Generalized Numeraire Portfolios

Giorgio De Santis, Bruno Gerard and Fulvio Ortu

University of California at Los Angeles, Anderson Graduate School of Management from Anderson Graduate School of Management, UCLA

Abstract: Given a set of assets, a numeraire portfolio (Long, 1990) is a self-financing portfolio with positive value and whose return process is a stochastic discount factors process. By relaxing the self-financing constraint, we define the generalized numeraire portfolios, and state necessary and sufficient conditions for their existence. We show that a set of assets admits generalized numeraire portfolios if and only if it is arbitrage free and at least one trading strategy has positive value. We also show that generalized numeraire portfolios are solutions to the optimal growth problem under the weaker constraint that the self-financing condition holds in conditional discounted expected value. Since the numeraire portfolio is unique (up to a scale factor), it generates only one admissible stochastic discount factor process. Generalized numeraire portfolios generate instead an infinite subset of, and under some conditions, all the admissible one-period stochastic discount factors. Finally, we propose some interesting tests that exploit the notion of generalized numeraire portfolios and provide preliminary empirical evidence.

Date: 2000-11-01
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.escholarship.org/uc/item/7m36d1tv.pdf;origin=repeccitec (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cdl:anderf:qt7m36d1tv

Access Statistics for this paper

More papers in University of California at Los Angeles, Anderson Graduate School of Management from Anderson Graduate School of Management, UCLA Contact information at EDIRC.
Bibliographic data for series maintained by Lisa Schiff ().