Abstract: As known as well,every investor has his preferences for risk and return in his investing activity.In other words,every investor’s activity should abide by an utility of risk-return.Following classical economic analysis,an utility function is called an indifference curve(IDC),and it is developed showing the magnitude and form of the risk-return trade-off in a mean-variance framework.Every investor has a family of indifference curves to represent his preferences for risk and return.How do an investor decide an IDC on which his optimal portfolio lie?In this paper,we solve this problem by applying a geometric method.First,we denote the efficient frontier of Markowitz model with the weights vector of portfolio.Second,we denote the IDCs with the weights vector of portfolio.By the rule of efficient selection of portfolio,we’re thus able to find this IDC.

Key words: indifference curve(IDC), efficient frontier, portfolio