IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/10447.html
   My bibliography  Save this paper

A Jackknife Estimator for Tracking Error Variance of Optimal Portfolios Constructed Using Estimated Inputs1

Author

Listed:
  • Gopal K. Basak
  • Ravi Jagannathan
  • Tongshu Ma

Abstract

We develop a jackknife estimator for the conditional variance of a minimum-tracking- error-variance portfolio constructed using estimated covariances. We empirically evaluate the performance of our estimator using an optimal portfolio of 200 stocks that has the lowest tracking error with respect to the S&P500 benchmark when three years of daily return data are used for estimating covariances. We find that our jackknife estimator provides more precise estimates and suffers less from in-sample optimism when compared to conventional estimators.

Suggested Citation

  • Gopal K. Basak & Ravi Jagannathan & Tongshu Ma, 2004. "A Jackknife Estimator for Tracking Error Variance of Optimal Portfolios Constructed Using Estimated Inputs1," NBER Working Papers 10447, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:10447
    Note: AP
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w10447.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
    2. Sharpe, William F., 1967. "Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(2), pages 76-84, June.
    3. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1683, August.
    4. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2005. "There is a risk-return trade-off after all," Journal of Financial Economics, Elsevier, vol. 76(3), pages 509-548, June.
    5. Dong-Hyun Ahn & Jennifer Conrad & Robert F. Dittmar, 2009. "Basis Assets," The Review of Financial Studies, Society for Financial Studies, vol. 22(12), pages 5133-5174, December.
    6. Schwert, G William & Seguin, Paul J, 1990. "Heteroskedasticity in Stock Returns," Journal of Finance, American Finance Association, vol. 45(4), pages 1129-1155, September.
    7. Olivier Ledoit & Michael Wolf, 2003. "Honey, I shrunk the sample covariance matrix," Economics Working Papers 691, Department of Economics and Business, Universitat Pompeu Fabra.
    8. Shanken, Jay, 1985. "Multivariate tests of the zero-beta CAPM," Journal of Financial Economics, Elsevier, vol. 14(3), pages 327-348, September.
    9. Foster, F Douglas & Smith, Tom & Whaley, Robert E, 1997. "Assessing Goodness-of-Fit of Asset Pricing Models: The Distribution of the Maximal R-Squared," Journal of Finance, American Finance Association, vol. 52(2), pages 591-607, June.
    10. Lahiri, S.N., 2002. "On The Jackknife-After-Bootstrap Method For Dependent Data And Its Consistency Properties," Econometric Theory, Cambridge University Press, vol. 18(1), pages 79-98, February.
    11. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2006. "Predicting volatility: getting the most out of return data sampled at different frequencies," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 59-95.
    12. MacKinlay, A. Craig, 1987. "On multivariate tests of the CAPM," Journal of Financial Economics, Elsevier, vol. 18(2), pages 341-371, June.
    13. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    14. Jobson, J. D. & Korkie, Bob, 1982. "Potential performance and tests of portfolio efficiency," Journal of Financial Economics, Elsevier, vol. 10(4), pages 433-466, December.
    15. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    16. Jorion, Philippe, 1986. "Bayes-Stein Estimation for Portfolio Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(3), pages 279-292, September.
    17. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    18. Kandel, Shmuel, 1984. "The likelihood ratio test statistic of mean-variance efficiency without a riskless asset," Journal of Financial Economics, Elsevier, vol. 13(4), pages 575-592, December.
    19. 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.
    20. 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.
    21. Foster, Dean P & Nelson, Daniel B, 1996. "Continuous Record Asymptotics for Rolling Sample Variance Estimators," Econometrica, Econometric Society, vol. 64(1), pages 139-174, January.
    22. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2004. "The MIDAS Touch: Mixed Data Sampling Regression Models," University of California at Los Angeles, Anderson Graduate School of Management qt9mf223rs, Anderson Graduate School of Management, UCLA.
    23. Elton, Edwin J & Gruber, Martin J, 1973. "Estimating the Dependence Structure of Share Prices-Implications for Portfolio Selection," Journal of Finance, American Finance Association, vol. 28(5), pages 1203-1232, December.
    24. repec:bla:jfinan:v:58:y:2003:i:4:p:1651-1684 is not listed on IDEAS
    25. Roll, Richard, 1985. "A note on the geometry of Shanken's CSR T2 test for mean/variance efficiency," Journal of Financial Economics, Elsevier, vol. 14(3), pages 349-357, September.
    26. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    27. Tse, Y K & Tsui, Albert K C, 2002. "A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 351-362, July.
    28. Fleming, Jeff & Kirby, Chris & Ostdiek, Barbara, 2003. "The economic value of volatility timing using "realized" volatility," Journal of Financial Economics, Elsevier, vol. 67(3), pages 473-509, March.
    Full references (including those not matched with items on IDEAS)

    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. Gopal K. Basak & Ravi Jagannathan & Tongshu Ma, 2009. "Jackknife Estimator for Tracking Error Variance of Optimal Portfolios," Management Science, INFORMS, vol. 55(6), pages 990-1002, June.
    2. Frahm, Gabriel & Memmel, Christoph, 2008. "Dominating estimators for the global minimum variance portfolio," Discussion Papers in Econometrics and Statistics 2/08, University of Cologne, Institute of Econometrics and Statistics.
    3. Nikolaus Hautsch & Lada M. Kyj & Peter Malec, 2015. "Do High‐Frequency Data Improve High‐Dimensional Portfolio Allocations?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(2), pages 263-290, March.
    4. Francisco Peñaranda & Enrique Sentana, 2024. "Portfolio management with big data," Working Papers wp2024_2411, CEMFI.
    5. Hautsch, Nikolaus & Voigt, Stefan, 2019. "Large-scale portfolio allocation under transaction costs and model uncertainty," Journal of Econometrics, Elsevier, vol. 212(1), pages 221-240.
    6. Herwartz, Helmut & Golosnoy, Vasyl, 2007. "Semiparametric Approaches to the Prediction of Conditional Correlation Matrices in Finance," Economics Working Papers 2007-23, Christian-Albrechts-University of Kiel, Department of Economics.
    7. Behr, Patrick & Guettler, Andre & Truebenbach, Fabian, 2012. "Using industry momentum to improve portfolio performance," Journal of Banking & Finance, Elsevier, vol. 36(5), pages 1414-1423.
    8. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    9. Santos, André Alves Portela & Ferreira, Alexandre R., 2017. "On the choice of covariance specifications for portfolio selection problems," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 37(1), May.
    10. repec:hum:wpaper:sfb649dp2013-014 is not listed on IDEAS
    11. Gregory Bauer & Keith Vorkink, 2007. "Multivariate Realized Stock Market Volatility," Staff Working Papers 07-20, Bank of Canada.
    12. Bob Korkie & Harry J. Turtle, 2002. "A Mean-Variance Analysis of Self-Financing Portfolios," Management Science, INFORMS, vol. 48(3), pages 427-443, March.
    13. Shanken, Jay & Zhou, Guofu, 2007. "Estimating and testing beta pricing models: Alternative methods and their performance in simulations," Journal of Financial Economics, Elsevier, vol. 84(1), pages 40-86, April.
    14. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," 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 1127-1220, Elsevier.
    15. Gilles Boevi Koumou, 2020. "Diversification and portfolio theory: a review," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(3), pages 267-312, September.
    16. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, September.
    17. Yan, Cheng & Zhang, Huazhu, 2017. "Mean-variance versus naïve diversification: The role of mispricing," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 48(C), pages 61-81.
    18. Hsu, Po-Hsuan & Han, Qiheng & Wu, Wensheng & Cao, Zhiguang, 2018. "Asset allocation strategies, data snooping, and the 1 / N rule," Journal of Banking & Finance, Elsevier, vol. 97(C), pages 257-269.
    19. James DiLellio, 2015. "A Kalman filter control technique in mean-variance portfolio management," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 39(2), pages 235-261, April.
    20. repec:hal:journl:peer-00741629 is not listed on IDEAS
    21. Plachel, Lukas, 2019. "A unified model for regularized and robust portfolio optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 109(C).
    22. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.

    More about this item

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • 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:nbr:nberwo:10447. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.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.