Skip to main content

Bayesian Networks for Portfolio Analysis and Optimization

  • Chapter
  • First Online:
Financial Decision Making Using Computational Intelligence

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 70))

Abstract

Portfolio analysis studies the impact of economic and financial scenarios on the performance of an investment portfolio, while portfolio optimization concerns asset allocation to achieve a trade-off between risk and return. In this chapter we exploit the interplay between modern portfolio theory and Bayesian networks to describe a new framework for portfolio analysis and optimization. Bayesian networks provide an effective way to interface models to data, allow efficient evidential reasoning, while their graphical language offers an intuitive interface by which the analyst can elicit his/her knowledge. The proposed framework leverages on evidential reasoning to understand the behavior of an investment portfolio in different economic and financial scenarios. It allows to formulate and solve a portfolio optimization problem, while coherently taking into account the investor’s market views. The Bayesian network framework for portfolio analysis and optimization is instantiated on the DJ Euro Stoxx 50 Index. Examples of portfolio analysis and optimization, exploiting evidential reasoning on Bayesian networks, are presented and discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. C. Albanese, K. Jackson, P. Wiberg, A new fourier transform algorithm for value at risk. Quant. Finance 4, 328–338 (2004)

    Article  MathSciNet  Google Scholar 

  2. R. Almgren, N. Chriss, Optimal portfolios from ordering information. J. Risk 9, 1–47 (2006)

    Google Scholar 

  3. D. Avramov, G. Zhou, Bayesian portfolio analysis. Annu. Rev. Financ. Econ. 2, 25–47 (2010)

    Google Scholar 

  4. F. Black, R. Litterman, Asset allocation: Combining investors views with market equilibrium. Journal of Fixed Income, 7–18 (1991)

    Google Scholar 

  5. G. Cooper, The computational complexity of probabilistic inference using bayesian belief networks. Artif. Intell. 42(2–3), 393–405 (1990)

    Article  MATH  Google Scholar 

  6. R. Dechter, Bucket elimination: A unifying framework for reasoning. Artif. Intell. 113, 41–85 (1999)

    Google Scholar 

  7. R. Demirer, R.R. Mau, C. Shenoy, Bayesian networks: A decision tool to improve portfolio risk analysis. J. Appl. Finance 16 (2006)

    Google Scholar 

  8. A. Edelman, Eigenvalues and Condition Numbers of Random Matrices. PhD thesis, Department of Mathematics, Massachussetts Institute of Technology (1989)

    Article  MATH  Google Scholar 

  9. E.J. Elton, M.J. Gruber, S.J. Brown, Modern Portfolio Theory and Investment Analysis (Wiley, New York, 2009)

    Google Scholar 

  10. N. Friedman, D. Geiger, M. Goldszmidt, Bayesian network classifiers. Mach. Learn. 29, 131–163 (1997)

    Article  MATH  Google Scholar 

  11. W.R. Gilks, S. Richardson, D.J. Spiegelhalter, Markov Chain Monte Carlo in Practice (Chapman and Hall, London, 1996)

    Google Scholar 

  12. D. Heckerman, D. Geiger, M. Chickering, Learning bayesian networks: The combination of knowledge and statistical data. Mach. Learn. 20, 197–243 (1995)

    Google Scholar 

  13. F.V. Jensen, T.D. Nielsen, Bayesian Networks and Decision Graphs (Springer, Berlin, 2007)

    Google Scholar 

  14. S.L. Lauritzen, D.J. Spiegelhalter, Local computations with probabilities on graphical structures and their application to expert systems (with discussion). J. Roy. Stat. Soc. 50, 157–224 (1988)

    Google Scholar 

  15. H. Markowitz, Portfolio selection. J. Finance 7, 77–91 (1952)

    Google Scholar 

  16. A. Meucci, Risk and Asset Allocation (Springer, Berlin, 2005)

    Google Scholar 

  17. A. Meucci, Beyond black-litterman in practice: A five-step recipe to input views on non-normal markets. Risk 19, 114–119 (2006)

    Google Scholar 

  18. A. Meucci, Fully flexible views: Theory and practice. Risk 21, 97–102 (2008)

    Google Scholar 

  19. A. Meucci, Enhancing the black-litterman and related approaches: Views and stress-test on risk factors. J. Asset Manag. 10, 89–96 (2009)

    Google Scholar 

  20. A. Meucci, Factors on demand. Risk 23, 84–89 (2010)

    Google Scholar 

  21. A. Meucci, Fully flexible bayesian networks. http://ssrn.com/abstract=1721302 (2010)

  22. A. Meucci, Linear vs. compounded returns-common pitfalls in portfolio management. GARP Risk Prof. “The Quant Classroom” series, 49–51 (2010)

    Google Scholar 

  23. A. Meucci, Review of linear factor models: Surprising common principles, the systematic-plus-idiosyncratic myth, and the misread relationship with financial theory, July (2010). http://ssrn.com/abstract=1635495

  24. A. Meucci, The prayer - Ten-step checklist for advanced risk and portfolio management. GARP Risk Prof. “The Quant Classroom” series, 54–60/34–41 (2011)

    Google Scholar 

  25. K.P. Murphy, The bayes net toolbox for matlab. Comput. Sci. Stat. 33 (2001)

    Google Scholar 

  26. K.P. Murphy, Dynamic Bayesian Networks: Representation, Inference and Learning. PhD thesis, UC Berkeley, Computer Science Division (2002)

    Google Scholar 

  27. R.E. Neapolitan, Learning Bayesian Networks (Prentice Hall, NJ, 2003)

    Google Scholar 

  28. M. Neil, N. Fenton, M. Tailor, Using bayesian networks to model expected and unexpected operational losses. Risk Anal. J. 25(4), 963–972 (2005)

    Google Scholar 

  29. U. Nodelman, C. Shelton, D. Koller, Continuous time Bayesian networks, in Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence (UAI) (2002), pp. 378–387. http://robotics.stanford.edu/~nodelman/publications.html

  30. T. Pavlenko, O. Chernyak, Credit risk modeling using bayesian networks. Int. J. Intell. Syst. 25(4), 326–344 (2010)

    Google Scholar 

  31. J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (Morgan Kaufmann, CA, 1988)

    Google Scholar 

  32. J. Pezier, Global portfolio optimization revisited: A least discrimination alternantive to black-litterman. ICMA Centre Discussion Papers in Finance (2007). http://www.icmacentre.ac.uk/files/pdf/dps/dp2007_07.pdf

  33. V. Plerou, V. Gopikrishnan, B. Rosenau, L. Amaral, T. Guhr, E. Stanley, Random matrix approach to cross-correlations in financial data. Phys. Rev. E 65, 1–17 (2002)

    Article  Google Scholar 

  34. J.P.B.M. Potters, L. Laloux, Financial applications of random matrix theory: Old laces and new pieces. Acta Phys. Pol. B 36(9), 2767–2784 (2005)

    Google Scholar 

  35. E. Qian, S. Gorman, Conditional distribution in portfolio theory. Financ. Analyst J. 57, 44–51 (2001)

    Google Scholar 

  36. S.T. Rachev, J.S.J. Hsu, B.S. Bagasheva, F.J. Fabozzi, Bayesian Methods in Finance (Wiley, New York, 2008)

    Google Scholar 

  37. R. Rebonato, Coherent Stress Testing: A Bayesian Approach to the Analysis of Financial Stress, Wiley (2010). ISBN: 0470666013

    Google Scholar 

  38. S. Roweis, Z. Ghahramani, A unifying review of linear gaussian models. Neural Comput. 11, 305–345 (1999). http://www.cs.nyu.edu/~roweis/papers/NC110201.pdf

    Google Scholar 

  39. S. Russell, P. Norvig, Artificial Intelligence: A Modern Approach, 3rd edn. (Prentice Hall, NJ, 2009)

    Google Scholar 

  40. W.F. Sharpe, Capital asset prices: A theory of market equilibrium under conditions of risk. J. Finance 3, 425–442 (1964)

    Google Scholar 

  41. C. Shenoy, P.P. Shenoy, Bayesian Networks: A Decision Tool to Improve Portfolio Risk Analysis. Working paper, School of Business, University of Kansas (1998)

    Google Scholar 

  42. D. Stefanica, A Primer for the Mathematics of Financial Engineering (FE Press, New York, 2008)

    Google Scholar 

  43. M. Tipping, C. Bishop, Mixtures of probabilistic principal component analyzers. Neural Comput. 11(2), 443–482 (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fabio Stella .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media New York

About this chapter

Cite this chapter

Villa, S., Stella, F. (2012). Bayesian Networks for Portfolio Analysis and Optimization. In: Doumpos, M., Zopounidis, C., Pardalos, P. (eds) Financial Decision Making Using Computational Intelligence. Springer Optimization and Its Applications, vol 70. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-3773-4_8

Download citation

Publish with us

Policies and ethics