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Simple Construction of the Efficient Frontier

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  • David Feldman
  • Haim Reisman

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.

Suggested Citation

  • David Feldman & Haim Reisman, 2003. "Simple Construction of the Efficient Frontier," European Financial Management, European Financial Management Association, vol. 9(2), pages 251-259, June.
    • Handle: RePEc:bla:eufman:v:9:y:2003:i:2:p:251-259
    DOI: 10.1111/1468-036X.00218
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    Cited by:

    1. Maria Teresa Medeiros Garcia & Daniel Alexandre Bourdain Santos Borrego, 2018. "Calculating the Efficient Frontier for the Portuguese Stock Market," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 24(4), pages 339-349, November.
    2. Ukhov, Andrey D., 2006. "Expanding the frontier one asset at a time," Finance Research Letters, Elsevier, vol. 3(3), pages 194-206, September.
    3. Rambaud, Salvador Cruz & Pérez, José García & Sánchez Granero, Miguel Ángel & Trinidad Segovia, Juan Evangelista, 2009. "Markowitz's model with Euclidean vector spaces," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1245-1248, August.
    4. Mihir Dash, 2018. "Modelling the Efficient Frontier: An Empirical Study in the Indian Stock Market," Journal of Applied Management and Investments, Department of Business Administration and Corporate Security, International Humanitarian University, vol. 7(2), pages 83-94, May.
    5. Teresa Garcia & Daniel Borrego, 2017. "Markowitz Efficient Frontier And Capital Market Line – Evidence From The Portuguese Stock Market," Portuguese Journal of Management Studies, ISEG, Universidade de Lisboa, vol. 22(1), pages 3-23.
    6. Bick, Avi, 2004. "The mathematics of the portfolio frontier: a geometry-based approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(2), pages 337-361, May.

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