The paper proposes an innovative framework for characterizing investors' behavior in portfolio selection. The approach is based on the realistic perspective of unknown investors' utility and incomplete information on returns distribution. Using a four-moment generalization of the Chebyshev inequality, an intuitive risk measure, risk horizon, is introduced with reference to the speed of convergence of a portfolio's mean return to its expectation. Empirical implementation provides evidence on the consistency of the approach with standard portfolio criteria such as, among others, the Sharpe ratio, a shortfall probability decay-rate optimization and a general class of flexible three-parameter utility functions.