Ambiguity When Performance Is Measured by the Securities Market Line

Imagine an idealized analog to the activities of professional money managers, a contest whose rules are as follows: (a) Each contestant selects a portfolio from a specified set of individual assets. (b) Returns are observed on the assets. (c) After each period of return observation, the portfolios are re-balanced to the initial selections. (d) After an interval consisting of several periods, "winners" and "losers" are declared for that interval. (e) Contestants choose a new portfolio, or keep the old one, and the process (b) through (d) is repeated. (f) After several intervals, consistent winners are declared to be superior port- folio managers and consistent losers are declared inferior. In the absence of any consistency, everyone is declared non-superior.