Piecewise linear risk function and portfolio optimization

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 transactions can be incorporated without making the problem intractable. Third, it enables two distributions to be distinguished with the same first and second moment but with different third moment. Fourth, the capital-market line can be generated and CAPM type equilibrium relations derived. The piecewise linear risk model was compared with the quadratic risk model using historical data of Tokyo Stock Market, whose results partly support the claims stated above.