| Sumario: | From the point of view of descriptive economic theory the main purpose of the theory of portfolio choice is the derivation of empirically meaningful restrictions on asset demand functions. Tobin's path-breaking paper was clearly focused on this objective. However, his model had some objectionable features which have frequently been pointed out by critics; see e.g. Arrow, Borch and Feldstein. First, it is based on very restrictive assumptions about the nature of preference orderings and/or subjective probabilities. Second, the quadratic utility function has some empirically unacceptable implications, e.g. that every risky asset is an inferior good; see e.g. Arrow. There exists by now a large literature on portfolio theory, much of which is concerned with generalizations of the mean-variance approach. However, this literature presents a confusing picture to the economist who approaches it with a background in the general theory of consumer demand, which most economists tend to regard as a model for any theory of individual choice. In that theory one begins with a very general set of assumptions, the most important of which—given the axioms ensuring the existence of a utility function are quasi-concavity and differentiability of the utility function. Once the results using this set of assumptions have been established, additional assumptions—like homogeneity, separability, etc.—can be introduced and more specialized results can be derived. In portfolio theory the situation is different. Here one typically starts out with a very special set of assumptions, like quadratic utility functions or normal probability distributions. Moreover, criticisms of such assumptions often take the form of introducing alternative assumptions like decreasing risk aversion, which, although they may be more attractive, are still rather special assumptions. What one would like to know is whether it is possible to derive a meaningful theory of asset demand given only weak conditions on utility functions and probability distributions of the sort that correspond to the above mentioned assumptions in consumer demand analysis. If that were possible, one would have established a standard against which more specialized results could be evaluated, just as the most general theory of consumer demand provides a standard for judging results that are derived from assumptions like separability, additivity, homogeneity, etc.
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