In this paper, we discuss measures of risk for uncertain outcomes of economic activity, which are based on the notion of the value of full information in stochastic programs. Information is measured in terms of σ-algebras. For multi-period income streams information is represented by filtrations, i.e. sequences of σ-algebras. The basic properties of our risk measures are multi-period coherence (“diversification decreases risk”), compound concavity (“random alternatives increase risk”) and convex monotonicity (“insurance decreases risk”).

The 1/N investment strategy, i.e. the strategy to split one’s wealth uniformly between the available investment possibilities, recently received plenty of attention in the literature. In this paper, we demonstrate that the uniform investment strategy is rational in situations where an agent is faced with a sufficiently high degree of model uncertainty in the form of ambiguous loss distributions. More specifically, we use a classical risk minimization framework to show that, for a broad class of risk measures, as the uncertainty concerning the probabilistic model increases, the optimal decisions tend to the uniform investment strategy. To illustrate the theoretical results of the paper, we investigate the Markowitz portfolio selection model as well as Conditional Value-at-Risk minimization with ambiguous loss distributions. Subsequently, we set up a numerical study using real market data to demonstrate the convergence of optimal portfolio decisions to the uniform investment strategy.