IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/20031.html
   My bibliography  Save this paper

Market Proxies, Correlation, and Relative Mean-Variance Efficiency: Still Living with the Roll Critique

Author

Listed:
  • Todd, Prono

Abstract

A test of the CAPM is developed conditional on a prior belief about the correlation between the true market return and the proxy return used in the test. Consideration is given to the effect of the proxy's mismeasurement of the market return on the estimation of the market model. Failure to grant this consideration biases tests towards rejection by overstating the inefficiency of the proxy. An extension of the proposed test to a CAPM with conditioning information links mismeasurement of the market return to time-variation in beta.

Suggested Citation

  • Todd, Prono, 2009. "Market Proxies, Correlation, and Relative Mean-Variance Efficiency: Still Living with the Roll Critique," MPRA Paper 20031, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:20031
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/20031/1/MPRA_paper_20031.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-927, July.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    4. Jagannathan, Ravi & Wang, Zhenyu, 1996. "The Conditional CAPM and the Cross-Section of Expected Returns," Journal of Finance, American Finance Association, vol. 51(1), pages 3-53, March.
    5. Shanken, Jay, 1987. "Multivariate proxies and asset pricing relations : Living with the Roll critique," Journal of Financial Economics, Elsevier, vol. 18(1), pages 91-110, March.
    6. Bodurtha, James N, Jr & Mark, Nelson C, 1991. "Testing the CAPM with Time-Varying Risks and Returns," Journal of Finance, American Finance Association, vol. 46(4), pages 1485-1505, September.
    7. 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.
    8. Adrian, Tobias & Franzoni, Francesco, 2009. "Learning about beta: Time-varying factor loadings, expected returns, and the conditional CAPM," Journal of Empirical Finance, Elsevier, vol. 16(4), pages 537-556, September.
    9. Lewellen, Jonathan & Nagel, Stefan, 2006. "The conditional CAPM does not explain asset-pricing anomalies," Journal of Financial Economics, Elsevier, vol. 82(2), pages 289-314, November.
    10. Harvey, Campbell R., 1989. "Time-varying conditional covariances in tests of asset pricing models," Journal of Financial Economics, Elsevier, vol. 24(2), pages 289-317.
    11. Rigobon, Roberto, 2002. "The curse of non-investment grade countries," Journal of Development Economics, Elsevier, vol. 69(2), pages 423-449, December.
    12. Hansen, Lars Peter & Jagannathan, Ravi, 1997. "Assessing Specification Errors in Stochastic Discount Factor Models," Journal of Finance, American Finance Association, vol. 52(2), pages 557-590, June.
    13. Pin-Huang Chou, 1996. "Using Bootstrap to Test Mean-Variance Efficiency of a Given Portfolio," Finance 9609002, University Library of Munich, Germany.
    14. Ferson, Wayne E, 1990. "Are the Latent Variables in Time-Varying Expected Returns Compensation for Consumption Risk?," Journal of Finance, American Finance Association, vol. 45(2), pages 397-429, June.
    15. Robert F. Dittmar, 2002. "Nonlinear Pricing Kernels, Kurtosis Preference, and Evidence from the Cross Section of Equity Returns," Journal of Finance, American Finance Association, vol. 57(1), pages 369-403, February.
    16. Christian M. Hafner, 2003. "Fourth Moment Structure of Multivariate GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 1(1), pages 26-54.
    17. Campbell, John Y, 1996. "Understanding Risk and Return," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 298-345, April.
    18. Fama, Eugene F. & French, Kenneth R., 1989. "Business conditions and expected returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 25(1), pages 23-49, November.
    19. John Y. Campbell & Tuomo Vuolteenaho, 2004. "Bad Beta, Good Beta," American Economic Review, American Economic Association, vol. 94(5), pages 1249-1275, December.
    20. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    21. Todd Prono, 2008. "GARCH-based identification and estimation of triangular systems," Supervisory Research and Analysis Working Papers QAU08-4, Federal Reserve Bank of Boston.
    22. Kandel, Shmuel & Stambaugh, Robert F, 1995. "Portfolio Inefficiency and the Cross-Section of Expected Returns," Journal of Finance, American Finance Association, vol. 50(1), pages 157-184, March.
    23. Rich, Robert W. & Raymond, Jennie & Butler, J. S., 1991. "Generalized instrumental variables estimation of autoregressive conditional heteroskedastic models," Economics Letters, Elsevier, vol. 35(2), pages 179-185, February.
    24. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    25. Keim, Donald B. & Stambaugh, Robert F., 1986. "Predicting returns in the stock and bond markets," Journal of Financial Economics, Elsevier, vol. 17(2), pages 357-390, December.
    26. Martin Lettau & Sydney Ludvigson, 2001. "Resurrecting the (C)CAPM: A Cross-Sectional Test When Risk Premia Are Time-Varying," Journal of Political Economy, University of Chicago Press, vol. 109(6), pages 1238-1287, December.
    27. James G. MacKinnon, 2007. "Bootstrap Hypothesis Testing," Working Paper 1127, Economics Department, Queen's University.
    28. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    29. MacKinlay, A Craig & Richardson, Matthew P, 1991. "Using Generalized Method of Moments to Test Mean-Variance Efficiency," Journal of Finance, American Finance Association, vol. 46(2), pages 511-527, June.
    30. Garry Phillips & Emma Iglesias, 2004. "Simultaneous Equations and Weak Instruments under Conditionally Heteroscedastic Disturbances," Econometric Society 2004 Far Eastern Meetings 567, Econometric Society.
    31. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    32. Kandel, Shmuel & Stambaugh, Robert F., 1987. "On correlations and inferences about mean-variance efficiency," Journal of Financial Economics, Elsevier, vol. 18(1), pages 61-90, March.
    33. 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.
    34. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Michael C. Nwogugu, 2020. "Decision-Making, Sub-Additive Recursive "Matching" Noise And Biases In Risk-Weighted Stock/Bond Index Calculation Methods In Incomplete Markets With Partially Observable Multi-Attribute Pref," Papers 2005.01708, arXiv.org.
    2. Todd Prono, 2008. "GARCH-based identification and estimation of triangular systems," Supervisory Research and Analysis Working Papers QAU08-4, Federal Reserve Bank of Boston.
    3. Michael Nwogugu, 2020. "Regret Theory And Asset Pricing Anomalies In Incomplete Markets With Dynamic Un-Aggregated Preferences," Papers 2005.01709, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Todd Prono, 2006. "GARCH-based identification of triangular systems with an application to the CAPM: still living with the roll critique," Working Papers 07-1, Federal Reserve Bank of Boston.
    2. Prono, Todd, 2015. "Market proxies as factors in linear asset pricing models: Still living with the roll critique," Journal of Empirical Finance, Elsevier, vol. 31(C), pages 36-53.
    3. Lewellen, Jonathan & Nagel, Stefan & Shanken, Jay, 2010. "A skeptical appraisal of asset pricing tests," Journal of Financial Economics, Elsevier, vol. 96(2), pages 175-194, May.
    4. Maio, Paulo & Santa-Clara, Pedro, 2012. "Multifactor models and their consistency with the ICAPM," Journal of Financial Economics, Elsevier, vol. 106(3), pages 586-613.
    5. Bali, Turan G., 2008. "The intertemporal relation between expected returns and risk," Journal of Financial Economics, Elsevier, vol. 87(1), pages 101-131, January.
    6. Adrian, Tobias & Franzoni, Francesco, 2009. "Learning about beta: Time-varying factor loadings, expected returns, and the conditional CAPM," Journal of Empirical Finance, Elsevier, vol. 16(4), pages 537-556, September.
    7. Amit Goyal, 2012. "Empirical cross-sectional asset pricing: a survey," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(1), pages 3-38, March.
    8. John Y. Campbell, 2000. "Asset Pricing at the Millennium," Journal of Finance, American Finance Association, vol. 55(4), pages 1515-1567, August.
    9. Stefano Gubellini, 2014. "Conditioning information and cross-sectional anomalies," Review of Quantitative Finance and Accounting, Springer, vol. 43(3), pages 529-569, October.
    10. Vendrame, Vasco & Guermat, Cherif & Tucker, Jon, 2018. "A conditional regime switching CAPM," International Review of Financial Analysis, Elsevier, vol. 56(C), pages 1-11.
    11. Auer Benjamin R., 2012. "Lassen sich CAPM, HCAPM und CCAPM durch konsumbasierte zeitvariable Parameterspezifikation rehabilitieren? / Can Time-varying Parameter Specification Based on Consumption Variables Rehabilitate CAPM, ," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 232(5), pages 518-544, October.
    12. Stefan Nagel, 2013. "Empirical Cross-Sectional Asset Pricing," Annual Review of Financial Economics, Annual Reviews, vol. 5(1), pages 167-199, November.
    13. Todd Prono, 2008. "GARCH-based identification and estimation of triangular systems," Supervisory Research and Analysis Working Papers QAU08-4, Federal Reserve Bank of Boston.
    14. Roh, Tai-Yong & Lee, Changjun & Min, Byoung-Kyu, 2019. "Consumption growth predictability and asset prices," Journal of Empirical Finance, Elsevier, vol. 51(C), pages 95-118.
    15. John Y. Campbell & Tuomo Vuolteenaho, 2004. "Bad Beta, Good Beta," American Economic Review, American Economic Association, vol. 94(5), pages 1249-1275, December.
    16. Liu, Ludan, 2008. "It takes a model to beat a model: Volatility bounds," Journal of Empirical Finance, Elsevier, vol. 15(1), pages 80-110, January.
    17. Ludvigson, Sydney C., 2013. "Advances in Consumption-Based Asset Pricing: Empirical Tests," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 799-906, Elsevier.
    18. Committee, Nobel Prize, 2013. "Understanding Asset Prices," Nobel Prize in Economics documents 2013-1, Nobel Prize Committee.
    19. Todd, Prono, 2010. "Simple GMM Estimation of the Semi-Strong GARCH(1,1) Model," MPRA Paper 20034, University Library of Munich, Germany.
    20. Motohiro Yogo, 2006. "A Consumption‐Based Explanation of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 61(2), pages 539-580, April.

    More about this item

    Keywords

    Asset pricing; CAPM; portfolio efficiency; multivariate testing; bootstrap hypothesis testing; triangular systems; endogeneity; identification; GMM; conditional heteroskedasticity; GARCH;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:20031. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.