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Uncertainty in Second Moments: Implications for Portfolio Allocation

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  • David Daewhan Cho
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    Abstract

    This paper investigates the uncertainty in variance and covariance of asset returns. It is commonly believed that these second moments can be estimated very accurately. However, time varying volatility and nonnormality of asset returns can lead to imprecise variance estimates. Using CRSP value weighted monthly returns from 1926 to 2001, this paper shows that the variance is less accurately estimated than the expected return. In addition, a mean variance investor will incur significant certainty equivalent loss due to the uncertainty in second moments. Applying the Fama French 3 factor model to 25 size, BE/ME sorted portfolios from 1963 to 2001, the loss due to the variance estimation can be shown to be as large as the loss due to the expected return estimation. Moreover, as the number of assets in the portfolio increases, the loss due to the variance uncertainty becomes larger. This provides a possible explanation to the home bias puzzle.

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    File URL: http://repec.org/esFEAM04/up.4188.1073936201.pdf
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    Bibliographic Info

    Paper provided by Econometric Society in its series Econometric Society 2004 Far Eastern Meetings with number 431.

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    Date of creation: 11 Aug 2004
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    Handle: RePEc:ecm:feam04:431

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    Related research

    Keywords: Portfolio allocation; estimation risk; time varying volatility; home bias; bayesian analysis;

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    References

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    1. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
    2. Jun-Koo Kang & Rene M. Stulz, 1995. "Why Is There a Home Bias? An Analysis of Foreign Portfolio Equity Ownership in Japan," NBER Working Papers 5166, National Bureau of Economic Research, Inc.
    3. repec:att:wimass:9220 is not listed on IDEAS
    4. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
    5. Joshua D. Coval & Tobias J. Moskowitz, 1999. "Home Bias at Home: Local Equity Preference in Domestic Portfolios," Journal of Finance, American Finance Association, vol. 54(6), pages 2045-2073, December.
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    8. Lubos Pastor & Robert F. Stambaugh, . "Comparing Asset Pricing Models: An Investment Perspective," Rodney L. White Center for Financial Research Working Papers 16-99, Wharton School Rodney L. White Center for Financial Research.
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    10. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
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    17. Bai, Xuezheng & Russell, Jeffrey R. & Tiao, George C., 2003. "Kurtosis of GARCH and stochastic volatility models with non-normal innovations," Journal of Econometrics, Elsevier, vol. 114(2), pages 349-360, June.
    18. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    19. Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-29, December.
    20. 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.
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