Mean-Variance Portfolio Optimization Based on Ordinal Information

We propose a new approach that allows for incorporating qualitative views, such as ordering information, into estimates of future asset returns within the Black-Litterman model. We develop a mathematical framework and numerical computation methods for this setting. We find importance sampling to be the most appropriate numerical approach in terms of accuracy and computation time. Using empirical stock market data, we find our extended Black-Litterman model to process ordering information on future asset returns better than two previously suggested approaches. Our new estimator is successfully evaluated in the context of mean-variance portfolio optimization.