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Capm Risk Adjustment For Exact Aggregation Over Financial Assets


  • LIU, YI


Barnett originated the Divisia monetary aggregates, which in continuous time exactly track any monetary aggregator function under perfect certainty. With user costs measuring the prices of the services of components, Barnett's aggregates are based on Francois Divisia's derivation of the Divisia line integral from the first-order conditions for optimizing behavior by economic agents under perfect certainty. We derive an extended Divisia index from the first-order conditions (Euler equations) that apply under risk. Our extended Divisia index is the first extension of index number theory into the domain of decision making under risk and thereby produces a route for the extension of all index number theory to permit non-risk-neutrality. We generate simulated data from a modeled rational consumer and investigate the tracking accuracy of the extended Divisia index to the consumer's exact aggregator function.

Suggested Citation

  • Barnett, William A. & Liu, Yi & Jensen, Mark, 1997. "Capm Risk Adjustment For Exact Aggregation Over Financial Assets," Macroeconomic Dynamics, Cambridge University Press, vol. 1(2), pages 485-512, June.
  • Handle: RePEc:cup:macdyn:v:1:y:1997:i:02:p:485-512_00

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    1. 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.
    2. William A. Barnett & Shu Wu, 2011. "On User Costs of Risky Monetary Assets," World Scientific Book Chapters, in: Financial Aggregation And Index Number Theory, chapter 3, pages 85-105, World Scientific Publishing Co. Pte. Ltd..
    3. William A. Barnett & Van H. Nguyen, 2021. "Constructing Divisia Monetary Aggregates for Singapore," JRFM, MDPI, vol. 14(8), pages 1-15, August.
    4. 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..
    5. 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..
    6. Barnett, William A. & Liu, Jinan, 2019. "User cost of credit card services under risk with intertemporal nonseparability," Journal of Financial Stability, Elsevier, vol. 42(C), pages 18-35.
    7. Tin, Jan, 1999. "Short-run and long-run demand for financial assets A microeconomic perspective," International Review of Economics & Finance, Elsevier, vol. 8(4), pages 467-478, November.
    8. Kelly, Logan J. & Barnett, William A. & Keating, John W., 2011. "Rethinking the liquidity puzzle: Application of a new measure of the economic money stock," Journal of Banking & Finance, Elsevier, vol. 35(4), pages 768-774, April.
    9. Yemba, Boniface P., 2022. "User cost of foreign monetary assets under dollarization," Finance Research Letters, Elsevier, vol. 49(C).
    10. 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, chapter 1, pages 1-51, World Scientific Publishing Co. Pte. Ltd..
    11. William Barnett & Shu Wu, 2004. "Intertemporally non-separable monetary-asset risk adjustment and aggregation," Economics Bulletin, AccessEcon, vol. 5(13), pages 1-9.
    12. 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.
    13. 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.
    14. 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.
    15. Elger Thomas & Binner Jane M., 2004. "The UK Household Sector Demand for Risky Money," The B.E. Journal of Macroeconomics, De Gruyter, vol. 4(1), pages 1-22, March.
    16. Barnett, William A. & Han, Qing & Zhang, Jianbo, 2021. "Monetary services aggregation under uncertainty: A behavioral economics extension using Choquet expectation," Journal of Economic Behavior & Organization, Elsevier, vol. 182(C), pages 437-447.
    17. Barnett, William A., 2014. "The joint services of money and credit," MPRA Paper 60336, University Library of Munich, Germany.
    18. repec:ebl:ecbull:v:5:y:2004:i:13:p:1-9 is not listed on IDEAS
    19. Kelly, Logan, 2007. "Measuring the Economic Stock of Money," MPRA Paper 4914, University Library of Munich, Germany.
    20. Binner, Jane M. & Chaudhry, Sajid & Kelly, Logan & Swofford, James L., 2018. "“Risky” monetary aggregates for the UK and US," Journal of International Money and Finance, Elsevier, vol. 89(C), pages 127-138.
    21. Paul Schreyer, 2009. "Comment on "A General-Equilibrium Asset-Pricing Approach to the Measurement of Nominal and Real Bank Output"," NBER Chapters, in: Price Index Concepts and Measurement, pages 320-328, National Bureau of Economic Research, Inc.
    22. Richard G. Anderson & Jason J. Buol, 2005. "Revisions to user costs for the Federal Reserve Bank of St. Louis monetary services indices," Review, Federal Reserve Bank of St. Louis, vol. 87(Nov), pages 735-750.
    23. Travis D. Nesmith, 2005. "Solving stochastic money-in-the-utility-function models," Finance and Economics Discussion Series 2005-52, Board of Governors of the Federal Reserve System (U.S.).
    24. James J. Heckman & Apostolos Serletis, "undated". "Introduction to Internally Consistent Modeling, Aggregation, Inference, and Policy," Working Papers 2014-73, Department of Economics, University of Calgary, revised 29 Sep 2014.

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