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Risk Return Relationship in the Portfolio Selection Models
Texas A & M International University, Laredo, TX, USA
Clarion University of Pennsylvania, Clarion, PA, USA
Clarion University of Pennsylvania, Clarion, PA, USA
Department of Finance, Zeigler College of Business, Bloomsburg University of Pennsylvania, Bloomsburg, PA, USA
- 1 Texas A & M International University, Laredo, TX, USA
- 2 Clarion University of Pennsylvania, Clarion, PA, USA
- 3 Clarion University of Pennsylvania, Clarion, PA, USA
- 4 Department of Finance, Zeigler College of Business, Bloomsburg University of Pennsylvania, Bloomsburg, PA, USA
Theoretical Economics Letters·Volume 08 (2018)·Pages 358–366·Published 7 February 2018·DOI10.4236/tel.2018.83025
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Abstract
In this paper, we calculate four different kinds of means —AM, GM, HM, and GDM—to investigate the risk-return contour using Markowitz risk minimization and Sharpe’s angle maximization models. For a given value (target portfolio return), the rank order of risk or variance-covariance ( υ ) can change. In the vertical segment of an efficient frontier curve, we observed v(GDM) > v(HM) > v(GM) > v(AM). At higher k values, the rank changes to v(GDM) > v(HM) > v(AM) > v(GM). That is to say, ranking a portfolio using different kinds of means may well give different rankings depending on what k value one is evaluating. It is also shown the harmonic mean should not be used in the case of a small negative growth rate in stock prices.
KeywordsArithmetic MeanGeometric MeanGolden MeanHarmonic MeanMarko-witz Risk MinimizationSharpe’s Angle Maximization
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