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Markowitz Portfolio Theory

  • Arlie O. Petters
  • Xiaoying Dong
Chapter
Part of the Springer Undergraduate Texts in Mathematics and Technology book series (SUMAT)

Abstract

We introduce Harry Markowitz’s mathematical model for how to distribute an initial capital across a collection of risky securities to create an efficient portfolio, namely, one with the least risk given an expected return and largest expected return given a level of portfolio risk. This chapter covers: the set up of the Markowitz portfolio model, which includes modeling security returns, the issue of multivariate normality, weights, short selling, portfolio return, portfolio risk, and portfolio log returns; two-security portfolio theory; the efficient frontier for N securities with and without short selling; the global minimum-variance portfolio, diversified portfolio, and Mutual Fund Theorem; utility functions and utility maximization; and diversification.

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Copyright information

© Arlie O. Petters and Xiaoying Dong 2016

Authors and Affiliations

  • Arlie O. Petters
    • 1
  • Xiaoying Dong
    • 1
  1. 1.Department of MathematicsDuke UniversityDurhamUSA

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