The 1/N investment strategy is optimal under high model ambiguity

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.

► We investigate risk optimal portfolios under ambiguous information about returns. ► Ambiguity is measured in a nonparametric way by the Kantorovich distance. ► As ambiguity rises, the portfolio decisions approach uniform portfolio weights. ► The results of the paper hold for most commonly used convex risk functionals.