Mean-variance portfolio optimization based on ordinal information

Eranda Cela, Stephan Hafner, Roland Mestel*, Ulrich Pferschy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Article number105989
Number of pages19
JournalJournal of Banking and Finance
Publication statusPublished - Jan 2021


  • Black-Litterman model
  • Portfolio optimization
  • Qualitative views
  • Return estimation

ASJC Scopus subject areas

  • Control and Optimization
  • Economics and Econometrics
  • Finance

Fields of Expertise

  • Mobility & Production

Treatment code (Nähere Zuordnung)

  • Theoretical


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