of things right … Idreesz is correct as well as CP … Tangent line has to be drawn from the Risk Free Rate point on Y axis. So, there can only be ONE tangent line from THAT point and not plenty as you understood it. And the portfolio on efficient frontier where tangent line meets the frontier IS the Market Portfolio. And such Market Portfolio would have maximum Sharpe Ratio.