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Abstract:
Continuous-time stochastic processes have become central to many disciplines, yet the fact that they are approximations to physically realizable phenomena is often overlooked. We quantify one aspect of the approximation errors of continuous-time models by investigating the replication errors that arise from delta hedging derivative securities in discrete time. We characterize the asymptotic distribution of these replication errors and their joint distribution with other assets as the number of discrete time periods increases. We introduce the notion of "temporal granularity" for continuous-time stochastic processes, which allows us to quantify the extent to which discrete-time implementations of continuous-time models can track the payoff of a derivative security. We show that granularity is a function of the contract specifications of the derivative security, and of the degree of market completeness. We derive closed form expressions for the granularity of geometric Brownian motion and of an Ornstein-Uhlenbeck process for call and put options, and perform Monte Carlo simulations that illustrate the practical relevance of granularity.

Abstract:
Milton Friedman argued that irrational traders will consistently lose money, won't survive and, therefore, cannot influence long run asset prices. Since his work, survival and price impact have been assumed to be the same. In this paper, we demonstrate that survival and price impact are two independent concepts. The price impact of irrational traders does not rely on their long-run survival and they can have a significant impact on asset prices even when their wealth becomes negligible. We also show that irrational traders' portfolio policies can deviate from their limits long after the price process approaches its long-run limit. In contrast to a partial equilibrium analysis, these general equilibrium considerations matter for the irrational traders' long-run survival.

Irrational Traders, Price Impact, Price Influence, Survival, Irrationality, Long Run Prices

Abstract:
Milton Friedman argued that irrational traders will consistently lose money, won't survive and, therefore, cannot influence long run asset prices. Since his work, survival and price impact have been assumed to be the same. In this paper, we demonstrate that survival and price impact are two independent concepts. The price impact of irrational traders does not rely on their long-run survival and they can have a significant impact on asset prices even when their wealth becomes negligible. We also show that irrational traders' portfolio policies can deviate from their limits long after the price process approaches its long-run limit. In contrast to a partial equilibrium analysis, these general equilibrium considerations matter for the irrational traders' long-run survival.

Irrational Traders, Price Impact, Price Influence, Survival, Irrationality, Long Run Prices

Abstract:
Milton Friedman argued that irrational traders will consistently lose money, won't survive and, therefore, cannot influence long run equilibrium asset prices. Since his work, survival and price influence have been assumed to be the same. Often partial equilibrium analysis has been relied upon to examine the survival of irrational traders and to make inferences on their influence on prices. In this paper, we demonstrate that survival and influence on prices are two independent concepts. The price impact of irrational traders does not rely on their long-run survival and they can have a significant impact on asset prices even when their wealth becomes negligible. In addition, in contrast to a partial equilibrium analysis, general equilibrium considerations matter since the ability of irrational traders to impact prices even when their wealth is diminishing can significantly affect their chances for long-run survival. In sum, in a long-run equilibrium, we explicitly show that price impact can occur whether or not the irrational traders survive. In related work, we show that even if the irrational traders survive they may have no price impact.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
American option pricing problem is one of the most computationally intensive problems in derivative pricing theory. The complications arise from the fact that the holder of the option has the right to exercise it at any one of the pre-specified exercise dates. Hence, to price such an option, one must solve an optimal stopping problem, which maximizes the value of the option over all possible exercise strategies. When applied to problems with multiple assets or realistic price dynamics, standard pricing algorithms suffer from the well-known curse of dimensionality. Several approximate pricing algorithms have been proposed in the literature in an attempt to use simulation methods to overcome the limitations of traditional pricing techniques. The accuracy of most such algorithms could not be rigorously evaluated, as they only provide a lower bound on the true option price. In "Pricing American Options: A Duality Approach", M. Haugh and L. Kogan develop a new duality theory for optimal stopping problems and use it to design a simulation method that allows one to compute the upper bounds on the true value of the American option price starting from any approximation to the option price. This simulation method possesses desirable tightness properties, i.e., as long as the initial approximation is close to the true option price, so is the upper bound. Since the algorithm does not depend on the specifics of how the initial approximation to the option price was obtained, it can be used in conjunction with any algorithm for approximating American option prices.

Abstract:
We develop a new method for pricing American options. The main practical contribution of this paper is a general algorithm for constructing upper and lower bounds on the true price of the option using any approximation to the option price. We show that our bounds are tight, so that if the initial approximation is close to the true price of the option, the bounds are also guaranteed to be close. We also explicitly characterize the worst-case performance of the pricing bounds. The computation of the lower bound is straightforward and relies on simulating the suboptimal exercise strategy implied by the approximate option price. The upper bound is also computed using Monte Carlo simulation. This is made feasible by the representation of the American option price as a solution of a properly defined dual minimization problem, which is the main theoretical result of this paper. Our algorithm proves to be accurate on a set of sample problems where we price call options on the maximum and the geometric mean of a collection of stocks. These numerical results suggest that our pricing method can be successfully applied to problems of practical interest.

Asset pricing, dynamic programming, simulation, American option, optimal stopping, duality

Abstract:
In this article, we show how to analyse analytically the equilibrium policies and prices in an economy with a stochastic investment opportunity set and incomplete financial markets, when agents have power utility over both intermediate consumption and terminal wealth, and face portfolio constraints. The exact local comparative statistics and approximate but analytical expression for the portfolio policy and asset prices are obtained by developing a method based on perturbation analysis to expand around the solution for an investor with log utility. We then use this method to study a general equilibrium exchange economy with multiple agents who differ in their degree of risk aversion and face borrowing constraints. We characterize explicitly the consumption and portfolio policies and also the properties of asset returns. We find that the volatility of stock returns increases with the cross-sectional dispersion of risk aversion, with the cross-sectional dispersion in portfolio holdings, and with the relaxation of the constraint on borrowing. Moreover, tightening the borrowing constraint lowers the risk-free interest rate and raises the equity premium in equilibrium.

Asset allocation, stochastic investment opportunities, incomplete markets, borrowing constraints, asymptotic analysis

Abstract:
In this article, we show how to analyze analytically the equilibrium policies and prices in an economy with a stochastic investment opportunity set and incomplete financial markets, when agents have power utility over both intermediate consumption and terminal wealth, and face portfolio constraints. The exact local comparative statics and approximate but analytical expression for the portfolio policy and asset prices are obtained by developing a method based on perturbation analysis to expand around the solution for an investor with log utility. We then use this method to study a general equilibrium exchange economy with multiple agents who differ in their degree of risk aversion and face borrowing constraints. We characterize explicitly the consumption and portfolio policies and also the properties of asset returns. We find that the volatility of stock returns increases with the cross-sectional dispersion of risk aversion, with the cross-sectional dispersion in portfolio holdings, and with the relaxation of the constraint on borrowing. Moreover, tightening the borrowing constraint lowers the risk-free interest rate and raises the equity premium in equilibrium.

Abstract:
In this article, we examine analytically the optimal consumption and portfolio policies in an economy with incomplete financial markets where agents have power utility over intermediate consumption and bequest, and face portfolio constraints and a stochastic investment opportunity set. The source of changes in the investment opportunity set could be a stochastic instantaneous interest rate, stochastic volatility, and/or a stochastic risk premium. We find analytically the conditions under which investment in the risky asset can increase with risk aversion. We then nest this portfolio problem in a general equilibrium setting (for a production economy and also for an exchange economy) with multiple agents who differ in their degree of risk aversion. We derive the optimal portfolio policies when the evolution of the investment opportunity set is determined endogenously and also characterize explicitly the interest rate, stock price and risk premium in general equilibrium. The exact local comparative statics and approximate but analytical expressions for the optimal policies are obtained by developing a method based on perturbation analysis to expand around the solution for an investor with log utility.

Asset allocation, stochastic investment opportunities, incomplete markets, borrowing constraints, asymptotic analysis

Abstract:
We explicitly link expected stock returns to firm characteristics such as firm size and book-to-market ratio in a dynamic general equilibrium production economy. Despite the fact that stock returns in the model are characterized by an intertemporal CAPM with the market portfolio as the only factor, size and book-to-market play separate roles in describing the cross-section of returns. These firm characteristics appear to predict stock returns because they are correlated with the true conditional market beta of returns. These cross-sectional relations can subsist after one controls for a typical empirical estimate of market beta. This lends support to the view that the documented ability of size and book-to-market to explain the cross-section of stock returns is not necessarily inconsistent with a single-factor conditional CAPM model.

Production based asset pricing, beta, size and book-to-market factors, CAPM, business cycle properties of stock returns

Abstract:
We explicitly link expected stock returns to firm characteristics such as firm size and book-to-market ratio in a dynamic general equilibrium production economy. Despite the fact that stock returns in the model are characterized by an intertemporal CAPM with the market portfolio as the only factor, size and book-to-market play separate roles in describing the cross-section of returns. These firm characteristics appear to predict stock returns because they are correlated with the true conditional market beta of returns. These cross-sectional relations can subsist after one controls for a typical empirical estimate of market beta. This lends support to the view that the documented ability of size and book-to-market to explain the cross-section of stock returns is not necessarily inconsistent with a single-factor conditional CAPM model. Our model also gives rise to a number of additional implications for the cross-section of returns. In this paper, we focus on the business cycle properties of returns and firm characteristics. Our results appear consistent with the limited existing evidence and provide a benchmark for future empirical studies.
cycle properties

General equilibrium, the cross-section of returns, beta, size, book-to-market ratio, firm heterogeneity, business

Abstract:
The demand for durable goods is more cyclical than that for nondurable goods and services. Consequently, the cash flows and stock returns of durable-good producers are exposed to higher systematic risk. Using the benchmark input-output accounts of the National Income and Product Accounts, we construct portfolios of durable-good, nondurable-good, and service producers. In the cross-section, an investment strategy that is long on the durable-good portfolio and short on the service portfolio earns a risk premium exceeding 4 percent annually. In the time series, an investment strategy that is long on the durable-good portfolio and short on the market portfolio earns a countercyclical risk premium. We explain these findings in a general equilibrium asset-pricing model with endogenous production.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
The demand for durable goods is more cyclical than that for nondurable goods and services. Consequently, the cash flows and stock returns of durable-good producers are exposed to higher systematic risk. Using the benchmark input-output accounts of the National Income and Product Accounts, we construct portfolios of durable-good, nondurable-good, and service producers. In the cross-section, an investment strategy that is long on the durable-good portfolio and short on the service portfolio earns a risk premium exceeding 4 percent annually. In the time series, an investment strategy that is long on the durable-good portfolio and short on the market portfolio earns a countercyclical risk premium. We explain these findings in a general equilibrium asset-pricing model with endogenous production.

Cash flow, Durable goods, Factor-mimicking portfolio, Input-output accounts, Stock returns

Abstract:
Many classical dynamic models of asset pricing, such as Lucas's exchange economy and Cox, Ingersoll and Ross's production economy, use a representative investor framework to study the determination of asset prices. This approach renders the computation of equilibrium elegantly simple and contributes much to our understanding of how underlying economic structures such as preferences, endowments and production technologies, influence asset prices. On the other hand, heterogeneity among investors is a prevailing feature in capital markets. In reconciling with this empirical observation, the contribution of the literature on aggregation is to identify conditions under which individual preferences can be aggregated and thus provide the theoretical justification for such a representative agent framework. Despite these important aggregation results, a representative investor framework assumes away many interesting issues such as the relation between cross-sectional wealth distribution, the behavior of asset prices and trading patterns. To tackle these issues, heterogeneity has to be modeled explicitly. We consider a pure exchange economy populated by a continuum of agents. Agents in our model have "catching up with the Joneses" preferences and differ only in the curvature of their utility functions. Capital markets in our model are complete. We study equilibrium asset prices and individual consumption-portfolio policies both numerically and analytically, using asymptotic analysis. Because of the "catching up with the Joneses" feature of preferences, our economy exhibits stationary long-run behavior, unlike the analogous economy populated by agents with separable preferences. We show that heterogeneity can have a drastic effect on the behavior of asset prices, in particular, on their conditional moments. Dynamic re-distribution of wealth among the agents in heterogeneous economies leads to time-variation in aggregate risk aversion and market price of risk, generating empirically observed negative relation between conditional return volatility and expected returns on one hand and the level of stock prices on the other hand. This stands in contrast with the behavior of homogeneous economies with the same preferences, in which such relation is positive. Moreover, the heterogeneous model is shown to be capable of generating various empirical phenomena of asset prices. Our work is closely related to a recent paper by Campbell and Cochrane (1999), in which a particular representative-agent model with catching up with the Joneses preferences is shown to replicate numerous empirically observed features of stock returns. In their model of preferences, Campbell and Cochrane assume that the local curvature of the utility function of the representative agent is decreasing in the level of consumption, inducing counter-cyclical variation in Sharpe ratio. In addition, they use a carefully crafted nonlinear process for the social standard of living (the distinctive feature of catching up with the Joneses preferences, called exogenous habit level by Campbell and Cochrane) to control the volatility of interest rates. As we demonstrate in this paper, a heterogeneous economy can give rise to similar qualitative and quantitative properties of stock returns through a different economic mechanism and with far simpler assumptions about individual preferences: constant curvature of the utility function and linear process for the standard of living.

Abstract:
The performance of a given portfolio policy can in principle be evaluated by comparing its expected utility with that of the optimal policy. Unfortunately, the optimal policy is usually not computable in which case a direct comparison is impossible. In this paper we solve this problem by using the given portfolio policy to construct an upper bound on the unknown maximum expected utility. This construction is based on a dual formulation of the portfolio optimization problem. When the upper bound is close to the expected utility achieved by the given portfolio policy, the potential utility loss of this policy is guaranteed to be small. Our algorithm can be used to evaluate portfolio policies in models with incomplete markets and position constraints. We illustrate our methodology by analyzing the static and myopic policies in markets with return predictability and constraints on short sales and borrowing.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
The performance of a given portfolio policy can in principle be evaluated by comparing its expected utility with that of the optimal policy. Unfortunately, the optimal policy is usually not computable in which case a direct comparison is impossible. In this paper we solve this problem by using the given portfolio policy to construct an upper bound on the unknown maximum expected utility. This construction is based on a dual formulation of the portfolio optimization problem. When the upper bound is close to the expected utility achieved by the given portfolio policy, the potential utility loss of this policy is guaranteed to be small. Our algorithm can be used to evaluate portfolio policies in models with incomplete markets and position constraints. We illustrate our methodology by analyzing the static and myopic policies in markets with return predictability and constraints on short sales and borrowing.

Portfolio Choice, Duality, Dynamic Programming, Constraints, Monte Carlo, Simulation

Abstract:
The hypothesis that financial markets punish traders who make relatively inaccurate forecasts and eventually eliminate the effect of their beliefs on prices is of fundamental importance to the standard modeling paradigm in asset pricing. We establish necessary and sufficient conditions for agents making inferior forecasts to survive and to affect prices in the long run in a general setting with minimal restrictions on endowments, beliefs, or utility functions. We show that the market selection hypothesis is valid for economies with bounded endowments or bounded relative risk aversion, but it cannot be substantially generalized to a broader class of models. Instead, survival is determined by a comparison of the forecast errors to risk attitudes. The price impact of inaccurate forecasts is distinct from survival because price impact is determined by the volatility of traders' consumption shares rather than by their level. Our results also apply to economies with state-dependent preferences, such as habit formation.

Market Selection, Heterogeneous Beliefs, State-Dependent Utility, Survival, Price Impact

Abstract:
In this article, we wish to understand: (i) the valuation of a non-redundant derivative in an economy where agents are heterogenous, (ii) the role of such a derivative in an investor's dynamic portfolio strategy, and (iii) the effect of introducing this derivative on the prices of more primitive securities, such as a stock and bond. We do this by studying a dynamic general equilibrium exchange economy in continuous time with two agents who differ in their degree of risk aversion, and where both the endowment and its growth rate are stochastic. We study two versions of this economy: in the first, only a stock and a zero-supply instantaneously riskless bond are available for trading, so that financial markets are incomplete; in the second version of this economy, we introduce a derivative that allows the agent to hedge perfectly the risk arising from the stochastic growth rate of endowment. Our main contribution is to characterize in closed form (using asymptotic analysis) the equilibrium in these two versions of the economy, including an expression for the price of the derivative in the second economy. We then compare analytically the portfolio policies and prices across the two versions of the economy. We find that the introduction of a derivative leads to an increase in the interest rate, expected return on the stock and the volatility of stock returns.

Asset pricing, derivative valuation, portfolio choice, incomplete markets

Abstract:
We document a new stylized fact regarding the term-structure of futures volatility. We show thatthe relation between the volatility of futures prices and the slope of the term structure of prices isnon-monotone and has a %u201CV-shape%u201D'. This aspect of the data cannot be generated by basic modelsthat emphasize storage while this fact is consistent with models that emphasize investmentconstraints or, more generally, time-varying supply-elasticity. We develop an equilibrium model inwhich futures prices are determined endogenously in a production economy in which investment isboth irreversible and is capacity constrained. Investment constraints affect firms' investmentdecisions, which in turn determine the dynamic properties of their output and consequently implythat the supply-elasticity of the commodity changes over time. Since demand shocks must beabsorbed either by changes in prices, or by changes in supply, time-varying supply-elasticity resultsin time-varying volatility of futures prices. Calibrating this model, we show it is quantitativelyconsistent with the aforementioned %u201CV-shape%u201D relation between the volatility of futures prices andthe slope of the term-structure.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
We document a new stylized fact regarding the term-structure of futures volatility. We show that the relationship between the volatility of futures prices and the slope of the term structure of prices is non-monotone and has a V-shape. This aspect of the data cannot be generated by basic models that emphasize storage while this fact is consistent with models that emphasize investment constraints or, more generally, time-varying elasticity of supply. We develop an equilibrium model in which futures prices are determined endogenously in a production economy in which investment is both irreversible and is capacity constrained. Investment constraints affect firms investment decisions, which in turn determine the dynamic properties of their output and consequently imply that the elasticity of supply of the commodity changes over time. Since demand shocks must be absorbed either by changes in prices, or by changes in supply, time-varying supply elasticity results in time-varying volatility of futures prices. Calibrating this model, we show it is quantitatively consistent with the aforementioned V-shape term-structure of futures prices.

Futures, investment contraints, production economy, SMM

Abstract:
Mutual funds with large capital inflows exert upward price pressure on stocks they purchase as they invest their new capital. We use this price pressure as a relatively exogenous overvaluation indicator, and examine whether managers time SEOs and personal sales. We document that: (i) inflow-driven buying pressure by mutual funds has a pronounced price impact on stocks; (ii) the odds of an SEO increase by about 78%, and managers personally sell about 8.5% more stock, in the four quarters following the buying pressure. This suggests managers are able to identify the overvaluation and transfer wealth from new to current shareholders.

SEO, Market Timing, Price Impact, Trading Pressure, Mutual Fund

Abstract:
The market value of a firm can be decomposed into two fundamental parts: the value of assets in place and the value of future growth opportunities. We propose a theoretically-motivated procedure for measuring heterogeneity in growth opportunities across firms. We identify firms with high growth opportunities based on the covariance of their stock returns with the investment-specific productivity shock. We find that, empirically, our procedure is able to identify economically significant and theoretically consistent differences in firms' investment behavior, as well as risk and risk premia in their stock returns. Our empirical findings are quantitatively consistent with a calibrated structural model of firms' growth.

Abstract:
Given a European derivative security with an arbitrary payoff function and a corresponding set of" underlying securities on which the derivative security is based, we solve the dynamic replication problem: find a" self-financing dynamic portfolio strategy involving only the underlying securities that most closely" approximates the payoff function at maturity. By applying stochastic dynamic programming to the minimization of a" mean-squared-error loss function under Markov state-dynamics, we derive recursive expressions for the optimal-replication strategy that are readily implemented in practice. The approximation error or " " of the optimal-replication strategy is also given recursively and may be used to quantify the "degree" of market incompleteness. " To investigate the practical significance of these -arbitrage strategies examples including path-dependent options and options on assets with stochastic volatility and jumps. "

Abstract:
We study asset-pricing implications of innovation in a general-equilibrium overlapping-generations economy. Innovation increases the competitive pressure on existing firms and workers, reducing the profits of existing firms and eroding the human capital of older workers. Due to the lack of inter-generational risk sharing, innovation creates a systematic risk factor, which we call ``displacement risk.'' This risk helps explain several empirical patterns, including the existence of the growth-value factor in returns, the value premium, and the high equity premium. We assess the magnitude of displacement risk using estimates of inter-cohort consumption differences across households and find support for the model.

Asset Pricing, Equity Premium, Value Premium, Intergenerational Risk, Innovation, Displacement Risk

Abstract:
We analyze a general equilibrium exchange economy with a continuum of agents who have "catching up with the Joneses" preferences and differ only with respect to the curvature of their utility functions. While individual risk aversion does not change over time, dynamic redistribution of wealth among the agents leads to countercyclical time variation in the Sharpe ratio of stock returns. We show that both the conditional risk premium and the return volatility are negatively related to the level of stock prices. Therefore, our model exhibits many of the empirically observed properties of aggregate stock returns, for example, patterns of autocorrelation in returns, the "leverage effect" in return volatility, and long-horizon return predictability.

Abstract:
We analyze a general equilibrium exchange economy with a continuum of agents who have 'catching up with the Joneses' preferences and differ only with respect to the curvature of their utility functions. While individual risk aversion does not change over time, dynamic redistribution of wealth among the agents leads to countercyclical time variation in the Sharpe ratio of stock returns. We show that both the conditional risk premium and the return volatility are negatively related to the level of stock prices, as observed empirically. Therefore, our model exhibits many of the empirically observed properties of aggregate stock returns, e.g., patterns of autocorrelation in returns, the 'leverage effect' in return volatility and long-horizon return predictability. For comparison, otherwise similar representative agent economies with the same type of preferences exhibit counter-factual behavior, e.g., a constant Sharpe ratio of returns and procyclical risk premium and return volatility.

Abstract:
We study asset-pricing implications of innovation in a general-equilibrium overlapping-generations economy. Innovation increases the competitive pressure on existing firms and workers, reducing the profits of existing firms and eroding the human capital of older workers. Due to the lack of inter-generational risk sharing, innovation creates a systematic risk factor, which we call "displacement risk." This risk helps explain several empirical patterns, including the existence of the growth-value factor in returns, the value premium, and the high equity premium. We assess the magnitude of displacement risk using estimates of inter-cohort consumption differences across households and find support for the model.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
The hypothesis that financial markets punish traders who make relatively inaccurate forecasts and eventually eliminate the effect of their beliefs on prices is of fundamental importance to the standard modeling paradigm in asset pricing. We establish necessary and sufficient conditions for agents making inferior forecasts to survive and to affect prices in the long run in a general setting with minimal restrictions on endowments, beliefs, or utility functions. We show that the market selection hypothesis is valid for economies with bounded endowments or bounded relative risk aversion, but it cannot be substantially generalized to a broader class of models. Instead, survival is determined by a comparison of the forecast errors to risk attitudes. The price impact of inaccurate forecasts is distinct from survival because price impact is determined by the volatility of traders’ consumption shares rather than by their level. Our results also apply to economies with state-dependent preferences, such as habit formation.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
This paper analyzes the links between the firms investment technology and financial asset prices within a general equilibrium production economy. The model assumes that real investment is irreversible and subject to convex adjustment costs. It shows how these basic features of real investment naturally generate rich dynamics of stock returns. Firm investment activity and firm characteristics, particularly the market-to-book ratio, or q, are functions of the state of the economy and therefore contain information about the dynamic behavior of stock returns. The model implies that the relation between real investment, q, and stock returns is conditional in nature. During low-q periods when the irreversibility constraint is binding, the relation between the conditional volatility and expected returns on one hand, and the market-to-book ratio and investment rate on the other hand should be negative. During high-q periods when the constraint on the rate of investment is binding, the relation should change sign to positive. Empirical tests based on industry portfolios are supportive of the model predictions for the behavior of conditional return volatility, but provide no evidence in favor of the implications for expected return.

Investment, Irreversibility, General equilibrium, Leverage effect, book-to-market

Abstract:
We construct a dynamic general equilibrium production economy to explicitly link expected stock returns to firm characteristics such as firm size and the book-to-market ratio. Stock returns in the model are completely characterized by a conditional CAPM. Size and book-to-market are correlated with the true conditional market beta and therefore appear to predict stock returns. The cross-sectional relations between firm characteristics and returns can subsist even after one controls for typical empirical estimates of beta. These findings suggest that the empirical success of size and book-to-market can be consistent with a single-factor conditional CAPM model.

Asset Pricing, Stock Returns, Book-to-market, Size, Equilibrium, Cross-section, Production, Investment, Business Cycle, Aggregation, Heterogeneity

Abstract:
We propose a study of an important source of stock market risk, the displacement risk. We focus on the fundamental inequality among firms and consumers with respect to technological innovation. New firms are the primary innovators who increase the overall productivity, but also steal business from older firms. Likewise, skills of younger households are better aligned with new technologies, while the human capital of older agents does not quite keep up with technological progress. Innovation activity increases total output while reducing the share of existing firms' profits in aggregate output. This displacement risk makes households reluctant to own stocks, particularly those of value firms, whose output is relatively exposed to the risk of increased innovation and competition by new firms, while assigning hedging value to growth firms, which profit from innovation. We propose a quantitative general-equilibrium model of displacement risk and offer an intuitive fundamental explanation of several basic empirical asset-pricing facts, including the high value premium, the high equity premium, and the low and stable risk-free rate. Our preliminary calibration results suggest that our model performs well quantitatively. Moreover, our model has unique empirical implications connecting historical returns on value and growth stocks to cross-sectional differences in consumption among households. Preliminary empirical analysis supports these implications of our theory.