The Structure of the Cost of Capital Under Uncertainty

Abstract

In the analysis of models of competitive markets under uncertainty, different approaches can be distinguished. One approach, typically dealt with in welfare economics, is the specification of environmental conditions that are sufficient for the existence of equilibrium prices, with all the corollary implications for the efficiency of the competitive system. Prominent examples of this approach are the works of Arrow [2], Debreu [3] and Radner [12]. Another approach, typical to the analysis of capital markets, is concerned more with the structure of equilibrium prices, rather than their existence. Under this approach, basic interest lies in the implications of various given assumptions about the preferences of individuals (e.g. risk aversion) on the relationship between various properties of capital assets and their equilibrium prices, which are initially assumed to exist. Such studies extend from the classical investigations, such as Hicks [6] and Lutz [10], on the term to maturity of “riskless” capital assets, to recent ones concerned primarily with the issue of risk, such as Sharpe [13], Lintner [9], Hirshleifer [7,8] and others. 1 The present study represents an attempt at a slightly different approach. We postulate the existence of equilibrium prices for capital assets under uncertainty, and then proceed to analyze the properties implicit in their definition. It is shown that some results can be derived without recourse to the way individuals make decisions, their detailed preferences or their subjective assessments of probabilities. ∗ The author appreciates the must useful comments of two referees. 1 For example, see also Diamond [4], Green [5], and Myers [11] - all using the same ArrowDebreu framework of uncertainty used here.