Constructing the Best Trading Strategy: A New General Framework
  We introduce a new general framework for constructing the best trading strategy for a given historical indicator. We construct the unique trading strategy with the highest expected return. This optimal strategy may be implemented directly, or its expected return may be used as a benchmark to evaluate how far away from the optimal other proposed strategies for the given indicators are. Separately, we also construct the unique trading strategy with the highest information ratio. In the normal case, when the traded security return is near zero, and for reasonable correlations, the performance differences are economically insignificant. However, when the correlation approaches one, the trading strategy with the highest expected return approaches its maximum information ratio of 1.32 while the trading strategy with the highest information ratio goes to infinity. 
Philip Z. Maymin and Zakhar G. Maymin
q-fin.PM