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Uncertainty in Second Moments: Implications for Portfolio Allocation


  • David Daewhan Cho


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.

Suggested Citation

  • David Daewhan Cho, 2004. "Uncertainty in Second Moments: Implications for Portfolio Allocation," Econometric Society 2004 Far Eastern Meetings 431, Econometric Society.
  • Handle: RePEc:ecm:feam04:431

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    References listed on IDEAS

    1. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
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    More about this item


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

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions


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