On Optimal Instrumental Variables Generators, with an Application to Hedge Fund Returns



In this paper, we propose a new benchmarking procedure lying on cumulants for computing the factor loadings in financial models of returns. We apply this technique to the well-known augmented Fama and French (J Fin Econ 43(2):153–193, 1997) model and compare it with another technique of ours based on higher moments. Our new procedure confirms the fact that the alpha is supposed to decrease when we disaggregate HFR indices to the level of individual funds while correcting for specification errors. Our new technique is therefore useful for hedge funds selection or ranking based on the alpha of Jensen corrected for specification errors. This technique will also be useful for calibrating other financial models of returns like the simple market model or the conditional alpha and beta models.


Hedge funds returns Alpha of Jensen Financial models Cumulants Higher moments Specification errors Aggregation bias 


C10 G10 G20 


  1. Chan, H. W., & Faff, R. W. (2005). Asset pricing and the illiquidity premium. Financial Review, 40(4), 429–458.CrossRefGoogle Scholar
  2. Chen, N. F., Roll, R., & Ross, S. (1986). Economic forces and the stock market. Journal of Business, 59(3), 572–621.Google Scholar
  3. Christopherson, J. A., Ferson, W. E., & Glassman, D. A. (1998). Conditioning manager alphas on economic information: another look at the persistence of performance. Review of Financial Studies, 11(1), 111–142.CrossRefGoogle Scholar
  4. Coën, A., & Racicot, F. E. (2007). The CAPM revisited: evidence from errors in variables. Economics Letters, 95(3), 443–450.CrossRefGoogle Scholar
  5. Dagenais, M. G., & Dagenais, D. L. (1997). Higher moment estimators for linear regression models with errors in the variables. Journal of Econometrics, 76(1–2), 193–221.CrossRefGoogle Scholar
  6. Durbin, J. (1954). Errors in variables. International Statistical Review, 22(1/3), 23–32.CrossRefGoogle Scholar
  7. Fama, E. F., & French, K. R. (1997). Industry costs of equity. Journal of Financial Economics, 43(2), 153–193.CrossRefGoogle Scholar
  8. Fama, E. F., & MacBeth, J. D. (1973). Risk, return, and equilibrium: empirical tests. Journal of Political Economy, 81(3), 607–636.CrossRefGoogle Scholar
  9. Ferson, W. E., & Schadt, R. W. (1996). Measuring fund strategy and performance in changing economic conditions. Journal of Finance, 51(2), 425–461.CrossRefGoogle Scholar
  10. Harvey, C., & Siddique, A. (2000). Conditional skewness in asset pricing. Journal of Finance, 55(3), 1263–1295.CrossRefGoogle Scholar
  11. Hausman, J. A. (1978). Specification tests in econometrics. Econometrica, 46(6), 1251–1271.CrossRefGoogle Scholar
  12. Kraus, A., & Litzenberger, R. (1976). Skewness preference and the valuation of risk assets. Journal of Finance, 31(4), 1085–1100.CrossRefGoogle Scholar
  13. Lim, K. G. (1989). A new test of the three-moment capital asset pricing model. Journal of Financial and Quantitative Analysis, 24(2), 205–216.CrossRefGoogle Scholar
  14. MacKinnon, J. G. (1992). Model specification tests and artificial regressions. Journal of Economic Litterature, 30(1), 102–146.Google Scholar
  15. Pal, M. (1980). Consistent moment estimators of regression coefficients in the presence of errors in variables. Journal of Econometrics, 14(3), 349–364.CrossRefGoogle Scholar
  16. Pindyck, R. S., & Rubinfeld, D. L. (1998). Econometric models and economic forecasts (4th ed.). New York: McGraw-Hill.Google Scholar
  17. Racicot, F. E (2003). Measurement errors on economic and financial variables. In Three essays on the analysis of economic and financial data, chap.3, Ph.D. thesis, ESG-UQAM.Google Scholar
  18. Racicot, F. E., & Théoret, R. (2007). The beta puzzle revisited: A panel study of hedge fund returns. Journal of Derivatives & Hedge Funds, 13(2), 125–147.CrossRefGoogle Scholar
  19. Racicot, F. E., & Théoret, R. (2008). On comparing hedge fund strategies using new Hausman-based estimators. Journal of Derivatives & Hedge Funds, 14(1), 9–30.CrossRefGoogle Scholar
  20. Rubinstein, M. (1973). The fundamental theorem of parameter-preference security valuation. Journal of Financial and Quantitative Analysis, 8(1), 61–69.CrossRefGoogle Scholar
  21. Samuelson, P. A. (1970). The fundamental approximation theorem of portfolio analysis in terms of means, variances and higher moments. Review of Economic Studies, 37(4), 537–542.CrossRefGoogle Scholar
  22. Watson, C. T. (2003). GMM and the Fama and French model: the role of instruments. Economics Department, UCLA, Working Paper.Google Scholar

Copyright information

© International Atlantic Economic Society 2008

Authors and Affiliations

  1. 1.Department of Administrative SciencesUniversity of Quebec—Outaouais, UQOGatineau (Hull)Canada
  2. 2.Department of FinanceUniversity of Quebec—Montreal, UQAMMontrealCanada

Personalised recommendations