The Impact of Credit Rating Agencies on Capital Markets Spyros Terovitis ∗ † April 13, 2016 Abstract In this paper I argue that the reason for potential problems emerging from Credit Rating Agencies (CRAs) is more pathological than the literature recognizes; even in the absence of conflicts of interest or other distortions resulting from players’ behavior, the market structure itself can be a source of inefficiency. I develop a setting, where, in the benchmark case, the CRA is capable of perfect monitoring and reveals its private information truthfully and costlessly. I explore the impact of such a “sincere” CRA on the interest rate and the probabilities of project financing and default. I find that even under these- near-utopian-, conditions the introduction of a CRA may not be beneficial. Specifically, a CRA may lead to under-financing of projects with positive net present value that would otherwise be financed; a higher expected interest rate; and a higher expected probability of default. These findings arise from the feedback effect inherent in capital markets, and the asymmetric impact the effect has on firms of different quality. I argue that restricting CRAs to provide hard evidence with their ratings might have a negative effect on the probabilities of project financing and default. JEL Classification: D82, D83, and G24 Keywords: Credit Rating Agencies, Feedback Effect, Financial Regulation. ∗ I am grateful to Motty Perry and Ilan Kremer for their support and their very useful comments. Moreover, I would like to thank Herakles Polemarchakis, Dan Bernhardt, Vasiliki Skreta, Giulio Trigilia and the participants at the European Winter Meeting of the Econometric Society, the RES Annual Conference 2015, the Game Theory and Applications UECE Meeting and the Warwick Workshop. I also wish to thank the Royal Economic Society as well as the State Scholarships Foundation of Greece for the financial support. † University of Warwick, Department of Economics, Coventry, CV4 7AL, United Kingdom, email: [email protected] 1 Introduction The 2007-2008 financial crisis raised unprecedented scrutiny on Credit Rating Agencies (CRAs). CRAs have been accused of failing to predict the financial crisis (Mason and Rosner, 2007), of following investor opinions rather than leading them (Richard and Steward, 2003) and most importantly of facing conflicts of interest which leads to rating inflation (Mathis, McAndrews, and Rochet 2009, Bolton, Freixas, and Shapiro 2012). In this paper I argue that the reason for potential problems emerging from CRAs is more pathological than the literature recognizes; potential sources of inefficiencies lie not only in the conflicts of interest, the way the players act, and the possibility that they are not rational, but in the market structure itself. To show this, I develop a model where: there are no conflicts of interest; ratings are accurate and truthful; and there is no price (rating fee) distortion. Even in this ideal environment, the introduction of a CRA may lead to higher expected probability of default and under-financing of projects with positive NPV that would be financed in the absence of a CRA. CRAs play a significant role in the market by affecting major economic variables, such as the interest rate and the probability of default. The main mechanism through which credit ratings affect such variables is by shaping of investors’ beliefs, and hence investment decisions. Unlike meteorologists, who predict the weather without affecting it, CRAs produce ratings that do affect the quality of the asset they rate. Kuhner (2001) points out that a credit rating can take the form of a self-fulfilling prophecy. Similarly, Manso (2013), captures the self-fulfilling prophecy nature of ratings by showing that a rating deterioration may trigger a “death spiral” . The feedback effect inherent in capital markets lies in the heart of my model. I develop a model of project’s financing where the entrepreneur is privately informed about his project’s efficiency level, and he cannot commit to exerting effort. The information asymmetry about the entrepreneur’s type is partly resolved by a CRA. Following CRAs’ common practice, i.e., issuing ratings that correspond to a predetermined level of creditworthiness, I cluster entrepreneurs into two categories: entrepreneurs with high expected cost of effort (HEC) and entrepreneurs with low expected cost of effort (LEC). This distinction captures the different levels of efficiency in project implementation. Thus, HEC entrepreneurs are of low credit-worthiness and LEC entrepreneurs are of high credit-worthiness. The inherent information asymmetry about the entrepreneur’s efficiency 1 level, together with the absence of commitment to exerting effort, allows me to endogenously determine the probability of default. In such an environment, a feedback effect emerges: the interest rate is determined by the expected probability of default, which in turn determines the realized probability of default. I argue that once one takes the market structure into consideration, better information by introducing a CRA, may not result in a better outcome from a social perspective. The reason is that in a setting characterized by information asymmetry and lack of commitment, introducing better information bears an inherent trade-off: it alleviates the information asymmetry problem but it exacerbates the adverse effect of non-commitment. The main findings suggest that the impact of introducing an intermediary depends on the features of the environment. In particular, the introduction of a CRA: (i) leads to higher expected default probability when the entrepreneur is efficient enough to raise funds independently of the presence of a CRA (mild information asymmetry), (ii) leads to under-financing, when financing of an HEC entrepreneur is feasible only if he is pooled with an LEC entrepreneur (moderate information asymmetry), and (iii) alleviates under-financing, when financing of an LEC entrepreneur is feasible only if he can be differentiated by an HEC entrepreneur (severe information asymmetry). I characterize the level of accuracy of the CRA’s private signal which maximizes welfare, and I show that some degree of inaccuracy or rating inflation might be optimal. Also I consider the case where the CRA charges the profit-maximizing fee. I find that a positive fee adversely affects the probability of default, but it does not affect the probability of market breakdown. The intuition behind the findings presented in the previous paragraph relates to the feedback effect in capital markets and its asymmetric impact on firms of different quality. In order to understand this asymmetry, one should first understand how the feedback effect works in practice. Lack of commitment implies that the entrepreneur exerts effort only if the cost of doing so is below a certain threshold, ĉ. This cost is known to the entrepreneur but unknown to the investors. In this setup the probability of default coincides with the probability of the cost of effort being above ĉ. Consider the case where an investor wishes to finance an entrepreneur. First, he forms his beliefs about the probability of default, and then, based on these beliefs he demands an interest rate which allows him to break even. The raised funds adjusted by the interest rate (capital cost) need to be paid back by the entrepreneur. For an entrepreneur whose cost of effort is such that he 2 is indifferent between exerting and not exerting effort, adding the capital cost makes the project unprofitable, thus, the implementation threshold decreases. The lower implementation threshold coincides with a higher probability of default, which results in investors demanding a higher interest rate. This cycle continues until the interest rate converges to its equilibrium value. Because the impact of the feedback effect is smaller for a more efficient entrepreneur, the negative effect of a downgrade dominates the positive effect of an upgrade. Along these lines, Kliger and Sarig (2000), use a natural experiment to show that credit ratings affect the cost of capital and Kisgen (2006) shows that a firm’s structural decision is directly affected by credit ratings. The finding that the introduction of a CRA can lead to under-financing of a positive NPV project that would otherwise be financed is another consequence of the non-commitment assumption. The underlined intuition is captured in the following example: Consider a case where an HEC entrepreneur has a bad rating and investors require an interest rate which makes exerting effort not profitable. Investors anticipate that if the entrepreneur is financed, then he will not exert effort, and, as a result, they are not willing to finance him. Now consider the case where there is no CRA and an HEC entrepreneur is mixed with an LEC entrepreneur. The investors are now more optimistic, and they require a lower interest rate. If the lower interest rate turns the choice of exerting effort from unprofitable to profitable, investors anticipate that effect, and they are willing to finance the entrepreneur. Finally, I address whether restricting a CRA to provide hard evidence leads to better outcomes. Notice that the hard-evidence assumption effectively restricts the rating policy to truthful disclosure, which, in turn, diminishes the role of the CRA. Relaxing the hard-evidence assumption gives rise to a model similar to the Bayesian Persuasion model developed by Kamenica and Gentzkow (2009). In this environment I explore the optimal disclosure policy when the CRA can commit in advance to it. I show that when the CRA can pre-commit to a disclosure rule, rating inflation can be part of the equilibrium. I differ from the related literature (Mathis et al., 2009) by showing that rating inflation can emerge even if the fee is not rating contingent. Specifically, I find that the optimal disclosure policy is either a truthful revelation of the type, or a babbling equilibrium where no information is revealed. The optimal disclosure policy implies that the presence of a CRA alone can alleviate market break-down, and increase financing opportunities compared to a regime where the CRA needs to provide hard evidence. Hence, restricting a CRA to provide hard evidence 3 might worsen financing opportunities. Another implication of the optimal disclosure policy is that, compared to the regime without CRA, a CRA can improve financing opportunities of an LEC type but it can not improve financing opportunities of an HEC type. Because the introduction of a CRA in capital markets can be also interpreted as a revelation of a signal about the creditworthiness of a party, this paper has implications about the optimal information disclosure policy imposed by a government. For instance, a key question after the recent crisis is whether the results of stress tests for banks should be revealed (Goldstein and Leitner, 2013). The answer that my analysis suggests is that no disclosure could be welfare enhancing, unless the market breaks down in the absence of additional information. In addition, this work produces implications related to the sovereign debt in eurozone countries. Finally, my work suggests that future research should take into account capital markets’ characteristic feedback effect in order to analyze whether a conflict of interest exists, and, if so, whether this affects the quality of the reported ratings. This finding opens the doors to policy considerations and raises concerns regarding CRAs regulation. This paper is organized as follows: Section 2 reviews the related literature. Section 3 introduces the model. Section 4 presents the three different regimes. Section 5 explores the impact of introducing a CRA. Section 6 relaxes the assumption of hard evidence and explores the optimal rating policy when the CRA can commit ex ante to it. Section 7 allows the agent to choose a profit-maximizing fee. Section 8 discusses and concludes. 2 Literature Review My paper relates primarily to two strands of the literature: the literature dealing with the effect of CRAs on real economic variables, and the literature that recognizes the adverse effect of information. Much of the literature on CRAs focuses on the quality of the reported ratings. There are three main approaches to analyzing the quality of reported ratings: (i) by testing if there is a conflict of interest, (ii) by examining the way the CRA chooses to disclose its private information, and (iii) by modeling behavioral biases of investors, and ratings shopping by issuers. The most popular way the literature addresses the question of whether the CRA has an incentive to be truthful is by testing the validity of the main argument used by CRAs in response to the 4 criticism of rating inflation, i.e., the reputation-concerns argument. According to this, inflating the ratings would harm a CRA’s reputation, and ultimately force it out of the market; hence, such conflict of interests does not exist. Mathis et al. (2009) develop a model with rating-contingent fees and they demonstrate that the reputation-concerns argument only works when enough of the CRA’s income comes from sources other than rating complex projects. Bouvard and Levy (2012) also test the reputation concerns argument. They show that a higher reputation for transparency is not always desirable because while it results in a higher sale price conditional on the certification, it comes at the cost of a lower probability of being certified. Another strand of literature links the quality of ratings with information disclosure. Lizzeri (1999) adopts a mechanism design approach. He shows that a monopolist CRA only reveals the minimum level of information, but if there are multiple CRAs, information is disclosed fully. In contrast, Faure-Grimaud, Peyrache, and Quesada (2007) adopt contingent fees and ex post efficient contracts, and they show that competition reduces information revelation. Several papers attribute rating inflation to behavioral biases of investors and to ratings shopping by issuers: if investors are not sophisticated enough to understand that a rating is not necessarily accurate, then an issuer has an incentive to buy good ratings, and a CRA wants to inflate its ratings to attract customers. Bolton et al. (2012) develop a model with the interaction of sophisticated and naive investors, and the results show that a duopoly is generally less efficient than a monopoly, because the entrepreneur has the opportunity to shop for a good rating to exploit naive investors. Skreta and Veldkamp (2009) obtain similar findings, where the direct implication of rating shopping is the systemic bias in disclosed ratings, even if each CRA produces unbiased ratings. Opp, Opp, and Harris (2013) show that ratings inflation can emerge if the face value - not the informational value - of the rating that matters. This is the case when rating-contingent regulation is required for institutional investors. My central approach deviates from this literature; I focus on a seemingly best case scenario where the CRA always reports its private information truthfully, and hard evidence supports each rating. This environment does not allow for a conflict of interest. As I recognize the ability of ratings to affect the creditworthiness of a project, I focus on the impact of CRAs on capital markets. Save for Boot, Milbourn, and Schmeits (2006), Kuhner (2001), Manso (2013) and to some extent Mathis et al. (2009), the literature has ignored this effect. Boot et al. (2006) propose that credit ratings can serve as a coordination mechanism in situations where multiple equilibria exist. Mathis et al. 5 (2009) show that the behavior of CRAs can lead to reputation cycles, with implications for credit spreads. Kuhner (2001) shows that when CRAs care about reputation, they are more likely to reveal their private information if their ratings cannot become self-fulfilling ex post. Manso (2013) deals with the feedback effect of credit ratings. He describes an environment where a single CRA interacts repeatedly with a firm that holds performance-sensitive debt, and whose payout flows are linked to its rating. This framework enables him to incorporate the feedback effect of credit ratings in a dynamic credit-rating model. He finds that when forming its rating policy the CRA should focus not only on ratings accuracy, but also on the effect of the ratings on the borrower’s probability of survival. This paper differs from Manso (2013) in three important dimensions: (i) the nature of the feedback effect, (ii) the information available to the CRA and (iii) the paper’s main focus. This paper examines the feedback effect inherent in capital markets rather than the feedback effect of ratings. In my setup the credit rating affects the project’s credit quality but, as opposed to Manso (2013), the project’s quality does not affect the CRA’s rating behavior. Thus, this paper explores the feedback loop between the project’s quality and the investors’ decisions rather than the feedback loop between project’s quality and credit rating. The second departure from Manso (2013) is that the CRA has an information advantage over potential investors. In Manso (2013) the cash flow process, which is the only parameter which determines firm’s creditworthiness, is observed by all market participants. In contrast, in this paper the CRA observes a private signal about the firm’s creditworthiness. That characteristic enables me to provide micro-foundations for the impact of CRAs on the cost of capital. Another departure from Manso (2013) concerns the methodology underlying the determing of capital cost. In Manso (2013) the capital cost depends on ratings exogenously, whereas in this paper, the capital cost is endogenously determined, capturing all the parameters of the model. Finally, regarding the main focus of the paper, Manso (2013) is interested in exploring the effect of the rating policy, i.e., the function which maps the cash flow into a rating, in the economy. This work focuses instead on the impact of providing information via a CRA on capital markets. Contrary to this model which highlights the feedback effect inherent in capital markets, Goldstein and Guembel (2008) develop a model which allows for a feedback effect in financial markets. They build a model where investors might be more informed than the firm about parameters which 6 determined profitability of a project. As a result, price reaction is informative, and it could be used by the firm in determining its investment strategy, something which allows uninformed investors to manipulate prices and affect real economic decisions. This papers differ from Goldstein and Guembel (2008) by assuming that the firm and not the investors has information advantage and by focusing on the capital-raising game rather the allocational role of prices. In addition, my work pertains to the literature on the adverse welfare consequence of information disclosure. Hirshleifer (1971) argues that an increase in the amount of information leads to welfare reduction because it destroys hedging opportunities. More recently, Amador and Weill (2010) show that the effect of releasing partial information about a monetary or productivity shock is twofold: on the one hand, providing more information benefits the economy; but on the other hand, it forces households to value the newly released public information more and their private information less. As a result, the situation leads to reduction of the endogenous informational content of prices. Kondor (2013) shows that when the correlation across the private information of different groups is low, the release of public information increases disagreement among short-horizon traders about the expected selling price. Kurlat and Veldkamp (2012) argue that disclosure of information reduces an asset’s risk and hence its return. As a result, high-risk, high-return investments disappear and investor welfare falls. The mechanism through which better information can be harmful differs from the existing literature. I suggest that the welfare reduction is a consequence of the coexistence of asymmetric information and lack of commitment which generates an asymmetric impact of the feedback effect on downward and upward deviations in beliefs of investors after the introduction of more information (CRA). This paper also relates to the literature on Bayesian Persuasion. In Section 8 I show that if the CRA is not obliged to provide supporting evidence for its ratings, and if it can commit to a rating policy, then the emerging setup is similar to Kamenica and Gentzkow (2009). Finally, my paper contributes to the literature on optimal security design. It shows that when the probability of implementing a project is endogenous, and when entrepreneurs know at the time of contracting their realized return, the main finding of Nachman and Noe (1994) holds. 7 3 Benchmark Model I consider a setting with three types of risk neutral players: a cashless entrepreneur, a CRA, and investors of mass 1. The entrepreneur holds a project whose implementation requires investment of size 1 which is raised by selling securities.1 The project returns R if it is successful and 0 if it fails2 , where R is known to all parties3 . The project is successful with probability 1 as long as the entrepreneur exerts effort. If no effort is exerted, then project fails with certainty. 4 The project’s final outcome is observed by all parties. Exerting effort implies a cost, c, and the entrepreneur cannot commit to exerting effort. There is asymmetric information between the entrepreneur and investors; only the entrepreneur observes the cost of effort. The entrepreneur’s cost of effort is a priori unknown to potential investors. The information investors have is that the entrepreneur is of low expected cost (LEC) with probability λ and of high expected cost (HEC) with probability 1−λ. Investors also know that the effort cost of an LEC (HEC) entrepreneur is drawn by a distribution with fL (fH ) and FL (FH ) standing for the probability density and cumulative distribution function respectively. Throughout this paper I assume that an HEC entrepreneur First Order Stochastically Dominates (FOSD) an LEC entrepreneur, i.e., FL (c0 ) ≤ FH (c0 ). Thus, an entrepreneur of LEC can be interpreted as the (in expectation) efficient entrepreneur and an entrepreneur of HEC as the inefficient entrepreneur.5 I restrict the analysis to the case where both LEC and HEC entrepreneur have positive net expected return, i.e., R > 1 + E[ci ] for each i ∈ {H, L}. Unlike potential investors, the CRA can monitor whether the entrepreneur is of LEC or HEC. The intuition behind this assumption is the following: First, it captures the empirical observation that CRAs have better information compared to outside investors about the creditworthiness of firm because CRAs have more experience in monitoring, because they have a more complete picture of the market conditions. Second, it reflects the fact that regardless of the experience that CRAs 1 Raising funds in exchange of a security is the reduced form of a setup where the entrepreneur sells a security at a price P in order to finance a project of size 1 ≥ P . The reason is that a direct consequence of a pooling equilibrium in the contracting stage is that there is a loss for the efficient entrepreneur (LEC), thus, he does not have incentive to raise more than the capital required for the investment, i.e. P = 1. 2 This is without loss of generality as long as the return in case of failure, RF is lower than R 3 The main findings are robust to the case where R is drawn from a distribution which is known to the entrepreneur and investors 4 The main findings are robust if we instead assume that exerting effort increases the probability of success. 5 The main findings are robust for any number of types of the entrepreneur. 8 may have, they are not able to know more about the creditworthiness of a firm than what the firm itself does. The reason the CRA only knows the type of the firm, i.e., the distribution from which the actual cost is derived and not the realized return, relates to two particular characteristics of the rating industry: the monitoring method and the clustering of ratings. Regarding the monitoring method, CRAs usually base their ratings on a mix of indexes. Hence, two firms with similar index values are likely to receive similar rating, even though the indexes do not reflect other parameters that are vital for a firm’s profitability. Regarding the clustering of ratings, one of the characteristics of the industry is that CRAs issue ratings following a specific rating scale and refrain from giving predictions about the exact economic outcome. The rest of this subsection is devoted to the timing of the events, the problems that each party faces, and the equilibrium concept. A more detailed analysis of each player’s problem follows in Section 4. Timing The timing of the events is as follows: 1) Nature determines the effort cost c̃ and the type of the entrepreneur. 2) The CRA announces its rating fee, H (zero in the benchmark model). 3) The entrepreneur decides: (i) whether to ask for a rating from the CRA, and (ii) the contract he offers. 4) Investors observe the rating (if any) and the contract, and then decide whether to invest. 5) Conditional on financing, the entrepreneur chooses whether to implement the project. 6) The contract is executed. The CRA’s Problem I assume that the CRA truthfully reveals its private information. This assumption could be justified by the observation that CRAs usually provide evidence supplementary to their ratings. In the benchmark model I consider a CRA that can costlessly monitor the type of the entrepreneur, and does not charge a rating fee. These assumptions suppress any conflict of interest and allow me: i) 9 to focus on the effect that a CRA has on capital markets by providing better information, and ii) to explore the welfare implications of introducing a CRA. In Section 6, I relax the hard evidence assumption whereas in Section 7, I relax the zero-fee assumption. Entrepreneur’s Problem First, the entrepreneur decides whether to ask for a rating. In doing so, he takes into consideration: i) the expected rating, ii) what would be the contract that he would issue with and without rating, and iii) whether he would exert effort in each case. In the benchmark model where the rating fee is zero, an LEC entrepreneur can costlessly differentiate himself, which enables him to promise a lower return to investors6 . In contrast, an HEC entrepreneur has no incentive to ask for a rating, because by doing so, he would reveal his type. Thus, the problem of choosing whether to ask for a rating becomes trivial; only an LEC entrepreneur ask for a rating. Second, the entrepreneur decides the contract which maximizes his expected profit. It is shown that the profit-maximizing contract promises a payment W if the the return is R and zero otherwise. This simple form of the optimal contract is a consequence of non-verifiability (or only partial verifiability) of the cost of effort. I analyze the optimality of such contract in following subsection. Third, given the rating and the optimal contract, the entrepreneur decides whether to exert effort. Recall that for a project to be successful: i) the investment needs to take place, and ii) the entrepreneur has to exert effort. Thus, the entrepreneur’s utility in each case would be: U (ef f ort) = R − W − c̃ U (not ef f ort) = 0 Hence, the entrepreneur exerts effort as long as: c̃ ≤ R − W ≡ ĉ (1) A critical variable of the model is the threshold level ĉ. The intuition behind this is straightforward, and it captures the fact that the entrepreneur will exert effort only if the benefit from doing so, R − W , does not exceed the cost, c̃. 6 The costless differentiation is not possible when the CRA can charge a profit maximizing fee. 10 It is crucial to mention here that the main findings would be unaffected if the entrepreneur observes a signal about the realized cost rather than the realized cost itself. The reason I present the case where the entrepreneur observes the realized cost is mathematical convenience. In the Appendix, I prove the coincidence of the two models. I define as default the case where the entrepreneur fails to pay back his loan. In this model, a default occurs when the project returns zero, which coincides with the case where no effort is exerted. This leads to the following definition of the probability of default. Definition 1 (Probability of default): The probability of default, d, coincides with the probability of financing an entrepreneur whose realized cost of effort exceeds ĉ: d ≡ P rob(def ault) = P rob(c > ĉ) (2) Similarly, the survival probability, s, coincides with the probability of financing an entrepreneur whose realized cost of effort is below ĉ: s ≡ P rob(not def ault) = P rob(c ≤ ĉ) (3) Because ĉ is negatively related to the payment W , the probability of default is positively related to the endogenously determined W .7 To avoid the trivial case in which the firm can finance through the issuance of risk-free debt, I assume that there are values of c such that the entrepreneur chooses to default even if the implied interest rate is zero, i.e. W = 1. The Investors’ Problem Investors form their beliefs about the probability that the entrepreneur exerts effort, and they require an interest rate that satisfies their participation constraint. I assume perfectly competitive capital markets. Consequently, the participation constraint of investors binds and enables me to 7 What matters for the main findings is that the effort exertion threshold, which determines the probability of default, is negatively related to the payment W . Alternatively, this could be achieved by assuming that the project succeeds with certainty when the entrepreneur exerts effort with cost c and succeeds with probability q if there is no effort. In such a setup the entrepreneur chooses to exert effort if an only if c̃ ≤ (R − W )(1 − q) which is associated to a probability of success equal to P rob(c ≤ ĉ) + qP rob(c > ĉ) = q + (1 − q) E[P rob(c ≤ ĉ)|Ω]. 11 determine the equilibrium interest rate by the investor’s zero profit condition: W E[s|Ω] = 1 (4) where the LHS is the expected benefit and the RHS is the borrowed capital. More specifically, W stands for the payment the entrepreneur promises, and s̃ for the investors’ beliefs about the probability of not defaulting given their information set Ω. Following Definition 1: E[s|Ω] ≡ E[P rob(c ≤ ĉ)|Ω] (5) The investors are willing to finance the project as long as E[P rob(c ≤ ĉ)|Ω] ≥ W −1 . Thus, it is the investors’ beliefs about the probability of default - not the probability of default itself that determine the interest rate. By substituting (1) into (5), given the information set, and by substituting of (5) into (4), we obtain: E[P rob(c ≤ R − W )|Ω = W −1 (6) which determines the equilibrium payment. The feedback effect can be seen in the previous fixedpoint equation; positive probability of default implies a positive interest rate (W > 1) which increases the probability of default, which in turn increases the interest rate. The Optimal Contract I now return to the entrepreneur’s problem, and, more specifically, to optimality of the suggested contract. A contract, w, defines the payment in each state of the world, i.e., the realized value of c, c̃, and the final output (R or 0). Recall that the cost of effort is not verifiable. Lack of verifiability of the cost gives rise to two main implications: i) the contract pins down to two relevant-in-equilibrium payments, and ii) the equilibrium in the capital raising problem is pooling. We explore these two implications sequentially. Regarding the equilibrium payments, note that the entrepreneur’s limited liability implies that the payment in case where the output is zero is also zero. Thus, the only case where the payment can be positive is when the projects succeeds. Suppose now that the contract w implies different 12 payment for different values of the realized cost. The entrepreneur would never find it optimal to report a realized value of cost which does not correspond to the minimum payment, wmin . Hence, in equilibrium the only relevant payments would be 0 if the project’s return is 0, and wmin if the return is R. To explore the lack of a separating equilibrium, we follow the intuition of Nachman and Noe (1994). Suppose that a separating equilibrium exists where wc̃0 is a contract offered by type c = c̃0 and wc̃00 is a contract offered by type c = c̃00 with c̃00 > c̃0 . In case type c = c̃00 mimics type c = c̃0 the gains for type c̃00 (if effort is exerted) is the difference between the expected payment under contract wc̃0 , Ec̃00 wc̃0 and the expected payment under contract wc̃00 , Ec̃00 wc̃00 . Notice that this difference is always non-negative since it can never be the case that type c = c̃00 chooses to exert effort (thus, it has a positive return) and type c = c̃0 chooses not to exert effort. This is true because the utility of type c = c̃00 is always lower than the utility of type c = c̃0 . Thus, we can focus on pooling equilibria where the all types of entrepreneur offer the same contract w. Note also that there might be more than one pooling equilibrium, which leads us to the following definition. Definition 2 (Equivalent Contracts): Contracts with payments contingent to the reported value of effort cost have the same expected return, and, hence, they are equivalent, if and only if they have the same minimum positive payment. The previous analysis allows me to assume without loss of generality that the contract is contingent on the project’s return instead of the reported value because the two contracts imply the same payment in equilibrium. Hence, the contract is associated with the following return for potential investors: Investor’s return W if return R 0 otherwise (7) I now deal with the uniqueness of the optimal contract. An entrepreneur who is not planning to exert effort mimics an entrepreneur who exerts effort by offering the same contract. Thus, the expected revenue of potential investors is W times the probability of financing an entrepreneur who exerts effort, which coincides with the probability that W < R − c. This last point implies that an efficient entrepreneur who plans to exert effort in equilibrium, should choose the value of W 13 taking into consideration the probability of default, such that the investors’ zero-profit condition is satisfied. Note that depending on the distribution of effort cost c there could be multiple combinations of payment-default probabilities that satisfy the zero-profit condition. However, the only combination/equilibrium which survives is the one that corresponds to the lowest value of W , W ∗ , because this equilibrium dominates all other equilibria from the entrepreneur’s perspective. The question that emerges is whether such contracts are observed in capital markets. Offering such contracts is a method of financing similar to debt financing; the entrepreneur issues bonds that return min{(1 + r), V }, where V is the firm’s value and r the interest rate. Since the entrepreneur has no wealth other than what the project returns, the value of the firm will be either R if effort is exerted, or 0 otherwise. Note also that if (1 + r) ≥ V the entrepreneur would choose to not exert effort because this would lead to negative profit. Hence, the return can only be (1 + r) if the project is implemented (V = R), or 0 if the project is not implemented (V = 0). Direct consequence of this is that the suggested contract is quantitative the same with debt financing where 1 + r = W . For the rest of the analysis I adopt the debt-financing interpretation. Given the form of optimal contract, equations (1), (4) ,and (6) are replaced by (9), (10), and (11). c̃ ≤ R − (1 + r) ≡ ĉ (8) (1 + r) E[s|Ω] = 1 (9) E[P rob(c ≤ R − (1 + r))|Ω] = (1 + r)−1 (10) For notational convenience I denote E[P rob(c ≤ R − (1 + r))|Ω] with s̃. Thus, s̃ captures investors beliefs about the probability of effort exertion given the information set Ω. The previous analysis highlights the importance of investors’ beliefs about the default probability on the determination of the equilibrium interest rate. The introduction of a CRA affects investors’ beliefs as follows: if the entrepreneur receives a bad rating then investor believe that he is an HEC type, which implies that investors downgrade their beliefs about the implementation cost compared to the case where there is no CRA. Similarly, if the entrepreneur receives a good rating, then investors believe that he is an LEC type which implies that investors upgrade their beliefs compared to the case with no CRA. Since the ĉ is related to survival probability, investors require a higher (lower) interest rate to finance such an HEC (LEC) entrepreneur compared to the status 14 quo. In addition, after the initial expectations about the implementation cost have been formed, a feedback mechanism arises as follows: a lower (higher) ĉ coincides with higher (lower) expected default probability, which implies a higher (lower) required interest rate by the investors, which, in turn, leads to an even higher (lower) default probability, triggering another feedback loop. Every loop leads to a smaller change in the interest rate, until it converges to the equilibrium interest rate. The main reason for convergence is that for an HEC (LEC) entrepreneur the conditional on survival probability c decreases (increases) after each loop. Equilibrium Concept The equilibrium concept is Perfect Bayesian Equilibrium, under which: (i) the CRA chooses the rating fee (H) that maximizes its expected revenue (forced to be zero in the basic model), (ii) the entrepreneur chooses whether to ask for a rating, the contract (W̄ ), and whether to implement the project to maximize his expected profits, and (iii) investors make financing decisions which maximize their utility. Each player’s beliefs about the others player’s strategies in equilibrium are correct. 4 Regime with and without CRA In this section I characterize the equilibrium in two different regimes: (i) an Imperfect Information without CRA regime and (ii) an Imperfect Information with CRA regime. In the Appendix, I present the regime of Perfect Information. Note that the following analysis holds for any probability density function of the cost as long as the FOSD assumption is satisfied. In the Appendix, I present the case there the cost of effort is uniformly distributed. 4.1 Imperfect & Asymmetric Information without CRA As opposed to the entrepreneur who observes the actual cost of effort, investors only know the entrepreneur is of LEC type with probability λ and of HEC type with probability (1 − λ). Because investors cannot distinguish between the different types of an entrepreneur, there is only one interest rate, rII . 15 The Investors’ Problem: As investors have no additional information, they use their prior beliefs to form their beliefs about the probability of default: s̃II = P rob(c̃ ≤ ĉ|LEC)P rob(LEC) + P rob(c̃ ≤ ĉ|HEC)P rob(HEC) =⇒ s̃II = λs̃L + (1 − λ)s̃H s̃L ≡ P rob(c̃ ≤ ĉ|LEC) = FL (ĉ) and (11) s̃H ≡ P rob(c̃ ≤ ĉ|HEC) = FH (ĉ) where FL (ĉ) is the c.d.f of the cost of an LEC entrepreneur and FH (ĉ) is the c.d.f of the cost of an HEC entrepreneur. Thus, s̃II = λFL (ĉ) + (1 − λ)FH (ĉ) = ΨII (ĉ) (12) Equilibrium Interest rate: The equilibrium existence condition is given by the Equilibrium Existence Theorem if I replace Ψ(ĉ) with Φ(ĉ|Ω) . The equilibrium interest rate is given by: ∗ (1 + rII ) = s̃−1 II 4.2 (13) Imperfect & Asymmetric Information with CRA In this section I introduce a CRA that monitors the true distribution of the entrepreneur’s cost of effort and, by assumption, reveals this distribution truthfully and costlessly. The analysis in this regime accounts for CRA’s problem in the determination of the equilibrium interest rate. The CRA affects the equilibrium interest rate by shaping investors’ beliefs by affecting their information set. As a result, the equilibrium interest rates are conditional on the rating. The Entrepreneur’s Problem: In this regime, the entrepreneur’s problem is augmented by the choice of whether to ask for a rating. The decision to ask for a rating depends on what the CRA can monitor (-i.e., the type of the entrepreneur (LEC or HEC)), and not on the actual cost. An LEC entrepreneur asks for a rating since he expect to receive a good rating and differentiate himself from an HEC type which will in turn enable him to pay a lower interest rate. An HEC entrepreneur is indifferent between asking and not asking for a rating. The intuition is that if he asks for a rating his type will be disclosed. Similarly, if he does not ask for a rating, investors will infer his type 16 because not asking for a rating is not consistent with an LEC type. Without loss of generality I assume that an HEC entrepreneur asks for a rating and receives a bad rating. Recall that the threshold ĉ depends on the interest rate which depends investors beliefs which depend on the rating. Thus, there are two critical values for the effort cost, ĉGR if the rating is good and ĉBR if the rating is bad. The Investors Problem: Investors form their beliefs conditional on the rating, with s̃GR denoting the beliefs following a good rating and s̃BR denoting the beliefs following a bad rating. s̃ ≡ s̃GR = P rob(c̃ ≤ ĉGR |LEC)P rob(LEC|GR) + P rob(c̃ ≤ ĉGR |HEC)P rob(HEC|GR) s̃BR = P rob(c̃ ≤ ĉBR |LEC)P rob(LEC|BR) + P rob(c̃ ≤ ĉBR |HEC)P rob(HEC|BR) Note that P rob(LEC|GR) = 1 and P rob(HEC|BR) = 1, as the CRA truthfully and accurately reports its private information. Hence, I can re-write investor beliefs as follows: s̃ ≡ s̃GR = P rob(c̃ ≤ ĉL |LEC) = FL (ĉGR ) if Good Rating (14) s̃BR = P rob(c̃ ≤ ĉH |HEC) = FH (ĉBR ) if Bad Rating Investors would be willing to finance an entrepreneur with a rating as long as s̃GR ≥ (1 + rGR )−1 and an entrepreneur a bad rating as long as s̃BR ≥ (1 + rBR )−1 . Equilibrium Interest rates: The solution to the problem of the CRA, entrepreneur and investor ∗ ∗ combined determines the equilibrium interest rates rGR and rBR for an entrepreneur with good or bad (or no) rating respectively. (1 + r∗ ) = ∗ ) = (F (ĉ −1 (1 + rGR L GR )) if Good Rating (1 + r∗ ) = (FH (ĉBR ))−1 BR if Bad Rating 17 (15) 5 Impact of a CRA In the previous sections I derived the equilibrium conditions under three different regimes. In addition I provided the conditions under which the market does not collapse. This section compares those regimes in terms of three vital market variables: the expected interest rate, the expected default probability, and the probability of project financing. 5.1 Important Variables Once the equilibrium interest rate is derived, I can easily find the expected/market interest rate and the expected/market default probability, rM and dM respectively. The expected interest rate (default probability) consists of the interest rate (default probability) for each type of entrepreneur, i, weighted by the probability the entrepreneur is of type i, where i ∈ {H, L} with H standing for HEC and L standing for LEC. As ratings are perfectly accurate, a good rating is associated with an LEC entrepreneur and a bad rating is associated with an HEC entrepreneur. Thus, ∗ ∗ ∗ (1 + rM ) = λ(1 + rH ) + (1 − λ)(1 + rL ) (16) d∗M = λd∗L + (1 − λ)d∗H = λ(1 − s∗L ) + (1 − λ)(1 − s∗H ) = 1 − s∗M (17) where d∗L = P rob(c ≥ ĉ∗GR |LEC) = 1 − FL (ĉ∗GR ) and d∗H = P rob(c ≥ ĉ∗BR |HEC) = 1 − FH (ĉ∗BR ) 5.2 Comparison I present the effect of introducing a CRA on these variables for both an LEC and an HEC entrepreneur; however, my main goal is to provide a welfare analysis by focusing on the effect at the market level. Recall that a social planner whose objective is to maximize net surplus will finance both types of entrepreneurs, since they are of positive NPV. In what follows, I define as “market survival for an LEC (HEC) entrepreneur” when FL (r)(FH (r)) satisfies the sufficient condition of the Equilibrium Existence Theorem, i.e., financing takes place if the type is known to be LEC (HEC). Similarly, I define as “market survival independently of whether a CRA exists” when ΨII (r) satisfies that condition, i.e. financing takes place for investors’ prior beliefs about the entrepreneur’s type. 18 5.2.1 In terms of equilibrium interest rates Proposition 1 (Equilibrium Interest Rates) If information asymmetry is mild such as the market survives independently of whether a CRA exists, then the relation among the equilibrium interest rates is given by: ∗ ∗ ∗ (1 + rGR ) < (1 + rII ) < (1 + rBR ) (18) ∗ , is always lower In addition, the expected equilibrium interest rate in the absence of a CRA, rM ∗ than the expected equilibrium interest rate when a CRA exists, r̄CRA : ∗ ∗ ∗ ∗ ∗ ) (1 + rM ) ≡ (1 + rII ) < λ(1 + rGR ) + (1 − λ)(1 + rBR ) ≡ (1 + r̄CRA (19) ∗ − r ∗ > r ∗ − r ∗ ; the introduction of a CRA A direct implication of Proposition 1 is that rBR GR II II results in an increase in the interest rate for an HEC entrepreneur that exceeds the reduction in the interest rate that an LEC entrepreneur receives. FL (r) FH (r) 0.5FL (r) + 0.5FH (r) (1 + r)−1 1 G 0.8 N A 0.6 B 0.4 r 0.2 0.4 0.6 0.8 1 1.2 1.4 Graph 1: Interest rate and default probability with and without CRA Here I present a graphical illustration of the proof and the underlined intuition. A more detailed proof is provided in the Appendix. Graph 1, where the interest rate is on horizontal axis, illustrates the equilibrium interest rates for the case where the entrepreneur is of an LEC or of an HEC type with equal probability, and the cost of effort is uniformly distributed. The two implications of First 19 Order Stochastic Dominance assumption are that: i) the graphical illustration of FL (r) lies above the graphical illustration of FH (r), and ii), the difference FL (r) − FH (r) is increasing in r. Points G and B indicate the equilibrium interest rate of an LEC and an HEC entrepreneur when a CRA exists. Point N indicates the equilibrium interest rate when there is no CRA.8 Part one follows directly from the FOSD assumption. Part two relates to the convexity of (1 + r)−1 . Note that (1 + r)−1 is a downward convex function of r, so the point denoted by N always lies to the left of the point A that determines the expected interest rate when a CRA exists. Hence, the interest rate when there is no CRA always exceed the expected interest rate when a CRA exists. Introducing a CRA has a negative effect on an HEC and a positive effect on an LEC entrepreneur. I show that the former always offsets the latter in the case where asymmetric information is not severe enough to lead to market collapse. These findings arise from the feedback effect in capital markets and its asymmetric impact on firms of different quality. In order to understand this asymmetry, it is crucial to first understand how the feedback effect works in practice. After investors observe the rating and form their beliefs about the expected effort cost and the probability of default, they demand an interest rate which allows them to break even. The raised funds adjusted by the interest rate (capital cost) need to be paid back by the entrepreneur. For an entrepreneur who was indifferent between exerting effort or not, adding the capital cost makes exerting effort unprofitable, and thus the implementation threshold ,ĉ, drops. The lower implementation threshold coincides with a higher probability of default, which results in investors demanding a higher interest rate. This cycle continues until the interest rate converges to its equilibrium value. Every loop leads to continuous updates in beliefs about the probability of default, and the expected interest rates, but the effects decrease with each loop. This is a consequence of the always decreasing expected cost conditional on exerting effort, which capturing the fact that the least efficient entrepreneurs have already defaulted. The feedback effect implies that the change in the interest rate is smaller for more-efficient entrepreneurs, i.e., the equilibrium interest rate is a convex function of the unconditional expected cost (the expected cost in the case the entrepreneur finances his project with his own funds). A 8 ∗ ∗ ∗ ∗ ∗ ∗ ∗ In G: (1 + rGR )−1 = FL (rGR ), in B: (1 + rBR )−1 = FH (rBR ) and in N : (1 + rGR )−1 = 0.5FL (rGR ) + 0.5FH (rBR ) 20 direct consequence of this is that the negative effect on an HEC entrepreneur will dominate the positive effect on an LEC entrepreneur because the former has a lower unconditional expected cost. 5.2.2 In terms of Default Probability Proposition 2 (Probability of Default) If information asymmetry is mild such as the market survives independently of whether a CRA exists, the relation among the equilibrium probabilities of default is: ∗ ∗ ∗ ∗ dL (rGR ) < dL (rII ) < dH (rII ) < dH (rBR ) (20) In addition, the expected probability of default in absence of a CRA, d∗M , is lower than the expected probability of default when a CRA exists, d¯∗CRA : ∗ ∗ ∗ ∗ d∗M ≡ λdL (rII ) + (1 − λ)dH (rII ) < λdL (rGR ) + (1 − λ)dH (rBR ) ≡ d¯∗CRA (21) The first part of the proposition is a consequence of the FOSD assumption. The second part is directly connected to part two of Proposition 1: In Graph 1, point N is always above point A. See Appendix for a more detailed proof. Another fundamental aspect of capital markets is the financing opportunities. The following Proposition explores the impact of introducing a CRA on financing opportunities given the creditworthiness of the entrepreneur. Proposition 3 (Probability of Financing) In a regime with a CRA, the probability of financing an LEC entrepreneur is weakly higher than the probability of financing an HEC entrepreneur. The probability of financing of an LEC (HEC) entrepreneur in a regime without CRA is weakly lower (higher) than in a regime with CRA. There is a non-empty set of values of the parameters for which the introduction of CRA alleviates underfinancing, and a non-empty set of values for which it leads to under-financing of entrepreneur with positive rate of return. 21 FL (r) λFL (r) + (1 − λ)FH (r) FH (r) (1 + r)−1 1 FL (r) λFL (r) + (1 − λ)FH (r) FH (r) (1 + r)−1 1 0.5 0.5 r 1 2 3 4 r 5 Graph 2: CRA alleviates under-financing 1 2 3 4 5 Graph 3: CRA leads to under-financing The intuition underlying Proposition 3 can be seen graphically. For any value of r, r̄, FL (r̄) lies above λFL (r̄) + (1 − λ)FH (r̄) which lies above FH (r̄). Hence, for any productivity level, it is more likely that an LEC entrepreneur will be financed if he can distinguish himself from an HEC entrepreneur, and similarly, it is more likely that an HEC entrepreneur is financed if he is pooled with an LEC entrepreneur. The last part of the proposition is depicted in Graph 2 and 3. Recall that a benevolent planner would finance both types, given that they are of positive NPV. The left panel illustrates the case where asymmetric information is severe and an LEC entrepreneur is able to raise capital only if he can differentiate himself. Hence, introducing a CRA alleviates under-financing. The right panel illustrates the case where an HEC entrepreneur is able to raise capital only if he is pooled with an LEC entrepreneur. Thus, introducing a CRA restricts this pooling from happening, and leads to under-financing of an HEC entrepreneur even though it is socially optimal to finance a positive NPV type. The intuition behind the last observation is related to the fact that an entrepreneur cannot commit to exerting effort. The distortion stemming from the lack of commitment is greater the lower ex-ante efficiency of the entrepreneur. Hence, pooling an HEC with an LEC entrepreneur alleviates the resulting inefficiency. This is evident in the case where an HEC entrepreneur can not be funded in isolation, though he can be funded by being pooled with an LEC entrepreneur. The reason is that pooling leads investors to attribute lower probability of default, which, in turn, reduces the interest rate they require. If the lower interest rate alters the choice of exerting effort 22 from unprofitable to profitable, then, investors anticipate this, and they are willing to finance the entrepreneur. 5.2.3 Optimal Level of Rating Precision A direct consequence of Propositions 1-3 is that better monitoring does not necessarily corresponds to welfare improvement. For example, consider an environment where the CRA receives a signal about the entrepreneur’s type, and the social planner is able to affect the precision of this signal through, for instance, regulating the evidence that an entrepreneur should provide to the CRA. A natural question is what would be the precision level that would maximize financing opportunities. To explore this I allow for the following modifications: I assume that the CRA receives a signal which can be either good or bad, σ = {GS, BS} which reveals the true state with probability α, i.e., P rob(LEC|GS) = P rob(HEC|BS) = α where α ∈ (0.5, 1] is known to all parties involved.9 To avoid any unnecessary complications I assume without loss of generality that the CRA reveals his private signal truthfully, i.e., the CRA gives a good rating if the signal is good, and a bad rating if the signal is bad. The level of optimal precision is given in Proposition 4. Proposition 4: (Optimal Level of Precision) The level of precision α that maximizes an entrepreneur’s financing opportunities does not necessarily coincide with 1 (perfectly precise signal). If an HEC entrepreneur can not be financed if his type is perfectly revealed, then, the financing opportunities are maximized for an α which is weakly smaller than one. The optimal level of precision, α∗ , solves: FL (r̃BR )(1 − α∗ ) + FH (r̃BR )α∗ = (1 + r̃BR )−1 Proof. See Appendix. 9 For α = 1 the signal is perfectly informative. 23 (22) The following Corollary summarizes the impact of introducing a CRA and Figure 1a and 1b illustrate the impact of introducing a CRA when the cost is uniformly distributed. Corollary 1 (Impact of better Information) The introduction of a CRA: (i) leads to a higher expected default probability and interest rate when both an LEC and an HEC entrepreneur can be finance independently of whether a CRA exists. (Area A) (ii) leads to under-financing, when an HEC entrepreneur’a financing can be sustained only if he is pooled with an LEC entrepreneur. (Area B) (iii) alleviates under-financing, when the LEC entrepreneur’s financing can be sustained only if an LEC entrepreneur can be differentiated by an HEC entrepreneur. (Area C) Note that as the probability of the entrepreneur being LEC, λ, increases, area B spreads over area C. The intuition is straightforward, as the information asymmetry becomes less severe, the adverse effect of non-commitment which is amplified by the introduction of a CRA dominates. I have developed a framework characterized by asymmetric information and a lack of commitment to exerting effort. In this environment, resolving part of the information asymmetry amplifies the impact of non-commitment. Thus, there is an inherent trade-off of introducing a CRA; on one hand, the CRA’s introduction alleviates the information-asymmetry problem, but on the other hand, it exacerbates the adverse effect of non-commitment. It can been shown that if the entrepreneur can commit to exerting effort, then better information is always welfare enhancing- an outcome, that may not be true if the entrepreneur is unable to commit. The net welfare effect of a CRA depends on the relative extent of each problem. For instance, if the information asymmetry is severe, -such as in case of a market collapse in the absence of a CRA, then introducing a CRA is welfare enhancing. Antithetically, if the information asymmetry is mild, then introducing a CRA amplifies the adverse impact of non-commitment of the less efficient entrepreneurs- a situation results in a welfare drop. 24 Figure 1a: Equilibrium existence regions for: cL ∼ U [0, c̄], cL ∼ U [γc̄, c̄], R = 5 & λ = 0.5 Figure 1b: Equilibrium existence regions for: cL ∼ U [0, c̄], cL ∼ U [γc̄, c̄], R = 5 & λ = 0.8 25 6 Optimal Disclosure Policy In the previous analysis I assumed that the ratings should be accompanied by hard evidence. This assumption restricts the rating policy to truthful disclosure. Even though this assumption is convenient when it comes to the determination of the impact of better information, it diminishes the role of a CRA. In this section I relax the hard-evidence assumption and I explore the optimal rating policy when the CRA can ex-ante commit to it. The rationale behind relaxing the assumption of hard evidence is that although it is true that CRAs provide supporting evidence with the ratings, there could be cases where the evidence does not perfectly reveal the true type. The CRA designs its rating policy with the objective of maximizing its expected profits, E[Π|ΩCRA ] = E[(p − d)D|ΩCRA ] where p, c and D stand for the rating fee, the cost of acquiring a signal, and the demand for ratings respectively. In order to disentangle the rating policy from the decision of acquiring a private signal and the rating fee determination, I assume that: i) the CRA can receive a signal about the entrepreneur’s type at cost d = 0, and that ii) the CRA is price(fee)-taker and the fee, p, is not rating-contingent.10 Price-taker CRA implies that the objective of maximizing expected revenues coincides with the objective of maximizing the expected demand, E[D|ΩCRA ] = E[λILEC + (1 − λ)IHEC |ΩCRA ] where ILEC (IHEC ) equals 1 if an LEC (HEC) type ask for a rating and zero otherwise. Note that the entrepreneur will only ask for a rating if he expects that having a rating will enable him to raise capital at a lower cost. Thus, the objective of maximizing demand pins down to designing a disclosure rule such that the entrepreneur will ask for a rating independently of his type. For this set of assumptions, the objective of the CRA is effectively the same with the planner’s objective, i.e. financing of both types. This setup is similar to the persuasion model developed in Kamenica and Gentzkow (2009) 10 The fee is substantially small, such that the entrepreneur may buy a rating as long as he is able to raise capital. 26 where a sender (CRA) observes a private signal (type of entrepreneur), and then sends a message (rating) to a receiver (investor) ,who, in turn, takes an action (decides whether to finance and the interest rate in case of financing), which affects the pay-off of both the sender and receiver. The persuasion game is relevant when the message is pivotal, i.e., it can affect the action/financing choice. This is the case in an environment where if the type of the entrepreneur is unknown only an LEC entrepreneur would be financed, i.e. for values of r such that FL (r) > (1 + r)−1 and FH (r) ≤ (1 + r)−1 . To avoid unnecessary complications I assume that the signal can be of two values, good and bad (σ̃ = {GS, BS}) and that it perfectly reveals the true type of the entrepreneur, i.e. P r(LEC|GS) = 1 and P r(HEC|BS) = 1. The disclosure policy is a mapping from a signal realization to a rating, where the rating can similarly take two values, good and bad (R̃ = {GR, BR}). Thus, the disclosure policy is denoted by a quadruple DP : {P r(GR|GS), P r(BR|GS), P r(GR|BS), P r(BR|BS)}. Since P r(GR|GS) is compliment to P r(BR|GS) and P r(GR|BS) is compliment to P r(BR|BS) the disclosure policy is simplified to DP : {αG , αB } where αG = P rob(GR|GS) and αB = P rob(BR|BS).11 Recall that as long as both ratings are issued in equilibrium, the market survives if there is at least a value of r such that the following conditions hold: P r(LEC|GR)FL (r) + P r(HEC|GR)FH (r) ≥ (1 + r)−1 P r(LEC|BR)FL (r) + P r(HEC|BR)FH (r) ≥ (1 + r)−1 where the first (second) condition refers to the case where a good (bad) rating is issued. By implementing the Bayes rule I can re-write the previous conditions as follows: (1 − αB )(1 − λ) αG λ FL (r) + FH (r) ≥ (1 + r)−1 αG λ + (1 − αB )(1 − λ) αG λ + (1 − αB )(1 − λ) (1 − αG )λ αB (1 − λ) FL (r) + FH (r) ≥ (1 + r)−1 (1 − αG )λ + αB (1 − λ) (1 − αG )λ + αB (1 − λ) From the first order stochastic dominance assumption it holds that FL (r) > FH (r) for any r, which 11 Truthful disclosure is implemented when αG = αB = 1. 27 implies that the market survives and financing takes place as long as the probability the investors allocate to the event that the entrepreneur is of LEC type is sufficiently large. Let me define as λ̂ the minimum probability that investors should allocate to the entrepreneur being of LEC type such as financing takes place. λ̂ solves: λ̂FL (r) + (1 − λ̂)FH (r) = (1 + r)−1 Thus, a CRA can achieve project financing for both types (ILEC = IHEC = 1) as long as αG and αB are chosen in a way that investors’ beliefs about the probability the entrepreneur is of LEC type exceed λ̂ for both good and bad rating. This translates into the CRA choosing a combination of αG and αB such that: M in{ (1 − αG )λ αG λ , } = λ̂ αG λ + (1 − αB )(1 − λ) (1 − αG )λ + αB (1 − λ) An emerging question is to what extent the CRA can affect investor’s beliefs and more specifically, what is the maximum λ̂, λ̂max , that could be achieved by a CRA when it can pre-commit to a disclosure policy. λ̂max solves the following problem: Maximize M in{P r(LEC|GR), P r(LEC|BR)} αG ,αB subject to 0 ≤ αG ≤ 1 and 0 ≤ αB ≤ 1 The solution satisfy the following equation: ∗ ∗ αG = 1 − αB (23) and the updated beliefs are given by: ∗ ∗ ∗ ∗ λ̂max ≡ P r(LEC|αG , αB , GR) = P r(LEC|αG , αB , BR) = λ Note that the equilibrium that maximizes financing opportunities is a babbling equilibrium. In a babbling equilibrium the updated beliefs equal the prior beliefs which coincide with investors’ 28 beliefs in a regime without CRA. Proposition 5:(Optimal Disclosure Policy) The optimal disclosure policy when the CRA’s objective is to maximize its profit is: ∗ = 1 − α∗ (babbling equilibrium) if there is an r such that λF (r) + (1 − λ)F (r) ≥ (1 + r)−1 i) αG L H B ∗ = α∗ = 1 (truthful disclosure) otherwise. ii) αG B One implication of Proposition 5 is that compared to the regime without CRA, a CRA can not improve financing opportunities of an HEC type, even in a setup where it is not obliged to provide supporting evidence,and it is able to commit to a disclosure rule. Rating Inflation and its Impact ∗ and α∗ which satisfy (23), and for α∗ high enough such as an LEC entrepreneur has For αG B G ∗ > 0. A strictly positive stronger incentive than an HEC entrepreneur to ask for a rating, αB ∗ 0 implies that the CRA inflates its rating, i.e., an HEC entrepreneur receives a rating which αB corresponds to an entrepreneur of higher level of creditworthiness. Rating inflation has been documented in the literature on Credit Rating Agencies. The underlined mechanism behind the rating inflation differs from the related literature, where rating inflation is a consequence of a rating-contingent fee. In this paper, we show that rating inflation arises due to the CRA’s incentive to attract HEC entrepreneurs, which takes place by distorting the ratings in order to make sure that an HEC will be able to raise capital after he asks for a rating. Also, in terms of welfare, we show that once we allow for the feedback effect inherent in capital markets, rating inflation might lead to financing of entrepreneur with positive NPV, that would not otherwise be financed. A direct consequence of this finding is that restricting CRAs to provide hard evidence with their ratings might have a negative effect on the probabilities of project financing and default. Corollary 2: Impact of Rating Inflation When the CRA can pre-commit to a disclosure rule, rating inflation can be part of the equilibrium even if the fee is not rating-contingent. In addition, rating inflation might lead to financing of positive NPV projects that would not otherwise be financed. 29 7 Profit-Maximizing Fee In this section I allow the CRA to choose a profit-maximizing fee. A direct consequence of the weakly positive rating fee is that it modifies the implementation threshold, ĉ. The comparison with the case where the rating fee is restricted to zero allows me to isolate the distortion that a rating fee imposes. The Entrepreneur’s Problem: The entrepreneur’s problem is more complex than before: now, before facing the problem of the security choice or whether to exert effort , he has to choose whether to ask for a rating. An HEC entrepreneur has no incentive to ask for a rating, because by doing this he would reveal his type. I first explore the incentives of an LEC entrepreneur in the case where the market does not collapse in the absence of a good rating. Whether an LEC entrepreneur has incentive to ask for a rating depends on which of the following two forces dominates. On one hand, asking for a rating differentiates him from an HEC entrepreneur, and allows him to promise a lower interest rate, r̂R instead of rII . On the other hand, asking for a rating implies that he needs to borrow a higher amount in order to cover the rating fee, H, apart from the investment cost. Thus, an LEC entrepreneur faces a trade-off between repaying a smaller loan (of 1, instead of 1 + H) with higher interest rate (rII instead of r̂R ), or a larger loan with lower interest rate.12 The choice of asking for a rating does not affect the payoff in the situation in which the entrepreneur chooses to not exert effort. Thus, in an environment where a rating is unnecessary for financing, the entrepreneur chooses the maximum of: U (without rating) = max{R − (1 + rII ) − c̃, 0} U (with rating) = max{R − (1 + r̂R )(1 + H) − c̃, 0} (24) (25) where the max function reflects the fact that the entrepreneur always has the choice to not exert effort. An LEC entrepreneur asks for a rating as long as: (1 + r̂R )(1 + H) ≤ (1 + rII ) (26) 12 Here I implicitly assume that there is a lag between the time that the CRA gives the rating and the time CRA is paid. Due to rational expectations of the CRA, such setup is feasible if the entrepreneur can commit to pay the fee after the loan is taken. 30 and he exerts effort as long as: c̃ ≤ ĉ ≡ max{R − (1 + rII ), R − (1 + r̂R )(1 + H)} (27) I now proceed to the case where the market collapses in the absence of a rating. It is shown the CRA charges H̄ max , hence, an LEC entrepreneur exerts effort as long as his utility is greater than or equal to zero, which is his outside option. Taking into consideration the CRA’s problem, I re-write the implementation threshold of an LEC entrepreneur , ĉL , as: ĉL ≡ ∗ ĉL = R − 1 + rII c̄ˆL = R − (1 + r̄R )(1 + H̄ max ) If rating & rating not necessary (28) If rating & rating necessary The related threshold for an HEC entrepreneur is: ĉH ≡ R − (1 + rN R ) (29) The CRA’s Problem: The CRA understands that only an LEC entrepreneur has incentive to ask for a rating; thus, it chooses the rating fee H, such that an LEC entrepreneur is indifferent between having a rating or not. The functional form of H max is related to the entrepreneur’s outside option, which is determined by whether financing is feasible without a rating. If having a rating is not necessary for financing, the CRA will charge a fee that makes an LEC entrepreneur indifferent between asking for a rating and differentiating himself, or not asking for a rating and pooling with an HEC entrepreneur. In contrast, when the absence of a good rating leads to no financing, the entrepreneur’s outside option is zero. Hence the profit-maximizing CRA extracts all the surplus, i.e., it charges the maximum fee for which an equilibrium exists. Hence, the following conditions characterize the profit maximizing rating fee:13 H max ≡ H max = (rII −r̂R ) (1+r̂R ) If rating is not necessary for financing (30) H̄ max : F (ĉ|H = H̄ max ) = 0.5 If rating is necessary for financing 13 H̄ max = arg max H s.t.(1 + r̂R )−1 = F (ĉ|H = H̄ max ) 31 The Investors’ Problem: Investors know whether project financing is feasible without the rating and they update their beliefs after they observe whether the entrepreneur has a rating. Because the CRA reports its private information truthfully and charges a fee that an LEC entrepreneur buys a rating in equilibrium: P rob(LEC|GR) = 1 and P rob(HEC|N R) = 1. Hence, investors’ beliefs are as follows: s̃ = s̃R = FL (ĉL ) If GR & rating not necessary for financing s̃R̄ = FL (c̄ˆL ) s̃N R = FH (ĉH ) If GR & rating necessary for financing (31) If No Rating Investors would be willing to finance an entrepreneur with a rating as long as s̃R ≥ (1 + rR )−1 , if rating is necessary, and as long as s̃R̄ ≥ (1 + rR̄ )−1 , if rating is not necessary. Similarly, investors would be willing to finance an entrepreneur with no rating as long as s̃N R ≥ (1 + rN R )−1 . 7.1 Equilibrium Interest rates The combined problems of the CRA, entrepreneur and the investors determine the equilibrium ∗ and r ∗ interest rates rR N R for an entrepreneur with or without rating respectively. (1 + ∗ rR ) ≡ (1 + r∗R ) = FL (ĉL )−1 (1 + r̄∗ ) = FL (c̄ˆL )−1 = 2 R If GR & rating not necessary (32) If GR & rating necessary ∗ −1 (1 + rN R ) = FH (ĉH ) (33) ∗ of an LEC entrepreneur is affected by the probability of the Observe that the interest rate rR entrepreneur being LEC: a higher λ, or a lower the cost of an HEC entrepreneur, reduces the ∗ , improves the outside option of an LEC entrepreneur, and results in a lower rating interest rate rII fee and interest rate. Moreover, the higher the fee, the higher the probability of default. As an HEC entrepreneur does not ask for a rating, the probability of default and his expected surplus are unaffected. Proposition 6: (Effect of Profit Maximizer CRA) Allowing the CRA to be profit-maximizing fee leads to a (weakly) positive fee that is negatively related to the probability λ and the cost of effort. This fee: (i) (weakly) increases the interest rate 32 and the probability of default of an LEC entrepreneur, (ii) (weakly) decreases expected surplus of an LEC entrepreneur and the market expected surplus, and (iii) does not affect the probability of project financing. Proof. See Appendix. 8 Concluding Remarks and Future Research In this paper I argue that the reason for potential problems emerging from Credit Rating Agencies is more pathological than the literature recognizes; even in the absence of conflicts of interest or other distortions resulting from players’ behavior, the market structure itself can be a source of inefficiency. I argue that if the economy is characterized by entrepreneurs with low expected efficiency (LEC), introducing a CRA enables entrepreneurs with relatively high expected efficiency (LEC) to distinguish themselves and raise the necessary funds for undertaking the investment. On the antipode, if the economy is dominated by entrepreneurs with high expected efficiency, introducing a CRA could raise the expected interest rate and the expected probability of default, and lead to under-financing of HEC entrepreneurs who have positive expected productivity. Moreover, I evaluate the suggested regulation policy of restricting CRAs to provide hard evidence with their ratings, and I argue this policy might have an adverse effect on the probabilities of project financing and default. My findings have implications on the optimal information disclosure policy imposed by a government or a Central Bank. For instance, a key question after the recent crisis is whether the results of stress tests for banks should be revealed. My analysis suggests that no disclosure of the stress tests results could be welfare enhancing, unless the market breaks down in the absence of additional information. This is a result of the amplification in the probability of bad banks; default, which dominates the beneficial effect on good banks. Goldstein and Leitner (2013) 14 arrive at a similar conclusion by adopting a different setting. Corollary 1 could also relate to the recent debate on the borrowing interests rates that countries 14 Disclosure of some information may be necessary to prevent a market breakdown, but disclosing too much destroys risk-sharing opportunities 33 in the eurozone face. Interest rates differ across countries due to differences in credit risk; this has resulted in some peripheral countries borrowing with high spreads, which kept rising over time and eventually led to some countries being close to default. This paper suggests that a policy that requires countries with lower credit risk to guarantee for countries with high credit risks could be welfare enhancing. My analysis also suggests that future research examining whether conflicts of interest could affect rating quality should account for the feedback effect that characterizes capital markets. Note that the feedback effect in capital markets implies a self-fulfilling effect of ratings: two projects with the same efficiencies, but different ratings, have different default probabilities. The literature has overlooked the self-fulfilling effect of ratings- a concept that could be applied in future work in the context of testing arguments on reputation concerns; CRAs claim that in practice there is no conflict of interests because by issuing inaccurate ratings a CRA would harm its reputation which, in turn, would lead to a loss of market share. However, one could imagine a simple model where the project can be of a good or bad type, with the bad type always failing and the good type succeeding with a positive probability if it receives a good rating, and failing otherwise. In that regime, it is not obvious that the CRA will always give a good rating to a good project because if it does so, and the project fails, the CRA’s reputation will drop substantially. The mechanism explained in the previous paragraph opens the door to policy considerations, and it raises concerns regarding CRAs’ regulation. A message from this paper is that regulation of CRAs has yet to consider their ability to affect crucial variables, such as the probability of default. 34 References Amador, M. and P.-O. Weill (2010): “Learning from Prices: Public Communication and Welfare,” Journal of Political Economy, 118, 866–907. Bolton, P., X. Freixas, and J. Shapiro (2012): “The Credit Ratings Game,” Journal of Finance, 67, 85–112. Boot, A. W. A., T. T. Milbourn, and A. Schmeits (2006): “Credit Ratings as Coordination Mechanisms,” Review of Financial Studies, 19, 81–118. Bouvard, M. and R. Levy (2012): “Two-sided reputation in certification markets,” Available at SSRN 2178119. 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(2001): “Financial Rating Agencies: Are They Credible? Insights Into The Reporting Incentives Of Rating Agencies In Times Of Enhanced Systemic Risk,” Schmalenbach Business Review (sbr), 53, 2–26. Kurlat, P. and L. Veldkamp (2012): “Should We Regulate Financial Information?” Nyu working paper. Lizzeri, A. (1999): “Information Revelation and Certification Intermediaries,” RAND Journal of Economics, 30, 214–231. Manso, G. (2013): “Feedback Effects of Credit Ratings,” Journal of Financial Economics, forthcoming. Mason, J. and J. Rosner (2007): “Where did the risk go? How misapplied bond ratings cause mortgage backed securities and collateralized debt obligation market disruptions,” Working Paper. Mathis, J., J. McAndrews, and J.-C. Rochet (2009): “Rating the raters: Are reputation concerns powerful enough to discipline rating agencies?” Journal of Monetary Economics, 56, 657–674. Nachman, D. C. and T. H. Noe (1994): “Optimal design of securities under asymmetric information,” Review of Financial Studies, 7, 1–44. Opp, C. C., M. M. Opp, and M. Harris (2013): “Rating agencies in the face of regulation,” Journal of Financial Economics, 108, 46–61. Richard, B. and M. Steward, eds. (2003): Principles of Corporate finance, McGraw-Hill. Skreta, V. and L. Veldkamp (2009): “Ratings shopping and asset complexity: A theory of ratings inflation,” Journal of Monetary Economics, 56, 678–695. 36 Appendix A: A.1 Equilibrium Existence Theorem In order to find the conditions for the existence of an equilibrium I use the Bolzano Theorem: for two real numbers rα and rβ , rα < rβ , if G(r) is (i) a continuous function and (ii) G(rα ) , G(rβ ) are of opposite signs, then there exists an r∗ ∈ [rα , rβ ] such that G(r∗ ) = 0. To find the equilibrium conditions I set E[P rob(c ≤ ĉ)|Ω] ≡ Φ(ĉ|Ω) where ĉ = R − (1 + r) and I create a new function, G(r) = (1 + r)−1 − Φ(ĉ|Ω), which satisfies (i) as Φ(ĉ|Ω) and (1 + r)−1 are continuous functions. To show that (ii) is satisfied I set rα = 0 for which the function (1 + r)−1 reaches its maximum value, 1. For such value of r, G(0) is non-negative as Φ(ĉ|Ω, r = 0) ≤ 1. Hence, for an equilibrium to exist it suffices to show that there is an r̃ such that G(r̃) < 0. Graph 4 present the case where at least one equilibrium exists, and Graph 5 the case where there is no equilibrium. Φ(r) G(r) (1 + r)−1 1 Φ(r) G(r) (1 + r)−1 1 0.5 0.5 r 1 2 3 4 r 5 Graph 4: Equilibrium exists A.2 1 2 3 4 5 Graph 5: Equilibrium does not exist Feedback effect in practice Before I proceed in exploring the effect of introducing a CRA, I provide a numerical example which illustrates how the feedback works. Assume that c ∼ U [0, 8] and R = 7.5. Under these assumptions and based on the previous analysis, investors’ belief about the probability of exerting effort is given by s = 7.5−(1+r) . 8 The entrepreneur’s objective is to minimize the interest rate paid to investors. 37 If the entrepreneur promises an interest rate equal to zero, then the probability of exerting effort, which coincides with the probability the project producing a positive return (R) and investor being paid, is 0.812. These values of r and s imply an expected return of 0.812 × (1 + 0%) = 0.812. As the expected return is below the cost of financing, the entrepreneur will have to increase the interest rate to 23% such as investors break even (0.812 × (1 + 23%) = 1). The increase in the interest rate triggers a decrease in the probability of exerting effort to 0.783, since for a set of values of c the entrepreneur does not find exerting effort profitable any more. Consequently, the entrepreneur should promise an even higher interest rate in order to satisfy investors’ participation constraint, which will in turn result in a decrease in the probability of exerting effort. Note that each feedback loop produces an increase of the interest rate and the probability of not implementing of always decreasing magnitude. This is a consequence of the fact that after each loop, the conditional value of c decreases. This process continuous until the equilibrium (s∗ = 0.77 and r∗ = 28%) is reached. Table 1 illustrates the described reasoning for different distributions of c. Round s (1 + r) s(1 + r) s (1 + r) s(1 + r) s (1 + r) s(1 + r) 1st 0.812 1 0.65 1 0.65 0.812 0.541 1 0.541 2nd 0.812 1.230 1 0.65 1.538 1 0.541 1.846 1 3rd 0.783 1.230 0.963 0.582 1.538 0.895 0.471 1.846 0.869 4th 0.783 1.276 1 0.869 1.677 1 0.471 2.122 1 5th 0.777 1.276 0.990 0.578 1.677 0.969 0.448 2.122 0.950 6th 0.768 1.287 1 0.578 1.71 1 0.448 2.231 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nth 0.7765 1.287 1 0.576 1.734 1 0.432 2.313 1 Table 1: Feedback loops and equilibrium values of r and s for different distributions of c. Columns 2-4: c ∼ U ni[0, 8], Columns 5-7: c ∼ U ni[0, 10], Columns 8-10: c ∼ U ni[0, 12] The process described in the previous paragraph is only a mental exercise; the equilibrium is reached immediately, i.e. the entrepreneur promises an interest rate which is consistent with the probability of exerting effort and investors break even. A crucial remark illustrated in Table 1, which is going to be useful for the analysis that follows, is that the more pessimistic the investors about the efficiency of the entrepreneur are (captured by 38 the increase in the expected cost), the higher the impact of the feedback effect in the probability of exerting effort. One can see this by comparing the probability of exerting effort before and after the feedback effect takes place for different efficiency levels (different distributions). For c ∼ U [0, 8] the feedback effect leads to a decrease from 0.812 to 0.775. For c ∼ U [0, 10] the feedback effect resulted in a decrease from 0.65 to 0.576 and for c ∼ U [0, 12] in a decrease from 0.541 to 0.432. A.3 Perfect Information - First Best In order to find the first best, I analyze the regime where both the entrepreneur and the observe the actual productivity, c̃, before the financing decision. The entrepreneur’s problem is identical to the one explained in Section 3: the entrepreneur implements the project as long as condition (1) is satisfied. The Investors’ Problem: In this regime investors know with certainty whether the entrepreneur will choose to exert effort for a given interest rate. Hence, investors beliefs are: s̃P I = 1 if c̃ < ĉ 0 otherwise (34) Equilibrium Interest Rate: Substituting (11) into (10) yields the equilibrium interest rate rP∗ I . The equilibrium interest rate depends on the effort cost - which is now observable - , as follows: rP∗ I = if c̃ < R − (1 + rP∗ I ) 0 not defined (35) otherwise Hence, there are two cases. If c̃ > R − 1, the entrepreneur does not exert effort (s̃ = 0), independently of the interest rate, and such an entrepreneur is never funded. If c̃ < R − (1 + rP∗ I ), the entrepreneur always exerts effort, the project is funded and, due to perfectly competitive capital markets, rP∗ I = 0. A.4 Proof of Main Propositions Firstly I provide the proof of Proposition 2 as it will be used in the proof of Proposition 1. 39 A.4.1 Proof of Proposition 2 Proof. Recall that when the type of the entrepreneur is known then the probability of default is P rob(c̃ > ĉ) ≡ 1 − F (ĉ), where ĉ is the value of c below which the entrepreneur chooses to not exert effort. In this setup is ĉ = R − (1 + r). For part one of the proposition I use the fact that F (ĉ) is a non-decreasing function of ĉ. I only present the case for an LEC entrepreneur. Similarly I can prove part one for an HEC entrepreneur. ∗ (1 + r ∗ ) if there is (there is not) an intermediary. FOSD An LEC entrepreneur promises 1 + rGR II ∗ ∗ and by plugging this into relation (1) I derive the relation between implies that 1 + rGR < 1 + rII the effort exertion thresholds, ĉGR > ĉII . The last part of the proof stems from the fact that F (ĉ) is a non-decreasing function as it stands for the c.d.f. of c. Hence, F (ĉG ) > F (ĉII ) which implies a lower probability of default in the case where a CRA exists. FL (r) FH (r) 0.5FL (r) + 0.5FH (r) (1 + r)−1 1 G Ḡ 0.8 0.6 B̄ 0.4 B0 B r 0.2 0.4 0.6 0.8 1 1.2 1.4 Graph 6: r and s̃ with and without CRA In order to show part b of the proposition I use the assumption of FOSD. The distance of point G (B) from the x-axis denotes the survival probability of an LEC (HEC) entrepreneur when a CRA exists. Similarly, the distance of point Ḡ (B̄) from the x-axis denotes the survival probability of an LEC (HEC) entrepreneur when there is no CRA. From FOSD, the difference of the vertical distance of G and Ḡ from the x-axis is smaller than the the difference of the distance of B and B̄ from the x-axis. Hence, any linear combination of Ḡ and B̄, λḠ + (1 − λ)B̄, will corresponds to a point which is above the point which corresponds to the linear combination of Ḡ and B̄ (for same 40 λ), λG + (1 − λ)B 0 . This is translated into: ∗ ∗ ∗ ∗ λFL (rII ) + (1 − λ)FH (rII ) ≥ λFL (rGR ) + (1 − λ)FH (rBR ) (36) which implies part b of the Proposition: ∗ ∗ ∗ ∗ λ[1 − FL (rGR )] + (1 − λ)[1 − FH (rBR )] ≥ λ[1 − FL (rII )] + (1 − λ)[1 − FH (rII )] A.4.2 (37) Proof of Proposition 1 Proof. Recall that the entrepreneur exerts effort as long as c̃ < R−(1+rk ) and that the equilibrium interest rate condition for each case is given by: (1 + rk∗ )−1 = ∗ ) FL (rGR ∗ ) FH (rBR λFL (r∗ ) + (1 − λ)FH (r∗ ) II II if k = GR if k = BR (38) if k = II (no CRA) For part one I use the assumption of the FOSD assumption. The proof is rather intuitive and is based on the fact that for a given interest rate r, the probability of default is weakly higher for an HEC project. As F is an non-increasing function of ĉ and ĉ is a decreasing function of r, the curve of FL (r) crosses the curve of (1 + r)−1 before the curve of FH (r) does, which implies that ∗ ) < (1 + r ∗ ). Similarly, the curve λF (r) + (1 − λ)F (r) crosses the curve of (1 + r)−1 (1 + rGR L H BR on the right of the curve of FL (r) and on the left of the curve of FH (r) does, which implies that ∗ ∗ < r∗ . rGR < rII BR In order to show part two I will use Proposition 2. From part two of Proposition 2 I know: ∗ ∗ ∗ ∗ λFL (rII ) + (1 − λ)FH (rII ) ≥ λFL (rGR ) + (1 − λ)FH (rBR ) 41 (39) After I substitute the zero profit conditions into equation (38) I get: ∗ −1 ∗ ∗ ∗ (1 + rII ) ≥ λ(1 + rGR )−1 + (1 − λ)(1 + rBR )−1 =⇒ (1 + rII )≤ ∗ )(1 + r ∗ ) (1 + rGR BR ∗ ) + (1 − λ)(1 + r ∗ ) λ(1 + rBR GR (40) If I show that: ∗ ∗ λ(1 + rGR ) + (1 − λ)(1 + rBR )≥ ∗ )(1 + r ∗ ) (1 + rGR BR ∗ ) + (1 − λ)(1 + r ∗ ) λ(1 + rBR GR (41) then, given (38) it should also hold that: ∗ ∗ ∗ λ(1 + rGR ) + (1 − λ)(1 + rBR ) ≥ (1 + rII ) (42) Hence, in order to show part b of Proposition 2, it suffices to show that (40) holds. (40) implies: ∗ )(1 + r ∗ ) + (1 − λ)λ[(1 + r ∗ )2 + (1 + r ∗ )2 ] + (1 − λ)2 (1 + r ∗ )(1 + r ∗ ) ≥ λ2 (1 + rGR BR BR GR GR BR ∗ )(1 + r ∗ ) =⇒ (1 + rGR BR ∗ )(1 + r ∗ ) + (1 − λ)λ(1 + r ∗ )2 + (1 − λ)λ(1 + r ∗ )2 ≥ 0 =⇒ 2(λ2 − λ)(1 + rGR BR GR BR ∗ )2 + (1 + r ∗ )2 − 2(1 + r ∗ )(1 + r ∗ )] ≥ 0 =⇒ (1 − λ)λ[(1 + r ∗ ) − (1 + r ∗ )]2 ≥ 0 (1 − λ)λ[(1 + rGR BR GR BR GR BR which is true since λ ∈ (0, 1). A.4.3 Proof of Proposition 3 Proof. Part one of Proposition 3 implies as c is a random variable then, for any given r, r̄: FL (r̄) ≥ (1 + r̄)−1 =⇒ FH (r̄) ≥ (1 + r̄)−1 which is satisfied as FL (r̄) ≥ FH (r̄) from the FOSD assumption. Part two of Proposition 3 for an LEC entrepreneur implies that for any given r, r̄: ∗ ) ≥ (1 + r̄)−1 =⇒ F (r ∗ ) ≥ (1 + r̄)−1 FL (rGR L II which is satisfied as FL is non-increasing. The proof for the HEC entrepreneur and the nonimplementation cost is identical. 42 The case where the introduction of CRA alleviates under-financing of project with positive rate of return refers to a state of the world where an LEC entrepreneur is financed only if it can differentiate itself from a HEC entrepreneur. This is true when there exists r# such that the following conditions are satisfied: λFL (r# ) + (1 − λ)FH (r# ) < (1 + r# )−1 (43) FL (1 + r# ) ≥ (1 + r# )−1 (44) FL (r# ) > (1 + r# )−1 > λFL (r# ) + (1 − λ)FH (x + r# ) (45) The two conditions combined: which is a non-empty set as as FL (r# ) ≥ FH (r# ) from the FOSD assumption. The case where the introduction of a CRA leads to under-financing of project with positive rate of return refers to a state of the world where an HEC entrepreneur is financed only if they are mixed with an LEC entrepreneur. This case emerges when there exists r## such that the following conditions are satisfied: λFL (r## ) + (1 − λ)FH (r## )) ≥ (1 + r## )−1 FL (r## ) < (1 + r## )−1 (46) (47) The two conditions combined: λFL (r## ) + (1 − λ)FH (r## )) > (1 + r## )−1 > FL (r## ) which is a non-empty set as FL (r## ) ≥ FH (r## ) from the FOSD assumption. 43 (48) A.4.4 Proof of Proposition 4 Following the assumption that the CRA costlessly reveals its private signal and given that the CRA’s precision level is represented by α the investors beliefs are formed as follows: s̃ ≡ s̃GS = FL (ĉ)α + FH (ĉ)(1 − α) if Good Signal s̃BS = FL (ĉ)(1 − α) + FH (ĉ)α if Bad Signal (49) Given the level of precision α the equilibrium condition for an entrepreneur with a good or a bad signal respectively, are: (1 + r̃∗ ) = (1 + r̃∗ ) = [FL (ĉ)α + FH (ĉ)(1 − α)]−1 GS if Good Signal (1 + r̃∗ ) = [FL (ĉ)(1 − α) + FH (ĉ)α]−1 BS if Bad Signal (50) Note that since α > 0.5, if the market survives after a bad signal, this must be also true after a good signal. For a given α = α̃ there is at least an interest rate r, r̃ for which the the following two conditions can be satisfied simultaneously FL (r̃BR )(1 − α̃) + FH (r̃BR )α̃ ≥ (1 + r̃BR )−1 (1 + r̃BR|α=1 )−1 ≥ FH (r̃BR|α=1 ) (51) (52) where the first relation implies that for α = α̃ an HEC entrepreneur raises funds and the second relation implies that for α = 1 (benchmark case) an HEC entrepreneur can not raise funds. The two relations can hold simultaneously since FH (r̃) < FL (r̃) from the FOSD assumption. A.4.5 Proof of Proposition 5 Proof. I start by proving part three which explains the use of the word “weakly” in the Proposition. This finding arises from the value of the optimal rating fee; the fee is strictly positive as long as there is at least one value of r such that FL (r|H = 0) ≥ (1 + r)−1 . As a positive fee that would shift the FL (r) curve downwards, this condition suffices that an equilibrium exists. The fee is zero if for any r but r∗ FL (r|H = 0) < (1 + r)−1 and FL (r∗ |H = 0) ≥ (1 + r∗ )−1 hold simultaneously. Observe that these two conditions reflect the minimum value of FL for which the market does not 44 collapse, which is unaffected by the profit maximizer assumption due to the non-positive fee. Hence market survival is insensitive to the profit-maximizing CRA assumption. I put the word “weakly” in a parenthesis, as this case is an almost zero-probability event. Now it is easy to show that part one hold. For part one I simply use the fact that the ĉL is an decreasing function of H max and FL is a non-decreasing function of ĉL . Hence, FL (r|H = H max ) ≤ FL (r|H = 0), and the equilibrium interest rate given by (1 + r∗ )−1 = FL (r∗ ), will be higher if the CRA charges the profit maximizing fee. For part two it is trivial to show that the HEC entrepreneur’s expected surplus is unaffected. Regarding the expected surplus of an LEC entrepreneur, there is a decrease as a consequence the definition of the rating fee which implies that for any given implementation threshold, ĉ, part of the entrepreneur’s surplus will be extracted by the CRA. 45 A.5 Case where the Entrepreneur observes a signal about the realised cost The aim of this section is to show the coincidence of a model where the entrepreneur observes the realized cost with the model where the entrepreneur observes an informative signal about the realized cost. To do so, I explore the case where the entrepreneur receives a signal, σc̃ about the realized cost c̃. For mathematical convenience and without loss of generality assume that this signal is unbiased: σc̃ = c̃ + where ∼ N (0, σ2 ). This interpretation implies that if the realized signal is σc̃0 then bayesian updating results in E[c̃|σc̃ = σc̃0 ] = σc̃0 . I first deal with the implications on the Entrepreneur’s problem. Recall that exerting effort is profitable as long as c̃ ≤ R − W . Since the entrepreneur observes σc̃ and not c̃, his critical condition for exerting effort will depend on σc̃ (rather than c̃). Thus, the entrepreneur exerts effort as long as E[c̃|σc̃ ] ≤ R − W which is true if σc̃ ≤ R − W . Hence the effort exertion threshold ĉ ≡ R − W switches to σ̂c̃ ≡ R − W . I now deal with the implications on the Investor’s problem. Recall that investors’ beliefs about the probability of the entrepreneur exerting effort determine W . Following the analysis of the previous paragraph, the investors’ beliefs about that probability equals E[P rob(σc̃ ≤ σ̂c̃ )|Ω] instead of E[P rob(c ≤ ĉ)|Ω] where Ω is investor’s information set. Observe that even though ĉ = σ̂c̃ , in general E[P rob(σc̃ ≤ σ̂c̃ )|Ω] differs from E[P rob(c ≤ ĉ)|Ω]. In order to show that the two models ˆc̃ such that E[P rob(σc̃ ≤ σ̂ ˆc̃ )|Ω] = are identical, it is enough to show that there exists a unique σ̂ ˆc̃ produces the same model. Hence, the E[P rob(c ≤ ĉ)|Ω]. If this is the case, then replacing ĉ with σ̂ ˆc̃ which satisfies the aforementioned property exists. whole exercise pins down to showing that a σ̂ The proof of that is straightforward. Since the cumulative distribution function of σc̃ and c̃ is a continuous and strictly increasing function, then for each W there is a unique ĉ associated to ˆ ˆc̃ the value E[P rob(c ≤ ĉ)|Ω]. In addition, for each value of E[P rob(s ≤ ŝ)|Ω], there is a unique σ̂ ˆc̃ for which E[P rob(σc̃ ≤ σ̂ ˆc̃ )|Ω] = E[P rob(c ≤ ĉ)Ω]. associated with it. Hence, there exists a unique σ̂ 46 A.6 Uniform Distribution In this section I assume that the cost of effort is uniformly distributed with cL ∼ U [αc̄, βc̄] and cH ∼ U [γc̄, δc̄]. The analysis is meaningful only if the probability of default is strictly positive. The probability of default is zero if effort is exerted for any c̃. From the entrepreneur’s problem this is true when c̃ ≤ R − 1. Additionally, I keep the assumption that the implied expected rate of i] return of both types is non-negative ( R−1−E[c|c∼c 1+E[c|c∼ci ] ≥ 0). In order to satisfy these two conditions and simplify calculations I set α = 0 and β = δ = 1. The parameter γ captures the efficiency level of the HEC type compare to the efficiency level of the LEC type; as γ approaches 1, the efficiency level of the HEC type approaches the efficiency level of the LEC type. A.6.1 Imperfect Information Case without CRA After I incorporate the entrepreneur’s problem, investors’ beliefs are given by: s̃II ≡ λs̃L + (1 − λ)s̃H = λ R − (1 + rII ) R − (1 + rII ) − γc̄ + (1 − λ) c̄ c̄(1 − γ) (53) ∗ , is given by: Substituting s̃II into the ZPC, the equilibrium interest rate, r̄II ∗ 1 + rII = [(1 − λγ)(R) − γc̄(1 − λ)] − p [(1 − λγ)(R) − γc̄(1 − λ)]2 − 4(1 − λγ)(1 − γ)c̄ 2(1 − λγ) (54) It can be shown that the probability of being LEC (λ) and the return of the project (R) is positively related to the probability of market survival. In contrast, the cost of effort is negatively related to the probability of market survival. For this set of distributions, the equilibrium condition is quadratic in r. In the case where the equation has two distinct roots, the smallest one is associated is with lower interest rates and lower default probability and it is the the only equilibrium since it is the combination of interest rate and probability of default which maximizes entrepreneur’s profits. A.6.2 Imperfect Information Case with non-profit maximizer CRA The investor’s beliefs depend on the rating as follows: s̃ = s̃GR = s̃BR = R−(1+rGR ) c̄ R−(1+rBR )−γc̄ c̄(1−γ) 47 if Good Rating if Bad Rating (55) The equilibrium interest rates are given by: ∗ 1+r = 1 + r∗ BR √ 2 −4c̄ ∗ 1 + rGR = R− R 2 √ (R−γc̄)− (R−γc̄)2 −4c̄(1−γ) = 2 if Good Rating (56) if Bad Rating The market existence condition for an HEC entrepreneur is (R − γc̄)2 ≥ 4c̄(1 − γ) and for an LEC entrepreneur it is R2 ≥ 4c̄. When these conditions are satisfied, the introduction of CRA leads to inferior results, as it does not improve financing opportunities and it increases the expected default probability. An interesting case is when an HEC entrepreneur is not efficient enough to restrict market breakdown, but he can raise capital if he pools with an LEC entrepreneur because the emerging 2 ≥ 4c̄(1 − γ) > (R − γc̄)2 ). interest rate is smaller and easier to be sustained ( [(1−λγ)R−γc̄(1−λ)] (1−λγ) Without a CRA both types are financed, in contrast to the case where a CRA exists and restricts this pooling from happening, and only an LEC entrepreneur is financed. Hence, the introduction of a CRA leads to under-financing of an entrepreneur with positive expected net return. Lastly, when an LEC entrepreneur can be financed only if they can be distinguished from an 2 HEC entrepreneur ( [(1−λγ)R−γc̄(1−λ)] < 4c̄ ≤ R2 ), then, the absence of a CRA leads to market (1−λγ)(1−γ) breakdown and neither an LEC nor an HEC entrepreneur is financed. Thus, the introduction of a CRA restricts the market of an LEC entrepreneur from collapsing, alleviating the problem of underfinancing. Figures 1a and 1b illustrate the effect of introducing a CRA for different combinations of c̄, γ and λ. More specifically, • Area A: Both an LEC and an HEC entrepreneur are financed, independently on whether a CRA exists; CRA increase the probability of default. • Area B: An HEC entrepreneur is financed only in the absence of a CRA. An LEC entrepreneur is financed independently on whether a CRA exists; CRA leads to under-financing. • Area C: An HEC entrepreneur is not financed independently on whether a CRA exists. An LEC entrepreneur is finance only if a CRA exists; CRA alleviates under-financing. • Area D: Neither an LEC nor an HEC entrepreneur is financed, independently on whether a CRA exists; CRA plays no role. 48 A.6.3 Imperfect Information Case with profit maximizer CRA Investors observe the rating and whether a rating is necessary for financing ([(1−λγ)R−γc̄(1−λ)]2 ≥ 4(1 − λγ)(1 − γ)c̄), and they form their beliefs about the probability of default as follows: R−(1+rR )(1+H max ) s̃GR = c̄ R−(1+r̄ )(1+ H̄ max ) R s̃ ≡ s̃GR ¯ = c̄ NR) s̃N R = R−(1+r c̄ If GR & rating not necessary If GR & rating necessary (57) If No Rating The CRA’s, the entrepreneurs and the investors’ problems combined determine the equilibrium ∗ and r ∗ interest rates rR N R for an entrepreneur with or without rating respectively. (1 + ∗ rR ) ≡ (1 + r∗ ) = R (1 + c̄ ∗ ) R−(1+rII ∗)=2 (1 + r̄R ∗ rN R) = if rating not necessary (58) if rating necessary (R − γc̄) − p (R − γc̄)2 − 4c̄(1 − γ) 2 (59) As Proposition 6 states, the market existence conditions are unaffected by the profit maximizing assumption. 49

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# The Impact of Credit Rating Agencies on Capital Markets Spyros Terovitis