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CAPM Risk Adjustment for Exact Aggregation Over Financial Assets
Barnett, William A. Liu, Yi Jensen, Mark
Barnett, William A.
Liu, Yi
Jensen, Mark
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Abstract
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.
Description
This is the authors' accepted manuscript. The publisher's version is available electronically from doi:10.1017/S1365100597003088
Date
1997-06-01
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Publisher
Cambridge University Press
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Keywords
Aggregation, Index number theory, Risk, Capital asset pricing
Citation
Barnett, William A., Liu, Yi, and Jensen, Mark "The CAPM Risk Adjustment for Exact Aggregation over Financial Assets," with Yi Liu and Mark Jensen, Macroeconomic Dynamics, vol 1, no 2, 1997, pp. 485-512. http://dx.doi.org/10.1017/S1365100597003088