Don't use quotients to calculate performance

Quotients, ratios, are among the most applied tools for measuring performance of mutual funds and investment portfolios, the Jensen index being an exception to the general rule. In this paper, we show some problems that arise when quotients are applied, closely related to their statistical meaning, which is too often forgotten. We also raise some advantages of the use of linear penalization, introducing a little known methodology for performance measurement. With this purpose, this paper's approach is comprehensive: we conceptually analyze performance indexes' geometric and statistical meaning, complementing this with a numerical example and empirical testing that confirm our view. This paper's main contribution is to demonstrate and empirically test how the use of quotients to measure performance may create problems due to their denominators, which may be solved by applying linear penalization.