Asset allocation with multiple analysts’ views: a robust approach

  • I-Chen Lu
  • Kai-Hong Tee
  • Baibing LiEmail author
Original Article


Retail investors often make decisions based on professional analysts’ investment recommendations. Although these recommendations contain up-to-date financial information, they are usually expressed in sophisticated but vague forms. In addition, the quality differs from analyst to analyst and recommendations may even be mutually conflicting. This paper addresses these issues by extending the Black–Litterman (BL) method and developing a multi-analyst portfolio selection method, balanced against any over-optimistic forecasts. Our methods accommodate analysts’ ambiguous investment recommendations and the heterogeneity of data from disparate sources. We prove the validity of our model, using an empirical analysis of around 1000 daily financial newsletters collected from two top 10 Taiwanese brokerage firms over a 2-year period. We conclude that analysts’ views contribute to the investment allocation process and enhance the portfolio performance. We confirm that the degree of investors’ confidence in these views influences the portfolio outcome, thus extending the idea of the BL model and improving the practicality of robust optimisation.


Analysts’ recommendation Black–Litterman model Fuzzy logic Portfolio selection Robust optimisation 

JEL Classification




  1. Aastveit, K.A., F. Ravazzolo, and H.K. Van Dijk. 2018. Combined density nowcasting in an uncertain economic environment. Journal of Business & Economic Statistics 36 (1): 131–145.Google Scholar
  2. Bartkowiak, M., and A. Rutkowska. 2017. Black–Litterman model with multiple experts’ linguistic Views. In Soft Methods for Data Science, 35–43. Cham: Springer.Google Scholar
  3. Becker, F., M. Gürtler, and M. Hibbeln. 2015. Markowitz versus Michaud: Portfolio optimization strategies reconsidered. The European Journal of Finance 21 (4): 269–291.Google Scholar
  4. Ben-Tal, A., and A. Nemirovski. 1998. Robust convex optimization. Mathematics of Operations Research 23 (4): 769–805.Google Scholar
  5. Bertsimas, D., V. Gupta, and I.C. Paschalidis. 2012. Inverse optimization: A new perspective on the Black–Litterman model. Operations Research 60 (6): 1389–1403.Google Scholar
  6. Black, F., and R.B. Litterman. 1991. Asset allocation: Combining investor views with market equilibrium. The Journal of Fixed Income 1 (2): 7–18.Google Scholar
  7. Black, F., and R. Litterman. 1992. Global portfolio optimization. Financial Analysts Journal 48 (5): 28–43.Google Scholar
  8. Blasco, N., P. Corredor, and E. Ferrer. 2018. Analysts herding: When does sentiment matter? Applied Economics 50 (51): 5495–5509.Google Scholar
  9. Carlsson, C., and R. Fuller. 2001. On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets and Systems 122 (2): 315–326.Google Scholar
  10. Carlsson, C., and R. Fuller. 2002. A possibilistic approach to selecting portfolios with highest utility score. Fuzzy Sets and Systems 131 (1): 13–21.Google Scholar
  11. Chopra, V.K., and W.T. Ziemba. 1993. The effect of errors in means, variances, and covariances on optimal portfolio choice. Journal of Portfolio Management 19 (2): 6–11.Google Scholar
  12. de Jong, M. 2018. Portfolio optimisation in an uncertain world. Journal of Asset Management 19 (4): 216–221.Google Scholar
  13. DeMiguel, V., L. Garlappi, and R. Uppal. 2009. Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? The Review of Financial Studies 22 (5): 1915–1953.Google Scholar
  14. Fabozzi, F.J., P. Kolm, D. Pachamanova, and S. Forcadi. 2007. Robust portfolio optimization: Recent trends and future directions. Journal of Portfolio Management 433 (3): 40–48.Google Scholar
  15. Fabozzi, F.J., D. Huang, and G. Zhou. 2010. Robust portfolio: Contributions from operations research and finance. Annals of Operations Research 176 (1): 191–220.Google Scholar
  16. Fernandes, J.L.B., J.R.H. Ornelas, and O.A.M. Cusicanqui. 2012. Combining equilibrium, resampling, and analyst’s views in portfolio optimization. Journal of Banking & Finance 36 (5): 1354–1361.Google Scholar
  17. Gregory, C., K. Darby-Dowman, and G. Mitra. 2011. Robust optimization and portfolio selection: The cost of robustness. European Journal of Operational Research 212 (2): 417–428.Google Scholar
  18. Gupta, P., M.K. Mehlawat, and A. Saxena. 2008. Asset portfolio optimization using fuzzy mathematical programming. Information Sciences 178 (6): 1734–1755.Google Scholar
  19. Hsu, C.C., and B.A. Sandford. 2007. The Delphi technique: Making sense of consensus. Practical Assessment, Research & Evaluation 12 (10): 1–8.Google Scholar
  20. Huang, D., S. Zhu, F. Fabozzi, and M. Fukushima. 2010. Portfolio selection under distributional uncertainty: A relative robust CVaR approach. European Journal of Operational Research 203 (1): 185–194.Google Scholar
  21. Kaya, H. 2017. Managing ambiguity in asset allocation. Journal of Asset Management 18 (3): 63–187.Google Scholar
  22. Kelley, E.K., and P.C. Tetlock. 2013. How wise are crowds? Insights from retail orders and stock returns. The Journal of Finance 68 (3): 1229–1265.Google Scholar
  23. Lutgens, F., and P. Schotman. 2010. Robust portfolio optimization with multiple experts. Review of Finance 14 (2): 343–383.Google Scholar
  24. Markowitz, H.M. 1952. Portfolio selection. The Journal of Finance 7 (1): 77–91.Google Scholar
  25. McAlinn, K., and M. West. 2019. Dynamic Bayesian predictive synthesis in time series forecasting. Journal of Econometrics 210 (1): 155–169.Google Scholar
  26. Meucci, A. 2010. Black–Litterman approach. In Encyclopedia of Quantitative Finance. Wiley.Google Scholar
  27. O’Toole, R. 2017. The Black–Litterman model: Active risk targeting and the parameter tau. Journal of Asset Management 18 (7): 580–587.Google Scholar
  28. Puri, M.L., and D.A. Ralescu. 1986. Fuzzy random variables. Journal of Mathematical Analysis and Applications 114 (2): 409–422.Google Scholar
  29. Schöttle, K., and R. Werner. 2009. Robustness properties of mean–variance portfolios. Optimization 58 (6): 641–663.Google Scholar
  30. Schöttle, K., R. Werner, and R. Zagst. 2010. Comparison and robustification of Bayes and Black–Litterman models. Mathematical Methods of Operations Research 71 (3): 453–475.Google Scholar
  31. Triantaphyllou, E. 2000. In Multi-criteria Decision Making Methods: A Comparative Study. London: Springer.Google Scholar
  32. Trueman, B. 1994. Analyst forecasts and herding behavior. The Review of Financial Studies 7 (1): 97–124.Google Scholar
  33. van der Schans, M., and H. Steehouwer. 2017. Time-dependent Black–Litterman. Journal of Asset Management 18 (5): 371–387.Google Scholar
  34. Watada, J. 1997. Fuzzy portfolio selection and its applications to decision making. Tatra Mountains Mathematical Publications 13: 219–248.Google Scholar
  35. West, M., and J. Crosse. 1992. Modelling probabilistic agent opinion. Journal of the Royal Statistical Society. Series B (Methodological) 54 (1): 285–299.Google Scholar
  36. Zadeh, L. 1965. Fuzzy sets. Information and Control 8 (3): 338–353.Google Scholar
  37. Ziemba, W.T. 2009. Use of stochastic and mathematical programming in portfolio theory and practice. Annals of Operations Research 166 (1): 5–22.Google Scholar

Copyright information

© Springer Nature Limited 2019

Authors and Affiliations

  1. 1.Department of Accounting and FinanceUniversity of NorthamptonNorthamptonUK
  2. 2.School of Business and EconomicsLoughborough UniversityLoughboroughUK

Personalised recommendations