IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpfi/9602001.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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.

Suggested Citation

  • William A. Barnett & Yi Liu, 1996. "The CAPM-Extended Divisia Monetary Aggregate with Exact Tracking under Risk," Finance 9602001, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpfi:9602001
    Note: Type of Document - Microsoft Word; prepared on Macintosh; to print on Postscript; pages: 24 ; figures: None.. See
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/fin/papers/9602/9602001.pdf
    Download Restriction: no

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/fin/papers/9602/9602001.ps.gz
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fisher, Franklin M. & Shell, Karl, 1972. "The Economic Theory of Price Indices," Elsevier Monographs, Elsevier, edition 1, number 9780122577505 edited by Shell, Karl.
    2. William A. Barnett & Douglas Fisher & Apostolos Serletis, 2006. "Consumer Theory and the Demand for Money," World Scientific Book Chapters, in: Money And The Economy, chapter 1, pages 3-43, World Scientific Publishing Co. Pte. Ltd..
    3. 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.
    4. Maurice Salles, 2016. "Social choice," Chapters, in: Gilbert Faccarello & Heinz D. Kurz (ed.), Handbook on the History of Economic Analysis Volume III, chapter 36, pages 518-537, Edward Elgar Publishing.
    5. Rotemberg, Julio J & Driscoll, John C & Poterba, James M, 1995. "Money, Output, and Prices: Evidence from a New Monetary Aggregate," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 67-83, January.
    6. 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.
    7. Feldstein, Martin & Stock, James H., 1996. "Measuring money growth when financial markets are changing," Journal of Monetary Economics, Elsevier, vol. 37(1), pages 3-27, February.
    8. William Barnett, 2005. "Monetary Aggregation," Macroeconomics 0503017, University Library of Munich, Germany.
    9. 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.
    10. 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.
    11. 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.
    12. 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 519-543, June.
    13. 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.
    14. Hulten, Charles R, 1973. "Divisia Index Numbers," Econometrica, Econometric Society, vol. 41(6), pages 1017-1025, November.
    15. Belongia, Michael T, 1996. "Measurement Matters: Recent Results from Monetary Economics Reexamined," Journal of Political Economy, University of Chicago Press, vol. 104(5), pages 1065-1083, October.
    16. 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.
    17. William A. Barnett & Melvin Hinich & Piyu Yue, 1989. "Monitoring monetary aggregates under risk aversion," Proceedings, Federal Reserve Bank of St. Louis, pages 189-245.
    18. Moulin, Herve, 1994. "Social choice," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 31, pages 1091-1125, Elsevier.
    19. Charles Blackorby & William Schworm, 1984. "The Structure of Economies with Aggregate Measures of Capital: A Complete Characterization," Review of Economic Studies, Oxford University Press, vol. 51(4), pages 633-650.
    20. Barnett, William A., 1978. "The user cost of money," Economics Letters, Elsevier, vol. 1(2), pages 145-149.
    21. Fischer, Stanley, 1974. "Money and the Production Function," Economic Inquiry, Western Economic Association International, vol. 12(4), pages 517-533, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Barnett, William A, 1997. "Which Road Leads to Stable Money Demand?," Economic Journal, Royal Economic Society, vol. 107(443), pages 1171-1185, July.
    3. William A. Barnett & Yi Liu, 1996. "Beyond the Risk Neutral Utility Function," Macroeconomics 9602001, University Library of Munich, Germany.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. William A. Barnett & Yi Liu & Haiyang Xu & Mark Jensen, 1996. "The CAPM Risk Adjustment Needed for Exact Aggregation over Financial Assets," Econometrics 9602003, University Library of Munich, Germany.
    2. Barnett, William A, 1997. "Which Road Leads to Stable Money Demand?," Economic Journal, Royal Economic Society, vol. 107(443), pages 1171-1185, July.
    3. William A. Barnett & Yi Liu, 1996. "Beyond the Risk Neutral Utility Function," Macroeconomics 9602001, University Library of Munich, Germany.
    4. William A. Barnett & Milka Kirova & Meenakshi Pasupathy, 1996. "Technology Modeling: Curvature is not Sufficient for Regularity," Econometrics 9602002, University Library of Munich, Germany, revised 24 Jun 1999.
    5. William A. Barnett & Melvin J. Hinich & Piyu Yue, 2011. "The Exact Theoretical Rational Expectations Monetary Aggregate," World Scientific Book Chapters, in: Financial Aggregation And Index Number Theory, chapter 2, pages 53-84, World Scientific Publishing Co. Pte. Ltd..
    6. Barnett, William A. & Chauvet, Marcelle, 2011. "How better monetary statistics could have signaled the financial crisis," Journal of Econometrics, Elsevier, vol. 161(1), pages 6-23, March.
    7. William Barnett & Barry E. Jones & Milka Kirova & Travis D. Nesmith & Meenakshi Pasupathy1, 2004. "The Nonlinear Skeletons in the Closet," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200403, University of Kansas, Department of Economics, revised May 2004.
    8. William A. Barnett & Marcelle Chauvet & Heather L. R. Tierney, 2011. "Measurement Error in Monetary Aggregates: A Markov Switching Factor Approach," World Scientific Book Chapters, in: Financial Aggregation And Index Number Theory, chapter 7, pages 207-249, World Scientific Publishing Co. Pte. Ltd..
    9. Ryan S. Mattson & Philippe de Peretti, 2014. "Investigating the Role of Real Divisia Money in Persistence-Robust Econometric Models," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00984827, HAL.
    10. Barnett, William A. & Keating, John W. & Kelly, Logan J., 2008. "Toward a bias corrected currency equivalent index," Economics Letters, Elsevier, vol. 100(3), pages 448-451, September.
    11. William A. Barnett & Marcelle Chauvet, 2011. "International Financial Aggregation and Index Number Theory: A Chronological Half-Century Empirical Overview," World Scientific Book Chapters, in: Financial Aggregation And Index Number Theory, volume 2, chapter 1, pages 1-51, World Scientific Publishing Co. Pte. Ltd..
    12. William Barnett & Liting Su, 2014. "The Joint Services of Money and Credit," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201407, University of Kansas, Department of Economics, revised Dec 2014.
    13. Duca, John V. & VanHoose, David D., 2004. "Recent developments in understanding the demand for money," Journal of Economics and Business, Elsevier, vol. 56(4), pages 247-272.
    14. Barnett, William & Chauvet, Marcelle & Leiva-Leon, Danilo & Su, Liting, 2016. "Nowcasting nominal gdp with the credit-card augmented Divisia monetary aggregates," MPRA Paper 73246, University Library of Munich, Germany.
    15. Barnett, William & Chauvet, Marcelle & Leiva-Leon, Danilo & Su, Liting, 2016. "Nowcasting Nominal GDP with the Credit-Card Augmented Divisia Monetary," Studies in Applied Economics 59, The Johns Hopkins Institute for Applied Economics, Global Health, and the Study of Business Enterprise.
    16. Richard G. Anderson & Barry E. Jones & Travis D. Nesmith, 1997. "Special report: The monetary services index project of the Federal Reserve Bank of St. Louis: introduction to the St. Louis monetary services index project," Review, Federal Reserve Bank of St. Louis, issue Jan, pages 25-30.
    17. John W. Keating & Logan J. Kelly & A. Lee Smith & Victor J. Valcarcel, 2019. "A Model of Monetary Policy Shocks for Financial Crises and Normal Conditions," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 51(1), pages 227-259, February.
    18. Belongia, Michael T. & Ireland, Peter N., 2019. "The demand for Divisia Money: Theory and evidence," Journal of Macroeconomics, Elsevier, vol. 61(C), pages 1-1.
    19. Barnett, William A. & Su, Liting, 2019. "Risk Adjustment Of The Credit-Card Augmented Divisia Monetary Aggregates," Macroeconomic Dynamics, Cambridge University Press, vol. 23(S1), pages 90-114, September.
    20. Jane M. Binner & Alicia M. Gazely & Shu‐Heng Chen & Bin‐Tzong Chie, 2004. "Financial Innovation and Divisia Money in Taiwan: Comparative Evidence from Neural Network and Vector Error‐Correction Forecasting Models," Contemporary Economic Policy, Western Economic Association International, vol. 22(2), pages 213-224, April.

    More about this item

    Keywords

    CAPM Divisia aggregation index risk money;

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpfi:9602001. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.