Financial Markets and Portfolio Management

, Volume 28, Issue 4, pp 307–336 | Cite as

Why not use SDF rather than beta models in performance measurement?

  • Jonas Gusset
  • Heinz ZimmermannEmail author


This paper analyzes performance measurement based on stochastic discount factors, compared to beta models traditionally used in computing funds’ (Jensen) alphas. From a theoretical point of view, standard alphas suffer from several limitations. Our paper addresses this issue from an empirical point of view using a sample of Swiss mutual funds from 2000 to 2011. Our results suggest that the key for a “fair” comparison between stochastic discount function (SDF) and beta models is the specification of the set of primitive assets used to calibrate the SDF function. Once this is established, the size of (absolute) performance differences considerably decreases between the two model families. However, there are sizeable performance deviations in the cross-section of funds if conditioning information is incorporated in the tests, up to some 20 basis points per month, or about 2.3 % per year. In almost all cases, the SDF-alphas are lower than the standard (Jensen) alphas. In absolute terms, the average SDF-based underperformance of the funds is way larger than the average total expense ratio (TER) of the funds, both in a conditional and unconditional setting.


Performance measurement Conditioning information Mutual funds 

JEL Classification

G12 G23 


  1. Aragon, G., Ferson, W.: Portfolio performance evaluation. Found. Trends Financ. 2, 83–190 (2006)CrossRefGoogle Scholar
  2. Bakshi, G., Chen, Z.: Asset pricing without consumption or market portfolio data. Working Paper, College Park, University of Maryland (1998)Google Scholar
  3. Bekaert, G., Liu, J.: Conditioning information and variance bounds on pricing kernels. Rev. Financ. Stud. 17, 339–378 (2004)CrossRefGoogle Scholar
  4. Bessler, W., Drobetz, W., Zimmermann, H.: Conditional performance evaluation for German mutual equity funds. Eur. J. Financ. 15, 287–316 (2009)CrossRefGoogle Scholar
  5. Chen, Z., Knez, P.: Portfolio performance measurement: theory and applications. Rev. Financ. Stud. 9, 511–555 (1996)CrossRefGoogle Scholar
  6. Cochrane, J.: A cross-sectional test of an investment-based asset pricing model. J. Polit. Econ. 104, 572–621 (1996)CrossRefGoogle Scholar
  7. Cochrane, J.: Asset Pricing. Princeton University Press, New Jersey (2001)Google Scholar
  8. Dahlquist, M., Söderlind, P.: Evaluating portfolio performance with stochastic discount factors. J. Bus. 72, 347–384 (1999)CrossRefGoogle Scholar
  9. Dahlquist, M., Engström, S., Söderlind, P.: Performance and characteristics of Swedish mutual funds. J. Financ. Quant. Anal. 35, 409–423 (2000)CrossRefGoogle Scholar
  10. Dybvig, P., Ross, S.: The analytics of performance measurement using and a security market line. J. Financ. 40, 401–416 (1985b)CrossRefGoogle Scholar
  11. Fama, E., French, K.: Common risk factors in the returns on stocks and bonds. J. Financ. Econ. 33, 3–56 (1993)CrossRefGoogle Scholar
  12. Farnsworth, H., Ferson, W., Jackson, D., Todd, S.: Performance evaluation with stochastic discount factors. J. Bus. 75, 473–504 (2002)CrossRefGoogle Scholar
  13. Ferson, W., Lin, J.: Alpha and performance measurement: the effect of investor heterogeneity. Working Paper (2012)Google Scholar
  14. Ferson, W., Qian, M.: Conditional performance evaluation: revisited. Working Paper, Boston College (2004)Google Scholar
  15. Ferson, W.: Investment Performance: a review and synthesis. In: Constantinides, G., Harris, M., Stulz, R. (eds.) Handbook of Economics and Finance (2012)Google Scholar
  16. Ferson, W., Harvey, C.: The risk and predictability of international equity returns. Rev. Financ. Stud. 6, 527–566 (1993)CrossRefGoogle Scholar
  17. Ferson, W., Korajczyk, R.: Do arbitrage pricing models explain the predictability of stock returns? J. Bus. 68, 309–349 (1995)CrossRefGoogle Scholar
  18. Ferson, W., Schadt, R.: Measuring fund strategy and performance in changing economic conditions. J. Financ. 51, 425–461 (1996)CrossRefGoogle Scholar
  19. Ferson, W., Harvey, C.: Conditioning variables and cross-section of stock returns. J. Financ. 54, 1325–1360 (1999)CrossRefGoogle Scholar
  20. Ferson, W., Henry, T., Kisgen, D.: Evaluating government bond fund performance with stochastic discount factors. Rev. Financ. Stud. 19, 423–456 (2006)CrossRefGoogle Scholar
  21. Ferson, W.: Investment performance evaluation. Ann. Rev. Financ. Econ. 2, 207–234 (2010)CrossRefGoogle Scholar
  22. Garrett, I., Hyde, S., Lozano, M.: Trade-offs between efficiency and robustness in the empirical evaluation of asset pricing models. Working Paper (2011)Google Scholar
  23. Gibbons, M., Ross, S., Shanken, J.: A test for the efficiency of a given portfolio. Econometrica 57, 1121–1152 (1989)CrossRefGoogle Scholar
  24. Griese, K., Kempf, A.: Lohnt aktives Fondsmanagement aus Anlegersicht? Ein Vergleich von Anlagestrategien in aktiv und passiv verwalteten Aktienfonds. Zeitschrift für Betriebswirtschaft 73, 201–224 (2003)Google Scholar
  25. Hansen, L.: Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054 (1982)CrossRefGoogle Scholar
  26. Hansen, L., Jagannathan, R.: Implications of security market data for models of dynamic economies. J. Polit. Econ. 99, 225–262 (1991)CrossRefGoogle Scholar
  27. Hansen, L., Jagannathan, R.: Assessing specification errors in stochastic discount factor models. J. Financ. 52, 557–590 (1997)CrossRefGoogle Scholar
  28. Jagannathan, R., Wang, Z.: Empirical evaluation of asset pricing models: a comparison of the SDF and beta methods. J. Financ. 57, 2337–2367 (2002)CrossRefGoogle Scholar
  29. Jensen, M.: The performance of mutual funds in the period 1945–1964. J. Financ. 23, 389–416 (1968)CrossRefGoogle Scholar
  30. Jobson, J., Korkie, B.: Potential performance and tests of portfolio efficiency. J. Financ. Econ. 10, 433–466 (1982)CrossRefGoogle Scholar
  31. Kan, R., Zhou, G.: Empirical asset pricing: the beta method versus the stochastic discount factor method. Working Paper. University of Toronto and Washington University, St. Louis (2002)Google Scholar
  32. Kan, R., Robotti, C.: Specification tests of asset pricing models using excess returns. J. Empir. Financ. 15, 816–838 (2008)CrossRefGoogle Scholar
  33. Lewellen, J.: Predicting returns with financial ratios. J. Financ. Econ. 74, 209–235 (2004)CrossRefGoogle Scholar
  34. Lewellen, J., Nagel, S., Shanken, J.: A skeptical appraisal of asset pricing tests. J. Financ. Econ. 96, 175–194 (2010)CrossRefGoogle Scholar
  35. MacKinlay, C.: Multifactor models do not explain deviations from the CAPM. J. Financ. Econ. 38, 3–28 (1995)CrossRefGoogle Scholar
  36. Malkiel, B.: Returns from investing in equity mutual funds 1971 to 1991. J. Financ. 50, 549–572 (1995)CrossRefGoogle Scholar
  37. Mehra, R., Prescott, E.: The equity premium: a puzzle. J. Monet. Econ. 15, 145–162 (1985)CrossRefGoogle Scholar
  38. Silva, F., Cortez, M.C., Armada, M.: Conditioning information and European bond fund performance. Eur. Financ. Manag. 9, 201–230 (2003)CrossRefGoogle Scholar
  39. Söderlind, P.: An interpretation of SDF based performance measures. European Finance Review 3, 233–237 (1999)CrossRefGoogle Scholar
  40. White, H.: A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48, 817–838 (1980)CrossRefGoogle Scholar

Copyright information

© Swiss Society for Financial Market Research 2014

Authors and Affiliations

  1. 1.WWZ Department of Finance, Wirtschaftswissenschaftliches Zentrum WWZUniversität BaselBaselSwitzerland

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