PIECEWISE LINEAR RISK FUNCTION AND PORTFOLIO OPTIMIZATION

Abstract

A new portfolio optimization model using a piecewise linear risk function is proposed. This model is similar to, but has several advantages over the classical Markowitz's quadratic risk model. First, it is much easier to generate an optimal portfolio since the problem to be solved is a linear program instead of a quadratic program. Second, integer constraints associated with real transaction can be incorporated without making the problem intractable. Third, it enables us to distinguish two distributions with the same first and second moment but with different third moment. Fourth, we can generate the capital-market line and derive CAPM type equilibrium relations. We compared the piecewise linear risk model with the quadratic risk model using historical data of Tokyo Stock Market, whose results partly support the claims stated above.