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

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  • William Barnett

    (Department of Economics, The 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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Bibliographic Info

Paper provided by University of Kansas, Department of Economics in its series WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS with number 201213.

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Length: 24 pages
Date of creation: Sep 2012
Date of revision: Sep 2012
Handle: RePEc:kan:wpaper:201213

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  1. William Barnett, 2005. "Monetary Aggregation," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200510, University of Kansas, Department of Economics, revised Mar 2005.
  2. Blackorby, Charles & Schworm, William, 1984. "The Structure of Economies with Aggregate Measures of Capital: A Complete Characterization," Review of Economic Studies, Wiley Blackwell, vol. 51(4), pages 633-50, October.
  3. Stahl, Dale O, II, 1983. "Quasi-Homothetic Preferences, the Generalized Divisia Quantity Index, and Aggregation," Economica, London School of Economics and Political Science, vol. 50(197), pages 87-93, February.
  4. Belongia, Michael T, 1996. "Measurement Matters: Recent Results from Monetary Economics Reexamined," Journal of Political Economy, University of Chicago Press, vol. 104(5), pages 1065-83, October.
  5. Julio J. Rotemberg & John C. Driscoll & James M. Poterba, 1991. "Money, Output and Prices: Evidence from A New Monetary Aggregate," NBER Working Papers 3824, National Bureau of Economic Research, Inc.
  6. James H. Stock & Martin Feldstein, 1994. "Measuring Money Growth When Financial Markets Are Changing," NBER Working Papers 4888, National Bureau of Economic Research, Inc.
  7. William A. Barnett & Melvin Hinich & Piyu Yue, 1989. "Monitoring monetary aggregates under risk aversion," Proceedings, Federal Reserve Bank of St. Louis, pages 189-245.
  8. Feenstra, Robert C., 1986. "Functional equivalence between liquidity costs and the utility of money," Journal of Monetary Economics, Elsevier, vol. 17(2), pages 271-291, March.
  9. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "Multilateral Comparisons of Output, Input, and Productivity Using Superlative Index Numbers," Economic Journal, Royal Economic Society, vol. 92(365), pages 73-86, March.
  10. Barnett, William A., 1978. "The user cost of money," Economics Letters, Elsevier, vol. 1(2), pages 145-149.
  11. Hulten, Charles R, 1973. "Divisia Index Numbers," Econometrica, Econometric Society, vol. 41(6), pages 1017-25, November.
  12. Blackorby, Charles & Davidson, Russell & Schworm, William, 1991. "Implicit separability: Characterisation and implications for consumer demands," Journal of Economic Theory, Elsevier, vol. 55(2), pages 364-399, December.
  13. Constantinides, George M, 1990. "Habit Formation: A Resolution of the Equity Premium Puzzle," Journal of Political Economy, University of Chicago Press, vol. 98(3), pages 519-43, June.
  14. Blackorby Charles & Russell R. Robert, 1994. "The Conjunction of Direct and Indirect Separability," Journal of Economic Theory, Elsevier, vol. 62(2), pages 480-498, April.
  15. Barnett, William A., 1980. "Economic monetary aggregates an application of index number and aggregation theory," Journal of Econometrics, Elsevier, vol. 14(1), pages 11-48, September.
  16. Mark Rubinstein, 1976. "The Valuation of Uncertain Income Streams and the Pricing of Options," Bell Journal of Economics, The RAND Corporation, vol. 7(2), pages 407-425, Autumn.
  17. Fischer, Stanley, 1974. "Money and the Production Function," Economic Inquiry, Western Economic Association International, vol. 12(4), pages 517-33, December.
  18. Barnett, William A & Fisher, Douglas & Serletis, Apostolos, 1992. "Consumer Theory and the Demand for Money," Journal of Economic Literature, American Economic Association, vol. 30(4), pages 2086-2119, December.
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Cited by:
  1. Barnett, William A, 1997. "Which Road Leads to Stable Money Demand?," Economic Journal, Royal Economic Society, vol. 107(443), pages 1171-85, July.
  2. William Barnett & Yi Liu, 2012. "Beyond the Risk Neutral Utility Function," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201216, University of Kansas, Department of Economics, revised Sep 2012.
  3. 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.
  4. 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.
  5. Wesche, Katrin, 1996. "Aggregating Money Demand in Europe with a Divisia Index," Discussion Paper Serie B 392, University of Bonn, Germany.

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