The paper derives a general form of the term structure of interest rates. The following assumptions are made: (A.l) The instantaneous (spot) interest rate follows a diffusion process; (A.2) the price of a discount bond depends only on the spot rate over its term; and (A.3) the market is efficient. Under these assumptions, it is shown by means of an arbitrage argument that the expected rate of return on any bond in excess of the spot rate is proportional to its standard deviation. This property is then used to derive a partial differential equation for bond prices. The solution to that equation is given in the form of a stochastic integral representation. An interpretation of the bond pricing formula is provided. The model is illustrated on a specific case.

this paper with an empirical investigation into some of the risk factors and demographic variables that might explain these cross-sectional differences in portfolio composition. A number of previous studies have focused on the level and variability of wage income growth as one of the largest sources of undiversifiable income risk. Here we present evidence that, for the subset of the population that has significant stock holdings, income from entrepreneurial ventures (which we refer to as proprietary business income) represents a large source of undiversifiable risk that is more highly correlated with common stock returns. These findings motivate the investigation in the second part of the paper of a linear asset pricing model that incorporates proprietary income from privately held businesses as a risk factor.

This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work and on the trade-off between risk and return. Modern research seeks to understand the behavior of the stochastic discount factor ~SDF! that prices all assets in the economy. The behavior of the term structure of real interest rates restricts the conditional mean of the SDF, whereas patterns of risk premia restrict its conditional volatility and factor structure. Stylized facts about interest rates, aggregate stock prices, and cross-sectional patterns in stock returns have stimulated new research on optimal portfolio choice, intertemporal equilibrium models, and behavioral finance. This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work. Theorists develop models with testable predictions; empirical researchers document “puzzles”—stylized facts that fail to fit established theories—and this stimulates the development of new theories. Such a process is part of the normal development of any science. Asset pricing, like the rest of economics, faces the special challenge that data are generated naturally rather than experimentally, and so researchers cannot control the quantity of data or the random shocks that affect the data. A particularly interesting characteristic of the asset pricing field is that these random shocks are also the subject matter of the theory. As Campbell, Lo, and MacKinlay ~1997, Chap. 1, p. 3! put it: What distinguishes financial economics is the central role that uncertainty plays in both financial theory and its empirical implementation. The starting point for every financial model is the uncertainty facing investors, and the substance of every financial model involves the impact of uncertainty on the behavior of investors and, ultimately, on mar-* Department of Economics, Harvard University, Cambridge, Massachusetts

. The paper studies the problem of maximizing the expected utility of terminal wealth in the framework of a general incomplete semimartingale model of a financial market. We show that the necessary and sufficient condition on a utility function for the validity of several key assertions of the theory to hold true is the requirement that the asymptotic elasticity of the utility function is strictly less then one. 1. Introduction A basic problem of mathematical finance is the problem of an economic agent, who invests in a financial market so as to maximize the expected utility of his terminal wealth. In the framework of a continuous-time model the problem was studied for the first time by R. Merton in two seminal papers [27] and [28] (see also [29] as well as [32] for a treatment of the discrete time case). Using the methods of stochastic optimal control Merton derived a non-linear partial differential equation (Bellman equation) for the value function of the optimization problem. He al...

In this article we construct a model in which a consumer’s utility depends on the consumption history We describe a general equilibrium framework similar to Cox, Ingersoll, and Ross (1985a). A simple example is then solved in closedform in this general equilibrium setting to rationalize the observed stickiness of the consumption series relative to the fluctuations in stock market wealth. The sample paths of consumption generated from this model imply lower variability in consumption growth rates compared to those generated by models with separable utilizations. We then present a partial equilibrium model similar to Merton (1969, 1971) and extend Merton’s results on optimal consumption and portfolio rules to accommodate nonseparability in preferences. Asset pricing implications of our framework are briefly explored. The idea that a given bundle of consumption goods will provide the same level of satisfaction at any date regardless of one’s past consumption experience is implicit in models that use time-separable utility functions to represent preferences. Separable utility functions have been the mainstay in much of the literature on asset pricing and optimal consumption and portfolio The results reported in this article were first presented at the EFA meetings in Bern, Switzerland, in 1985 [see Sundaresan (1984)]. Subsequently the article was presented at a number of universities and conferences. I thank the participants at those presentations for their feedback. I am especially thankful to Doug Breeden, Michael Brennan, John Cox, Chi-fu Huang, and Krishna Ramaswamy for their thoughtful comments and criticisms. I also thank Tong-sheng Sun for explaining the simulation procedure for stochastic differential equations and for his comments and suggestions. I am responsible for any remaining errors. Correspondence should be sent to Suresh M. Sundaresan, Graduate

This paper solves the dynamic investment problem of a risk averse manager compensated with a call option on the assets he controls. Under the manager’s optimal policy, the option ends up either deep in or deep out of the money. As the asset value goes to zero, volatility goes to infinity. However, the option compensation does not strictly lead to greater risk seeking. Sometimes, the manager’s optimal volatility is less with the option than it would be if he were trading his own account. Furthermore, giving the manager more options causes him to reduce volatility. MANAGERS WITH CONVEX COMPENSATION SCHEMES play an important role in financial markets. This paper solves for the optimal dynamic investment policy for a risk averse manager paid with a call option on the assets he controls. The paper focuses on how the option compensation impacts the manager’s appetite for risk when he cannot hedge the option position. On one hand, the convexity of the option makes the manager shun payoffs that are likely to be near the money. Under the optimal policy, the manager

This paper presents a dynamic asset-pricing model under asymmetric information. Investors have different information concerning the future growth rate of dividends. They rationally extract information from prices as well as dividends and maximize their expected utility. The model has a closed-form solution to the rational expectations equilibrium. We find that existence of uninformed investors increases the risk premium. Supply shocks can affect the risk premium only under asymmetric information. Information asymmetry among investors can increase price volatility and negative autocorrelation in returns. Less-informed investors may rztionally behave like price chasers.

especially grateful for the thoughtful and thorough comments of the referee which greatly improved the paper. Geert Bekaert thanks the NSF for financial support.

In this article, I explicitly solve dynamic portfolio choice problems, up to the solution of an ordinary differential equation (ODE), when the asset returns are quadratic and the agent has a constant relative risk aversion (CRRA) coefficient. My solution includes as special cases many existing explicit solutions of dynamic portfolio choice problems. I also present three applications that are not in the literature. Application 1 is the bond portfolio selection problem when bond returns are described by ‘‘quadratic term structure models.’ ’ Application 2 is the stock portfolio selection problem when stock return volatility is stochastic as in Heston model. Application 3 is a bond and stock portfolio selection problem when the interest rate is stochastic and stock returns display stochastic volatility. (JEL G11) There is substantial evidence of time variation in interest rates, expected returns, and asset return volatilities. Interest rates change over time, and although expected stock returns are not directly observed, future stock returns seem to be predictable using term structure variables and scaled prices such as dividend yields. 1 Similarly, there is well-documented evidence

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