TITLE:
Risk Return Relationship in the Portfolio Selection Models
AUTHORS:
Ken Hung, C. W. Yang, Yifan Zhao, Kuo-Hao Lee
KEYWORDS:
Arithmetic Mean, Geometric Mean, Golden Mean, Harmonic Mean, Marko-witz Risk Minimization, Sharpe’s Angle Maximization
JOURNAL NAME:
Theoretical Economics Letters,
Vol.8 No.3,
February
12,
2018
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 kvalues, 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.