Ortu, Fulvio: Generalized Numeraire Portfolios
World Conference Econometric Society, 2000, Seattle

Giorgio deSantis, Goldman Sachs and Company
Bruno Gerard, University of California, Los Angeles
Fulvio Ortu, University of Southern California
Generalized Numeraire Portfolios
Session: C-13-25  Wednesday 16 August 2000  by Ortu, Fulvio
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 the generalized numeraire portfolios solve the problem of maximizing the logarithmic expected utility from terminal wealth, under the constraint that the feasible dynamic trading strategies be self-financing 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 empirical tests that exploit the notion of generalized numeraire portfolios and provide preliminary empirical evidence.


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