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Sampling Distribution of the Relative Risk Aversion Estimator: Theory and Applications

In: HANDBOOK OF FINANCIAL ECONOMETRICS, MATHEMATICS, STATISTICS, AND MACHINE LEARNING

Author

Listed:
  • Marvin J. Karson
  • David C. Cheng
  • Cheng Few Lee

Abstract

Brown and Gibbons (1985) developed a theory of relative risk aversion estimation in terms of average market rates of return and the variance of market rates of return. However, the exact sampling distributions of sampling distribution of an appropriate relative risk aversion estimator. First, we have derived theoretically the density of Brown and Gibbons’ maximum likelihood estimator. It is shown that the central t is not appropriate for estimating the significance of estimated relative risk aversion distribution. Then, we derived the minimum variance unbiased estimator by a linear transformation of Brown and Gibbons’ maximum likelihood estimator. The density function is neither a central nor a noncentral t distribution. Then, density function of this new distribution has been tabulated. There is an empirical example to illustrate the application of this new sampling distribution.

Suggested Citation

  • Marvin J. Karson & David C. Cheng & Cheng Few Lee, 2020. "Sampling Distribution of the Relative Risk Aversion Estimator: Theory and Applications," World Scientific Book Chapters, in: Cheng Few Lee & John C Lee (ed.), HANDBOOK OF FINANCIAL ECONOMETRICS, MATHEMATICS, STATISTICS, AND MACHINE LEARNING, chapter 65, pages 2323-2335, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789811202391_0065
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    More about this item

    Keywords

    Financial Econometrics; Financial Mathematics; Financial Statistics; Financial Technology; Machine Learning; Covariance Regression; Cluster Effect; Option Bound; Dynamic Capital Budgeting; Big Data;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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