摘要：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.
