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A Linear Belief Function Approach to Portfolio Evaluation

  • Liping Liu
  • Catherine Shenoy
  • Prakash P. Shenoy
Registered author(s):

    By elaborating on the notion of linear belief functions (Dempster 1990; Liu 1996), we propose an elementary approach to knowledge representation for expert systems using linear belief functions. We show how to use basic matrices to represent market information and financial knowledge, including complete ignorance, statistical observations, subjective speculations, distributional assumptions, linear relations, and empirical asset pricing models. We then appeal to Dempster's rule of combination to integrate the knowledge for assessing an overall belief of portfolio performance, and updating the belief by incorporating additional information. We use an example of three gold stocks to illustrate the approach.

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    File URL: http://arxiv.org/pdf/1212.2473
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    Paper provided by arXiv.org in its series Papers with number 1212.2473.

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    Date of creation: Oct 2012
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    Handle: RePEc:arx:papers:1212.2473
    Contact details of provider: Web page: http://arxiv.org/

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    1. Klaas Baks & Andrew Metrick & Jessica Wachter, . "Should Investors Avoid All Actively Managed Mutual Funds? A Study in Bayesian Performance Evaluation," Rodney L. White Center for Financial Research Working Papers 18-99, Wharton School Rodney L. White Center for Financial Research.
    2. Yacine AÏT-SAHALIA, & Michael W. BRANDT, 2001. "Variable Selection for Portfolio Choice," FAME Research Paper Series rp34, International Center for Financial Asset Management and Engineering.
    3. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
    4. Fama, Eugene F., 1996. "Multifactor Portfolio Efficiency and Multifactor Asset Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(04), pages 441-465, December.
    5. Samuelson, Paul A, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances, and Higher Moments," Review of Economic Studies, Wiley Blackwell, vol. 37(4), pages 537-42, October.
    6. John Y. Campbell, 2000. "Asset Pricing at the Millennium," NBER Working Papers 7589, National Bureau of Economic Research, Inc.
    7. Ronald Fisher, 1959. "Mathematical probability in the natural sciences," Metrika, Springer, vol. 2(1), pages 1-10, December.
    8. Lubos Pastor & Robert F. Stambaugh, 1998. "Costs of Equity Capital and Model Mispricing," NBER Working Papers 6490, National Bureau of Economic Research, Inc.
    9. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, 09.
    10. Lubos Pástor, 2000. "Portfolio Selection and Asset Pricing Models," Journal of Finance, American Finance Association, vol. 55(1), pages 179-223, 02.
    11. Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, vol. 57(5), pages 1121-52, September.
    12. Liu, Liping, 1999. "Approximate portfolio analysis," European Journal of Operational Research, Elsevier, vol. 119(1), pages 35-49, November.
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