THE STRONG CASE FOR THE GENERALIZED LOGARITHMIC UTILITY MODEL AS THE PREMIER MODEL OF FINANCIAL MARKETS

Authors

  • Robert Litzenberger,

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    • Stanford University
  • Mark Rubinstein

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    • Assistant Professor, Graduate School of Business Administration, University of California, Berkeley. Research for this paper was supported in part by a grant from the Dean Witter Foundation. A substantially expanded version of this article is to appear in a book of papers given at the “Conference on Financial Decision-Making Under Uncertainty” held at Ein Bokek, Israel, March 9–14, 1975. In particular, all proofs have been omitted from this reduced version.

Abstract

This paper begins by comparing the available well-developed micro-economic models in finance which recognize uncertainty. It is argued that models whose distinctive simplifying assumption restricts utility functions are superior to those which instead restrict probability distributions, both with respect to the realism of their assumptions and richness of their conclusions. In particular, the most successful model, based on generalized logarithmic utility (GLUM), is a multiperiod consumption/portfolio and equilibrium model in discrete-time which (1) requires decreasing absolute risk aversion; (2) tolerates increasing, constant, or decreasing proportional risk aversion; (3) assumes no exogenous specification of the contemporaneous or intertemporal stochastic process of security prices; (4) tolerates heterogeneity with respect to wealth, lifetime, time-and risk-preference and beliefs; (5) results in a complete specification of consumption/portfolio decision and sharing rules which include nontrivial multiperiod separation properties and explains demand for default-free bonds of various maturities and options; (6) leads to a solution to the aggregation problem; (7) results in a complete specification of the contemporaneous and intertemporal process of security prices which reveals necessary and sufficient conditions for an unbiased term structure and the market portfolio to follow a random walk as a natural outcome of equilibrium; (8) provides an empirically testable aggregate consumption function relating per capita consumption to per capita wealth and the present value of a perpetual default-free annuity which does not require inferences of ex ante beliefs from ex post data; (9) provides a nontrivial multiperiod extension of popular single-period security valuation models which is empirically testable; (10) yields a simple multiperiod valuation formula for an uncertain income stream even when this income is serially correlated over time.

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