Mean-variance portfolio optimization based on ordinal information

We propose a new approach to integrate qualitative views, in particular ordering relations among expected asset returns, in the well-known Black-Litterman (BL) framework. We assume investor views to be stochastic and adapt the BL-formula for the posterior expectation of asset returns, conditioned on ordering information. The new estimator is computed by applying an importance sampling technique. Using data from the EUROSTOXX 50 and the S&P 100, respectively, we empirically evaluate the forecast quality of our new approach in comparison to existing, but methodologically different, approaches from the literature and assess the performance of our model in a mean-variance portfolio context. We find that our approach mostly achieves the highest predictive power, irrespective of the dataset, the assumed level of accuracy of the ordering information, and mostly irrespective of the investor’s confidence in the qualitative view, even though the improvement resulting from our approach is moderate. We observe a similar behaviour in the context of portfolio performance analysis.