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

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Author Info

  • William A. Barnett

    (Washington University in St. Louis)

  • Yi Liu

    (University of S. Alabama)

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 EconWPA in its series Finance with number 9602001.

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Length: 24 pages
Date of creation: 12 Feb 1996
Date of revision:
Handle: RePEc:wpa:wuwpfi:9602001

Note: Type of Document - Microsoft Word; prepared on Macintosh; to print on Postscript; pages: 24 ; figures: None.. See
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Keywords: CAPM Divisia aggregation index risk money;

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References

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  1. Barnett, William A., 1978. "The user cost of money," Economics Letters, Elsevier, vol. 1(2), pages 145-149.
  2. 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.
  3. Hulten, Charles R, 1973. "Divisia Index Numbers," Econometrica, Econometric Society, vol. 41(6), pages 1017-25, November.
  4. 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.
  5. William Barnett, 2005. "Monetary Aggregation," Macroeconomics 0503017, EconWPA.
  6. 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.
  7. 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.
  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. 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.
  10. James H. Stock & Martin Feldstein, 1994. "Measuring Money Growth When Financial Markets Are Changing," NBER Working Papers 4888, National Bureau of Economic Research, Inc.
  11. 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.
  12. 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.
  13. Rotemberg, J.J. & Driscoll, J.C. & Poterba, J.M., 1991. "Money, Output, and Prices: Evidence from a New Monetary Aggregate," Working papers 585, Massachusetts Institute of Technology (MIT), Department of Economics.
  14. 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.
  15. 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.
  16. William A. Barnett & Melvin Hinich & Piyu Yue, 1989. "Monitoring monetary aggregates under risk aversion," Proceedings, Federal Reserve Bank of St. Louis, pages 189-245.
  17. Fischer, Stanley, 1974. "Money and the Production Function," Economic Inquiry, Western Economic Association International, vol. 12(4), pages 517-33, December.
  18. 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.
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Citations

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Cited by:
  1. 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.
  2. Wesche, Katrin, 1996. "Aggregating Money Demand in Europe with a Divisia Index," Discussion Paper Serie B 392, University of Bonn, Germany.
  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. William A. Barnett & Yi Liu, 1996. "Beyond the Risk Neutral Utility Function," Macroeconomics 9602001, EconWPA.
  5. Barnett, William A, 1997. "Which Road Leads to Stable Money Demand?," Economic Journal, Royal Economic Society, vol. 107(443), pages 1171-85, July.

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