Corporate earnings and the equity premium

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Abstract

Corporate cash flows are highly volatile and strongly procyclical. We examine the asset-pricing implications of the sensitivity of corporate cash flows to economic shocks within a continuous-time model in which dividends are a stochastic fraction of aggregate consumption. We provide closed-form solutions for stock values and show that the equity premium can be represented as the sum of three components which we call the consumption-risk, event-risk, and corporate-risk premia. Calibrated to historical data, the model implies a total equity premium many times larger than in the standard model. The model also generates levels of equity volatility consistent with those experienced in the stock market.

Introduction

Standard asset-pricing theory implies that equilibrium asset values can be expressed as the expected product of a pricing kernel and the cash flows from those assets. The ultimate ability of an asset-pricing model to explain the equity premium thus hinges on successfully identifying an appropriate pricing kernel and accurately modeling corporate cash flows.

Since the equity premium puzzle was identified by Mehra and Prescott (1985), considerable progress has been made in specifying pricing kernels.1 In contrast, less attention has been paid to the problem of modeling corporate cash flows within this framework. In fact, many papers in this literature sidestep this issue altogether by simply constraining aggregate dividends to equal aggregate consumption. Important exceptions include Merton (1971) and Santos and Veronesi (2001), who model aggregate corporate cash flows as consumption minus a labor income component. In a series of insightful recent papers, Barberis and Huang (2001) and Menzly 2002, Menzly 2003 model the cash flows of individual firms in a way that allows aggregate dividends to differ from aggregate consumption.2

Modeling cash flows separately from aggregate consumption is crucial since corporate cash flows have historically been far more volatile and sensitive to economic shocks than has aggregate consumption. For example, corporate earnings have been more than 10 times as volatile as consumption growth during the post-war period. Similarly, while aggregate consumption declined nearly 10% during the early stages of the Great Depression, aggregate corporate earnings were completely obliterated, falling more than 103%. In addition to being more volatile, corporate cash flows are also highly correlated with aggregate consumption because of their strong procyclical behavior. To provide specifics, during the period 1929–2001 the volatility of earnings growth was 29.5%, while the correlation between per capita real consumption and earning growth was 68.7%.

Intuitively, the reason for the extreme volatility and procyclicality of corporate earnings is that stockholders are residual claimants to corporate cash flows. Thus, the compensation of workers is a senior claim to cash flows. In other words, labor contracts provide workers with some degree of insurance against business cycle risk. These contracts make the fraction of labor income in output (or consumption) countercyclical, while the fraction of earnings in output is procyclical. Gomme and Greenwood (1995) document that these business-cycle-related changes in labor income and earnings can be found in many countries.

This paper extends the literature by modeling aggregate dividends as a small but highly volatile and procyclical component of aggregate consumption. The procyclicality and volatility of dividends directly affect the covariance between the pricing kernel and corporate cash flows and significantly affect equilibrium stock values. To capture the sensitivity of corporate cash flows to both the usual “small” economic shocks as well as to rare catastrophic “large” economic shocks, we extend the representative agent framework to allow aggregate dividends and consumption to follow distinct exponential-affine jump-diffusion processes. The ratio of aggregate dividends to consumption, which we designate the “corporate fraction”, plays a central role in the model.

From the first-order conditions of the representative agent, we obtain an explicit closed-form expression for the stock price. In turn, this allows us to derive a simple expression for the equity premium in which there are three distinct components. The first is the standard Mehra and Prescott (1985) equity premium proportional to the variance of consumption growth, which we call the consumption-risk premium. The second is proportional to the probability of a jump times the product of the jump sizes in consumption and the stock price. We designate this jump-related component the event-risk premium. The third is proportional to the covariance between the growth rates in consumption and the corporate fraction, and is designated the corporate-risk premium. This three-component model of the equity premium nests many of the previous models in the literature and provides a number of new insights about the determinants of the equity premium.

To illustrate the model's asset-pricing implications, we calibrate the model using parameters that approximate the properties of consumption and the corporate fraction during the past century. A novel feature of our approach is that we calibrate the model using imputed dividends (calculated by applying a payout ratio, which we assume to be constant, to aggregate corporate earnings) rather than using reported dividends. The rationale for this stems from the well-known tendency of firms to artificially smooth their dividends over time, thereby delinking reported dividends from actual corporate cash flows.

We show that the high sensitivity of imputed dividends to economic shocks maps into equity premia many times larger than in the standard framework. For example, using a risk aversion coefficient of five, the three components of the equity premium are 0.36%, 0.51%, and 1.39%, respectively, giving a total equity premium of 2.26%. Thus, the equity premium implied by the model is more than six times as large as the standard Mehra and Prescott (1985) equity premium (given by the first component). Similar results hold for a variety of other calibrations.

It is important to recognize, however, that the equity premium implied by the model is less than half as large as historical estimates. Thus, the model clearly does not provide a complete resolution of the equity premium puzzle.3 Moreover, the Euler equation for the risk-free bond in our model is the standard one, which means that we inherit Weil's (1989) risk-free rate puzzle. Our results do suggest, however, that combining our approach with other elements such as habit formation (as in Campbell and Cochrane, 1999) or investor heterogeneity in incomplete markets (see the discussion in Constantinides, 2002) could play an important role in the ultimate resolution of asset-pricing puzzles.

The remainder of this paper is organized as follows. Section 2 presents the asset-pricing model. Section 3 solves for the equity premium generated by the model and examines its properties. Section 4 discusses the properties of the corporate fraction. Section 5 describes how the model is calibrated. Section 6 examines the asset-pricing implications of the model. Section 7 summarizes the results and makes concluding remarks.

Section snippets

The model

We extend the Lucas (1978) and Mehra and Prescott (1985) framework by introducing an explicit model of corporate cash flows. In this model, corporate cash flows represent a small but highly volatile fraction of aggregate consumption. This sensitivity to economic shocks has a number of important asset-pricing implications.

We consider an economy populated by a representative agent who maximizes an expected power utility function of the formEtte−δ(s−t)Cs1−γ1−γds,where Ct represents consumption, γ

The equity premium

To explore the implications of the model for the equity premium, it is helpful to first simplify notation slightly. Let σC and σF denote the instantaneous volatility of percentage changes in consumption and the corporate fraction, respectively. More precisely, σC and σF denote the instantaneous volatility of the continuous portion of dC/C and dF/F, respectively. By a simple extension of the results in Cochrane (2001) to jump-diffusion processes, the appendix shows that the equity premium EP

Measuring the corporate fraction

One of distinguishing features of our framework is that dividends are explicitly modeled as a stochastic fraction of total consumption. Since this corporate fraction plays a key role throughout our framework, we describe how it is estimated and provide summary statistics about its properties.

In theory, the corporate fraction could be estimated by taking reported aggregate dividends and dividing them by aggregate consumption. In actuality, however, there are important reasons why the resulting

Model calibration

In examining the asset-pricing implications of the model, we provide a simple benchmark calibration that captures the historical properties of the data. To gain more insight into these asset-pricing implications, however, we also use a range of realistic alternative values for a number of key model parameters.

First, to hold fixed the properties of the pricing kernel throughout the analysis, the results are all based on a modest level of five for the risk aversion coefficient γ of the

Asset-pricing implications

Given our benchmark calibration, it is now straightforward to solve for the equity premium and its components. Table 2 reports the values of the equity premium implied by the benchmark calibration. Also reported in Table 2 are values implied by alternative sets of some of the key parameters of this model.

As shown, the total equity premium is 2.26% in the benchmark case. This equity premium consists of a 0.36% consumption-risk premium, a 0.51% event-risk premium, and a 1.39% corporate-risk

Conclusion

We explore the asset-pricing implications of allowing cash flows to differ from aggregate consumption in a representative agent model with power utility. To model cash flows, we specify processes for consumption and the fraction of dividends in aggregate consumption, which we call the corporate fraction. Consistent with their historical properties, these processes can be modeled as affine jump-diffusions. We show that equilibrium stock prices can be computed in closed form in this economy.

To

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    The authors would like to thank Tony Bernardo, John Cochrane, George Constantinides, Darrell Duffie, Jun Liu, Lee Ohanian, Pedro Santa-Clara, Tano Santos, Martin Schneider, and Pietro Veronesi. We are particularly grateful for the many helpful comments and suggestions of the editor William Schwert and of an anonymous referee. All errors are our responsibility.

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