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The CAPM-Extended Divisia Monetary Aggregate with Exact Tracking under Risk

Author

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  • William Barnett

    (Department of Economics, University of Kansas)

  • Yi Liu

    (Washington University in St.Louis)

Abstract

This paper extends the field of index number theory to the case of risk, by deriving the Divisia index from the Euler equations under risk, rather than from the first order conditions under perfect certainty, as was done by Francois Divisia. The result is an extended Divisia index which corrects for risk by subtracting from each risky user cost price a CCAPM beta term. The formula is derived and illustrated in terms of aggregation over monetary assets that yield risky return paid at the end of the period. Hence the beta correction is a function of the covariance between each rate of return and the consumption stream, and also depends upon the degree of risk aversion.
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Suggested Citation

  • William Barnett & Yi Liu, 2012. "The CAPM-Extended Divisia Monetary Aggregate with Exact Tracking under Risk," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201213, University of Kansas, Department of Economics, revised Sep 2012.
    • Handle: RePEc:kan:wpaper:201213
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    File URL: http://www2.ku.edu/~kuwpaper/2009Papers/201213.pdf
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    1. William A. Barnett & Yi Liu, 2000. "Beyond the Risk-neutral Utility Function," Palgrave Macmillan Books, in: Michael T. Belongia & Jane M. Binner (ed.), Divisia Monetary Aggregates, chapter 1, pages 11-27, Palgrave Macmillan.
    2. William A. Barnett, 2000. "Which Road Leads to Stable Money Demand?," Contributions to Economic Analysis, in: The Theory of Monetary Aggregation, pages 577-592, Emerald Group Publishing Limited.
    3. Alicia Gazely & Jane Binner & Graham Kendall, 2004. "Co-evolution vs. Neural Networks; An Evaluation of UK Risky Money," Computing in Economics and Finance 2004 258, Society for Computational Economics.
    4. Obben, James & Nugroho, Agus Eko, 2003. "Determinants Of The Funding Volatility Of Indonesian Banks: A Dynamic Model," Discussion Papers 23700, Massey University, Department of Applied and International Economics.
    5. Binner, Jane & Elger, Thomas & de Peretti, Philipe, 2002. "Is UK Risky Money Weakly Separable? A Stochastic Approach," Working Papers 2002:13, Lund University, Department of Economics.

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    More about this item

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates

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