Dynamic Spanning in the Consumption-Based Capital Asset Pricing Model

Posted: 11 Sep 2001

See all articles by Peter O. Christensen

Peter O. Christensen

Copenhagen Business School - Department of Finance

Svend Erik Graversen

University of Aarhus - Department of Mathematical Sciences

Kristian R. Miltersen

Copenhagen Business School

Abstract

Under the assumptions of the Consumption-based Capital Asset Pricing Model (CCAPM), Pareto optimal consumption allocations are characterized by each agent's consumption process being adapted to the filtration generated by the aggregate consumption process of the economy. The wealth processes of the agents, however, are adapted to the finer filtration generated by aggregate consumption and the conditional distribution of future aggregate consumption. Therefore, in order to achieve Pareto optimal consumption allocations, a sufficiently varied set of assets must exist such that any wealth process adapted to this finer filtration can be implemented by dynamically trading in that set of assets. We provide sufficient conditions for the existence of such a set of assets based on dynamically trading contingent claims on aggregate consumption. In addition, we give sufficient conditions for the existence of equilibria in a dynamically effectively complete market in which agents are only able to trade in contingent claims on aggregate consumption, the market portfolio of firms, and a (numeraire) zero-coupon bond. We demonstrate the role of short- and long-term contingent claims on aggregate consumption for the implementation of Pareto optimal allocations in the presence of short- and long-term risks. In addition, in the presence of personal risks, we demonstrate the role of insurance contracts.

Keywords: Consumption-based capital asset pricing model, CCAPM, dynamic trading

JEL Classification: G13

Suggested Citation

Christensen, Peter Ove and Graversen, Svend Erik and Miltersen, Kristian Risgaard, Dynamic Spanning in the Consumption-Based Capital Asset Pricing Model. Available at SSRN: https://ssrn.com/abstract=270115

Peter Ove Christensen (Contact Author)

Copenhagen Business School - Department of Finance ( email )

Solbjerg Plads 3
Frederiksberg, DK-2000
Denmark
+45 6140 3237 (Phone)

Svend Erik Graversen

University of Aarhus - Department of Mathematical Sciences ( email )

DK-8000 Aarhus
Denmark

Kristian Risgaard Miltersen

Copenhagen Business School ( email )

Solbjerg Plads 3
Frederiksberg C, DK - 2000
Denmark

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