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- Title
Risk Aversion and Wealth Effects on Portfolios with Many Assets.
- Authors
Cass, D.; Stiglitz, J.E.
- Abstract
This paper is concerned with describing the qualitative behaviour of alternative characterizations of portfolios with many assets or securities; in particular, we wish to know what can be said about changes in portfolios as wealth changes. At least three alternative characterizations seem available: (1) A portfolio can be characterized by the percentage of its value held in the form of a safe asset or money. Those like Tobin [5] and Arrow [1] who have attempted to derive properties of the demand curve for money from portfolio analysis have implicitly employed this characterization. (2) A portfolio can be characterized by certain statistical properties, e.g., its mean, variance, range, etc. (3) A portfolio can be characterized in terms of certainty equivalents: at what certain rate of return would the individual investor be indifferent between his (risky) portfolio and the portfolio consisting of just a safe asset with that rate of return? In Section 2 we present theorems describing the effect of changes in wealth on portfolios in terms of all three characterizations for the special case of two assets, one of which is perfectly safe. In Sections 3 and 4 we consider whether these theorems can be extended to situations where there are more than two assets. In Section 3, we show that if there are as many securities as states of nature, although the theorems relating to the second and third characterizations still obtain, that relating to the first does not. This suggests that without stringent conditions it does not appear possible to derive a simple theory of the demand for money from portfolio analysis. In Section 4, we show that only the theorem relating to certainty equivalents can be extended to the general case where there are more states of nature than securities.
- Subjects
PORTFOLIO management (Investments); SECURITIES; INVESTMENTS; RISK aversion; ASSET allocation; WEALTH
- Publication
Review of Economic Studies, 1972, Vol 39, Issue 3, p331
- ISSN
0034-6527
- Publication type
Article
- DOI
10.2307/2296363