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A Linear Belief Function Approach to Portfolio Evaluation

  • Liping Liu
  • Catherine Shenoy
  • Prakash P. Shenoy
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    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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    Paper provided by 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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    1. 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.
    2. Lubos Pástor, 2000. "Portfolio Selection and Asset Pricing Models," Journal of Finance, American Finance Association, vol. 55(1), pages 179-223, 02.
    3. Paul A. Samuelson, 1970. "The Fundamental Approximation Theorem of Portfolio Analysis in terms of Means, Variances and Higher Moments," Review of Economic Studies, Oxford University Press, vol. 37(4), pages 537-542.
    4. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
    5. John Y. Campbell, 2000. "Asset Pricing at the Millennium," NBER Working Papers 7589, National Bureau of Economic Research, Inc.
    6. Yacine Ait-Sahalia & Michael W. Brandt, 2001. "Variable Selection for Portfolio Choice," NBER Working Papers 8127, National Bureau of Economic Research, Inc.
    7. Klaas P. Baks, 2001. "Should Investors Avoid All Actively Managed Mutual Funds? A Study in Bayesian Performance Evaluation," Journal of Finance, American Finance Association, vol. 56(1), pages 45-85, 02.
    8. Ronald Fisher, 1959. "Mathematical probability in the natural sciences," Metrika, Springer, vol. 2(1), pages 1-10, December.
    9. Liu, Liping, 1999. "Approximate portfolio analysis," European Journal of Operational Research, Elsevier, vol. 119(1), pages 35-49, November.
    10. 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.
    11. 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.
    12. Lubos Pástor & Robert F. Stambaugh, 1999. "Costs of Equity Capital and Model Mispricing," Journal of Finance, American Finance Association, vol. 54(1), pages 67-121, 02.
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