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A Linear Belief Function Approach to Portfolio Evaluation

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  • Liping Liu
  • Catherine Shenoy
  • Prakash P. Shenoy
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    Abstract

    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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    Bibliographic Info

    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

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    Web page: http://arxiv.org/

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    1. Lubos Pástor & Robert F. Stambaugh, . "Costs of Equity Capital and Model Mispricing," Rodney L. White Center for Financial Research Working Papers, Wharton School Rodney L. White Center for Financial Research 4-98, Wharton School Rodney L. White Center for Financial Research.
    2. 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, Wiley Blackwell, vol. 37(4), pages 537-42, October.
    3. 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, Wharton School Rodney L. White Center for Financial Research 18-99, Wharton School Rodney L. White Center for Financial Research.
    4. John Y. Campbell, 2000. "Asset Pricing at the Millennium," NBER Working Papers 7589, National Bureau of Economic Research, Inc.
    5. Liu, Liping, 1999. "Approximate portfolio analysis," European Journal of Operational Research, Elsevier, Elsevier, vol. 119(1), pages 35-49, November.
    6. Lubo Pástor, . "Portfolio Selection and Asset Pricing Models," CRSP working papers 498, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
    7. Ronald Fisher, 1959. "Mathematical probability in the natural sciences," Metrika, Springer, Springer, vol. 2(1), pages 1-10, December.
    8. Ait-Sahalia, Y. & Brandt, M.W., 2001. "Variable Selection for Portfolio Choice," Papers, Manitoba - Department of Economics 34, Manitoba - Department of Economics.
    9. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, American Finance Association, vol. 19(3), pages 425-442, 09.
    10. Fama, Eugene F., 1996. "Multifactor Portfolio Efficiency and Multifactor Asset Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 31(04), pages 441-465, December.
    11. Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, Econometric Society, vol. 57(5), pages 1121-52, September.
    12. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, Elsevier, vol. 13(3), pages 341-360, December.
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