Wirtschaftswissenschaftliche Fakultät Department of Business Administration and Economics

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1 Wirtschaftswissenschaftliche Fakultät Department of Business Administration and Economics Are Rating Splits a Useful Indicator for the Opacity of an Industry? Achim Hauck Ulrike Neyer Diskussionspapier zur Volkswirtschaftslehre, Finanzierung und Besteuerung Nr. 3/008 Discussion Paper on Economics, Finance, and Taxation No. 3/008 Electronic copy available at:

2 Diese Diskussionspapierreihe ist im Internet im PDF-Format unter der Adresse verfügbar. Sie wird gemeinsam herausgegeben von: This Discussion Paper Series is available online in PDF format at and is jointly edited by: Prof. Dr. Christoph J. Börner* Tel.: +49 (0) Fax: +49 (0) Prof. Dr. Guido Förster* Tel.: +49 (0) Fax: +49 (0) Prof. Dr. Albrecht F. Michler* Tel.: +49(0) Fax: +49(0) Prof. Dr. Raimund Schirmeister* Tel.: +49(0) Fax: +49(0) Prof. Dr. Ulrike Neyer* Tel.: +49(0) Fax: +49(0) Prof. Dr. Heinz-Dieter Smeets* Tel.: +49-(0) Fax: +49-(0) *Adresse: Heinrich-Heine-Universität Düsseldorf Wirtschaftswissenschaftliche Fakultät Universitätsstraße Düsseldorf Deutschland *Address: Heinrich-Heine-University Dusseldorf Department of Business Administration and Economics Universitaetsstrasse Dusseldorf Germany Bei Nachfragen zu dieser Diskussionspapierreihe wenden Sie sich bitte an die derzeitige Koordinatorin: Prof. Dr. Ulrike Neyer. Please direct any enquiries to the current coordinator: Prof. Dr. Ulrike Neyer. Anmerkung: Beiträge zu dieser Diskussionspapierreihe sind vorläufige Papiere, die zur Diskussion und zu kritischen Anmerkungen anregen sollen. Die Analyse und Ergebnisse sind die des Autors (der Autoren) des jeweiligen Beitrages und spiegeln nicht unbedingt die Meinung anderer Mitglieder der Wirtschaftswissenschaftlichen Fakultät der Heinrich-Heine-Universität Düsseldorf wider. Jede Reproduktion als Ganzes oder in Teilen in Form einer anderen Veröffentlichung, ob in gedruckter oder elektronischer Form, ist nur mit der schriftlichen Zustimmung des Autors/der Autoren erlaubt. Note: Papers in this Discussion Paper Series are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the author(s) and do not indicate concurrence by other members of the Department of Business Administration and Economics at the Heinrich-Heine-University Dusseldorf. Any reproduction in the form of a different publication, whether printed or produced electronically, in whole or in part, is permitted only with the written authorisation of the author(s). Heinrich-Heine-Universität Düsseldorf 008 ISSN Electronic copy available at:

3 Are Rating Splits a Useful Indicator for the Opacity of an Industry? Achim Hauck Ulrike Neyer November 008 Abstract In empirical analyses, rating splits (disagreement between rating agencies) are commonly used as a proxy for the opacity of an industry. This is justified by the argument that a higher number of rating splits should be observed if a sector is more opaque. In this paper we challenge this view. We show that rating splits may occur if an industry is rather opaque but that they may also occur if an industry is rather transparent. Therefore, rating splits are not a useful indicator for opacity. Keywords: opaque assets; ratings; rating agencies; rating splits. JEL-Codes: G0, G4, G30 We like to thank Heinz-Dieter Smeets, Angélique Herzberg, Christian Fürtjes, Lucas Kramer, Andreas Wiesner, and participants of the HHU Economics Research Seminar for instructive comments and suggestions. The usual disclaimer applies. Corresponding author: Heinrich-Heine-University Düsseldorf, Department of Economics, Universitätsstraße 1, 405 Düsseldorf, Germany, Tel.: +49/(0)11/ , Fax.: +49/(0)11/ , achim.hauck@uni-duesseldorf.de Heinrich-Heine-University Düsseldorf, Department of Economics, Universitätsstraße 1, 405 Düsseldorf, Germany, Tel.: +49/(0)11/ , Fax.: +49/(0)11/ , ulrike.neyer@uniduesseldorf.de

4 1 Introduction Opacity is a relevant issue in economics. It has been argued that the recent turmoil on financial markets was amplified by the opacity of financial products (see, e.g., Borio, 008, Crouhy, Jarrow and Turnbull, 008). Moreover, it is conventional wisdom that opacity of firms is a major obstacle for obtaining outside funding. Following Morgan s (00) contribution, several empirical studies on opacity have used rating splits, i.e. disagreement between rating agencies on ratings, as a proxy for opacity. 1 This paper shows that this is inappropriate because rating splits may occur not only if an industry is opaque but also if it is transparent. We proceed as follows. Section presents our main argument. In section 3, we introduce the analytical framework. In section 4, we analyze the interrelation between opacity and rating splits. Section 5 concludes. The Main Argument Potential buyers of a bond are typically uncertain about its default probability. This is particularly true if information about the specific characteristics of the bond issuing firm is scarce. Then, buyers have to rely on, e.g., the industry-wide distribution of default probabilities which in general will be easier to obtain. Obviously, the larger is the range of this distribution, the higher is a bond s opacity. Rating agencies can reduce this opacity. They have a screening technology which provides information about the default characteristics of a certain bond. This allows them to update those expectations purely based on industry-wide information. The extent of opacity reduction increases in the quality of the screening technology. Consequently, there are two determinants of (post-screening) opacity: the range of possible default probabilities in an industry and the quality of the rating agencies screening technology. Empirical analyses show that some rating agencies rate more conservatively than others (Morgan 00, van Roy 005). Now, consider a bond for which a less conservative agency would give a letter rating A and a more conservative agency would give a letter rating B if they had to rate the bond before the screening process. That is, suppose that there would 1 See, e.g., Morgan (00) and Iannotta (006) who study the opacity of the financial and the nonfinancial sector or Bonaccorsi di Patti and Dell Ariccia (004) and Hyytinen and Pajarinen (008) who investigate the opacity of young and old firms. Other studies using this proxy are Pottier and Sommer (006) and Drucker and Puri (008).

5 be a rating split if the agencies had to base their ratings on the industry-wide distribution of default probabilities only. To clarify our main point, we consider two cases. Firstly, suppose that the industry is characterized by a large range of possible default probabilities and that the quality of the agencies screening technology is poor. In this case, in which the industry is rather opaque, screening by the rating agencies provides little helpful information so that the updated expected probability of default does not differ significantly from pre-screening expectations. Consequently, the rating split persists. Secondly, suppose that there is a small range of possible default probabilities in the industry and that the screening of the agencies is perfect. Then, the small range of possible default probabilities implies that the updated expected probability of default again does not differ significantly from pre-screening expectations. Therefore, also in this perfectly transparent industry, the rating split persists. Consequently, rating splits may occur in a transparent as well as in an opaque industry implying that they are not a useful indicator for opacity. 3 The Framework Consider two rating agencies and an industry that consists of a large number of firms. Each firm issues a bond in order to raise funds for investment. The firms in the industry are divided into two groups of equal size. The first group has an investment technology that yields a relatively safe return. Accordingly, bonds of this group will default with a low probability ρ l. The investments of the second group of firms are somewhat riskier. Their bonds are associated with a high default probability ρ h >ρ l. A potential buyer of a bond cannot observe to which group the issuing firm belongs. Therefore, without further information he expects the bond to default with probability ρ = 1 ρ l + 1 ρ h. This lack of information creates a useful role for the rating agencies. They have access to a screening technology that provides a noisy signal s about a bond s true default probability. The signal can be either s l or s h and satisfies (see figure 1): Pr [s l ρ l ]=Pr[s h ρ h ]= 1+q, where Pr[s i ρ i ] with i = l, h denotes the conditional probability of s i for a given ρ i and q [0; 1] represents the quality of the screening technology as a higher q leads to a higher probability that the signal coincides with the true default probability. 3

6 1 1 low default probability highdefault probability l h 1 q 1 q 1 q 1 q signal s l signal s h signal s l signal s h Figure 1: Default probability and signal The agencies use the signal to update their ex-ante, i.e. their pre-screening expectations ρ about a bond s default probability according to Bayes rule. Thus, a positive signal s l implies that the agencies expect a default with probability: E[ρ s l ]=(1 q) ρ + qρ l. (1) That is, if the signal is useless, q = 0, the agencies will not update their expectations, E[ρ s l ]= ρ. However, if q > 0, the signal s l will be informative implying that the expected default probability will be below ρ. Moreover, since E[ρ s l] q < 0, the expected default probability E[ρ s l ] will decrease if the quality of the signal increases. If q =1 so that the signal is perfectly informative, the expected default probability will coincide with the true probability of default, E[ρ s l ]=ρ l. The implications of a negative signal s h are analogous. Bayes rule then implies: E[ρ s h ]=(1 q) ρ + qρ h. () As one would expect, E[ρ s h ] is increasing in q, is equal to ρ for q = 0 and equal to ρ h for q =1. Following Morgan (00), we assume that each rater transforms the updated expected default probability into a letter rating A or B. When deciding on the rating, agency j =1, aims at minimizing its expected reputational costs E[Cj mis ] of misrating. As in Morgan (00), we use this term in an ex-post sense so that there are two forms of misrating. First, there will be ex-post overrating if a bond defaults after having obtained an A. Then, the rater incurs a cost C o j > 0. Consequently, when giving an A, the expected reputational 4

7 costs are E[C mis j A] =E[ρ s i ]Cj o. Second, ex-post underrating refers to a situation where a B-rated bond does not default. Then, the cost to the agency is Cj u > 0 so that the expected reputational costs of a B-rating are E[Cj mis B] =(1 E[ρ s i ]) Cj u. The bond thus obtains an A-rating from agency j only if E[Cj mis condition translates to: A] E[C mis j B]. This E [ρ s i ] C u j C o j + Cu j =: K j. (3) If (3) is not met, the bond gets a B. Hence, a prerequisite for an A-rating is that the agency s expectation about the bond s default probability is below a certain threshold level K j, where the threshold is fully determined by the individual over- and underrating costs. 4 Opacity and Rating Splits A natural measure of opacity is the variance of the bond s default probability after the signal has been observed by the agencies. For any given signal s i, this ex-post variance satisfies: ] σρ = E [(ρ E[ρ s i ]) s i = 1 ( 1 q ) (ρ h ρ l ). 4 Accordingly, we obtain: Lemma The industry will become more opaque if (i) q decreases or (ii) (ρ h ρ l ) increases. The lemma clarifies that there can be a high level of opacity for two reasons. Firstly, opacity will be high if the agencies have a poor screening technology, i.e. if q is small. Then, signals are relatively imprecise implying that the agencies are hardly able to discriminate between high risk and low risk bonds. Secondly, opacity will be high if the range ρ h ρ l of possible default probabilities is large. A rating split will occur if the agencies disagree on a bond s rating so that one agency gives an A-rating and the other assigns a B to the bond. To clarify our main point, it is sufficient to analyze the case K 1 > ρ K. That is, the first agency is relatively conservative in the sense that it would give a B-rating if no signal were available while the second agency is unconservative. Without a signal, it would give an A. Then, the decision rule (3) together with the respective expectations as given either by (1) or () implies: 5

8 Proposition There will be a rating split if (i) s = s l and q< ρ K 1 1 (ρ h ρ l ) =: q 1 or (ii) s = s h and q K ρ 1 =: q. (ρ h ρ l ) Concerning the two determinants of the opacity of an industry, the proposition states that there will be a rating split if the quality of the screening technology is poor (low q) and/or if the range of possible default probabilities ρ h ρ l is small. The intuition for this result is straightforward. Due to the different reputational costs of misrating between the rating agencies, there is a rating split before the screening process. This split will disappear after the screening process only if the received signal leads to a sufficiently large change in the assessment of the bond s default probability. However, this will not happen, i.e., the split will persist, if the quality of the screening technology is poor or if the range of the possible probabilities of default is small anyhow. Recall from the lemma that the opacity of an industry decreases in q and increases in the range ρ h ρ l. Therefore, there may be rating splits in an extremely opaque industry (low q, high range), but also in a perfectly transparent industry (high q, low range). 5 Conclusion This paper has shown that a rating split can either indicate that the screening technology is of little use to the rating agencies implying that an industry is rather opaque. Or, it can indicate that the default probabilities of bonds issued in the industry are relatively homogeneous so that there is a low level of opacity. Therefore, rating splits cannot serve as a useful measure for opacity. References Bonaccorsi di Patti, E. and G. Dell Ariccia, 004, Bank competition and firm creation, Journal of Money, Credit and Banking 36, Borio, C., 008, The financial turmoil 007-?: A preliminary assessment and some policy considerations, BIS Working Papers No. 51, Bank for International Settlements, Basel. Crouhy, M., Jarrow, R. A. and S. M. Turnbull, 008, The subprime credit crisis of 007, Journal of Derivatives, forthcoming. Drucker, S. and M. Puri, 008, On loan sales, loan contracting, and lending relationships, Review of Financial Studies, doi: /rfs/hhn067. 6

9 Hyytinen, A. and M. Pajarinen, 008, Opacity of young businesses: Evidence from rating disagreement, Journal of Banking & Finance 3, Iannotta, G., 006, Testing for opaqueness in the European banking industry: Evidence from bond credit ratings, Journal of Financial Services Research 30, Morgan, D. P., 00, Rating banks: Risk and uncertainty in an opaque industry, American Economic Review 9, Pottier, S. W. and D. W. Sommer, 006, Opaqueness in the insurance industry: Why are some insurers harder to evaluate than others?, Risk Management and Insurance Review 9, Van Roy, P., 005, Credit ratings and the standardised approach to credit risk in Basel II, ECB Working Paper No. 517, European Central Bank, Frankfurt/Main. 7

10 Die folgenden Diskussionspapiere wurden seit Juni 008 veröffentlicht: The following Discussion Papers have been published since June 008: Finanzierungsentscheidungen mittelständischer Christoph Börner Unternehmer Eine empirische Analyse des Dietmar Grichnik Pecking-Order-Modells Franz Reize Solvig Räthke 008 Credit Default Swaps and the Stability of the Frank Heyde Banking Sector Ulrike Neyer Are Rating Splits a Useful Indicator for the Achim Hauck Opacity of an Industry? Ulrike Neyer