Equilibrium Asset Pricing Model Research Articles

An Intertemporal General Equilibrium Model of Asset Prices

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

A Theory of the Term Structure of Interest Rates

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

Comparative Dynamics of an Equilibrium Intertemporal Asset Pricing Model

This paper uses recursive competitive theory to develop a general equilibrium asset pricing model. In this framework all prices and rates of return are endogenously determined, thus enabling us to analyze the effects of changes in preferences, technological uncertainty, and expectations on the structure of security prices. In particular we focus on how the market risk premium varies with changes in the underlying economic environment, an issue which other asset pricing models have chosen not to address.

Temporal Resolution of Uncertainty in Stapleton and Subrahmanyam's "Multiperiod Equilibrium Asset Pricing Model"

Temporal Resolution of Uncertainty in Stapleton and Subrahmanyam's "Multiperiod Equilibrium Asset Pricing Model"

The Capital Asset Pricing Model and the Investment Horizon

TN following the mean-variance analysis developed by Markowitz (1952) and Tobin (1958), Sharpe (1964), Lintner (1965a, b) and Treynor (1961) have developed the theory for determination of asset prices under conditions of uncertainty. The equilibrium asset pricing model, and its implication for measuring ex post performance of individual securities, have been empirically tested by Lintner,1 Jensen (1968, 1972), Miller and Scholes (1972), Douglas (1969), Roll (1969) and others. The empirical results obtained by both Douglas and Lintner deviated from the theory of the model. Moreover, Miller and Scholes have run empirical tests similar to those of Douglas and Lintner and found a significant disparity between the theoretical model and the empirical evidence. They maintain that part of this discrepancy can be explained by possible statistical biases, measurement errors, and consideration of the skewness of the distribution of returns. Black, Jensen, and Scholes (1972) (hereafter B-J-S) confirm the systematic bias. Using monthly data covering a 35 year period, they discovered that, on average, high risk securities earned less than the amount predicted by the model. Similarly, earnings on low risk securities exceeded the amount predicted.2 Although these disparities clearly suggest some systematic empirical bias, we are not examining a possible statistical bias but a mathematical bias stemming from one of the assumptions underlying the capital asset pricing model (CAPM). To be more specific, the model assumes that all investors are single period, expected utility of terminal wealth maximizers. There is no particular restriction on the length of this period as long as it is identical for all investors. Clearly, the length of the true investment horizon affects asset prices under conditions of uncertainty. We claim that the disparities noted above may result from using data calculated for an investment horizon that differs from the true investment horizon. In the various empirical tests, the investment horizon has been selected arbitrarily. For example, Lintner and Miller and Scholes use annual data (i.e., they implicitly assume a one-year horizon), Douglas uses quarterly and annual data; Black, Jensen and Scholes, as well as Friend and Blume (1970), use monthly rates of return in their empirical tests, while Roll uses weekly data. It has been shown elsewhere by Levy (1972) that the Reward to Variability index (developed by Sharpe, 1966) is a function of the investment horizon assumed. Hence, there exists a systematic mathematical bias that is a function of the horizon assumed. The above theoretical findings are related to the theory of pricing capital assets, but deal only with efficient portfolios and not individual stocks. In this paper we illustrate that the assumed horizon plays a crucial role in empirical testing. Any deviation from the true horizon causes a systematic bias in the regression coefficient (i.e., in the security systematic risk). This in turn causes a systematic bias in the performance measures of each security, and hence the deviation between the theoretical model and the empirical evidence. The results of this paper are not limited to the theory of pricing capital assets; they are applicable to any econometric study in which the variables have multiplicative rather than additive properties. In such a case the regression coefficients will have a matheReceived for publication February 27, 1975. Revision accepted for publication March 8, 1976. The authors acknowledge the technical assistance of Moshe Smith and two anonymous referees. The first author has been partially financed by the Maurice Falk Foundation, and the second author has been financed by the Ford Foundation. 1 Lintner's paper Security Prices and Risk: The Theory and a Comparative Analysis of A.T.&T. and Leading Industrials was presented at the Conference on Economics of Regulated Public Utilities, June 24, 1965, Chicago. 2 Miller and Scholes show that the presence of certain biases could have accounted for the Douglas and Lintner findings. BJ-S maintain that the assumption of borrowing at riskless interest rates could have accounted for these deviations.