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Abstract:

We examine the role of earnings management in explaining the properties of asset prices and stock market participation. We demonstrate that investors’ uncertainty about the extent of manipulation can cause excess movements in stock price relative to fluctuations in output. When faced with information asymmetry about fundamentals in the presence of earnings management, investors demand a higher equity premium for bearing the additional risk associated with their payoffs. In addition, when investors have heterogeneous beliefs about managerial manipulation, the dispersion in belief endogenously gives rise to limited stock market participation. Our model suggests that the increasing stringency of corporate governance and varying composition of investors may have played a role in the contemporaneous run-up of market participation rates in the recent years.

Keywords: Earnings management, excess volatility, equity premium, limited stock market participation

JEL classification: D82, D83, G12, G14

Managerial manipulation of financial records can arise in a wide variety of contexts; for example, to window dress financial statements prior to public securities offerings, to increase corporate managers compensation, or to avoid violation of lending contracts. Corporate executives have incentives to manipulate earnings, and empirical research on earnings management indicates that they often do. 3 The purpose of this paper is to analyze the implication of earnings management for the behavior of asset prices and investment strategies, and thereby shed light on the role of information manipulation in accounting for observed patterns in the stock market.

We construct a simple rational expectations model in which managers have an incentive to portray unjustified success and distort the information content of financial statements, and the market is uncertain about the degree of manipulation. We show that by distinguishing between the cash flows received by equity holders and financial reports released by managers, and by allowing for learning about an unobservable degree of manipulation, it is possible to generate a simple asset pricing model with rational behavior which yields several stylized financial facts. We are primarily interested in the effects that earnings management has on price volatility, equity premium, and stock market participation.

One key feature of our framework is that rational investors are uncertain about the extent of manipulation. Financial statements conflate productivity shocks with earnings management in our model, and even fully rational investors cannot perfectly gauge the true state of the firm in equilibrium. In reality, because the degree of reporting discretion available varies with economic cycles, and managers are not all equally versed in manipulating financial records, shareholders often face bias in the financial results, but cannot determine the extent of the bias. Our model features the substantial discrepancy between market expectations and the firm’s underlying financial worth that characterizes many recent corporate scandals.

One implication of our model revolves around the understanding of excess volatility. It has been known for many years that stock prices undergo fluctuations that cannot be justified by subsequent dividends (Shiller (1981) and Leroy and Porter (1981)). In this paper, we show that imperfect information about manipulation generates additional variability in future dividends, and can cause excess movements in stock price relative to fluctuations in dividends. Our model suggests that market uncertainty about underlying states caused by earnings management may be one potential source that amplifies the volatility of relatively stable fundamentals into a fluctuating price series.

In addition, we find that the existence of earnings management can lead to equity premia higher than under truthful reporting. When investors face a significant degree of information asymmetry concerning the extent of manipulation, there is additional uncertainty in firm fundamentals. The perceived opaqueness of financial reporting drives up the equity premium investors demand. Put differently, risk-averse investors are compensated for increased volatility through higher returns on stocks in equilibrium.

The most important application of our model is to examine the relation between the market information about earnings management and the rates of stock market participation. We find that if we allow for beliefs about the degree of manipulation to vary across investors, limited market participation can arise endogenously in equilibrium. When the dispersion of investor beliefs about manipulation is large, investors sufficiently pessimistic about the credibility of financial reporting will consider the market price unjustified by firm value and optimally choose not to invest in stocks in equilibrium.

To study the influence of corporate governance and financial regulations on market participation, we characterize the condition under which the equilibrium rate of market participation increases with the cost of manipulation in our model. The impact of manipulation costs on market participation is determined by how demand for stocks is distributed across investors with heterogeneous beliefs. If the demand is sensitive to investor beliefs of manipulation, a small portion of the most optimistic investors can demand a large volume of stocks, thus driving up the stock price sufficiently high to force out other investors. If investors’ demand does not vary much with their beliefs, the equilibrium stock price must adjust to induce a large proportion of investors to hold stocks for the market to clear.

Increasing the cost of falsifying financial records has two effects on the distribution of investor demand. On the one hand, the degree of manipulation is reduced, and thus the demand heterogeneity across investors with differential beliefs becomes smaller. On the other hand, a decreased degree of manipulation brings with it reduced uncertainty of manipulation, causing investor demand to be more sensitive to investor beliefs. When the cost of manipulation is large, the first effect, that is, the effect of reduced importance of investor optimism, dominates, investor demand is less sensitive to investor beliefs when the manipulation cost increases. As a result, the equilibrium participation rate increases to clear the market.

The market participation rate also decreases with the dispersion in investor beliefs about manipulation in our model. Under limited participation, only investors relatively optimistic about reporting credibility invest in stocks. Thus when beliefs about the extent of manipulation become more dispersed, market participants on average have a more favorable view about the accountability of managers’ reports and thus the financial worth of the firm. The increased market optimism drives up the equilibrium market price, forcing more investors to withdraw from the market.

Our model builds on previous literature on earnings management. Fischer and Verrecchia (2000) show that more bias in earnings reports reduces the association between share price and reported earnings, and reduces the extent to which price reflects all available information. Guttman et al. (2006) use a signaling model similar to Fischer and Verrecchia (2000) to create an endogenous discontinuity in the distribution of reports. Kwon and Yeo (2009) consider a single-period model where the principal takes into account how compensation affects productive effort and market expectations when designing the optimal contract. In their paper, a rational market can simply recalibrate or discount the reported performance when the manager overstates earnings, and correctly guess the true performance. These papers do not address the issues of price volatility, equity premia, or market participation rates, which are the primary focuses of our paper.

Another branch of literature to which our analysis adheres studies asset pricing under asymmetric information, such as Detemple (1986), Wang (1993), and Cecchetti et al. (2000). In particular, Wang (1993) presents a dynamic asset-pricing model in which investors can be either informed or uninformed: the informed investors know the future dividend growth rate; the uninformed investors do not. He finds that the existence of uninformed investors can lead to risk premia and price volatility much higher than under symmetric and perfect information. Our paper studies the interplay between managers’ manipulative incentives and investors’ investment strategies, and provides a new explanation for the phenomenon of limited stock market participation.

Our paper is closely related to the literature on limited market participation. Allen and Gale (1994) and Williamson (1994) show that transaction cost and liquidity needs can create limited market participation. Vissing-Jorgensen (1999) and Yaron and Zhang (2000) examine the effect of fixed entry cost on investors’ participation decisions. Haliassos and Bertaut (1995) show that risk aversion, heterogeneous beliefs, habit persistence, time-nonseparability, and quantity constraints on borrowing do not account for the observed phenomenon. Among the models that have been proposed to explain why limited market participation may exist, most similar to ours is Cao et al. (2005). They consider uncertainty-averse investors who evaluate an investment strategy according to the expected utility under the worst case probability distribution in a set of prior distributions. They generate limited participation in the presence of model uncertainty and heterogeneous uncertainty-averse investors. This paper can be viewed as complementary to theirs in that our results indicate that limited participation can arise endogenously in the presence of earnings management without behavioral utility specifications. In addition, our model yields implications of how corporate governance policies and financial regulations influence market participation rates.

Existing studies have analyzed earnings management behavior and stylized financial facts in isolation, and there have not been many theoretical studies that investigate the systematic link between manipulation and financial anomalies. Sun (2010) represents an exception and shows that embedding a contracting problem into an otherwise standard asset-pricing model can account for a number of observed features of return volatility. In this paper, we instead study capital market considerations in managerial reporting decisions and incorporate heterogeneous investor beliefs of earnings manipulation. Furthermore, we examine the implications of information manipulation for the equilibrium equity premium and market participation rate, which are not addressed in Sun (2010).

We organize this paper as follows. Section 2 lays out the formal model, and we consider a simple environment in which the manager reports truthfully and investors are homogeneous and perfectly informed. This provides a benchmark case for our analysis. The equilibrium of the full model is characterized in Section 3. In Section 4, we investigate how investors’ uncertainty about managerial manipulation affects price volatility and equity premium. In Section 5, we extend the model to allow for heterogeneous investor beliefs about the extent of manipulation. Section 6 analyzes the equilibrium market participation rate. Section 7 concludes.

Figure 1: Model Timeline

We consider a simple one-period economy with a representative firm. True earnings are drawn from a normal distribution with mean and variance . The time line of Figure 1 chronicles the sequence of events in the model. Before the stock is traded in the market, the manager of the firm receives a private signal of the future realization of earnings, that is, , where is the productivity shock to the firm value and follows a normal distribution: . The manager is mandated to publish a report of his private signal, denoted by , which investors use to make their investment strategies. At the end of the period, final payoffs are established and earnings () are distributed to investors as dividends.

If the manager produces an inaccurate report, the manager incurs a personal cost, denoted by , where . The discrepancy between the original signal and the financial report, , is interpreted as the amount of manipulation undertaken by the manager. is a quadratic function of : , where is a known positive parameter, and is a parameter unknown to investors. The cost of manipulation thus involves a deterministic component () and a stochastic component (). can be interpreted as a policy parameter that is influenced by governance policies and regulatory stringency, and the value of is public information. We also assume that the marginal cost of inflating reports increases with the deviation from the original signal, which is determined by .

We assume that is a random draw from a normal distribution: . Investors know the distribution of , but the true value of remains the manager’s private information. 4 The unobserved heterogeneity of is intended to capture the notion that manipulating financial records often involves personal costs or benefits the market does not precisely know. For example, investors may not have perfect information about managers’ time horizon, personal stigma, the degree of risk-aversion, the costs involved in bribing auditors not to report a discrepancy in financial statements, or the amount of resources and effort required to modify financial records. Note that can be positive or negative, reflecting the fact that some managers have preferences towards positive manipulation and some managers have preferences towards negative manipulation. In particular, a manager with a negative prefers a larger (more positive) manipulation than a manager with a positive . In reality, we observe earnings manipulation in both directions. The financial report () thereby conflates the exogenous shock to the firm value and the amount of manipulation (influenced by ). This assumption of unobserved manipulation cost is motivated by the substantial discrepancy between investors’ expectations and the underlying financial worth of the firm highlighted by many recent financial scandals.

Let denote the price of the stock given the report . The manager’s utility is given by

The first term reflects the manager’s desire to maximize the share price of the firm. The second term is the manager’s cost of manipulating the report. Typically, managers prefer higher stock prices, as their managerial compensation is often directly or indirectly tied to the firm’s stock market performance. Another interpretation of this term is that managers want to boost share price before the firm’s initial public offerings.

The objective of the manager in this environment is to maximize his utility by choosing a reporting strategy represented by , subject to the market reaction.

where is the expected value given the report and is the variance given . This indicates a linear tradeoff between the mean and variance of terminal wealth. With CARA utility functions, investors’ demand for stocks is independent of their initial wealth. This implies that the equilibrium price and participation strategies are independent of the level of aggregate wealth and the wealth distribution of investors.

A Perfect Bayesian Equilibrium is defined as a reporting strategy for the manager, joint with a pricing function for investors, such that:

1. Given the manager’s reporting strategy and the pricing rule , investors maximize their expected utility. Beliefs are consistent with Bayes’ rule.
2. Given the pricing function, maximizes the utility of the manager.
3. Market clearing requires that the stock voluntarily held by investors (denoted by ) be equal to the total quantity of the stock.

Before we solve the full model, let us first consider the special case in which there is no possibility of manipulation, that is, . The equilibrium price under truthful reporting provides a benchmark for the value of the stock, and will serve as a basis for comparison with the stock price dynamics in the presence of manipulation that will be analyzed in Section 3.

Under truthful reporting, investors maximize their expected utility by choosing how much to invest in the firm’s stock and how much to park in a risk-free asset. Given investors’ portfolio choice, market clearing is then imposed to determine the equilibrium stock price. Let denote the equilibrium stock price given the report () in the absence of manipulation. We have the following result.

Proposition 1 Under truthful reporting, the firm’s stock price given the report, , can be expressed as

Proof. See Appendix A.

The equilibrium stock price is the risk adjusted present value of future dividends discounted at the risk-free rate. Here is the expected output. The term represents the discount on the stock price to compensate for the risk in the future dividends, which is proportional to investors’ risk-aversion coefficient and the variance of productivity shock. As increases, the price of the stock has to adjust to generate a higher expected return in order to induce investors to hold the stock.

Given the equilibrium price of the stock, the return on the firm’s stock, denoted by , is the true earnings () divided by the market price (). The expected excess return on equity under truthful reporting is . only depends on , which characterizes the risk associated with future dividends of the stock. Below we show that the price volatility and excess return on the firm’s stock increase with fundamental uncertainty .

Lemma 1 Stock price volatility () and equity premium () are increasing in .

Proof: See Appendix A.

When manipulation is possible, in our model truthful reporting (that is, ) does not in general constitute an equilibrium, because there is an incentive to alter the reporting strategy ex-post. If the market believed in the face value of the reports, the manager would have an incentive to overstate the report for an inflated share price.

In the presence of manipulation opportunities, the equilibrium stock price and excess return on the stock depend on the information structure of the economy. When investors have perfect information about manipulation costs ( as well as ), they correctly subtract out the manipulation component from the report when they value the firm. This type of signal jamming equilibrium is inefficient, because the manager takes a costly action to mislead but ends up misleading no one in the equilibrium. The cost associated with manipulation is borne by the manager; since no market player benefits from manipulating reports, it imposes a deadweight loss on the economy. This signal jamming equilibrium is standard in the literature 6. and in Appendix B we show that the behavior of the equilibrium stock price is identical to that in the benchmark case.

In the remaining part of this section we solve for the equilibrium of the full model specified in Section 2, in which investors know the probability distribution of but are unable to observe the actual value of . In reality, manipulation may carry higher regulatory costs for firms with stringent internal control systems over financial reporting, and may involve higher psychological costs for some managers than others. In addition, managers are not equally versed in inflating reports and are thus subject to differential learning costs. Investors do not know how costly it is for the manager of one particular firm to manipulate financial results.

The procedure we follow to obtain an equilibrium of the economy is similar to that of Grossman (1976). We first conjecture an equilibrium pricing function and an equilibrium reporting function. Based on the assumed pricing function, we solve the manager’s optimization problem, and based on the assumed reporting function, we solve the investors’ investment problem. The market clearing condition is then imposed to verify the conjectured pricing and reporting functions.

3.1 Manager’s Reporting Strategy

Since we expect the equilibrium stock price to resemble the functional form of the price in the benchmark case, we first guess that the price of the firm is a linear function of the report: . With the conjectured price function, the first-order condition for the manager’s problem (1) yields