Informationless Trading and Biases in Performance Measurement: Inefficiency of the Sharpe Ratio, Treynor Ratio, Jensen’s Alpha, the Information Ratio and DEA-Based Performance Measures and Related Measures

The Sharpe Ratio, Conditional Sharpe Ratio , Conditional Treynor Ratio , Treynor Ratio, Jensen’s Alpha , Appraisal Ratio , Sortino and Van der Meer Ratio (1991), Sortino, Van der Meer and Plantinga (1999) Ratio , Information Ratio , DEA-based Methods and the Henriksson-Merton market timing measure are all based on the Mean–Variance (“M-V”) Framework and are hereafter referred to as the “M-V Performance Measures.” This chapter explains why the M-V Performance Measures are grossly inaccurate and inefficient. The M-V Performance Measures have been theoretically and empirically shown to be inaccurate and unrealistic, primarily because returns cannot be accurately characterized by any mixture of distributions over time, and because Standard Deviations (SD) and returns are not sufficient to accurately define investors’ preferences. Value at Risk (VaR) and Expected Shortfall were addressed in Nwogugu (2005) and Nwogugu ( Applied Mathematics and Computation, 185 (1), 178–196).