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Bayesian Performance Evaluation

  • Klaas Baks
  • Andrew Metrick
  • Jessica Wachter

This paper proposes a Bayesian method of performance evaluation for investment managers. We begin with a flexible set of prior beliefs that can be elicited without any reference to probability distributions or their parameters. We then combine these prior beliefs with a general multi-factor model and derive an analytical solution for the posterior expectation of alpha', the intercept term from the model. This solution can be computed using only a few extra steps beyond maximum likelihood estimation and does not require a comprehensive or bias-free database. We then apply our methodology to a sample of domestic diversified equity mutual funds and ask what prior beliefs would imply zero investment in active managers?' To justify such a zero-investment strategy, we find that a mean-variance investor would need to believe that less than 1 out of every 100,000 managers has an expected alpha greater than 25 basis points per month. Overall, our analysis suggests that even when the average manager is expected to underperform passive benchmarks, it requires very strong prior beliefs to imply zero investment in managers with the best past performance.

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File URL: http://www.nber.org/papers/w7069.pdf
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 7069.

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Date of creation: Apr 1999
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Publication status: published as Newly titled "Should Investors Avoid All Actively Managed Mutual Funds? A Study in Bayesian Performance Evaluation", Journal of Finance (February 2001).
Handle: RePEc:nbr:nberwo:7069
Note: AP
Contact details of provider: Postal: National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.
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Web page: http://www.nber.org
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  1. Judith Chevalier & Glenn Ellison, 1999. "Are Some Mutual Fund Managers Better Than Others? Cross-Sectional Patterns in Behavior and Performance," Journal of Finance, American Finance Association, vol. 54(3), pages 875-899, 06.
  2. Frost, Peter A. & Savarino, James E., 1986. "An Empirical Bayes Approach to Efficient Portfolio Selection," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(03), pages 293-305, September.
  3. Stambaugh, Robert F., 1997. "Analyzing investments whose histories differ in length," Journal of Financial Economics, Elsevier, vol. 45(3), pages 285-331, September.
  4. 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.
  5. Kandel, Shmuel & McCulloch, Robert & Stambaugh, Robert F, 1995. "Bayesian Inference and Portfolio Efficiency," Review of Financial Studies, Society for Financial Studies, vol. 8(1), pages 1-53.
  6. Pastor, Lubos & Stambaugh, Robert F., 2000. "Comparing asset pricing models: an investment perspective," Journal of Financial Economics, Elsevier, vol. 56(3), pages 335-381, June.
  7. Daniel, Kent & Titman, Sheridan, 1997. " Evidence on the Characteristics of Cross Sectional Variation in Stock Returns," Journal of Finance, American Finance Association, vol. 52(1), pages 1-33, March.
  8. Carhart, Mark M, 1997. " On Persistence in Mutual Fund Performance," Journal of Finance, American Finance Association, vol. 52(1), pages 57-82, March.
  9. Klein, Roger W. & Bawa, Vijay S., 1976. "The effect of estimation risk on optimal portfolio choice," Journal of Financial Economics, Elsevier, vol. 3(3), pages 215-231, June.
  10. William N. Goetzmann & Stephen J. Brown, 2005. "Performance Persistence," Yale School of Management Working Papers ysm451, Yale School of Management.
  11. Jorion, Philippe, 1986. "Bayes-Stein Estimation for Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(03), pages 279-292, September.
  12. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
  13. Jorion, Philippe, 1991. "Bayesian and CAPM estimators of the means: Implications for portfolio selection," Journal of Banking & Finance, Elsevier, vol. 15(3), pages 717-727, June.
  14. Jorion, Philippe, 1985. "International Portfolio Diversification with Estimation Risk," The Journal of Business, University of Chicago Press, vol. 58(3), pages 259-78, July.
  15. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
  16. repec:fth:pennfi:72 is not listed on IDEAS
  17. Shanken, Jay, 1987. "A Bayesian approach to testing portfolio efficiency," Journal of Financial Economics, Elsevier, vol. 19(2), pages 195-215, December.
  18. Kandel, Shmuel & Stambaugh, Robert F, 1996. " On the Predictability of Stock Returns: An Asset-Allocation Perspective," Journal of Finance, American Finance Association, vol. 51(2), pages 385-424, June.
  19. 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.
  20. Ferson, Wayne E & Schadt, Rudi W, 1996. " Measuring Fund Strategy and Performance in Changing Economic Conditions," Journal of Finance, American Finance Association, vol. 51(2), pages 425-61, June.
  21. Keim, Donald B. & Madhavan, Ananth, 1997. "Transactions costs and investment style: an inter-exchange analysis of institutional equity trades," Journal of Financial Economics, Elsevier, vol. 46(3), pages 265-292, December.
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