Simple Construction of the Efficient Frontier

Abstract

We provide simple methods of constructing known results. At the core of our methods is the identification of a simple concise basis that spans the Capital Market Line (CML). We show that a portfolio whose risky assets weights are the product of the inverse variance-covariance matrix of (nonredundant) security rates of return times the vector of the excess expected rates of return over the risk-free rate is a CML portfolio. This portfolio and the risk-free security span the CML. In addition, with this basis, there is immediate construction of the efficient frontier of risky assets (the hyperbola), tangency portfolios, reflection portfolios, and a CAPM relationship. Our method is quick and simple. It is easy to derive, teach, implement, interpret, and remember.

Keywords: Portfolio frontier, efficient frontier, capital market line, asset pricing

JEL Classification: G10, G11, G12