Abstract: The majority of risk adjusted performance measures (RAPM) currently in use - e.g., Treynor ratio, (?/?)) ratio, Omega index, RoVaR, 'coherent' preference criteria, etc. - are incompat- ible with any sensible utility function and would be best avoided. We argue instead for the assessment of a maximum certainty equivalent excess return (CER*) criterion, or equivalent criteria, adapted to investment circumstances: alternative investments, return forecasts, and risk attitude. We explain the assessment of CER*s and give three applications: performance comparisons among traditional and alternative funds, optimal design of structured products, and explanation of the credit risk premium puzzle.