Rationalization of investment preference criteria

Jacques Pézier

Abstract

ABSTRACT

The majority of risk-reward or risk-adjusted performance measures currently in use (eg, the Treynor ratio, the α / β ratio, the Omega index, expected return over value at-risk, "coherent" preference criteria, etc/ are incompatible with any sensible utility function and are therefore unreliable, except possibly in limited circumstances.We argue instead for the use of an intuitive and essential criterion: the maximum certainty equivalent excess return (CER*). A proper assessment of a CER*
should take into account the availability of alternative investments, the return forecasts and the risk attitude of the investor.We explain the assessment of CER*
and give three applications: performance comparison among traditional and alternative funds, optimal design of structured products and explanation of the credit risk premium puzzle. We also suggest that CER*
or equivalent criteria such as generalized Sharpe ratios and generalized information ratios should be used for public reporting of fund performance and could serve as a basis for the design of executive incentive schemes.