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A Linear Belief Function Approach to Portfolio Evaluation

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  • Liping Liu
  • Catherine Shenoy
  • Prakash P. Shenoy

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.

Suggested Citation

  • Liping Liu & Catherine Shenoy & Prakash P. Shenoy, 2012. "A Linear Belief Function Approach to Portfolio Evaluation," Papers 1212.2473, arXiv.org.
  • Handle: RePEc:arx:papers:1212.2473
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    References listed on IDEAS

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    1. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
    2. Liu, Liping, 1999. "Approximate portfolio analysis," European Journal of Operational Research, Elsevier, vol. 119(1), pages 35-49, November.
    3. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    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. 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, February.
    6. 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, February.
    7. Ronald Fisher, 1959. "Mathematical probability in the natural sciences," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 2(1), pages 1-10, December.
    8. 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, September.
    9. 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 1121-1152, September.
    10. Yacine Aït-Sahalia, 2001. "Variable Selection for Portfolio Choice," Journal of Finance, American Finance Association, vol. 56(4), pages 1297-1351, August.
    11. Lubos Pástor, 2000. "Portfolio Selection and Asset Pricing Models," Journal of Finance, American Finance Association, vol. 55(1), pages 179-223, February.
    12. 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.
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