Modelling the role of credit rating agencies - Do they spark off a virtuous circle?∗ Christina E. Bannier†and Marcel Tyrell‡

28th August 2006

Abstract In this paper, we propose a model of credit rating agencies using the global games framework to incorporate information and coordination problems. By introducing a reduced-form utility function for the agency, we find that - in contrast to earlier work - rating announcements do not necessarily increase multiple equilibria incidences. For sufficiently highly-rated firms, public rating announcements and investors’ private information collection turn out to be complements rather than substitutes. Rating agencies may hence spark off a virtuous circle that increases aggregate information precision and raises market efficiency. We furthermore comment on the difference between solicited and unsolicited ratings and institutional investors’ influence.

JEL Classification: D82, G14, G33 Keywords: Information production, rating agencies, coordination problems, global game

∗

We received helpful comments from Alexander Bassen, Patrick Behr, Wolfgang B¨ uhler, Falko Fecht, Robert Gillenkirch, Andr´e G¨ uttler, Hendrik Hakenes, Martin Hellwig, Stephan Klasen, Jan Pieter Krahnen, Dirk Kr¨ uger, Christian Laux, Lukas Menkhoff, Martin Nell, Andreas Oestreicher, Anjolein Schmeits, Hartmut Schmidt, Isabel Schnabel, participants at Goethe-University Frankfurt Finance Seminar, Conference of the Swiss Society for Financial Market Research Zuerich, FIRS Conference Shanghai, MPI Econ Workshop Bonn. All errors are, of course, our own. † Department of Economics and Business Administration, Goethe-University Frankfurt, Mertonstr. 17-21, 60325 Frankfurt, Germany, Phone: +49 69 798 23386, Fax: +49 69 798 28951, E-mail: [email protected] ‡ Department of Economics and Business Administration, Goethe-University Frankfurt, Mertonsr. 17-21, 60325 Frankfurt, Germany, E-mail: [email protected]

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1

Introduction

Despite a lot of recent research effort, the role of credit rating agencies is still not very well understood. On the one hand, due to the secrecy of rating agencies about their work, the rating process itself remains unclear; on the other hand, observers still struggle to understand how the market perceives this process and how the rating influences the rated firms and their outstanding debt. Yet, the influence of credit rating agencies has steadily increased over the years, not least because of the adoption of the new global framework regulating banks’ capital known as Basel II. Due to the new Basel Accord, banks are required to hold a level of equity reserves that corresponds to their credit risk, which can either be assessed via internal rating systems or by making use of external rating expertise. Additionally, the complexity of many financial products, such as derivative and asset-backed securities, has made it very difficult for investors to assess credit risk on their own and has therefore raised the importance of rating agencies. Recent years have seen many empirical and descriptive research projects gathering a large number of stylized facts about the process of rating assessments and their influence on investment decisions. However, theoretical papers explaining these stylized facts remain rare. Up to now, it is for instance unclear why firms tend to ask for two rating assessments for their outstanding debt instead of a single rating (Baker and Mansi, 2002) or why rating changes lead to asymmetric market effects, depending on whether the initial rating is upgraded or downgraded (Vassalou and Xing, 2002; Hand, Holthausen, Leftwich, 1992). Another controversy refers to the recent practice of announcing unsolicited ratings i.e. “ratings that credit rating agencies conduct without being formally engaged to do so by the issuer” (IOSCO, 2003).1 Even though these unsolicited ratings open up competition among credit rating agencies since they allow smaller agencies to compete with the “Big Three” (Moody’s, Standard and Poor’s and Fitch), it is questionable why these ratings exist at all, as, due to their confinement on publicly-available information, they do not contain any new information over and above what has already been known to the market and are not paid for. Possibly, therefore, rating agencies do not only provide information but perform additional functions, for instance by serving as a coordination device for investors as has been suggested by Boot et al. (2006). Corroborating these fundamental uncertainties about the work and functioning of credit rating agencies are regular reports about a growing concern among market practitioners on their role (AFP, 2004), as well as proposals of a code of conduct and of a revision of the SEC’s recognition process of Nationally Recognized Statistical Rating Organizations (OICU-IOSCO, 2004; AFP, 2005). One main aspect in this controversy is the question whether the service that credit rating agencies offer actually contributes to a reduction in market uncertainty or rather increases it. The general concern and the obvious lack of understanding of the agencies’ objectives is reflected in the following statement by Thomas Friedman (1996): “There are two superpowers in the world today. There’s 1

Before the 1970s, credit rating agencies used to charge investors a fee for the provision of information about a bond’s default risk, a service that could reasonably be referred to as unsolicited ratings. Moving to a system where issuers were charged for assessing the risk of their outstanding debt mainly occurred because of the decreasing cost of photo-copying in the 1970s. In 1991, Moody’s reintroduced the practice of announcing unsolicited ratings which was quickly followed by other major agencies.

the United States and there’s Moody’s Bond Rating Service. The United States can destroy you by dropping bombs, and Moody’s can destroy you by downgrading your bonds. And believe me, it’s not clear sometimes, who’s more powerful.” The lack of a solid theoretical basis in grasping these issues has been perceived as one of the main shortcomings of the academic research to date.2 The current paper tries to fill this gap. As one of the first approaches in this respect, we consider a reduced-form utility function that allows the derivation of an agency’s optimal rating assessment. In accordance with empirical findings and anecdotal evidence, this function contains two different utility components, based on a reputation and coordination, respectively competition, objective.3 The main contribution of the paper focuses on the effects that rating announcements have on investors’ actions and how they may help to eliminate uncertainties in investment behavior. Additionally, we examine the difference between unsolicited and solicited ratings and study the reasons for their empirically-observed deviation. Finally, we analyze the influence of large, institutional investors on the investment process and explore whether they strengthen or weaken the rating’s effect. While our model remains within the institutional framework of the market for corporate credit ratings, our results may easily be transferred to a broader setting, for instance to sovereign credit ratings. As a recent example for a rating’s effect on market stability, we may also consider the current troubles of open-end property funds in Germany that have partly been triggered by rating announcements. These examples warrant a detailed analysis of the process of information certification and its influence on the stability of the assessed entities. Contrary to the results of an earlier paper by Carlson and Hale (2005), we find that the existence of rating agencies does not necessarily increase market uncertainty. Carlson and Hale (2005) conclude that rating agencies, by announcing their ratings publicly, increase the precision of public information on the market and hence make coordination among investors easier. In their model,4 a rating agency therefore fulfills both a function of information but also of coordination - with potentially detrimental results. Whereas for perfectly sound firms the risk of default is not affected by the rating, less than perfectly sound firms suffer from the occurrence of multiple equilibria. Here, investors cannot determine their optimal investment decision with certainty, since, based on the public rating assessment, both a prolongation of credit and a premature withdrawal of money may be rational, depending on the behavior of the aggregate investment decisions of the market (leading to a respective shift in price), so that a considerable amount of uncertainty prevails. In our model, in contrast, we can show that, despite the dual role of ratings, as long as the agency pursues additional aims to the usually assumed objective of maximizing her reputation, a unique equilibrium may be restored and uncertainties are eliminated. Moreover we find that for sufficiently highly-rated bonds, public rating announcements 2

This is also one of the main conclusions by Cantor (2004) in the editorial of the November 2004 Special Issue on Credit Ratings of the Journal of Banking and Finance. 3 The view that the credit rating industry is competitive and reputation-driven is the dominant one held by scholars. See for instance Cantor and Packer (1994) and Smith and Walter (2001) as advocates of this view but also Partnoy (2001) for an alternative position. 4 Carlson and Hale (2005) focus on sovereign debt ratings and investors’ influence on sovereign default. Yet, the model implications may also be applied to corporate markets.

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and private information collection are complements rather than substitutes. Hence, if investors have discretionary power over the precision of their private information, they are able to secure the prevalence of a unique equilibrium and reduce the probability of the rated entity’s default. Rating agencies may even spark off a “virtuous circle”: the more accurate the announced ratings are, the higher are investors’ incentives to increase the precision of their private information as well, which raises the efficiency of the market outcome. In our model, the observed difference between unsolicited and solicited ratings is ascribed to the gap between the rating agency’s private information and the market expectation about the firm’s credit quality. Hence, unsolicited ratings are seriously downward-biased for firms who could potentially disclose very optimistic private information about their credit quality to the agency, while the market a priori expects a much lower quality. Since the probability of default decreases with better, i.e. higher, ratings, our model relates the observed downward-bias of unsolicited ratings to an adverse selection problem between firms that believe to be of high quality and, consequently, request a (solicited) rating and those that believe to be of lower quality and therefore refrain to ask for a rating. Regarding the rating agency’s “ability” to assess the relative default risk of corporate bonds, we prove anecdotal evidence to be true that agencies of higher ability tend to announce more extreme ratings than do agencies of lower ability. This requires, however, that they do take into account their coordinating role additional to a maximization of their reputation. We then find that after observing good private information, a rating agency of higher ability will announce a higher rating than an agency of lower ability. The opposite holds for the case of bad information. Finally, we show that the existence of large, institutionalized investors (such as pension funds), that has often raised concerns, increases the probability of default for lowlyrated firms. This result stems from regulatory reasons that require pension funds to condition their investments on the assets’ ratings. A corporate rating downgrade may then result in a strong financial disruption, due to extensive withdrawals by institutional investors, that forces the firm into default. For sufficiently highly-rated, i.e. investmentgrade, firms, in contrast, the existence of institutional investors strengthens the virtuouscircle effect mentioned above as institutional investors usually maintain own research departments and hence dispose of very precise private information. This reduces the risk of default even more. To invest in the precision of their private information, however, is only beneficial for investors if the agencies’ ratings are also sufficiently precise. Thus, for this positive cycle to work, the quality and precision of ratings has to be assured continuously, which is one of the main demands that have consistently been brought before state hearings on legislative solutions regarding the work of credit rating agencies in the U.S. (AFP, 2005) The paper is related to various strands of the literature. The first is the literature on reputational concerns and reliability of information provided by certification intermediaries such as rating agencies. Mariano (2005) develops a model which analyzes this relationship in the context of both a monopolistic and a duopolistic certification industry.5 Because of a different modelling setup, her paper has to abstract from a potential 5

Also Benabou and Laroque (1992) and Morris (2001) are important examples of this literature.

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coordination function of the credit rating agency and does not consider multiplicity of equilibria. The second strand of literature builds on signalling models in the tradition of Spence (1973) and examines how different types of firms can signal their quality to the market when there is asymmetric information between firm insiders and market participants. Byoun and Shin (2002) model signalling behavior of firms in an environment in which firms can choose a rating agency as an information specialist who is able to obtain and convey information at lowest costs. They develop conditions for a separating equilibrium where only good firms signal their quality through the rating agency. Their paper differs from ours in many respects. Most importantly, it does not consider the interplay between private and public information and gives no active role to the credit rating agency. Most closely related to our work are the papers by Boot et al. (2006) and Carlson and Hale (2005). Boot et al. (2006) show that credit ratings can serve as a coordinating mechanism in situations of multiple equilibria. In addition, they explore in detail how a monitoring role vis-`a-vis a firm is put in place through the credit watch procedure used by credit rating agencies. In their model, the practice of institutional investors to condition their investment behavior on the rating enforces an implicit contract between the firm and the credit rating agency where the former promises not to misbehave because this may endanger her credit standing. While we share the focus on multiple equilibria with Boot et al. (2006), the methodological contribution of our paper is quite different. We apply the global games theory to examine under which conditions uniqueness of equilibrium can be achieved. This allows us to investigate in detail the role of a credit rating agency in providing information to the market rather than performing a monitoring role, when the rating simultaneously fulfills a coordinating function. Carlson and Hale (2005) also propose a model of rating agencies as an application of the global games methodology. However, they do not introduce an explicit utility function for the rating agency. Further differences between the two papers will be discussed where appropriate in the paper. The remainder of the paper is organized as follows. Section 2 describes the basic setup of our model. Section 3 derives the agency’s optimal rating. Section 4 discusses the condition for a unique equilibrium. Sections 5 to 7 analyze the difference between solicited and unsolicited ratings and their impact on investors’ actions. Section 8 concludes. Both papers develop repeated cheap talk models of a sender of information whose honesty is unknown to the information receivers.

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2

The model

2.1

Strategies, Information and Sequence of Events

In a very simple model we capture the interaction between a firm, a continuum of investors6 and a credit rating agency (CRA).7 The firm has outstanding debt from an ongoing business project that has to be repaid at maturity. Based on private and public information about the firm’s quality - including a published rating - investors have to decide whether or not to prolong credit in the intermediate period.8 Extensive premature withdrawal of credit may force the firm into default. We assume that the firm’s quality is a random variable θ, normally distributed with mean y and variance 1/a. The distribution of θ is common knowledge in the market and may as such be referred to as public information. The lower a, the higher is the firm’s fundamental risk, since firm quality θ may then deviate strongly from the ex-ante expected value y. While the distribution of θ is commonly known, the realization θ is not observable to market participants. Yet, each investor receives private information about firm quality: xi |θ ∼ N (θ, 1/b). The higher b, the more closely are investors’ private signals distributed around the unknown firm quality θ. In this respect, b denotes the precision of investors’ private information. Similarly, the rating agency collects information about the firm that results in a private signal of xA |θ ∼ N (θ, 1/c). Note that, conditional on θ, private signals are assumed to be independent of each other. The time line of the model is as follows: • In t = 0, the firm has outstanding debt that has to be repaid at a rate of R > 1 per unit of debt at maturity (t = 2). While market participants cannot observe the realization of firm quality θ, its fundamental situation, i.e. the distribution of θ, is common knowledge. The firm appoints a rating agency to assess its quality. • In t = 1, investors observe individual private signals xi about firm quality. The rating agency collects a private signal xA and subsequently announces the rating z - a statement on the firm’s quality - to the market. Investors update their beliefs and decide on whether to prolong credit (i.e. hold on to their investment) or withdraw early. Early withdrawal is not connected to any premium or punishment and hence delivers a payment of 1 per unit of capital. • The firm’s project can mature successfully in t = 2, if a proportion of less than θ of outstanding debt has been withdrawn prematurely. The firm then repays debt out of the realized project payoff, which is equal to V . Otherwise the firm 6

The assumption of atomistic investors is made in order to keep the analysis as simple as possible. It is not critical for the derivation of results as has been shown by Morris and Shin (2003). 7 The derivation of the “optimal” rating in section 3 will be based on the assumption of a continuum of information intermediaries. In equilibrium, therefore, all ratings will be equivalent, so that we only refer to one CRA in the present section. 8 The rating we consider comprises general information about the firm’s quality and hence comes close to the notion of “corporate ratings”. As we consider short-term debt financing such as for instance provided by commercial papers, the rating’s interpretation should not be narrowed down to bond ratings, which usually address the quality of medium- to long-term debt.

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Table 1: Investors’ strategies and payoffs default no default (l ≥ θ) (l < θ) prolong withdraw

0 1

R 1

defaults, a payoff of zero is obtained and credit is not repaid.9 In this simple formulation, project payoff V is a constant larger than R. Fundamental variable θ measures the firm’s ability to meet the financial disruption brought about by investors’ withdrawal of credit and hence measures the firm’s credit quality.10 Investors’ payoffs are summarized in table 1. Here, l represents the aggregate amount of early withdrawal, i.e. the proportion of investors that decide not to prolong credit.11

2.2

Equilibrium Without a CRA

In order to derive a benchmark result, let us first consider the case without a rating agency. Equilibrium values are denoted by subindices “W”. In this case, investors have to base their decisions of whether or not to prolong credit solely on the common prior about θ and on their private signals xi . From table 1 the following may easily be inferred. Since l, the proportion of investors that decide to withdraw their money prematurely, takes on values between 0 and 1, investors will always opt for withdrawal for θ < 0 and choose to prolong credit for θ > 1, the latter being the efficient equilibrium of the model. For θ ∈ [0, 1], however, both actions may constitute an equilibrium, depending on investors’ expectations about l. As these equilibria are based on self-fulfilling beliefs,12 the model delivers the undesirable feature of unpredictability of outcome for non-extreme firm fundamentals if the 9

This very simple payoff function implies that the recovery rate conditional on default is independent of θ (Morris and Shin, 2004). 10 Consider that a massive withdrawal of capital excessively shrinks the firm’s potential to raise new money and hence to repay outstanding debt at maturity. In the extreme, the firm might fear not to be able to repay credit in t = 2 and opts for default. The decision to default is not contractible ex-ante and gives rise to the moral hazard problem to be studied in the following. 11 The model may alternatively be applied to the case where the firm intends to conduct a new project and issues claims, e.g. bonds, to raise the necessary finance. Market participants decide whether or not to invest in t = 1 based on their private information and the public bond rating. The project can only be successful (i.e. yield a payoff of V ), if sufficiently many investors donate financing. These investors then obtain a fixed repayment of R in t = 2. If the raised amount of finance is below the critical level of 1 − θ, however, the project does not deliver any repayment. Firm quality θ hence represents the amount of internal financing. Note that the model also shows a parallel to the recently observed troubles of openend property funds in Germany. Open-end funds trade long-term investments for short-term liquidity but may choose to freeze trading at the current value of assets once too high liquidity outflows are observed. In December 2005 and January 2006, three funds were closed because of massive withdrawals of liquidity after a rating-downgrade announcement on two of the funds. 12 Whenever an investor believed that sufficiently many other investors might withdraw their loans early, it would be optimal for him to withdraw as well, thereby vindicating any investor’s decision to

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realization of θ were common knowledge. A remedy for the multiplicity problem is provided by heterogeneous information about firm quality θ, which lies at the heart of the model assumptions. Essentially, the depicted model (with imprecise private and public information) presents a global game in the sense of Carlsson and van Damme (1993), where each player noisily observes the game’s payoff structure (i.e. firm quality θ), which itself is determined by a random draw from a given class of games. Following the solution method of Morris and Shin (2003, 2004) we can derive a unique equilibrium, provided that private information about θ is sufficiently precise. The equilibrium can be shown to be given in trigger strategies, so that each investor will extend his loan whenever he obtains a private signal xi higher than a trigger value x∗W and will withdraw credit otherwise. Correspondingly, the firm ∗ is realized. Equilibrium values θ ∗ and x∗ will default if a quality value lower than θW W W are derived from the conditions that render agents indifferent between their respective actions as will be shown in the following. The marginal investor is indifferent between foreclosing and prolonging credit, if both actions deliver the same expected payoff: ∗ 1 = R · prob(θ ≥ θW |xi ) .

(1)

Here, it has been recognized that the project will only be successful if the firm’s quality ∗ . θ is larger than θW If there is no credit rating agency on the market, investors’ posterior beliefs about θ are given by: ! Ã 1 ay + bxi , . (2) θ|xi ∼ N a+b a+b Plugging this in (1) delivers the indifference condition for the individual investor: √ a+b ∗ a a + b −1 ³ R − 1 ´ xi = θW − y − Φ ≡ x∗W . b b b R

(3)

Hence, an investor will foreclose his loan early whenever he observes a private signal about firm quality lower than x∗W and rolls over otherwise. The firm’s project, however, needs a critical mass of (external) investment in order to proceed successfully, i.e. the project defaults whenever the proportion of withdrawn debt is higher than θ.13 The firm is therefore on the brink of default if: θ = l ≡ prob(x ≤ x∗W |θ) √ θ = Φ( b(x∗W − θ)) .

(4)

foreclose the loan, so that eventually they will all do so. If, in contrast, he expected others to extend their loans, it would be profit-maximizing for him to extend as well, leading to coordination on the efficient equilibrium. 13 This simplifying assumption may be rationalized as follows: if credit markets are fully competitive, investors will ask for a higher return R for the project, the larger the probability that the project will not succeed, i.e. the higher the proportion of investors that will not prolong credit. This increases the cost from pursuing the risky project over the choice of the “safe” default that renders a payoff of zero to both the firm and to investors. See also Boot et al. (2006).

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Note that due to the assumed independence of private signals, the proportion of investors withdrawing their loans prematurely (after observing sufficiently low private signals) is equivalent to the probability with which an individual investor obtains private information lower than x∗W . Combining indifference conditions (3) and (4) yields the equilibrium threshold value ∗ below which the firm’s project will optimally be abandoned, since the proportion of θW withdrawn capital is too high to warrant any further refinancing on the part of the firm. ∗ , however, the project will be continued with certainty, For quality values of θ above θW even though there might still be some credit foreclosure. This withdrawal of capital is ∗ is then yet sufficiently small as not to force the firm into default. Equilibrium value θW derived as: r ³ a a + b −1 ³ R − 1 ´´ ∗ ∗ θW = Φ √ (θW − y) − . (5) Φ b R b ∗ ∈ [0, 1], the optimal behavior in the extreme regions, θ < 0 and θ > 1, is As θW ∗ , a default is always unchanged.14 Note that for intermediate firm qualities, 0 < θ ≤ θW inefficient since it has not been triggered by a sufficiently bad firm quality but simply by the number of investors that decided to withdraw their money early.15 A default in this region could be prevented, if only sufficiently many investors decided to prolong credit. Uniqueness of equilibrium hence does not eliminate inefficiencies. Default occurring ∗ ] is also referred to as a coordination failure on the part of in the range of θ ∈ [0, θW investors.

As a sufficient condition for (overall) uniqueness of equilibrium, consider that the two indifference curves as represented by (3) and (4) must not cross more than once. Solving ∗ , it can easily be seen that a (4) for x and deriving both functions with respect to θW sufficient condition for a unique equilibrium is given by b > a2 /(2π). It requires that behavioral uncertainty, introduced via the variance in traders’ individual private signals, 1/b, does not become too strong as compared to fundamental uncertainty, represented by the variance 1/a of the firm’s quality value θ.16 Stated differently, private information on the part of investors must be sufficiently precise relative to the precision a of public information about θ.

2.3

Equilibrium With CRA

Now consider the case of a credit rating agency publicly announcing her rating in t = 1. For the time being, we assume the rating z to be exogenously given and normally 14

In fact, the uniquely optimal strategies in the extreme regions of θ are necessary in order to derive a unique equilibrium for all values of θ under heterogeneous information by iteratively eliminating dominated strategies (Morris and Shin, 2003). Under certain conditions, even only one such region may suffice to allow the derivation of a unique equilibrium for the whole range of fundamental values (Goldstein and Pauzner, 2005). 15 Default is efficient only for θ < 0, since in that case, even if all lenders decided to roll over, termination of the project would still be optimal for the firm. The same is true in the case with a rating agency being present. 16 What we call behavioral uncertainty corresponds to the notion of strategic uncertainty in Morris and Shin (2002, 2003, 2004). Both terms will be used interchangeably.

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distributed with a variance of 1/d. The optimal rating will endogenously be derived in section 3. The announcement of rating z brings additional public information to the market and leads investors to update their beliefs to: θ|xi , z ∼ N

´ ³ ay + bx + dz 1 i , . a+b+d a+b+d

Based on the same analysis as above, the unique equilibrium value for firm quality with a rating agency being present, θ∗ , is then derived as: Ã ! ³ ³ R − 1 ´´ √ 1 θ∗ = Φ √ a(θ∗ − y) + d(θ∗ − z) − a + b + dΦ−1 , (6) R b with the equilibrium value for private signals given by: √ a+b+d ∗ a d a + b + d −1 ³ R − 1 ´ ∗ x = θ − y− z− Φ . b b b b R

(7)

For quality values higher than θ∗ , the firm will never default since a sufficiently large number of investors will optimally decide to prolong credit. A firm quality less than θ∗ , in contrast, will always lead to a default by the firm. Uniqueness of equilibrium in the case where a credit rating agency is present requires that: (a + d)2 b> . 2π Note that this uniqueness condition is stricter than in the absence of a CRA as long as the precision of her rating, d, is perceived to be larger than zero. This is due to the fact that the announced rating increases the precision of information that is public in the market.

3

Optimal Rating

In the following, we will analyze a simple process for the generation of a rating. In essence, we assume a continuum of information intermediaries generating an assessment of the firm’s credit quality, θ, as such accounting for potential competitive pressures in the industry.17 As one distinguishing feature, our model considers technological spillovers in the generation of ratings. These network effects may stem from the implicit contractual relation between a rating institution and the rated entity, particularly obvious in the “credit watch” procedure (Boot et al., 2006), or from the often-mentioned feedback-effects that rating agencies claim to be triggered by rating announcements or 17

Recent years have seen the expansion of a large number of potential competitors to the established credit rating agencies (The Economist, 2005). Apart from smaller, country-specific rating agencies, there is also a growing importance of other predictors of default, for instance via financial derivatives such as credit default swaps.

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rating changes (Hill, 2004; Covitz and Harrison, 2003).18 Both channels establish a direct influence of the rating (or its impending announcement) on the credit quality of the firm.19 Consequently, in its rating assessment, each rating agency has not only to be concerned with its (exogenous) information about the firm’s quality but also with the statements of other information intermediaries that are influencing the firm’s credit quality. In this respect, by taking account of this additional “endogenous” source of information, our model displays richer rating characteristics than the model by Carlson and Hale (2005), who assume that the announced rating is equal to the private signal about firm quality that the agency observes, xA . Our model is also in contrast to Boot et al. (2006), where, essentially, the rating agency simply reconfirms information that has already been publicly available in the market, thereby giving rise to a “focal point” role. Rather, in our case the CRA chooses how much “new” private information to turn into public and how much “old” public information to confirm, depending on the weights attached to the objectives that it pursues in the rating assessment process. Taking the above deliberations into account, we assume that a rating agency tries to maximize expected profits. As we do not consider any additional services offered by a CRA, profits solely stem from fees paid by issuers for solicited ratings. The agency’s utility function therefore reflects its role as an intermediary between the issuer soliciting the rating and the investors using the rating information (Schwarcz, 2002), which is also described in the IOSCO code of conduct: “CRAs should endeavor to issue opinions that help reduce the asymmetry of information that exists between borrowers and debt and debt-like securities issuers, on one side, and lenders and the purchasers of debt and debt-like securities on the other.” (OICU-IOSCO, 2004). As a rating agency’s promise to announce reliable information about the rated entity is not enforceable, but, if violated, will have an effect on her reputation, we consider the following utility function, reminiscent of the optimality of discretionary contracts trading off reputational versus financial capital `a la Boot et al. (1993). Maximizing expected profits then requires minimizing the loss from information “disintermediation”, stated as follows: ¯ 2, ui (zi , θ) = −(1 − r)(zi − θ)2 − r(Li − L) with

Z Li =

0

1

(8)

(zj − zi )2 dj

18

Apart from a rating’s effect on the firm’s funding costs, in particular the existence of rating triggers gives rise to feedback-effects that may force rating agencies to be cautious in their rating process (Hill, 2004). This may become obvious for firms in financial turmoil. With respect to the Enron case, for instance, it has been mentioned that one reason why the rating agencies acted very late (arguably too late) was that they did not want to begin a downgrading spiral started off by a first downgrading followed by an increase in credit costs due to rating triggers, which would again have increased Enron’s probability of default, leading to an even lower rating etc (The Economist, 2005). 19 Additionally, the fact that rating agencies are known to be very conservative with regard to the risk of announcing “incorrect” rating assessments, leads them to tend to “err on the side of caution” (Golin, 2001). While the concept of conservatism has also been used as an explanation of the downward bias of unsolicited ratings that lack the additional ingredient of private information (Van Roy, 2005), it is reasonable to believe that CRAs’ favor of conservatism leads them to stick relatively close to the industry’s average rating.

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and

Z ¯= L

1

0

Lj dj .

The first part in the utility function displays the CRA’s objective to reduce information asymmetries between issuers and investors as far as possible by disclosing a rating zi that is as close as possible to the unknown firm quality θ. This reputation objective enters the utility function with a weight of (1 − r). The second part mirrors the network effects of technological spillovers in agencies’ rating assessments, recognizing that ratings have a feedback-effect on the “true” firm quality.20 It is hence reasonable for each rating institution to take into account the industry’s “average” rating and to try to minimize the distance between the own and the average rating.21 This competition objective, that has also been brought forward in a different context by Morris and Shin (2002) based on the “beauty contest” theme by Keynes, is attached a weight of r.22 In this simple reduced-form utility function, we do not consider costs from information collection. This is corroborated by the fact that agencies are obviously willing to process information even without financial compensation, as shown by the existence of unsolicited ratings. As such, the agency’s utility function solely comprises reputation and competition objectives as the main drivers of the generated rating information zi . Derivation of the optimal rating requires the following steps. A full description is given in appendix A. The optimal rating zi will maximize the CRA’s expected utility function and is, thus, given by: zi = (1 − r)E(θ|xA ) + rE(¯ z |xA ) , (9) where z¯ denotes the average rating. If we assume a linear R strategy as optimal for a rating agency, we may average over all ratings, i.e. z¯ = zj dj. Plugging this in the optimal rating function (9) and comparing coefficients delivers the following “optimal” 20

The latter argument is reminiscent of the discussion on “fair value” versus “book value” reporting systems by Plantin et al. (2005). They argue that market prices affect the market outcome through their influence on the actions of market participants, so that an endogenous source of volatility arises via this feedback-loop. 21 Agencies’ rating choices therefore display strategic complementarities. I.e., it is the more rewarding to announce a “high” rating, the larger the number of other rating agencies that also announce a high rating and vice versa. For the effects of strategic substitutability on information generation, see also Hellwig and Veldkamp (2006). 22 Additional proof of the beauty-contest argument and even more detailed hypotheses come from a recent German experience. On June 19, 2005, the so-called “Gew¨ ahrtr¨ agerhaftung” and “Anstaltslast”, a maintenance obligation and implied liability of the German public sector for the state banks’ public debt, was abolished by the German government because of pressure by the EU competition commission. Contrary to what has been expected, however, the state banks’ ratings did not deteriorate after the event. Rather, the required two ratings for each bank remained at a very high level. Rating counsellors publicly stated at the time that competition between rating agencies leads them to reduce their business risk by announcing average ratings, while only agencies of very high ability and long-standing experience dare to disclose “extreme” ratings (Von Heusinger, 2005). This hypothesis will be taken up again in section 5.

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rating, given the CRA’s private and public information about firm quality θ: zi (xA , y) =

(1 − r)c a xA + y. a + (1 − r)c a + (1 − r)c

(10)

As can be seen, the optimal rating is influenced by the CRA’s private information about the firm, xA , and the prior expected firm quality, y. Hence, the agency not only reconfirms already publicly available information, y, but additionally turns (part of) her private information xA into public. The factors with which these two types of information enter the announced rating depend on the respective information precision. The more precise one type of information, the larger its weight in determining the optimal rating. It is moreover interesting to note that r, the weighting factor put on the competition objective, decreases the effect of xA but increases the effect of y. Therefore, the more importance the CRA attaches to the competition argument, the stronger will the optimal rating be influenced by the prior mean y and the less will it be affected by the CRA’s private information. Placing more emphasis on the reputation objective, in contrast, increases the impact of private information xA on the optimal rating. Only if the rating agency did not attach any importance to the competition objective, i.e. for r = 0, and accounted only for her reputation, would the factors with which the two types of information enter the rating depend only on their respective precision.23 Note that if investors know the CRA’s utility function, they are able to solve for the CRA’s private information xA about firm quality in equilibrium. Still, there is a difference between announcing the “optimal” rating z as derived above and announcing the signal xA directly, as has been studied by Carlson and Hale (2005). To see this, consider the investors’ posterior beliefs if they learn the agency’s signal xA directly, θ|xi , xA ∼ N

³ ay + bx + cx ´ 1 i A , a+b+c a+b+c

or if they learn the rating z θ|xi , z ∼ N

³ 2ay + bx + (1 − r)cx ´ 1 i A , . 2a + b + (1 − r)c 2a + b + (1 − r)c

Particularly with respect to the variance of posterior beliefs, it can be seen that if the CRA attaches a relatively low weight to the reputation objective, the variance of investors’ posterior beliefs will be higher after observing the rating z than after observing the CRA’s private signal xA . The opposite holds if a high weight is attached to the reputation objective.24 Hence, the CRA’s mode of information processing and distributing plays a subtle role in affecting particularly higher-order moments of beliefs.25 23

Were private information on the part of the CRA completely precise i.e. for c → ∞, our results would coincide with the ones obtained by Carlson and Hale. For a → ∞ (i.e. for completely precise initial public information), in contrast, our results are essentially identical to the ones by Boot et al. (2006). 24 For 1 − r < 1 − a/c, the variance conditional on z is lower, for 1 − r > 1 − a/c, the variance conditional on xA is lower. 25 For a more detailed analysis on similar issues see also Hellwig and Veldkamp (2006).

13

4 4.1

The Role of the Credit Rating Agency Uniqueness of Equilibrium

Since the announcement of a rating increases the precision of public information above that of the prior distribution of firm quality θ, a CRA will certainly have an effect on whether a unique or multiple equilibria prevail. In order to ensure uniqueness of equilibrium and prevent the ex-ante uncertainty connected to multiple equilibria, we know that the precision of investors’ private information must not become too low compared to the precision of information that is publicly available on the market. Hence, the sufficient condition for a unique equilibrium will become stricter after the rating announcement. From the optimal rating strategy (10), we know that z displays a variance of 1/[a + (1 − r)c], so that the uniqueness condition can be rewritten as: (2a + (1 − r)c)2 . (11) 2π For a unique equilibrium to hold, investors’ private information has to be sufficiently precise, not only relative to the precision of public information, a, but also relative to the precision of the CRA’s private information, c, since this is partly turned into public information via the rating announcement. The implication is also revealed in figure 1 that displays equilibrium selection depending on investors’ private information precision b. b >

No CRA

z

multiple equilibria }|

{z

unique equilibrium ∗ with rollover for θ ≥ θW }|

{-

a2 2π

b

z

multiple equilibria }|

unique equilibrium with rollover for θ ≥ θ∗ {z }| {-

0

a2 2π

0 With CRA

(2a+(1−r)c)2 2π

b

Figure 1: Equilibrium selection corresponding to investors’ private information precision b However, rearranging the uniqueness condition allows a slightly different view: ¯ √2πb − 2a ¯ ¯ ¯ (12) 1−r (2a + (1 − r)c)2 /(2π). Hence, after the additional investment in private information precision, a unique equilibrium will be restored even after the public rating announcement. Furthermore, note that investors’ attempt to maximize their proceeds from granting credit to the firm coincides with maximizing overall efficiency by minimizing the probability of default, prob(θ ≤ θ∗ ). Stage one of the game hence requires investors to compare the proceeds from the secondstage game that follow either from multiple equilibria, if they decided not to increase the precision of private information, or from a unique equilibrium after the investment in information precision. As in the former case equilibria are based on expectations regarding other investors’ actions, we assume the following beliefs: let α be the proportion of investors that are expected to withdraw their money early. From the equilibrium derivations in chapter 2 it follows that a firm default will occur whenever α > α∗ = θ ∗ , i.e. whenever the proportion of withdrawing investors is larger than the critical proportion that renders the firm indifferent between defaulting or not, stated in equation (4). As has been shown by Boot et al. (2006), if α is sufficiently high, it is then reasonable for all investors not to prolong credit. This is due to the fact that the beliefs of the withdrawing investors (that the firm will default) are confirmed in equilibrium, so that the remaining 1 − α investors rationally conjecture the same. If, in contrast, α < α∗ , all investors would prolong credit. Since the critical level α∗ is given by θ∗ , with26 Ã ! ³ ´´ √ 1 ³ ∗ ∗ −1 R − 1 ∗ θ = Φ √ a(θ − y) + d(θ − z) − a + b + dΦ , R b we find the following: the higher the expected credit quality, y, and the higher the credit rating, z, the lower is the critical proportion α∗ of investors believing in a firm default and therefore withdrawing credit, thereby moving the firm on the brink of default. Hence, the more likely will it be for given α that the critical proportion α∗ is surpassed so that in the multiple equilibria case the market will coordinate on an inefficient firm default. As investors in this case receive a payoff of zero, they will have an interest to invest into the precision of their private information in order to restore uniqueness of equilibrium as long as R · prob(θ ≥ θ∗ |xi ) − C(∆) > 0 . Note that the critical level of costs C(∆)crit that investors are willing to bear decreases in θ∗ as C(∆)crit = R · prob(θ ≥ θ∗ |xi ) . As is shown in appendix B, equilibrium value θ∗ decreases in the precision of the CRA’s private information, c, for sufficiently high ratings z. Results so far are summarized in the following propositions: 26

In order to simplify the notation, the precision of the rating is still denoted by d rather than a + (1 − r)c.

16

Proposition 2 For a2 /(2π) < b < (2a + (1 − r)c)2 /(2π), the rating announcement increases the number of equilibria. If the CRA announces a sufficiently high rating, investors have a high incentive to invest in the precision of their private information in order to eliminate multiple equilibria, thereby increasing the efficiency of the market outcome. Whenever a low rating is announced, however, the market is likely to coordinate on the most efficient among multiple equilibria without any investment in private information collection. Proposition 3 (Virtuous Circle) The more precise the announced rating is, the higher is the critical level of investment costs that investors are willing to bear in order to increase the precision of their private information, provided that the rating is sufficiently high. For sufficiently high ratings (e.g. investment-grade ratings), investors’ private information and public rating information therefore turn out to be complements, leading to an accelerating increase in efficiency. For sufficiently high ratings, investors therefore prefer a unique equilibrium over multiple equilibria and vice versa for low ratings. As a reason for this interesting result, consider that - even though this is not modelled explicitly27 - the expectation of a high firm quality as mirrored in a high rating z (and in a high prior expected value y) in a competitive credit market should lower the firm’s costs R from proceeding with the project, while the profit from default remains constant (equal to zero). In this instance, the proportion of investors that are willing to withdraw credit prematurely will be very small. This reduces the critical value α∗ that is rationally sustainable in equilibrium. For a given proportion of α, that is possibly institutionally determined (and hence independent of deliberations of rationality), it then becomes likely that α > α∗ so that precisely because of a high rating, the market moves towards the inefficient firm default in the multiple equilibria case. For sufficiently low ratings, exactly the opposite explanation would lead to the realization of the efficient equilibrium in which all investors prolong credit in a multiple equilibria regime.28 Interestingly, this difference in preferences for equilibrium outcomes coincides with regulatory requirements as far as institutional investors are concerned. In almost any country, institutional investors are required to invest only in sufficiently highly-rated (investment-grade, “m¨ undelsicher”, etc.) assets. At the same time, institutional investors usually dispose of own research and analysis departments that supply them with additional private information. This has often been taken as evidence for a too low precision of credit ratings, since otherwise it would not be worthwhile for investors to look for additional sources of information (Partnoy, 1999). According to our analysis, however, it is not the lack of precision in credit ratings but rather the opposite: rating announcements increase the precision of public information too strongly and hence destroy uniqueness of equilibrium. Regarding investment decisions in highly-rated bonds, however, investors prefer a unique equilibrium as this minimizes the probability of default. Hence, agents’ incentives to invest in information is highest when investment 27

For the modelling of the refinancing decision on the part of the firm and its strategic effects on equilibrium, see for instance Hubert and Sch¨ afer (2002). 28 Experimental evidence exists that without major incentives to act otherwise, agents tend to coordinate on the payoff-dominant among multiple equilibria (Heinemann et al., 2004).

17

is in firms with highly-graded bonds, which is exactly what institutional investors are confined to. Note that in contrast to Carlson and Hale (2005), the CRA in our setup does not disclose her private information to the market but a weighted function of her posterior information. If investors know the CRA’s specific utility function and if equilibrium is unique, they are able to deduce the expected probability of default. With multiple equilibria, this is no longer true. In this case, the rating agency in essence has a strategic choice of whether to announce a default probability that corresponds to the efficient or to the inefficient equilibrium. But still, investors could choose to reduce the uncertainty emerging from the multiplicity of equilibria by investing in the precision of their private information. Interestingly, investors choose to disregard the focal point role of CRAs when ratings are high. In the market for sufficiently highly-rated bonds, therefore, rating precision and the precision of private information are no longer substitutes. Rather, they become complements so that the announcement of a rating may spark-off a virtuous circle that increases information efficiency and injects a degree of stability in the market, thereby reducing the probability of firm default. The market for lowly-rated bonds, however, is characterized by substitutability between rating information and private information. Whenever a unique equilibrium prevailed before the rating announcement, the most efficient result can be achieved in the postannouncement phase if self-fulfilling beliefs and hence a degree of instability are tolerated.

5

Solicited Versus Unsolicited Ratings

In recent years, rating agencies have started to issue ratings that are not requested by the rated entity and that are not paid for. These “unsolicited” ratings rely only on public information. Empirical studies on unsolicited ratings have raised several questions regarding both the purpose and the informational content of these rating assessments. In our setup, unsolicited ratings may be characterized by c = 0, since no private information enters the rating process. The unsolicited rating zU is then given as zU = y as it is only influenced by public information. If we assume a solicited rating zS to be characterized by c > 0, it stands to reason whether it will be higher or lower than zU : zS − zU

=

(1 − r)c (xA − y) a + (1 − r)c

This delivers the intuitive result that the difference between solicited and unsolicited rating will be positive (negative) if the CRA’s private information, xA , turns out to be higher (lower) than the ex-ante expected firm quality, y. Corollary 1 For sufficiently high (low) private information of the CRA, xA , compared to the ex-ante expected firm quality, y, a solicited rating will be higher (lower) than an unsolicited rating. It is intuitive to see that the solicited rating zS as given by (10) increases in the face value of the rating agency’s private information, xA . For the influence of the agency’s 18

private information precision c, however, we find the following: ∂zS ∂c

=

a(1 − r) (xA − y) . [a + (1 − r)c]2

(13)

Corresponding to the result in corollary 1, the effect of c on the optimal solicited rating depends on the difference between the CRA’s private information and the prior information about firm quality, i.e. xA − y. Obviously, for xA > y this partial derivative will be positive and vice versa. Nevertheless, the provision of private information does not necessarily increase any agency’s private information precision c by the same amount. Rather, we may interpret a specific value of c > 0 as the “ability” of the CRA to gather and process the relevant information privately provided by the firm.29 What further implications can then be derived with regard to the effect of the CRA’s ability on the solicited rating? Based on the influence of c as given in (13), we find that for sufficiently high private information, i.e. for xA > y, the solicited rating increases in the weight attached to the competitive argument, r, provided that the CRA’s private information is of sufficient precision.30 The opposite holds for an increase in the importance given to the reputation objective. Hence, a rating agency of high ability, i.e. that disposes of very precise private information, will give a higher solicited rating for sufficiently good private information as compared to a CRA of poorer ability, if she attaches lower weight to her reputational aim and puts more emphasis on competitive concerns. For sufficiently bad private information, i.e. low xA , in contrast, she will give a lower solicited rating as a CRA of poor ability. Therefore, the hypothesis that only rating agencies of high ability can afford to deviate strongly from the average rating holds, provided that these agencies do not put too much weight on their reputational objective. In the case of a unique equilibrium we may reasonably assume this condition to be satisfied, as follows from uniqueness condition (12). Corollary 2 CRAs of sufficiently high ability will announce more extreme solicited ratings than agencies of lower ability, if they attach relatively low weight to their reputation objective. Analyzing the influence that fundamental uncertainty 1/a has on the optimal solicited rating, delivers: ∂zS ∂a

=

(1 − r)c (y − xA ) . [a + (1 − r)]2

Hence, for sufficiently good prior expectations with regard to the firm’s credit quality, i.e. for y > xA , higher fundamental uncertainty leads to an reduction of zS , while the opposite holds for bad prior expectations. As an intuition for this result, consider that higher fundamental uncertainty implies that the unknown firm quality θ might lie far apart from the ex-ante expected value y. For high values of y, there is a considerable 29

In this respect, the “ability” of a rating agency would require a solicited rating as a necessary condition. 30 For proof, see appendix C.

19

likelihood that θ will be much lower, which will be mirrored by a low rating, while the opposite is true for low values of y. Finally, how does the structure of the CRA’s utility function, i.e. the weights attached to reputation and competition objective, influence the solicited rating? Intuitively, we find that for a sufficiently optimistic prior expectation with regard to θ, i.e. for y > xA , the rating increases in r and decreases in 1 − r. The proof can be obtained from appendix D. Stated differently, the more weight a rating agency places on her reputation (as compared to competitive concerns), the lower will her rating be in case of bad private information about the firm and the higher will it be in case of good private information about θ. The opposite holds if she puts less emphasis on her reputation. The results are summed up in the following corollary: Corollary 3 For sufficiently high private information, the optimal solicited rating will (i) increase in fundamental uncertainty, 1/a, (ii) decrease in the weight attached to the competitive argument, r, and (iv) increase in the emphasis attached to the repuational aim. The opposite holds for sufficiently low private information. Before analyzing the effect that unsolicited and solicited ratings may have on the market outcome, let us consider their role with regard to the uniqueness of equilibrium. Even though the condition for a unique equilibrium is less strict if the rating agency announces only unsolicited ratings, as public information on the market in this case comprises only the common knowledge about the firm’s quality distribution, and hence complies with the uniqueness condition in the absence of a rating agency, the practice of generating unsolicited ratings endangers the virtuous circle originally triggered by the announcement of very precise rating assessments. Are our results in line with the empirical results on the difference between solicited and unsolicited ratings? There is more or less consensus in the empirical literature that unsolicited ratings are lower than solicited ones.31 However, there are two interpretations that are consistent with this difference that is also known in the literature as the “downward bias”. The first may be referred to as the “punishment hypothesis”. Under the punishment hypothesis, a rating agency that is compensated by issuers has an incentive to assign higher ratings to firms who pay for the service than to issuers who do not. Thus, rating agencies announce unsolicited ratings as a means to blackmail issuers. The second hypothesis may be denoted as the “private information hypothesis”. It states that lower unsolicited ratings are the result of self selection based on private information. Of course, this interpretation is more in line with our results. Interestingly, however, our model indicates that it is not the firm quality per se that influences the solicited rating but the difference between the CRA’s perception of firm quality, i.e. private signal xA , and the ex-ante expected firm quality, y. Notice that the power of a rating agency to select the equilibrium in case of multiple equilibria also contains an element of blackmailing. Interestingly, recent empirical studies confirm mainly the private information story (Byoun and Shin ,2003, and Gan, 2004). In addition, studies that investigate the stock market reaction of rating changes from unsolicited to solicited ratings find that markets seem to expect an upgrade and punish those firms whose ratings 31

See Byoun and Smith (2002), Poon (2003), Poon and Firth (2004), Gan (2004), and G¨ uttler and Behr (2005) for evidence in this regard.

20

remain unchanged (Behr and G¨ uttler, 2005). This is also consistent with our theory, as will be shown in the following section.

6

Market Effects

In the following, we assume that the condition for a unique equilibrium holds, i.e. that investors obtain private information of sufficient precision, respectively that the rating agency attaches a sufficiently low weight to her reputation concern. From the analysis in section 2 we know that the ex-ante probability of default is given by: √ prob (default) = prob(θ ≤ θ∗ ) = Φ( a(θ∗ − y)) . Obviously, the default probability increases in equilibrium value θ∗ , so that all model parameters that reduce θ∗ will decrease the incidence of default as well. With rational expectations, investors will learn that the rating’s precision d is given by a + (1 − r)c. Plugging this into the equilibrium equation for θ delivers: ³ 1 ³ ¡ ¢ θ∗ = Φ √ a 2θ∗ − y − (1 − r)z +(1 − r)c(θ∗ − z) b ³ R − 1 ´´´ p − 2a + b + (1 − r)cΦ−1 . (14) R As can easily be seen, the probability of default decreases in the ex-ante expected firm quality, y, in the announced rating, z, and in the offered repayment rate, R. But how does θ∗ compare to the equilibrium value in the absence of a credit rating ∗ ? From the following comparison: agency, θW ∗ θW ∗ θW

> θ∗

⇔

1 R−1 √ (1 − r)c ∗ (θ − z) + Φ−1 ( )[ a + b > 2θ∗ − (1 − r)z + a a R p − 2a + b + (1 − r)c]

(15)

we find that the introduction of a rating agency reduces the probability of default as long as the rating agency announces a sufficiently high rating. From the preceding section we know that the difference between the solicited and the unsolicited rating rises along with the precision of the CRA’s private information if the face value of the CRA’s private signal deviates positively from y. Hence, for firms that are able to confide sufficiently optimistic information about their business prospects to the CRA despite a pessimistic prior expected firm quality, the probability of default will decrease after the announcement of a rating. This contributes to the above-mentioned “private information hypothesis”, that relates the difference between solicited and unsolicited ratings to an adverse selection problem. Our model is even more precise in showing that firms have a high incentive to request a solicited rating in order to reduce their probability of default, if they believe to be treated unfair by the market, i.e. whenever they believe to be able to disclose much more optimistic private information to the CRA than what has a priori been expected.32 32

In a sense, this result is related to Faure-Grimaud et al. (2006), who show that rating agencies

21

Proposition 4 In order to reduce the probability of default, firms will request a (solicited) rating if they believe that they are able to disclose more optimistic private information to the credit rating agency than what has a priori been expected by the market, i.e. for xA > y. Since equilibrium value θ∗ decreases in the announced rating, it follows naturally from corollary 3 that for sufficiently high xA , the probability of default will increase in fundamental uncertainty, 1/a and weight r. For sufficiently low private information xA , the opposite results are obtained. Hence, the introduction of a rating agency is not necessarily beneficial only for firms of high quality, as has been stated by Carlson and Hale (2005). Rather the benefits of a rating agency are contingent on a complex system of parameter variations.

7

Institutional Investors

Investors on bond markets can usually be categorized into two different groups. They are either small, individual market participants, or large and institutionalized investors. As institutional investors typically hold their own research departments, they are also presumably much better informed about firm quality than small investors. In order to bring this structure into our model, we assume in this section that the market consists of proportion λ of institutional investors that observe private information about the firm with precision ¯b, and proportion (1 − λ) of small investors with information of precision b, with ¯b ≥ b. In many countries, institutional investors are furthermore restricted with regard to their investment choice.33 We build this restriction in our model by assuming that institutional investors are only allowed to invest in bonds with a rating at least as high as z˜. In contrast to Boot et al. (2006), we do not, however, rely on the simplifying assumption that whenever a bond obtains a sufficiently high (usually investment-grade) rating all institutional investors always invest.34 Hence, in the following we assume that institutional investors have to withdraw for z < z˜, but do not necessarily have to prolong credit for z ≥ z˜. What does this market-segregation imply for the equilibrium? Whenever the CRA announces a rating z < z˜, we know that institutional investors never roll over their debt but always withdraw their money. Hence the condition for imminent default of the firm is changed to: √ θ = λ + (1 − λ)Φ( b(xi − θ)) . offering corporate governance scores (CGS), that may remain hidden from investors at the discretion of the rated entity, represent an optimal contract. They prove that firms decide to hide the score, if they are sufficiently uncertain about their quality at the time of hiring a certification intermediary. 33 In a dynamic asset pricing model, Pagratis (2005) examines the effects of ratings-based asset holdings on price volatility and market efficiency. He finds a tradeoff between volatility and efficiency if investors hold heterogeneous beliefs and are sufficiently risk-averse. 34 Even though the market sometimes is so tight that they have to rely on this strategy, we rather consider the case where institutional market participants may but not necessarily have to buy and hold investment-grade bonds.

22

This delivers a unique equilibrium value of θ1∗ : ³ 1 θ1∗ = λ + (1 − λ)Φ √ (a(2θ1∗ − y − (1 − r)z) + (1 − r)c(θ1∗ − z) b p R−1 ´ )) . − 2a + b + (1 − r)cΦ−1 ( R It is obvious to see that θ1∗ ≥ θ∗ , so that for sufficiently low ratings, i.e. z < z˜, the probability of default is increased by the existence of institutional investors. If the CRA instead announces a rating of z ≥ z˜, whether or not institutional investors roll over their loans depends on their posterior beliefs about θ, so that equilibrium value θ2∗ is given by: ³ 1 ³ θ2∗ = λΦ √ a(2θ2∗ − y − (1 − r)z) + (1 − r)c(θ2∗ − z) ¯b q ¡ R − 1 ¢´´ − 2a + ¯b + (1 − r)cΦ−1 R ³ 1 ³ +(1 − λ)Φ √ a(2θ2∗ − y − (1 − r)z) + (1 − r)c(θ2∗ − z) b p ¡ R − 1 ¢´´ − 2a + b + (1 − r)cΦ−1 . R While it always holds that θ2∗ ≤ θ1∗ , we find that θ2∗ ≤ θ∗ whenever repayment R > 2 (as a sufficient condition), while θ2∗ > θ∗ for R < 2, as: p p ¯ 2a + b + (1 − r)c] Φ−1 ( R−1 ∗ ∗ ∗ ∗ R )[ 2a + b + (1 − r)c − θ2 ≤ θ ⇔ θ2 − θ < 2a + (1 − r)c For R > 2, this inequality is satisfied because the l.h.s. is negative by assumption while the r.h.s. is positive. The following corollary sums up the results: Corollary 4 The existence of institutional investors reduces the probability of default for firms rated investment-grade, whenever sufficiently high repayment values R are offered. For ratings below investment-grade, however, their existence raises the risk of inefficient firm default due to regulatory reasons.

8

Conclusion

Due to the complexity of many financial products and the adoption of the Basel II accord, the importance of credit rating agencies has strongly increased. Lacking a convincing theoretical basis, empirical and descriptive studies have often come to the conclusion that the market for credit ratings is “curiously devoid of competition and oversight”, of which it desperately “needs more” (The Economist, 2005). Moody’s Bond Rating Service, a major rating institution, has even been declared as one of the “two superpowers in the world today” (Partnoy, 1999) - together with the United States-, and has been accused of being able to make a “grown man cry” (Euromoney, 1998) by destabilizing markets. Focussing on a rigorous theoretical analysis and accounting for a complex utility function, we find that credit rating agencies may nevertheless be a benefactor to financial 23

markets. In particular, they may spark off a virtuous circle that supports information aggregation, thereby increasing market efficiency. This result is due to the fact that rating announcements and private information collection prove to be complements rather than substitutes for sufficiently highly-rated bonds. On the downside, however, the recent practice of announcing unsolicited ratings that are based only on publicly available information destroys this virtuous circle. Anticipating the lower precision, bond holders reduce their investment in private information precision, which undermines the benevolent effect of credit ratings on information aggregation. Recently observed troubles of open-end real estate funds in Germany, that have partly been triggered by rating announcements, show that the effects are not restricted to the market for credit ratings but hold in a more general context. In particular, the market structure, reflecting the influence of large, institutionalized investors, seems to strengthen the impact of rating agencies on investment decisions, thereby corroborating the coordinating role that ratings may fulfill additionally to their information role.

24

References [1] Association for Financial Professionals (AFP), 2004, 2004 Credit Rating Agency Survey, available at http://www.afponline.org/pub/pdf/pr 20050208 kaitz.pdf. [2] Association for Financial Professionals (AFP), 2005, Statement of James A. Kaitz before the House Financial Services Committee, Wednesday, June 29, 2005. [3] Baker, H.K., S.A. Mansi, 2002, Assessing Credit Rating Agencies by Bond Issuers and Institutional Investors, Journal of Business Finance & Accounting 29, 13671398. uttler, 2005, The Stock Market Reaction to Changes of Unsolicited [4] Behr, P, A. G¨ Ratings. Working Paper Goethe-University Frankfurt. [5] Benabou, R., G. Laroque, 1992, Using Privileged Information to Manipulate Markets: Insiders, Gurus and Credibility, Quarterly Journal of Economics 107, 921958. [6] Boot, A., S. Greenbaum, A. Thakor, 1993, Reputation and Discetion in Financial Contracting, American Economic Review 83(5), 1165-1183. [7] Boot, A., T. Milbourn, A. Schmeits, 2006, Credit Ratings as Coordination Mechanisms. Review of Financial Studies 19, 81-118. [8] Byoun, S., Y.S. Shin, 2002, Unsolicited Credit Ratings: Theory and Empirical Analysis. Working Paper. [9] Cantor, R., 2004, An Introduction to Recent Research on Credit Ratings, Journal of Banking and Finance 28, 2565-2573. [10] Cantor, R., F. Packer, 1994, The Credit Rating Industry, Federal Reserve Bank of New York Quarterly Review Summer-Fall, 1-26. [11] Carlson, M., G. Hale, 2005, Courage to Capital? A Model of the Effects of Rating Agencies on Sovereign Debt Roll-Over. Cowles Foundation Discussion Paper No 1506. [12] Carlsson, H., E. van Damme, 1993, Global Games and Equilibrium Selection, Econometrica 61, 989-1018. [13] Covitz, D.M., Harrison, P., 2003, Testing Conflicts of Interest at Bond Ratings Agencies with Market Anticipation: Evidence that Reputation Incentives Dominate, mimeo, Federal Reserve Board, Washington. [14] Euromoney, 1998, Rating Agencies Caught With Their Pants Down, January 15, p. 51. [15] Faure-Grimaud,A., Peyrache, E., Quesada, L., 2006, The Ownership of Ratings, mimeo, London School of Economics. [16] Gan, Y., 2004, Why Do Firms Pay for Bond Ratings When They Can Get Them for Free?. Job Market Paper Wharton School. 25

[17] Goldstein, I., Pauzner, A. 2005, Demand Deposit Contracts and the Probability of Bank Runs. Journal of Finance 60(3), 1293-1328. [18] Golin, J., 2001, The Bank Credit Analysis Handbook: A Guide for Analysts, Bankers and Investors, Wiley & Sons. [19] Hand, J., R. Holthausen, R. Leftwich, 1992, The Effect of Bond Rating Agency Announcements on Bond and Stock, The Journal of Finance 47(2), 733-752. [20] Heinemann, F., R. Nagel, P. Ockenfels, 2004, The Theory of Global Games on Test: Experimental Analysis of Coordination Games With Public and Private Information, Econometrica 72(5), 1583-1599. [21] Hellwig, C., L. Veldkamp, 2006, Knowing What Others Know: Coordination Motives in Information Acquisition, mimeo, University of California, Los Angeles. [22] Hill, C.A., 2004. Regulating the Rating Agencies. Washington University Law Quarterly 82, 43–95. [23] Hubert, F., Sch¨afer, D., 2002, Coordination Failure with Multiple-Source Lending: the Cost of Protection Against a Powerful Lender, Journal of Institutional and Theoretical Economics 158, 256-275. [24] IOSCO, 2003, Report on the activities of credit rating agencies, available at http://www.iosco.org/library/pubdocs/pdf/IOSCOPD153.pdf. [25] Lucas, R., 1972, Expectations and the Neutrality of Money, Journal of Economic Theory 4, 103-124. [26] Lucas, R., 1973, Some International Evidence on Output-Inflation Tradeoffs, American Economic Review 63, 326–334. [27] Mariano, B., 2005, Conformity and Competition in Financial Certification. London School of Economics Working Paper. [28] Morris, S., 2001, Political Correctness, Journal of Political Economy 109, 231-265 [29] Morris, S., H. Shin, 1999, Private versus Public Information in Coordination Problems, unpublished paper, Yale University. [30] Morris, S., H. Shin, 2002, Social Value of Public Information, American Economic Review, 52 (5), 1521-1534. [31] Morris, S., H. Shin, 2003, Global Games: Theory and Applications, in Dewatripont, M. et al. (eds): Advances in Economics and Econometrics, the Eighth World Congress, Cambridge University Press, (2003). [32] Morris, S., H. Shin, 2004, Coordination risk and the price of debt, European Economic Review 48, 133-153. [33] OICU-IOSCO, 2004, Code of Conduct Fundamentals for Credit Rating Agencies, December 2004. 26

[34] Pagratis, S., 2005, Asset Pricing, Asymmetric Information and Rating Announcements: Does Benchmarking on Ratings Matter? Bank of England Working Paper No 265. [35] Partnoy, F, 1999, The Siskel and Ebert of Financial Markets? Two Thumbs Down for the Credit Rating Agencies, Washington University Law Quarterly, Vol. 77, No. 3, pp. 619–715. [36] Partnoy, F., 2001, The Paradox of Credit Ratings. University of San Diego Law an Economics Research Paper No 20. [37] Phelps, E., 1970, Introduction, in E. Phelps et al. (eds): Microeconomic Foundations of Employment and Information Theory, 1–23, Norton, New York. [38] Plantin, G., H. Sapra, H.S. Shin, 2005, Marking-to-Market: Panacea or Pandora’s Box? Mimeo, Carnegie Mellon University, Pittsburgh. [39] Poon, W., 2003, Are Unsolicited Credit Ratings Biased Downwards?, Journal of Banking and Finance 27, 593-614. [40] Poon, W., M. Firth, 2004, Are Unsolicited Bank Ratings Lower? Preliminary Evidence from Fitch‘s Bank Individual Ratings, Working Paper. [41] Schwarzc, S., 2002, Private Ordering of Public Markets: The Rating Agency Paradox, University of Illinois Law Review, 1-28. [42] Spence, M., 1973, Job Market Signaling, Quarterly Journal of Economics 87, 355374. [43] Smith, R.C., I. Walter, 2001, Rating Agencies: Is There an Agency Issue?, Working Paper. [44] The Economist, 2005, Special Report Credit-rating agencies, March 26, 65–67. [45] Van Roy, P., 2005, Is there a difference in treatment between solicited and unsolicited bank ratings and, if so, why?, mimeo, ECARES, Universite Libre de Bruxelles. [46] Vassalou, M., Y. Xing, 2005, Abnormal Equity Returns Following Downgrades, mimeo, Columbia Business School. unstlinge der Investoren, Die Zeit, July 26, 2005. [47] Von Heusinger, R., 2005, G¨

27

Appendix Appendix A From the analysis in section 2 we know that the probability of firm default is given by prob(θ ≤ θ∗ ), while the CRA holds a posterior belief about the firm’s quality of: θ|xA ∼ N

³ ay + cx

A

a+c

,

1 ´ . a+c

The CRA’s expected utility function can therefore be derived as: ¯ A )2 Eui (zi , θ) = −(1 − r)(zi − E(θ|xA ))2 − rE(Li − L|x = −(1 − r)(zi − E(θ|xA ))2 Z 1 −rE(zi2 − 2zi z¯ + z¯2 − (zj2 − 2zj z¯ + z¯2 )dj|xA ) .

(16)

0

Derivation with respect to zi and setting equal to zero delivers the optimal rating as given in (9). Following Morris and Shin (2002), we assume a linear strategy as optimal for a rating agency: zi = k1 xA + k2 y . (17) This allows to average over all potential ratings: E(¯ z |xA ) = k1

ay + cxA + k2 y , a+c

(18)

since E(xAj |xAi ) = E(θ|xAi ). Plugging this into the optimal rating function (9) yields: zi =

(1 − r)c + rk1 c (1 − r)a + rk1 a + rk2 (a + c) xA + y. a+c a+c

Comparing coefficients to (17) gives us the weights attached to the three arguments of the optimal rating strategy: (1 − r)c , k1 = a + (1 − r)c and k2 =

a . a + (1 − r)c

Appendix B With rational expectations, investors will learn that the rating’s precision d is given by a + (1 − r)c. Plugging this into the equilibrium equation for θ delivers: ³ 1 ³ ¡ ¢ θ∗ = Φ √ a 2θ∗ − y − (1 − r)z +(1 − r)c(θ∗ − z) b ³ R − 1 ´´´ p − 2a + b + (1 − r)cΦ−1 . R

28

(19)

The derivation with respect to the CRA’s private information precision is then given by ∂θ∗ ∂c

³R − 1´ 1 ∂θ∗ ∂θ∗ (1 − r) = φ(·) · √ [2a + (1 − r)(θ∗ − z) + (1 − r)c − p Φ−1 ] ∂c ∂c R b 2 2a + b + (1 − r)c ³ ´ φ(·) √1b [(1 − r)(θ∗ − z) − √ 1−r Φ−1 R−1 ] R 2 2a+b+(1−r)c = 1 − φ(·) √1b (2a + (1 − r)c)

Obviously, this partial derivative is negative for z sufficiently high relative to θ*, such that the numerator becomes negative, while the denominator always stays positive due to the uniqueness condition.

Appendix C For the derivation of factor

(1−r)a , [a+(1−r)c]2

we find:

(1−r)a ∂ [a+(1−r)c] 2

∂r which is positive if c >

a 1−r

=

a[(1 − r)c − a] [a + (1 − r)c]3

and negative otherwise.

Appendix D ∂zS ac = (y − xA ) . ∂r [a + (1 − r)c]2 This partial derivative is positive for y > xA and negative otherwise. Exactly the opposite holds for the impact of (1 − r) on zS .

29

28th August 2006

Abstract In this paper, we propose a model of credit rating agencies using the global games framework to incorporate information and coordination problems. By introducing a reduced-form utility function for the agency, we find that - in contrast to earlier work - rating announcements do not necessarily increase multiple equilibria incidences. For sufficiently highly-rated firms, public rating announcements and investors’ private information collection turn out to be complements rather than substitutes. Rating agencies may hence spark off a virtuous circle that increases aggregate information precision and raises market efficiency. We furthermore comment on the difference between solicited and unsolicited ratings and institutional investors’ influence.

JEL Classification: D82, G14, G33 Keywords: Information production, rating agencies, coordination problems, global game

∗

We received helpful comments from Alexander Bassen, Patrick Behr, Wolfgang B¨ uhler, Falko Fecht, Robert Gillenkirch, Andr´e G¨ uttler, Hendrik Hakenes, Martin Hellwig, Stephan Klasen, Jan Pieter Krahnen, Dirk Kr¨ uger, Christian Laux, Lukas Menkhoff, Martin Nell, Andreas Oestreicher, Anjolein Schmeits, Hartmut Schmidt, Isabel Schnabel, participants at Goethe-University Frankfurt Finance Seminar, Conference of the Swiss Society for Financial Market Research Zuerich, FIRS Conference Shanghai, MPI Econ Workshop Bonn. All errors are, of course, our own. † Department of Economics and Business Administration, Goethe-University Frankfurt, Mertonstr. 17-21, 60325 Frankfurt, Germany, Phone: +49 69 798 23386, Fax: +49 69 798 28951, E-mail: [email protected] ‡ Department of Economics and Business Administration, Goethe-University Frankfurt, Mertonsr. 17-21, 60325 Frankfurt, Germany, E-mail: [email protected]

1

1

Introduction

Despite a lot of recent research effort, the role of credit rating agencies is still not very well understood. On the one hand, due to the secrecy of rating agencies about their work, the rating process itself remains unclear; on the other hand, observers still struggle to understand how the market perceives this process and how the rating influences the rated firms and their outstanding debt. Yet, the influence of credit rating agencies has steadily increased over the years, not least because of the adoption of the new global framework regulating banks’ capital known as Basel II. Due to the new Basel Accord, banks are required to hold a level of equity reserves that corresponds to their credit risk, which can either be assessed via internal rating systems or by making use of external rating expertise. Additionally, the complexity of many financial products, such as derivative and asset-backed securities, has made it very difficult for investors to assess credit risk on their own and has therefore raised the importance of rating agencies. Recent years have seen many empirical and descriptive research projects gathering a large number of stylized facts about the process of rating assessments and their influence on investment decisions. However, theoretical papers explaining these stylized facts remain rare. Up to now, it is for instance unclear why firms tend to ask for two rating assessments for their outstanding debt instead of a single rating (Baker and Mansi, 2002) or why rating changes lead to asymmetric market effects, depending on whether the initial rating is upgraded or downgraded (Vassalou and Xing, 2002; Hand, Holthausen, Leftwich, 1992). Another controversy refers to the recent practice of announcing unsolicited ratings i.e. “ratings that credit rating agencies conduct without being formally engaged to do so by the issuer” (IOSCO, 2003).1 Even though these unsolicited ratings open up competition among credit rating agencies since they allow smaller agencies to compete with the “Big Three” (Moody’s, Standard and Poor’s and Fitch), it is questionable why these ratings exist at all, as, due to their confinement on publicly-available information, they do not contain any new information over and above what has already been known to the market and are not paid for. Possibly, therefore, rating agencies do not only provide information but perform additional functions, for instance by serving as a coordination device for investors as has been suggested by Boot et al. (2006). Corroborating these fundamental uncertainties about the work and functioning of credit rating agencies are regular reports about a growing concern among market practitioners on their role (AFP, 2004), as well as proposals of a code of conduct and of a revision of the SEC’s recognition process of Nationally Recognized Statistical Rating Organizations (OICU-IOSCO, 2004; AFP, 2005). One main aspect in this controversy is the question whether the service that credit rating agencies offer actually contributes to a reduction in market uncertainty or rather increases it. The general concern and the obvious lack of understanding of the agencies’ objectives is reflected in the following statement by Thomas Friedman (1996): “There are two superpowers in the world today. There’s 1

Before the 1970s, credit rating agencies used to charge investors a fee for the provision of information about a bond’s default risk, a service that could reasonably be referred to as unsolicited ratings. Moving to a system where issuers were charged for assessing the risk of their outstanding debt mainly occurred because of the decreasing cost of photo-copying in the 1970s. In 1991, Moody’s reintroduced the practice of announcing unsolicited ratings which was quickly followed by other major agencies.

the United States and there’s Moody’s Bond Rating Service. The United States can destroy you by dropping bombs, and Moody’s can destroy you by downgrading your bonds. And believe me, it’s not clear sometimes, who’s more powerful.” The lack of a solid theoretical basis in grasping these issues has been perceived as one of the main shortcomings of the academic research to date.2 The current paper tries to fill this gap. As one of the first approaches in this respect, we consider a reduced-form utility function that allows the derivation of an agency’s optimal rating assessment. In accordance with empirical findings and anecdotal evidence, this function contains two different utility components, based on a reputation and coordination, respectively competition, objective.3 The main contribution of the paper focuses on the effects that rating announcements have on investors’ actions and how they may help to eliminate uncertainties in investment behavior. Additionally, we examine the difference between unsolicited and solicited ratings and study the reasons for their empirically-observed deviation. Finally, we analyze the influence of large, institutional investors on the investment process and explore whether they strengthen or weaken the rating’s effect. While our model remains within the institutional framework of the market for corporate credit ratings, our results may easily be transferred to a broader setting, for instance to sovereign credit ratings. As a recent example for a rating’s effect on market stability, we may also consider the current troubles of open-end property funds in Germany that have partly been triggered by rating announcements. These examples warrant a detailed analysis of the process of information certification and its influence on the stability of the assessed entities. Contrary to the results of an earlier paper by Carlson and Hale (2005), we find that the existence of rating agencies does not necessarily increase market uncertainty. Carlson and Hale (2005) conclude that rating agencies, by announcing their ratings publicly, increase the precision of public information on the market and hence make coordination among investors easier. In their model,4 a rating agency therefore fulfills both a function of information but also of coordination - with potentially detrimental results. Whereas for perfectly sound firms the risk of default is not affected by the rating, less than perfectly sound firms suffer from the occurrence of multiple equilibria. Here, investors cannot determine their optimal investment decision with certainty, since, based on the public rating assessment, both a prolongation of credit and a premature withdrawal of money may be rational, depending on the behavior of the aggregate investment decisions of the market (leading to a respective shift in price), so that a considerable amount of uncertainty prevails. In our model, in contrast, we can show that, despite the dual role of ratings, as long as the agency pursues additional aims to the usually assumed objective of maximizing her reputation, a unique equilibrium may be restored and uncertainties are eliminated. Moreover we find that for sufficiently highly-rated bonds, public rating announcements 2

This is also one of the main conclusions by Cantor (2004) in the editorial of the November 2004 Special Issue on Credit Ratings of the Journal of Banking and Finance. 3 The view that the credit rating industry is competitive and reputation-driven is the dominant one held by scholars. See for instance Cantor and Packer (1994) and Smith and Walter (2001) as advocates of this view but also Partnoy (2001) for an alternative position. 4 Carlson and Hale (2005) focus on sovereign debt ratings and investors’ influence on sovereign default. Yet, the model implications may also be applied to corporate markets.

3

and private information collection are complements rather than substitutes. Hence, if investors have discretionary power over the precision of their private information, they are able to secure the prevalence of a unique equilibrium and reduce the probability of the rated entity’s default. Rating agencies may even spark off a “virtuous circle”: the more accurate the announced ratings are, the higher are investors’ incentives to increase the precision of their private information as well, which raises the efficiency of the market outcome. In our model, the observed difference between unsolicited and solicited ratings is ascribed to the gap between the rating agency’s private information and the market expectation about the firm’s credit quality. Hence, unsolicited ratings are seriously downward-biased for firms who could potentially disclose very optimistic private information about their credit quality to the agency, while the market a priori expects a much lower quality. Since the probability of default decreases with better, i.e. higher, ratings, our model relates the observed downward-bias of unsolicited ratings to an adverse selection problem between firms that believe to be of high quality and, consequently, request a (solicited) rating and those that believe to be of lower quality and therefore refrain to ask for a rating. Regarding the rating agency’s “ability” to assess the relative default risk of corporate bonds, we prove anecdotal evidence to be true that agencies of higher ability tend to announce more extreme ratings than do agencies of lower ability. This requires, however, that they do take into account their coordinating role additional to a maximization of their reputation. We then find that after observing good private information, a rating agency of higher ability will announce a higher rating than an agency of lower ability. The opposite holds for the case of bad information. Finally, we show that the existence of large, institutionalized investors (such as pension funds), that has often raised concerns, increases the probability of default for lowlyrated firms. This result stems from regulatory reasons that require pension funds to condition their investments on the assets’ ratings. A corporate rating downgrade may then result in a strong financial disruption, due to extensive withdrawals by institutional investors, that forces the firm into default. For sufficiently highly-rated, i.e. investmentgrade, firms, in contrast, the existence of institutional investors strengthens the virtuouscircle effect mentioned above as institutional investors usually maintain own research departments and hence dispose of very precise private information. This reduces the risk of default even more. To invest in the precision of their private information, however, is only beneficial for investors if the agencies’ ratings are also sufficiently precise. Thus, for this positive cycle to work, the quality and precision of ratings has to be assured continuously, which is one of the main demands that have consistently been brought before state hearings on legislative solutions regarding the work of credit rating agencies in the U.S. (AFP, 2005) The paper is related to various strands of the literature. The first is the literature on reputational concerns and reliability of information provided by certification intermediaries such as rating agencies. Mariano (2005) develops a model which analyzes this relationship in the context of both a monopolistic and a duopolistic certification industry.5 Because of a different modelling setup, her paper has to abstract from a potential 5

Also Benabou and Laroque (1992) and Morris (2001) are important examples of this literature.

4

coordination function of the credit rating agency and does not consider multiplicity of equilibria. The second strand of literature builds on signalling models in the tradition of Spence (1973) and examines how different types of firms can signal their quality to the market when there is asymmetric information between firm insiders and market participants. Byoun and Shin (2002) model signalling behavior of firms in an environment in which firms can choose a rating agency as an information specialist who is able to obtain and convey information at lowest costs. They develop conditions for a separating equilibrium where only good firms signal their quality through the rating agency. Their paper differs from ours in many respects. Most importantly, it does not consider the interplay between private and public information and gives no active role to the credit rating agency. Most closely related to our work are the papers by Boot et al. (2006) and Carlson and Hale (2005). Boot et al. (2006) show that credit ratings can serve as a coordinating mechanism in situations of multiple equilibria. In addition, they explore in detail how a monitoring role vis-`a-vis a firm is put in place through the credit watch procedure used by credit rating agencies. In their model, the practice of institutional investors to condition their investment behavior on the rating enforces an implicit contract between the firm and the credit rating agency where the former promises not to misbehave because this may endanger her credit standing. While we share the focus on multiple equilibria with Boot et al. (2006), the methodological contribution of our paper is quite different. We apply the global games theory to examine under which conditions uniqueness of equilibrium can be achieved. This allows us to investigate in detail the role of a credit rating agency in providing information to the market rather than performing a monitoring role, when the rating simultaneously fulfills a coordinating function. Carlson and Hale (2005) also propose a model of rating agencies as an application of the global games methodology. However, they do not introduce an explicit utility function for the rating agency. Further differences between the two papers will be discussed where appropriate in the paper. The remainder of the paper is organized as follows. Section 2 describes the basic setup of our model. Section 3 derives the agency’s optimal rating. Section 4 discusses the condition for a unique equilibrium. Sections 5 to 7 analyze the difference between solicited and unsolicited ratings and their impact on investors’ actions. Section 8 concludes. Both papers develop repeated cheap talk models of a sender of information whose honesty is unknown to the information receivers.

5

2

The model

2.1

Strategies, Information and Sequence of Events

In a very simple model we capture the interaction between a firm, a continuum of investors6 and a credit rating agency (CRA).7 The firm has outstanding debt from an ongoing business project that has to be repaid at maturity. Based on private and public information about the firm’s quality - including a published rating - investors have to decide whether or not to prolong credit in the intermediate period.8 Extensive premature withdrawal of credit may force the firm into default. We assume that the firm’s quality is a random variable θ, normally distributed with mean y and variance 1/a. The distribution of θ is common knowledge in the market and may as such be referred to as public information. The lower a, the higher is the firm’s fundamental risk, since firm quality θ may then deviate strongly from the ex-ante expected value y. While the distribution of θ is commonly known, the realization θ is not observable to market participants. Yet, each investor receives private information about firm quality: xi |θ ∼ N (θ, 1/b). The higher b, the more closely are investors’ private signals distributed around the unknown firm quality θ. In this respect, b denotes the precision of investors’ private information. Similarly, the rating agency collects information about the firm that results in a private signal of xA |θ ∼ N (θ, 1/c). Note that, conditional on θ, private signals are assumed to be independent of each other. The time line of the model is as follows: • In t = 0, the firm has outstanding debt that has to be repaid at a rate of R > 1 per unit of debt at maturity (t = 2). While market participants cannot observe the realization of firm quality θ, its fundamental situation, i.e. the distribution of θ, is common knowledge. The firm appoints a rating agency to assess its quality. • In t = 1, investors observe individual private signals xi about firm quality. The rating agency collects a private signal xA and subsequently announces the rating z - a statement on the firm’s quality - to the market. Investors update their beliefs and decide on whether to prolong credit (i.e. hold on to their investment) or withdraw early. Early withdrawal is not connected to any premium or punishment and hence delivers a payment of 1 per unit of capital. • The firm’s project can mature successfully in t = 2, if a proportion of less than θ of outstanding debt has been withdrawn prematurely. The firm then repays debt out of the realized project payoff, which is equal to V . Otherwise the firm 6

The assumption of atomistic investors is made in order to keep the analysis as simple as possible. It is not critical for the derivation of results as has been shown by Morris and Shin (2003). 7 The derivation of the “optimal” rating in section 3 will be based on the assumption of a continuum of information intermediaries. In equilibrium, therefore, all ratings will be equivalent, so that we only refer to one CRA in the present section. 8 The rating we consider comprises general information about the firm’s quality and hence comes close to the notion of “corporate ratings”. As we consider short-term debt financing such as for instance provided by commercial papers, the rating’s interpretation should not be narrowed down to bond ratings, which usually address the quality of medium- to long-term debt.

6

Table 1: Investors’ strategies and payoffs default no default (l ≥ θ) (l < θ) prolong withdraw

0 1

R 1

defaults, a payoff of zero is obtained and credit is not repaid.9 In this simple formulation, project payoff V is a constant larger than R. Fundamental variable θ measures the firm’s ability to meet the financial disruption brought about by investors’ withdrawal of credit and hence measures the firm’s credit quality.10 Investors’ payoffs are summarized in table 1. Here, l represents the aggregate amount of early withdrawal, i.e. the proportion of investors that decide not to prolong credit.11

2.2

Equilibrium Without a CRA

In order to derive a benchmark result, let us first consider the case without a rating agency. Equilibrium values are denoted by subindices “W”. In this case, investors have to base their decisions of whether or not to prolong credit solely on the common prior about θ and on their private signals xi . From table 1 the following may easily be inferred. Since l, the proportion of investors that decide to withdraw their money prematurely, takes on values between 0 and 1, investors will always opt for withdrawal for θ < 0 and choose to prolong credit for θ > 1, the latter being the efficient equilibrium of the model. For θ ∈ [0, 1], however, both actions may constitute an equilibrium, depending on investors’ expectations about l. As these equilibria are based on self-fulfilling beliefs,12 the model delivers the undesirable feature of unpredictability of outcome for non-extreme firm fundamentals if the 9

This very simple payoff function implies that the recovery rate conditional on default is independent of θ (Morris and Shin, 2004). 10 Consider that a massive withdrawal of capital excessively shrinks the firm’s potential to raise new money and hence to repay outstanding debt at maturity. In the extreme, the firm might fear not to be able to repay credit in t = 2 and opts for default. The decision to default is not contractible ex-ante and gives rise to the moral hazard problem to be studied in the following. 11 The model may alternatively be applied to the case where the firm intends to conduct a new project and issues claims, e.g. bonds, to raise the necessary finance. Market participants decide whether or not to invest in t = 1 based on their private information and the public bond rating. The project can only be successful (i.e. yield a payoff of V ), if sufficiently many investors donate financing. These investors then obtain a fixed repayment of R in t = 2. If the raised amount of finance is below the critical level of 1 − θ, however, the project does not deliver any repayment. Firm quality θ hence represents the amount of internal financing. Note that the model also shows a parallel to the recently observed troubles of openend property funds in Germany. Open-end funds trade long-term investments for short-term liquidity but may choose to freeze trading at the current value of assets once too high liquidity outflows are observed. In December 2005 and January 2006, three funds were closed because of massive withdrawals of liquidity after a rating-downgrade announcement on two of the funds. 12 Whenever an investor believed that sufficiently many other investors might withdraw their loans early, it would be optimal for him to withdraw as well, thereby vindicating any investor’s decision to

7

realization of θ were common knowledge. A remedy for the multiplicity problem is provided by heterogeneous information about firm quality θ, which lies at the heart of the model assumptions. Essentially, the depicted model (with imprecise private and public information) presents a global game in the sense of Carlsson and van Damme (1993), where each player noisily observes the game’s payoff structure (i.e. firm quality θ), which itself is determined by a random draw from a given class of games. Following the solution method of Morris and Shin (2003, 2004) we can derive a unique equilibrium, provided that private information about θ is sufficiently precise. The equilibrium can be shown to be given in trigger strategies, so that each investor will extend his loan whenever he obtains a private signal xi higher than a trigger value x∗W and will withdraw credit otherwise. Correspondingly, the firm ∗ is realized. Equilibrium values θ ∗ and x∗ will default if a quality value lower than θW W W are derived from the conditions that render agents indifferent between their respective actions as will be shown in the following. The marginal investor is indifferent between foreclosing and prolonging credit, if both actions deliver the same expected payoff: ∗ 1 = R · prob(θ ≥ θW |xi ) .

(1)

Here, it has been recognized that the project will only be successful if the firm’s quality ∗ . θ is larger than θW If there is no credit rating agency on the market, investors’ posterior beliefs about θ are given by: ! Ã 1 ay + bxi , . (2) θ|xi ∼ N a+b a+b Plugging this in (1) delivers the indifference condition for the individual investor: √ a+b ∗ a a + b −1 ³ R − 1 ´ xi = θW − y − Φ ≡ x∗W . b b b R

(3)

Hence, an investor will foreclose his loan early whenever he observes a private signal about firm quality lower than x∗W and rolls over otherwise. The firm’s project, however, needs a critical mass of (external) investment in order to proceed successfully, i.e. the project defaults whenever the proportion of withdrawn debt is higher than θ.13 The firm is therefore on the brink of default if: θ = l ≡ prob(x ≤ x∗W |θ) √ θ = Φ( b(x∗W − θ)) .

(4)

foreclose the loan, so that eventually they will all do so. If, in contrast, he expected others to extend their loans, it would be profit-maximizing for him to extend as well, leading to coordination on the efficient equilibrium. 13 This simplifying assumption may be rationalized as follows: if credit markets are fully competitive, investors will ask for a higher return R for the project, the larger the probability that the project will not succeed, i.e. the higher the proportion of investors that will not prolong credit. This increases the cost from pursuing the risky project over the choice of the “safe” default that renders a payoff of zero to both the firm and to investors. See also Boot et al. (2006).

8

Note that due to the assumed independence of private signals, the proportion of investors withdrawing their loans prematurely (after observing sufficiently low private signals) is equivalent to the probability with which an individual investor obtains private information lower than x∗W . Combining indifference conditions (3) and (4) yields the equilibrium threshold value ∗ below which the firm’s project will optimally be abandoned, since the proportion of θW withdrawn capital is too high to warrant any further refinancing on the part of the firm. ∗ , however, the project will be continued with certainty, For quality values of θ above θW even though there might still be some credit foreclosure. This withdrawal of capital is ∗ is then yet sufficiently small as not to force the firm into default. Equilibrium value θW derived as: r ³ a a + b −1 ³ R − 1 ´´ ∗ ∗ θW = Φ √ (θW − y) − . (5) Φ b R b ∗ ∈ [0, 1], the optimal behavior in the extreme regions, θ < 0 and θ > 1, is As θW ∗ , a default is always unchanged.14 Note that for intermediate firm qualities, 0 < θ ≤ θW inefficient since it has not been triggered by a sufficiently bad firm quality but simply by the number of investors that decided to withdraw their money early.15 A default in this region could be prevented, if only sufficiently many investors decided to prolong credit. Uniqueness of equilibrium hence does not eliminate inefficiencies. Default occurring ∗ ] is also referred to as a coordination failure on the part of in the range of θ ∈ [0, θW investors.

As a sufficient condition for (overall) uniqueness of equilibrium, consider that the two indifference curves as represented by (3) and (4) must not cross more than once. Solving ∗ , it can easily be seen that a (4) for x and deriving both functions with respect to θW sufficient condition for a unique equilibrium is given by b > a2 /(2π). It requires that behavioral uncertainty, introduced via the variance in traders’ individual private signals, 1/b, does not become too strong as compared to fundamental uncertainty, represented by the variance 1/a of the firm’s quality value θ.16 Stated differently, private information on the part of investors must be sufficiently precise relative to the precision a of public information about θ.

2.3

Equilibrium With CRA

Now consider the case of a credit rating agency publicly announcing her rating in t = 1. For the time being, we assume the rating z to be exogenously given and normally 14

In fact, the uniquely optimal strategies in the extreme regions of θ are necessary in order to derive a unique equilibrium for all values of θ under heterogeneous information by iteratively eliminating dominated strategies (Morris and Shin, 2003). Under certain conditions, even only one such region may suffice to allow the derivation of a unique equilibrium for the whole range of fundamental values (Goldstein and Pauzner, 2005). 15 Default is efficient only for θ < 0, since in that case, even if all lenders decided to roll over, termination of the project would still be optimal for the firm. The same is true in the case with a rating agency being present. 16 What we call behavioral uncertainty corresponds to the notion of strategic uncertainty in Morris and Shin (2002, 2003, 2004). Both terms will be used interchangeably.

9

distributed with a variance of 1/d. The optimal rating will endogenously be derived in section 3. The announcement of rating z brings additional public information to the market and leads investors to update their beliefs to: θ|xi , z ∼ N

´ ³ ay + bx + dz 1 i , . a+b+d a+b+d

Based on the same analysis as above, the unique equilibrium value for firm quality with a rating agency being present, θ∗ , is then derived as: Ã ! ³ ³ R − 1 ´´ √ 1 θ∗ = Φ √ a(θ∗ − y) + d(θ∗ − z) − a + b + dΦ−1 , (6) R b with the equilibrium value for private signals given by: √ a+b+d ∗ a d a + b + d −1 ³ R − 1 ´ ∗ x = θ − y− z− Φ . b b b b R

(7)

For quality values higher than θ∗ , the firm will never default since a sufficiently large number of investors will optimally decide to prolong credit. A firm quality less than θ∗ , in contrast, will always lead to a default by the firm. Uniqueness of equilibrium in the case where a credit rating agency is present requires that: (a + d)2 b> . 2π Note that this uniqueness condition is stricter than in the absence of a CRA as long as the precision of her rating, d, is perceived to be larger than zero. This is due to the fact that the announced rating increases the precision of information that is public in the market.

3

Optimal Rating

In the following, we will analyze a simple process for the generation of a rating. In essence, we assume a continuum of information intermediaries generating an assessment of the firm’s credit quality, θ, as such accounting for potential competitive pressures in the industry.17 As one distinguishing feature, our model considers technological spillovers in the generation of ratings. These network effects may stem from the implicit contractual relation between a rating institution and the rated entity, particularly obvious in the “credit watch” procedure (Boot et al., 2006), or from the often-mentioned feedback-effects that rating agencies claim to be triggered by rating announcements or 17

Recent years have seen the expansion of a large number of potential competitors to the established credit rating agencies (The Economist, 2005). Apart from smaller, country-specific rating agencies, there is also a growing importance of other predictors of default, for instance via financial derivatives such as credit default swaps.

10

rating changes (Hill, 2004; Covitz and Harrison, 2003).18 Both channels establish a direct influence of the rating (or its impending announcement) on the credit quality of the firm.19 Consequently, in its rating assessment, each rating agency has not only to be concerned with its (exogenous) information about the firm’s quality but also with the statements of other information intermediaries that are influencing the firm’s credit quality. In this respect, by taking account of this additional “endogenous” source of information, our model displays richer rating characteristics than the model by Carlson and Hale (2005), who assume that the announced rating is equal to the private signal about firm quality that the agency observes, xA . Our model is also in contrast to Boot et al. (2006), where, essentially, the rating agency simply reconfirms information that has already been publicly available in the market, thereby giving rise to a “focal point” role. Rather, in our case the CRA chooses how much “new” private information to turn into public and how much “old” public information to confirm, depending on the weights attached to the objectives that it pursues in the rating assessment process. Taking the above deliberations into account, we assume that a rating agency tries to maximize expected profits. As we do not consider any additional services offered by a CRA, profits solely stem from fees paid by issuers for solicited ratings. The agency’s utility function therefore reflects its role as an intermediary between the issuer soliciting the rating and the investors using the rating information (Schwarcz, 2002), which is also described in the IOSCO code of conduct: “CRAs should endeavor to issue opinions that help reduce the asymmetry of information that exists between borrowers and debt and debt-like securities issuers, on one side, and lenders and the purchasers of debt and debt-like securities on the other.” (OICU-IOSCO, 2004). As a rating agency’s promise to announce reliable information about the rated entity is not enforceable, but, if violated, will have an effect on her reputation, we consider the following utility function, reminiscent of the optimality of discretionary contracts trading off reputational versus financial capital `a la Boot et al. (1993). Maximizing expected profits then requires minimizing the loss from information “disintermediation”, stated as follows: ¯ 2, ui (zi , θ) = −(1 − r)(zi − θ)2 − r(Li − L) with

Z Li =

0

1

(8)

(zj − zi )2 dj

18

Apart from a rating’s effect on the firm’s funding costs, in particular the existence of rating triggers gives rise to feedback-effects that may force rating agencies to be cautious in their rating process (Hill, 2004). This may become obvious for firms in financial turmoil. With respect to the Enron case, for instance, it has been mentioned that one reason why the rating agencies acted very late (arguably too late) was that they did not want to begin a downgrading spiral started off by a first downgrading followed by an increase in credit costs due to rating triggers, which would again have increased Enron’s probability of default, leading to an even lower rating etc (The Economist, 2005). 19 Additionally, the fact that rating agencies are known to be very conservative with regard to the risk of announcing “incorrect” rating assessments, leads them to tend to “err on the side of caution” (Golin, 2001). While the concept of conservatism has also been used as an explanation of the downward bias of unsolicited ratings that lack the additional ingredient of private information (Van Roy, 2005), it is reasonable to believe that CRAs’ favor of conservatism leads them to stick relatively close to the industry’s average rating.

11

and

Z ¯= L

1

0

Lj dj .

The first part in the utility function displays the CRA’s objective to reduce information asymmetries between issuers and investors as far as possible by disclosing a rating zi that is as close as possible to the unknown firm quality θ. This reputation objective enters the utility function with a weight of (1 − r). The second part mirrors the network effects of technological spillovers in agencies’ rating assessments, recognizing that ratings have a feedback-effect on the “true” firm quality.20 It is hence reasonable for each rating institution to take into account the industry’s “average” rating and to try to minimize the distance between the own and the average rating.21 This competition objective, that has also been brought forward in a different context by Morris and Shin (2002) based on the “beauty contest” theme by Keynes, is attached a weight of r.22 In this simple reduced-form utility function, we do not consider costs from information collection. This is corroborated by the fact that agencies are obviously willing to process information even without financial compensation, as shown by the existence of unsolicited ratings. As such, the agency’s utility function solely comprises reputation and competition objectives as the main drivers of the generated rating information zi . Derivation of the optimal rating requires the following steps. A full description is given in appendix A. The optimal rating zi will maximize the CRA’s expected utility function and is, thus, given by: zi = (1 − r)E(θ|xA ) + rE(¯ z |xA ) , (9) where z¯ denotes the average rating. If we assume a linear R strategy as optimal for a rating agency, we may average over all ratings, i.e. z¯ = zj dj. Plugging this in the optimal rating function (9) and comparing coefficients delivers the following “optimal” 20

The latter argument is reminiscent of the discussion on “fair value” versus “book value” reporting systems by Plantin et al. (2005). They argue that market prices affect the market outcome through their influence on the actions of market participants, so that an endogenous source of volatility arises via this feedback-loop. 21 Agencies’ rating choices therefore display strategic complementarities. I.e., it is the more rewarding to announce a “high” rating, the larger the number of other rating agencies that also announce a high rating and vice versa. For the effects of strategic substitutability on information generation, see also Hellwig and Veldkamp (2006). 22 Additional proof of the beauty-contest argument and even more detailed hypotheses come from a recent German experience. On June 19, 2005, the so-called “Gew¨ ahrtr¨ agerhaftung” and “Anstaltslast”, a maintenance obligation and implied liability of the German public sector for the state banks’ public debt, was abolished by the German government because of pressure by the EU competition commission. Contrary to what has been expected, however, the state banks’ ratings did not deteriorate after the event. Rather, the required two ratings for each bank remained at a very high level. Rating counsellors publicly stated at the time that competition between rating agencies leads them to reduce their business risk by announcing average ratings, while only agencies of very high ability and long-standing experience dare to disclose “extreme” ratings (Von Heusinger, 2005). This hypothesis will be taken up again in section 5.

12

rating, given the CRA’s private and public information about firm quality θ: zi (xA , y) =

(1 − r)c a xA + y. a + (1 − r)c a + (1 − r)c

(10)

As can be seen, the optimal rating is influenced by the CRA’s private information about the firm, xA , and the prior expected firm quality, y. Hence, the agency not only reconfirms already publicly available information, y, but additionally turns (part of) her private information xA into public. The factors with which these two types of information enter the announced rating depend on the respective information precision. The more precise one type of information, the larger its weight in determining the optimal rating. It is moreover interesting to note that r, the weighting factor put on the competition objective, decreases the effect of xA but increases the effect of y. Therefore, the more importance the CRA attaches to the competition argument, the stronger will the optimal rating be influenced by the prior mean y and the less will it be affected by the CRA’s private information. Placing more emphasis on the reputation objective, in contrast, increases the impact of private information xA on the optimal rating. Only if the rating agency did not attach any importance to the competition objective, i.e. for r = 0, and accounted only for her reputation, would the factors with which the two types of information enter the rating depend only on their respective precision.23 Note that if investors know the CRA’s utility function, they are able to solve for the CRA’s private information xA about firm quality in equilibrium. Still, there is a difference between announcing the “optimal” rating z as derived above and announcing the signal xA directly, as has been studied by Carlson and Hale (2005). To see this, consider the investors’ posterior beliefs if they learn the agency’s signal xA directly, θ|xi , xA ∼ N

³ ay + bx + cx ´ 1 i A , a+b+c a+b+c

or if they learn the rating z θ|xi , z ∼ N

³ 2ay + bx + (1 − r)cx ´ 1 i A , . 2a + b + (1 − r)c 2a + b + (1 − r)c

Particularly with respect to the variance of posterior beliefs, it can be seen that if the CRA attaches a relatively low weight to the reputation objective, the variance of investors’ posterior beliefs will be higher after observing the rating z than after observing the CRA’s private signal xA . The opposite holds if a high weight is attached to the reputation objective.24 Hence, the CRA’s mode of information processing and distributing plays a subtle role in affecting particularly higher-order moments of beliefs.25 23

Were private information on the part of the CRA completely precise i.e. for c → ∞, our results would coincide with the ones obtained by Carlson and Hale. For a → ∞ (i.e. for completely precise initial public information), in contrast, our results are essentially identical to the ones by Boot et al. (2006). 24 For 1 − r < 1 − a/c, the variance conditional on z is lower, for 1 − r > 1 − a/c, the variance conditional on xA is lower. 25 For a more detailed analysis on similar issues see also Hellwig and Veldkamp (2006).

13

4 4.1

The Role of the Credit Rating Agency Uniqueness of Equilibrium

Since the announcement of a rating increases the precision of public information above that of the prior distribution of firm quality θ, a CRA will certainly have an effect on whether a unique or multiple equilibria prevail. In order to ensure uniqueness of equilibrium and prevent the ex-ante uncertainty connected to multiple equilibria, we know that the precision of investors’ private information must not become too low compared to the precision of information that is publicly available on the market. Hence, the sufficient condition for a unique equilibrium will become stricter after the rating announcement. From the optimal rating strategy (10), we know that z displays a variance of 1/[a + (1 − r)c], so that the uniqueness condition can be rewritten as: (2a + (1 − r)c)2 . (11) 2π For a unique equilibrium to hold, investors’ private information has to be sufficiently precise, not only relative to the precision of public information, a, but also relative to the precision of the CRA’s private information, c, since this is partly turned into public information via the rating announcement. The implication is also revealed in figure 1 that displays equilibrium selection depending on investors’ private information precision b. b >

No CRA

z

multiple equilibria }|

{z

unique equilibrium ∗ with rollover for θ ≥ θW }|

{-

a2 2π

b

z

multiple equilibria }|

unique equilibrium with rollover for θ ≥ θ∗ {z }| {-

0

a2 2π

0 With CRA

(2a+(1−r)c)2 2π

b

Figure 1: Equilibrium selection corresponding to investors’ private information precision b However, rearranging the uniqueness condition allows a slightly different view: ¯ √2πb − 2a ¯ ¯ ¯ (12) 1−r (2a + (1 − r)c)2 /(2π). Hence, after the additional investment in private information precision, a unique equilibrium will be restored even after the public rating announcement. Furthermore, note that investors’ attempt to maximize their proceeds from granting credit to the firm coincides with maximizing overall efficiency by minimizing the probability of default, prob(θ ≤ θ∗ ). Stage one of the game hence requires investors to compare the proceeds from the secondstage game that follow either from multiple equilibria, if they decided not to increase the precision of private information, or from a unique equilibrium after the investment in information precision. As in the former case equilibria are based on expectations regarding other investors’ actions, we assume the following beliefs: let α be the proportion of investors that are expected to withdraw their money early. From the equilibrium derivations in chapter 2 it follows that a firm default will occur whenever α > α∗ = θ ∗ , i.e. whenever the proportion of withdrawing investors is larger than the critical proportion that renders the firm indifferent between defaulting or not, stated in equation (4). As has been shown by Boot et al. (2006), if α is sufficiently high, it is then reasonable for all investors not to prolong credit. This is due to the fact that the beliefs of the withdrawing investors (that the firm will default) are confirmed in equilibrium, so that the remaining 1 − α investors rationally conjecture the same. If, in contrast, α < α∗ , all investors would prolong credit. Since the critical level α∗ is given by θ∗ , with26 Ã ! ³ ´´ √ 1 ³ ∗ ∗ −1 R − 1 ∗ θ = Φ √ a(θ − y) + d(θ − z) − a + b + dΦ , R b we find the following: the higher the expected credit quality, y, and the higher the credit rating, z, the lower is the critical proportion α∗ of investors believing in a firm default and therefore withdrawing credit, thereby moving the firm on the brink of default. Hence, the more likely will it be for given α that the critical proportion α∗ is surpassed so that in the multiple equilibria case the market will coordinate on an inefficient firm default. As investors in this case receive a payoff of zero, they will have an interest to invest into the precision of their private information in order to restore uniqueness of equilibrium as long as R · prob(θ ≥ θ∗ |xi ) − C(∆) > 0 . Note that the critical level of costs C(∆)crit that investors are willing to bear decreases in θ∗ as C(∆)crit = R · prob(θ ≥ θ∗ |xi ) . As is shown in appendix B, equilibrium value θ∗ decreases in the precision of the CRA’s private information, c, for sufficiently high ratings z. Results so far are summarized in the following propositions: 26

In order to simplify the notation, the precision of the rating is still denoted by d rather than a + (1 − r)c.

16

Proposition 2 For a2 /(2π) < b < (2a + (1 − r)c)2 /(2π), the rating announcement increases the number of equilibria. If the CRA announces a sufficiently high rating, investors have a high incentive to invest in the precision of their private information in order to eliminate multiple equilibria, thereby increasing the efficiency of the market outcome. Whenever a low rating is announced, however, the market is likely to coordinate on the most efficient among multiple equilibria without any investment in private information collection. Proposition 3 (Virtuous Circle) The more precise the announced rating is, the higher is the critical level of investment costs that investors are willing to bear in order to increase the precision of their private information, provided that the rating is sufficiently high. For sufficiently high ratings (e.g. investment-grade ratings), investors’ private information and public rating information therefore turn out to be complements, leading to an accelerating increase in efficiency. For sufficiently high ratings, investors therefore prefer a unique equilibrium over multiple equilibria and vice versa for low ratings. As a reason for this interesting result, consider that - even though this is not modelled explicitly27 - the expectation of a high firm quality as mirrored in a high rating z (and in a high prior expected value y) in a competitive credit market should lower the firm’s costs R from proceeding with the project, while the profit from default remains constant (equal to zero). In this instance, the proportion of investors that are willing to withdraw credit prematurely will be very small. This reduces the critical value α∗ that is rationally sustainable in equilibrium. For a given proportion of α, that is possibly institutionally determined (and hence independent of deliberations of rationality), it then becomes likely that α > α∗ so that precisely because of a high rating, the market moves towards the inefficient firm default in the multiple equilibria case. For sufficiently low ratings, exactly the opposite explanation would lead to the realization of the efficient equilibrium in which all investors prolong credit in a multiple equilibria regime.28 Interestingly, this difference in preferences for equilibrium outcomes coincides with regulatory requirements as far as institutional investors are concerned. In almost any country, institutional investors are required to invest only in sufficiently highly-rated (investment-grade, “m¨ undelsicher”, etc.) assets. At the same time, institutional investors usually dispose of own research and analysis departments that supply them with additional private information. This has often been taken as evidence for a too low precision of credit ratings, since otherwise it would not be worthwhile for investors to look for additional sources of information (Partnoy, 1999). According to our analysis, however, it is not the lack of precision in credit ratings but rather the opposite: rating announcements increase the precision of public information too strongly and hence destroy uniqueness of equilibrium. Regarding investment decisions in highly-rated bonds, however, investors prefer a unique equilibrium as this minimizes the probability of default. Hence, agents’ incentives to invest in information is highest when investment 27

For the modelling of the refinancing decision on the part of the firm and its strategic effects on equilibrium, see for instance Hubert and Sch¨ afer (2002). 28 Experimental evidence exists that without major incentives to act otherwise, agents tend to coordinate on the payoff-dominant among multiple equilibria (Heinemann et al., 2004).

17

is in firms with highly-graded bonds, which is exactly what institutional investors are confined to. Note that in contrast to Carlson and Hale (2005), the CRA in our setup does not disclose her private information to the market but a weighted function of her posterior information. If investors know the CRA’s specific utility function and if equilibrium is unique, they are able to deduce the expected probability of default. With multiple equilibria, this is no longer true. In this case, the rating agency in essence has a strategic choice of whether to announce a default probability that corresponds to the efficient or to the inefficient equilibrium. But still, investors could choose to reduce the uncertainty emerging from the multiplicity of equilibria by investing in the precision of their private information. Interestingly, investors choose to disregard the focal point role of CRAs when ratings are high. In the market for sufficiently highly-rated bonds, therefore, rating precision and the precision of private information are no longer substitutes. Rather, they become complements so that the announcement of a rating may spark-off a virtuous circle that increases information efficiency and injects a degree of stability in the market, thereby reducing the probability of firm default. The market for lowly-rated bonds, however, is characterized by substitutability between rating information and private information. Whenever a unique equilibrium prevailed before the rating announcement, the most efficient result can be achieved in the postannouncement phase if self-fulfilling beliefs and hence a degree of instability are tolerated.

5

Solicited Versus Unsolicited Ratings

In recent years, rating agencies have started to issue ratings that are not requested by the rated entity and that are not paid for. These “unsolicited” ratings rely only on public information. Empirical studies on unsolicited ratings have raised several questions regarding both the purpose and the informational content of these rating assessments. In our setup, unsolicited ratings may be characterized by c = 0, since no private information enters the rating process. The unsolicited rating zU is then given as zU = y as it is only influenced by public information. If we assume a solicited rating zS to be characterized by c > 0, it stands to reason whether it will be higher or lower than zU : zS − zU

=

(1 − r)c (xA − y) a + (1 − r)c

This delivers the intuitive result that the difference between solicited and unsolicited rating will be positive (negative) if the CRA’s private information, xA , turns out to be higher (lower) than the ex-ante expected firm quality, y. Corollary 1 For sufficiently high (low) private information of the CRA, xA , compared to the ex-ante expected firm quality, y, a solicited rating will be higher (lower) than an unsolicited rating. It is intuitive to see that the solicited rating zS as given by (10) increases in the face value of the rating agency’s private information, xA . For the influence of the agency’s 18

private information precision c, however, we find the following: ∂zS ∂c

=

a(1 − r) (xA − y) . [a + (1 − r)c]2

(13)

Corresponding to the result in corollary 1, the effect of c on the optimal solicited rating depends on the difference between the CRA’s private information and the prior information about firm quality, i.e. xA − y. Obviously, for xA > y this partial derivative will be positive and vice versa. Nevertheless, the provision of private information does not necessarily increase any agency’s private information precision c by the same amount. Rather, we may interpret a specific value of c > 0 as the “ability” of the CRA to gather and process the relevant information privately provided by the firm.29 What further implications can then be derived with regard to the effect of the CRA’s ability on the solicited rating? Based on the influence of c as given in (13), we find that for sufficiently high private information, i.e. for xA > y, the solicited rating increases in the weight attached to the competitive argument, r, provided that the CRA’s private information is of sufficient precision.30 The opposite holds for an increase in the importance given to the reputation objective. Hence, a rating agency of high ability, i.e. that disposes of very precise private information, will give a higher solicited rating for sufficiently good private information as compared to a CRA of poorer ability, if she attaches lower weight to her reputational aim and puts more emphasis on competitive concerns. For sufficiently bad private information, i.e. low xA , in contrast, she will give a lower solicited rating as a CRA of poor ability. Therefore, the hypothesis that only rating agencies of high ability can afford to deviate strongly from the average rating holds, provided that these agencies do not put too much weight on their reputational objective. In the case of a unique equilibrium we may reasonably assume this condition to be satisfied, as follows from uniqueness condition (12). Corollary 2 CRAs of sufficiently high ability will announce more extreme solicited ratings than agencies of lower ability, if they attach relatively low weight to their reputation objective. Analyzing the influence that fundamental uncertainty 1/a has on the optimal solicited rating, delivers: ∂zS ∂a

=

(1 − r)c (y − xA ) . [a + (1 − r)]2

Hence, for sufficiently good prior expectations with regard to the firm’s credit quality, i.e. for y > xA , higher fundamental uncertainty leads to an reduction of zS , while the opposite holds for bad prior expectations. As an intuition for this result, consider that higher fundamental uncertainty implies that the unknown firm quality θ might lie far apart from the ex-ante expected value y. For high values of y, there is a considerable 29

In this respect, the “ability” of a rating agency would require a solicited rating as a necessary condition. 30 For proof, see appendix C.

19

likelihood that θ will be much lower, which will be mirrored by a low rating, while the opposite is true for low values of y. Finally, how does the structure of the CRA’s utility function, i.e. the weights attached to reputation and competition objective, influence the solicited rating? Intuitively, we find that for a sufficiently optimistic prior expectation with regard to θ, i.e. for y > xA , the rating increases in r and decreases in 1 − r. The proof can be obtained from appendix D. Stated differently, the more weight a rating agency places on her reputation (as compared to competitive concerns), the lower will her rating be in case of bad private information about the firm and the higher will it be in case of good private information about θ. The opposite holds if she puts less emphasis on her reputation. The results are summed up in the following corollary: Corollary 3 For sufficiently high private information, the optimal solicited rating will (i) increase in fundamental uncertainty, 1/a, (ii) decrease in the weight attached to the competitive argument, r, and (iv) increase in the emphasis attached to the repuational aim. The opposite holds for sufficiently low private information. Before analyzing the effect that unsolicited and solicited ratings may have on the market outcome, let us consider their role with regard to the uniqueness of equilibrium. Even though the condition for a unique equilibrium is less strict if the rating agency announces only unsolicited ratings, as public information on the market in this case comprises only the common knowledge about the firm’s quality distribution, and hence complies with the uniqueness condition in the absence of a rating agency, the practice of generating unsolicited ratings endangers the virtuous circle originally triggered by the announcement of very precise rating assessments. Are our results in line with the empirical results on the difference between solicited and unsolicited ratings? There is more or less consensus in the empirical literature that unsolicited ratings are lower than solicited ones.31 However, there are two interpretations that are consistent with this difference that is also known in the literature as the “downward bias”. The first may be referred to as the “punishment hypothesis”. Under the punishment hypothesis, a rating agency that is compensated by issuers has an incentive to assign higher ratings to firms who pay for the service than to issuers who do not. Thus, rating agencies announce unsolicited ratings as a means to blackmail issuers. The second hypothesis may be denoted as the “private information hypothesis”. It states that lower unsolicited ratings are the result of self selection based on private information. Of course, this interpretation is more in line with our results. Interestingly, however, our model indicates that it is not the firm quality per se that influences the solicited rating but the difference between the CRA’s perception of firm quality, i.e. private signal xA , and the ex-ante expected firm quality, y. Notice that the power of a rating agency to select the equilibrium in case of multiple equilibria also contains an element of blackmailing. Interestingly, recent empirical studies confirm mainly the private information story (Byoun and Shin ,2003, and Gan, 2004). In addition, studies that investigate the stock market reaction of rating changes from unsolicited to solicited ratings find that markets seem to expect an upgrade and punish those firms whose ratings 31

See Byoun and Smith (2002), Poon (2003), Poon and Firth (2004), Gan (2004), and G¨ uttler and Behr (2005) for evidence in this regard.

20

remain unchanged (Behr and G¨ uttler, 2005). This is also consistent with our theory, as will be shown in the following section.

6

Market Effects

In the following, we assume that the condition for a unique equilibrium holds, i.e. that investors obtain private information of sufficient precision, respectively that the rating agency attaches a sufficiently low weight to her reputation concern. From the analysis in section 2 we know that the ex-ante probability of default is given by: √ prob (default) = prob(θ ≤ θ∗ ) = Φ( a(θ∗ − y)) . Obviously, the default probability increases in equilibrium value θ∗ , so that all model parameters that reduce θ∗ will decrease the incidence of default as well. With rational expectations, investors will learn that the rating’s precision d is given by a + (1 − r)c. Plugging this into the equilibrium equation for θ delivers: ³ 1 ³ ¡ ¢ θ∗ = Φ √ a 2θ∗ − y − (1 − r)z +(1 − r)c(θ∗ − z) b ³ R − 1 ´´´ p − 2a + b + (1 − r)cΦ−1 . (14) R As can easily be seen, the probability of default decreases in the ex-ante expected firm quality, y, in the announced rating, z, and in the offered repayment rate, R. But how does θ∗ compare to the equilibrium value in the absence of a credit rating ∗ ? From the following comparison: agency, θW ∗ θW ∗ θW

> θ∗

⇔

1 R−1 √ (1 − r)c ∗ (θ − z) + Φ−1 ( )[ a + b > 2θ∗ − (1 − r)z + a a R p − 2a + b + (1 − r)c]

(15)

we find that the introduction of a rating agency reduces the probability of default as long as the rating agency announces a sufficiently high rating. From the preceding section we know that the difference between the solicited and the unsolicited rating rises along with the precision of the CRA’s private information if the face value of the CRA’s private signal deviates positively from y. Hence, for firms that are able to confide sufficiently optimistic information about their business prospects to the CRA despite a pessimistic prior expected firm quality, the probability of default will decrease after the announcement of a rating. This contributes to the above-mentioned “private information hypothesis”, that relates the difference between solicited and unsolicited ratings to an adverse selection problem. Our model is even more precise in showing that firms have a high incentive to request a solicited rating in order to reduce their probability of default, if they believe to be treated unfair by the market, i.e. whenever they believe to be able to disclose much more optimistic private information to the CRA than what has a priori been expected.32 32

In a sense, this result is related to Faure-Grimaud et al. (2006), who show that rating agencies

21

Proposition 4 In order to reduce the probability of default, firms will request a (solicited) rating if they believe that they are able to disclose more optimistic private information to the credit rating agency than what has a priori been expected by the market, i.e. for xA > y. Since equilibrium value θ∗ decreases in the announced rating, it follows naturally from corollary 3 that for sufficiently high xA , the probability of default will increase in fundamental uncertainty, 1/a and weight r. For sufficiently low private information xA , the opposite results are obtained. Hence, the introduction of a rating agency is not necessarily beneficial only for firms of high quality, as has been stated by Carlson and Hale (2005). Rather the benefits of a rating agency are contingent on a complex system of parameter variations.

7

Institutional Investors

Investors on bond markets can usually be categorized into two different groups. They are either small, individual market participants, or large and institutionalized investors. As institutional investors typically hold their own research departments, they are also presumably much better informed about firm quality than small investors. In order to bring this structure into our model, we assume in this section that the market consists of proportion λ of institutional investors that observe private information about the firm with precision ¯b, and proportion (1 − λ) of small investors with information of precision b, with ¯b ≥ b. In many countries, institutional investors are furthermore restricted with regard to their investment choice.33 We build this restriction in our model by assuming that institutional investors are only allowed to invest in bonds with a rating at least as high as z˜. In contrast to Boot et al. (2006), we do not, however, rely on the simplifying assumption that whenever a bond obtains a sufficiently high (usually investment-grade) rating all institutional investors always invest.34 Hence, in the following we assume that institutional investors have to withdraw for z < z˜, but do not necessarily have to prolong credit for z ≥ z˜. What does this market-segregation imply for the equilibrium? Whenever the CRA announces a rating z < z˜, we know that institutional investors never roll over their debt but always withdraw their money. Hence the condition for imminent default of the firm is changed to: √ θ = λ + (1 − λ)Φ( b(xi − θ)) . offering corporate governance scores (CGS), that may remain hidden from investors at the discretion of the rated entity, represent an optimal contract. They prove that firms decide to hide the score, if they are sufficiently uncertain about their quality at the time of hiring a certification intermediary. 33 In a dynamic asset pricing model, Pagratis (2005) examines the effects of ratings-based asset holdings on price volatility and market efficiency. He finds a tradeoff between volatility and efficiency if investors hold heterogeneous beliefs and are sufficiently risk-averse. 34 Even though the market sometimes is so tight that they have to rely on this strategy, we rather consider the case where institutional market participants may but not necessarily have to buy and hold investment-grade bonds.

22

This delivers a unique equilibrium value of θ1∗ : ³ 1 θ1∗ = λ + (1 − λ)Φ √ (a(2θ1∗ − y − (1 − r)z) + (1 − r)c(θ1∗ − z) b p R−1 ´ )) . − 2a + b + (1 − r)cΦ−1 ( R It is obvious to see that θ1∗ ≥ θ∗ , so that for sufficiently low ratings, i.e. z < z˜, the probability of default is increased by the existence of institutional investors. If the CRA instead announces a rating of z ≥ z˜, whether or not institutional investors roll over their loans depends on their posterior beliefs about θ, so that equilibrium value θ2∗ is given by: ³ 1 ³ θ2∗ = λΦ √ a(2θ2∗ − y − (1 − r)z) + (1 − r)c(θ2∗ − z) ¯b q ¡ R − 1 ¢´´ − 2a + ¯b + (1 − r)cΦ−1 R ³ 1 ³ +(1 − λ)Φ √ a(2θ2∗ − y − (1 − r)z) + (1 − r)c(θ2∗ − z) b p ¡ R − 1 ¢´´ − 2a + b + (1 − r)cΦ−1 . R While it always holds that θ2∗ ≤ θ1∗ , we find that θ2∗ ≤ θ∗ whenever repayment R > 2 (as a sufficient condition), while θ2∗ > θ∗ for R < 2, as: p p ¯ 2a + b + (1 − r)c] Φ−1 ( R−1 ∗ ∗ ∗ ∗ R )[ 2a + b + (1 − r)c − θ2 ≤ θ ⇔ θ2 − θ < 2a + (1 − r)c For R > 2, this inequality is satisfied because the l.h.s. is negative by assumption while the r.h.s. is positive. The following corollary sums up the results: Corollary 4 The existence of institutional investors reduces the probability of default for firms rated investment-grade, whenever sufficiently high repayment values R are offered. For ratings below investment-grade, however, their existence raises the risk of inefficient firm default due to regulatory reasons.

8

Conclusion

Due to the complexity of many financial products and the adoption of the Basel II accord, the importance of credit rating agencies has strongly increased. Lacking a convincing theoretical basis, empirical and descriptive studies have often come to the conclusion that the market for credit ratings is “curiously devoid of competition and oversight”, of which it desperately “needs more” (The Economist, 2005). Moody’s Bond Rating Service, a major rating institution, has even been declared as one of the “two superpowers in the world today” (Partnoy, 1999) - together with the United States-, and has been accused of being able to make a “grown man cry” (Euromoney, 1998) by destabilizing markets. Focussing on a rigorous theoretical analysis and accounting for a complex utility function, we find that credit rating agencies may nevertheless be a benefactor to financial 23

markets. In particular, they may spark off a virtuous circle that supports information aggregation, thereby increasing market efficiency. This result is due to the fact that rating announcements and private information collection prove to be complements rather than substitutes for sufficiently highly-rated bonds. On the downside, however, the recent practice of announcing unsolicited ratings that are based only on publicly available information destroys this virtuous circle. Anticipating the lower precision, bond holders reduce their investment in private information precision, which undermines the benevolent effect of credit ratings on information aggregation. Recently observed troubles of open-end real estate funds in Germany, that have partly been triggered by rating announcements, show that the effects are not restricted to the market for credit ratings but hold in a more general context. In particular, the market structure, reflecting the influence of large, institutionalized investors, seems to strengthen the impact of rating agencies on investment decisions, thereby corroborating the coordinating role that ratings may fulfill additionally to their information role.

24

References [1] Association for Financial Professionals (AFP), 2004, 2004 Credit Rating Agency Survey, available at http://www.afponline.org/pub/pdf/pr 20050208 kaitz.pdf. [2] Association for Financial Professionals (AFP), 2005, Statement of James A. Kaitz before the House Financial Services Committee, Wednesday, June 29, 2005. [3] Baker, H.K., S.A. Mansi, 2002, Assessing Credit Rating Agencies by Bond Issuers and Institutional Investors, Journal of Business Finance & Accounting 29, 13671398. uttler, 2005, The Stock Market Reaction to Changes of Unsolicited [4] Behr, P, A. G¨ Ratings. Working Paper Goethe-University Frankfurt. [5] Benabou, R., G. Laroque, 1992, Using Privileged Information to Manipulate Markets: Insiders, Gurus and Credibility, Quarterly Journal of Economics 107, 921958. [6] Boot, A., S. Greenbaum, A. Thakor, 1993, Reputation and Discetion in Financial Contracting, American Economic Review 83(5), 1165-1183. [7] Boot, A., T. Milbourn, A. Schmeits, 2006, Credit Ratings as Coordination Mechanisms. Review of Financial Studies 19, 81-118. [8] Byoun, S., Y.S. Shin, 2002, Unsolicited Credit Ratings: Theory and Empirical Analysis. Working Paper. [9] Cantor, R., 2004, An Introduction to Recent Research on Credit Ratings, Journal of Banking and Finance 28, 2565-2573. [10] Cantor, R., F. Packer, 1994, The Credit Rating Industry, Federal Reserve Bank of New York Quarterly Review Summer-Fall, 1-26. [11] Carlson, M., G. Hale, 2005, Courage to Capital? A Model of the Effects of Rating Agencies on Sovereign Debt Roll-Over. Cowles Foundation Discussion Paper No 1506. [12] Carlsson, H., E. van Damme, 1993, Global Games and Equilibrium Selection, Econometrica 61, 989-1018. [13] Covitz, D.M., Harrison, P., 2003, Testing Conflicts of Interest at Bond Ratings Agencies with Market Anticipation: Evidence that Reputation Incentives Dominate, mimeo, Federal Reserve Board, Washington. [14] Euromoney, 1998, Rating Agencies Caught With Their Pants Down, January 15, p. 51. [15] Faure-Grimaud,A., Peyrache, E., Quesada, L., 2006, The Ownership of Ratings, mimeo, London School of Economics. [16] Gan, Y., 2004, Why Do Firms Pay for Bond Ratings When They Can Get Them for Free?. Job Market Paper Wharton School. 25

[17] Goldstein, I., Pauzner, A. 2005, Demand Deposit Contracts and the Probability of Bank Runs. Journal of Finance 60(3), 1293-1328. [18] Golin, J., 2001, The Bank Credit Analysis Handbook: A Guide for Analysts, Bankers and Investors, Wiley & Sons. [19] Hand, J., R. Holthausen, R. Leftwich, 1992, The Effect of Bond Rating Agency Announcements on Bond and Stock, The Journal of Finance 47(2), 733-752. [20] Heinemann, F., R. Nagel, P. Ockenfels, 2004, The Theory of Global Games on Test: Experimental Analysis of Coordination Games With Public and Private Information, Econometrica 72(5), 1583-1599. [21] Hellwig, C., L. Veldkamp, 2006, Knowing What Others Know: Coordination Motives in Information Acquisition, mimeo, University of California, Los Angeles. [22] Hill, C.A., 2004. Regulating the Rating Agencies. Washington University Law Quarterly 82, 43–95. [23] Hubert, F., Sch¨afer, D., 2002, Coordination Failure with Multiple-Source Lending: the Cost of Protection Against a Powerful Lender, Journal of Institutional and Theoretical Economics 158, 256-275. [24] IOSCO, 2003, Report on the activities of credit rating agencies, available at http://www.iosco.org/library/pubdocs/pdf/IOSCOPD153.pdf. [25] Lucas, R., 1972, Expectations and the Neutrality of Money, Journal of Economic Theory 4, 103-124. [26] Lucas, R., 1973, Some International Evidence on Output-Inflation Tradeoffs, American Economic Review 63, 326–334. [27] Mariano, B., 2005, Conformity and Competition in Financial Certification. London School of Economics Working Paper. [28] Morris, S., 2001, Political Correctness, Journal of Political Economy 109, 231-265 [29] Morris, S., H. Shin, 1999, Private versus Public Information in Coordination Problems, unpublished paper, Yale University. [30] Morris, S., H. Shin, 2002, Social Value of Public Information, American Economic Review, 52 (5), 1521-1534. [31] Morris, S., H. Shin, 2003, Global Games: Theory and Applications, in Dewatripont, M. et al. (eds): Advances in Economics and Econometrics, the Eighth World Congress, Cambridge University Press, (2003). [32] Morris, S., H. Shin, 2004, Coordination risk and the price of debt, European Economic Review 48, 133-153. [33] OICU-IOSCO, 2004, Code of Conduct Fundamentals for Credit Rating Agencies, December 2004. 26

[34] Pagratis, S., 2005, Asset Pricing, Asymmetric Information and Rating Announcements: Does Benchmarking on Ratings Matter? Bank of England Working Paper No 265. [35] Partnoy, F, 1999, The Siskel and Ebert of Financial Markets? Two Thumbs Down for the Credit Rating Agencies, Washington University Law Quarterly, Vol. 77, No. 3, pp. 619–715. [36] Partnoy, F., 2001, The Paradox of Credit Ratings. University of San Diego Law an Economics Research Paper No 20. [37] Phelps, E., 1970, Introduction, in E. Phelps et al. (eds): Microeconomic Foundations of Employment and Information Theory, 1–23, Norton, New York. [38] Plantin, G., H. Sapra, H.S. Shin, 2005, Marking-to-Market: Panacea or Pandora’s Box? Mimeo, Carnegie Mellon University, Pittsburgh. [39] Poon, W., 2003, Are Unsolicited Credit Ratings Biased Downwards?, Journal of Banking and Finance 27, 593-614. [40] Poon, W., M. Firth, 2004, Are Unsolicited Bank Ratings Lower? Preliminary Evidence from Fitch‘s Bank Individual Ratings, Working Paper. [41] Schwarzc, S., 2002, Private Ordering of Public Markets: The Rating Agency Paradox, University of Illinois Law Review, 1-28. [42] Spence, M., 1973, Job Market Signaling, Quarterly Journal of Economics 87, 355374. [43] Smith, R.C., I. Walter, 2001, Rating Agencies: Is There an Agency Issue?, Working Paper. [44] The Economist, 2005, Special Report Credit-rating agencies, March 26, 65–67. [45] Van Roy, P., 2005, Is there a difference in treatment between solicited and unsolicited bank ratings and, if so, why?, mimeo, ECARES, Universite Libre de Bruxelles. [46] Vassalou, M., Y. Xing, 2005, Abnormal Equity Returns Following Downgrades, mimeo, Columbia Business School. unstlinge der Investoren, Die Zeit, July 26, 2005. [47] Von Heusinger, R., 2005, G¨

27

Appendix Appendix A From the analysis in section 2 we know that the probability of firm default is given by prob(θ ≤ θ∗ ), while the CRA holds a posterior belief about the firm’s quality of: θ|xA ∼ N

³ ay + cx

A

a+c

,

1 ´ . a+c

The CRA’s expected utility function can therefore be derived as: ¯ A )2 Eui (zi , θ) = −(1 − r)(zi − E(θ|xA ))2 − rE(Li − L|x = −(1 − r)(zi − E(θ|xA ))2 Z 1 −rE(zi2 − 2zi z¯ + z¯2 − (zj2 − 2zj z¯ + z¯2 )dj|xA ) .

(16)

0

Derivation with respect to zi and setting equal to zero delivers the optimal rating as given in (9). Following Morris and Shin (2002), we assume a linear strategy as optimal for a rating agency: zi = k1 xA + k2 y . (17) This allows to average over all potential ratings: E(¯ z |xA ) = k1

ay + cxA + k2 y , a+c

(18)

since E(xAj |xAi ) = E(θ|xAi ). Plugging this into the optimal rating function (9) yields: zi =

(1 − r)c + rk1 c (1 − r)a + rk1 a + rk2 (a + c) xA + y. a+c a+c

Comparing coefficients to (17) gives us the weights attached to the three arguments of the optimal rating strategy: (1 − r)c , k1 = a + (1 − r)c and k2 =

a . a + (1 − r)c

Appendix B With rational expectations, investors will learn that the rating’s precision d is given by a + (1 − r)c. Plugging this into the equilibrium equation for θ delivers: ³ 1 ³ ¡ ¢ θ∗ = Φ √ a 2θ∗ − y − (1 − r)z +(1 − r)c(θ∗ − z) b ³ R − 1 ´´´ p − 2a + b + (1 − r)cΦ−1 . R

28

(19)

The derivation with respect to the CRA’s private information precision is then given by ∂θ∗ ∂c

³R − 1´ 1 ∂θ∗ ∂θ∗ (1 − r) = φ(·) · √ [2a + (1 − r)(θ∗ − z) + (1 − r)c − p Φ−1 ] ∂c ∂c R b 2 2a + b + (1 − r)c ³ ´ φ(·) √1b [(1 − r)(θ∗ − z) − √ 1−r Φ−1 R−1 ] R 2 2a+b+(1−r)c = 1 − φ(·) √1b (2a + (1 − r)c)

Obviously, this partial derivative is negative for z sufficiently high relative to θ*, such that the numerator becomes negative, while the denominator always stays positive due to the uniqueness condition.

Appendix C For the derivation of factor

(1−r)a , [a+(1−r)c]2

we find:

(1−r)a ∂ [a+(1−r)c] 2

∂r which is positive if c >

a 1−r

=

a[(1 − r)c − a] [a + (1 − r)c]3

and negative otherwise.

Appendix D ∂zS ac = (y − xA ) . ∂r [a + (1 − r)c]2 This partial derivative is positive for y > xA and negative otherwise. Exactly the opposite holds for the impact of (1 − r) on zS .

29