THE ARROW-PRATT MEASURES of risk aversion for von Neumann-Morgenstern utility functions have become workhorses for analyzing problems in the microeconomics of uncertainty. They have been used to characterize the qualitative properties of demand in insurance and asset markets, to examine the properties of risk taking in taxation models, and to study the interaction between risk and life-cycle savings problems to name just a few applications. Equally importantly, they have generated the linear risk tolerance class of utility functions which has provided canonical examples in such diverse areas as portfolio theory and the theory of teams. Despite these successes, there have been a number of areas for which the results have been weaker than hoped. It is natural to use the risk aversion measures to compare the behavior of individuals in risky choice situations. For example, consider the individual portfolio choice problem in a two asset world with a riskless asset and a risky asset. If individual A has a uniformly higher Arrow-Pratt coefficient of risk aversion than individual B, then B will always choose a portfolio combination with more wealth invested in the risky asset. But, suppose that both assets are risky. Now, there is no obvious sense in which the more risk averse individual can be said to hold a less risky portfolio, but it seems strange that such a simple alteration should destroy the analytics which support the basic intuition. Similarly, consider the basic insurance problem. If one individual, A, is more risk averse than another, B, in the Arrow-Pratt sense, it follows that A will pay a larger premium to insure against a random loss than will B. Typically, though, an individual evaluates partial rather than total insurance, that is, only some gambles can be insured against and others must be retained. In this case, even when the gambles which are retained are independent from those which are insured, it is no longer true that the individual whose Arrow-Pratt measure of risk aversion is higher will pay a larger insurance premium. The situation is no better when we consider comparative statics exercises for a single individual. Decreasing absolute risk aversion in the sense of Arrow and

This paper develops a continuous time general equilibrium model of a simple but complete economy and uses it to examine the behavior of asset prices. In this model, asset prices and their stochastic properties are determined endogenously. One principal result is a partial differential equation which asset prices must satisfy. The solution of this equation gives the equilibrium price of any asset in terms of the underlying real variables in the economy. IN THIS PAPER, we develop a general equilibrium asset pricing model for use in applied research. An important feature of the model is its integration of real and financial markets. Among other things, the model endogenously determines the stochastic process followed by the equilibrium price of any financial asset and shows how this process depends on the underlying real variables. The model is fully consistent with rational expectations and maximizing behavior on the part of all agents. Our framework is general enough to include many of the fundamental forces affecting asset markets, yet it is tractable enough to be specialized easily to produce specific testable results. Furthermore, the model can be extended in a number of straightforward ways. Consequently, it is well suited to a wide variety of applications. For example, in a companion paper, Cox, Ingersoll, and Ross [7], we use the model to develop a theory of the term structure of interest rates. Many studies have been concerned with various aspects of asset pricing under uncertainty. The most relevant to our work are the important papers on intertemporal asset pricing by Merton [19] and Lucas [16]. Working in a continuous time framework, Merton derives a relationship among the equilibrium expected rates of return on assets. He shows that when investment opportunities are changing randomly over time this relationship will include effects which have no analogue in a static one period model. Lucas considers an economy with homogeneous individuals and a single consumption good which is produced by a number of processes. The random output of these processes is exogenously determined and perishable. Assets are defined as claims to all or a part of the output of a process, and the equilibrium determines the asset prices. Our theory draws on some elements of both of these papers. Like Merton, we formulate our model in continuous time and make full use of the analytical tractability that this affords. The economic structure of our model is somewhat similar to that of Lucas. However, we include both endogenous production and

This paper uses an intertemporal general equilibrium asset pricing model to study the term structure of interest rates. In this model, anticipations, risk aversion, investment alternatives, and preferences about the timing of consumption all play a role in determining bond prices. Many of the factors traditionally mentioned as influencing the term structure are thus included in a way which is fully consistent with maximizing behavior and rational expectations. The model leads to specific formulas for bond prices which are well suited for empirical testing. 1. INTRODUCTION THE TERM STRUCTURE of interest rates measures the relationship among the yields on default-free securities that differ only in their term to maturity. The determinants of this relationship have long been a topic of concern for economists. By offering a complete schedule of interest rates across time, the term structure embodies the market's anticipations of future events. An explanation of the term structure gives us a way to extract this information and to predict how changes in the underlying variables will affect the yield curve. In a world of certainty, equilibrium forward rates must coincide with future spot rates, but when uncertainty about future rates is introduced the analysis becomes much more complex. By and large, previous theories of the term structure have taken the certainty model as their starting point and have proceeded by examining stochastic generalizations of the certainty equilibrium relationships. The literature in the area is voluminous, and a comprehensive survey would warrant a paper in itself. It is common, however, to identify much of the previous work in the area as belonging to one of four strands of thought. First, there are various versions of the expectations hypothesis. These place predominant emphasis on the expected values of future spot rates or holdingperiod returns. In its simplest form, the expectations hypothesis postulates that bonds are priced so that the implied forward rates are equal to the expected spot rates. Generally, this approach is characterized by the following propositions: (a) the return on holding a long-term bond to maturity is equal to the expected return on repeated investment in a series of the short-term bonds, or (b) the expected rate of return over the next holding period is the same for bonds of all maturities. The liquidity preference hypothesis, advanced by Hicks [16], concurs with the importance of expected future spot rates, but places more weight on the effects of the risk preferences of market participants. It asserts that risk aversion will cause forward rates to be systematically greater than expected spot rates, usually

[In a portfolio problem with given asset returns, the portfolio efficient set is the set of portfolios chosen by any risk averse agent. Using an approach of Peleg and Yaari [13], we characterize the portfolio efficient set and derive some of its properties. In particular, we show that it may not be convex, proving that a central result of mean variance theory, the efficiency of the market portfolio, does not generalize. Finally, a characterization of the efficiency of several observations gives a version of revealed preference theory for incomplete markets.]

A test for the ex ante efficiency of a given portfolio of assets is analyzed. The relevant statistic has a tractable small sample distribution. Its power function is derived and used to study the sensitivity of the test to the portfolio choice and to the number of assets used to determine the ex post mean-variance efficient frontier. Several intuitive interpretations of the test are provided, including a simple mean-standard deviation geometric explanation. A univariate test, equivalent to our multivariate-based method, is derived, and it suggests some useful diagnostic tools which may explain why the null hypothesis is rejected. Empirical examples suggest that the multivariate approach can lead to more appropriate conclusions than those based on traditional inference which relies on a set of dependent univariate statistics.