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Rationalizing the Policy of Credit Rating Agencies² Karl L. Keiber, WHU Otto Beisheim Graduate School of Management Gunter Löffler, University of Ulm* Abstract This paper analyzes the policy of rating agencies and provides two ra- tionales which might account for the empirical observation that rating agencies sometimes do not reveal relevant information through their bond ratings. We find that the stickiness of ratings can be advanta- geous for investors if mandatory portfolio revisions due to rating- based investment guidelines are subject to transaction costs, or if some investors are privately informed about default risk. The intuition for the latter is that sticky ratings can balance the conflicting interests of uninformed investors, who benefit from public rating information, and informed investors, whose advantage is diminished by ratings. Keywords: credit ratings, rating agency, stickiness, conservatism, corporate bond. JEL classification: G20, G33. * Corresponding author: Gunter Löffler, Department of Finance, University of Ulm, Helmholtzstrasse 18, 89069 Ulm, Germany. Phone: ++49-731-5023597 e-mail: loeffler@mathematik.uni-ulm.de ² We thank Richard Cantor for helpful conversations. The comments by Marc Gürtler as well as by participants of the 11th Annual Meeting of the German Finance Association 2004 are gratefully acknowledged. Financial support from Moody's Investors Service is gratefully acknowledged, too. Any errors are our responsibility. Comments are welcome. 1 Introduction Credit rating agencies often face criticism for being to slow to change ratings. Yet, they do not aspire to be "high-frequency sources of information" (Fons, 2002, p. 13). According to official statements, ratings are intended to be both accurate and stable, implying that "some short-term default prediction may be sacrificed" (Cantor and Mann, 2003, p.4). Agencies state that this policy meets the needs of issuers and investors. Since ratings are widely used in investment guidelines and bond indices, investors value stability because rating changes might trigger costly transactions. Issuers value stability because it gives them opportunity to change their financial condition in order to avoid downgrades. So far, the academic literature has not examined the pros and cons of such a rating policy. Focusing on the investor side, we aim at providing a theoretical foundation for the observed rating management practices. Consistent with the arguments put forward by rating agencies, we abstract from agency problems and model optimal rating behavior if the rating agencies' goal is to maximize the expected utility of investors. We first confirm the transaction cost argument put forward by rating agencies. In our model. single-trip transaction costs below 0.1% are sufficient to prevent investors from adjusting their portfolio to new information — implying that investors may be indifferent between timely ratings and ones that are kept stable despite changes in fundamentals. If exogenous investment restrictions trigger sub-optimal transactions upon rating changes, this indifference can turn into a preference for stable ratings. The general applicability of this argument, however, is debatable. Many restrictions focus on the investment grade boundary, and bond indices are based on the agencies' classification into seven letter grades rather than on the refined systems with 21 grades.1 Thus, there are rating changes that are of little relevance for the opportunity set of investors. In such cases, it is not evident why investors should not prefer to have timely rating information, and then decide on their own whether it is sufficient to warrant a portfolio revision or not. Our second, and novel rationale for rating stability is more general in that it is not build on exogenous restrictions, but on asymmetric information among investors. If some investors are privately informed about the credit quality of an issuer, public rating information has two opposing effects. It increases the utility of investors who are not fully informed, but it reduces the informational advantage of informed investors. A rating policy that does not react to small 1 In the system of Standard & Poor's for example, letter grades are AAA, AA, A, BBB, BB, B and C. Modified grades are marked by adding "+", nothing, or "–" to these letter grades. 2 changes in issuer default risk can be optimal in that it maximizes the average utility of informed and uniformed investors. The related literature includes empirical papers which find that ratings do not fully reflect available information. Delianedis and Geske (1999) show that ratings lag market-based measures of default risk which use only publicly available information; Carey and Hrycay (2001) and Kealhofer (2003) find ratings to be relatively stable compared to quantitative measures of default risk; Kealhofer (2003) also compares the default prediction power of ratings and a market-based credit risk measure and concludes that the latter is superior. Through simulations, Löffler (2003, 2004) demonstrates that the stylized empirical facts could result from two elements of the agencies' rating policy, the through-the-cycle approach and the propensity to avoid frequent rating reversals. Altman and Rijken (2004) examine actual rating data and reach similar conclusions. In essence, rating through the cycle means that the horizon used in assessing default risk is longer than the usual one-year horizon. If changes in default risk are negatively autocorrelated, shocks tend to be corrected over time, and a through-the-cycle rating will be more stable than a rating measuring one-year default risk. We do not model autocorrelation in our paper because we focus on the question of whether an agency that uses a certain concept of default risk should refrain from incorporating information that is relevant for this concept. Our results thus are not conditioned on the rating horizon. The type of policy we examine is more closely linked to the policy of changing a rating only “when it is unlikely to be reversed within a relatively short period of time” (Cantor, 2001, p. 175). While Löffler (2003) and Altman and Rijken (2004) build their analysis on the actual, discrete rating scale used by rating agencies, we assume a continuous scale. Our results are thus more general and not conditioned on a specific rating scale. In contrast to our analysis, extant theoretical papers on the provision of rating information are built on adverse selection and moral hazard problems. In a general analysis of intermediaries that can be applied to ratings, Ramakrishnan and Thakor (1984) and Lizzeri (1999) show that there may be equilibria in which the signal provided by the intermediary is uninformative. Boot, Milbourn and Schmeits (2004) propose that ratings could serve as coordinating mechanism. Boom (2001) studies the demand for ratings and the price setting behavior of a rating agency. The remainder of the paper proceeds as follows. Section 2 presents the model underlying our analyses. In section 3, we propose an implementation of the model. Section 4 studies numerically the impact of transactions cost and private information on investors’ expected 3 utility under various rating policies and collects some numerical comparative static results. Section 5 concludes. 2 Model We study investor portfolio choice in a one-period world with two assets. The first asset is a credit risky zero coupon bond which has face value N and matures at the end of the period. The second asset is a riskless bond. At the beginning of the period the agents do not know whether the credit risky bond will end up in default or not. At the end of the period all uncertainty is resolved. The riskiness of the credit risky bond is captured by its default probability π , and its recovery rate δ in the case of default. The investors are assumed to be rational. Their preferences are represented by a von Neumann-Morgenstern utility function and the investors are expected utility maximizers. At the beginning of the period, at date t = 0 , they determine the split of their initial wealth between the credit risky bond and the riskless bond such that it maximizes the expected utility of their end of period wealth. The investors’ initial wealth is assumed to amount to unity, W0 = 1 . The utility function U is isoelastic and defined over the end of period wealth, U (W ) = 1 1−γ W 1−γ , where W denotes the end of period wealth at date t = 1 , and γ represents the Pratt-Arrow coefficient of relative risk aversion. The credit risky bond is priced by means of risk-neutral valuation. The risk neutral default probability can be derived from the default probability π by applying Merton’s (1974) structural model. In this model, default occurs at maturity if the value of the firm V lies below the value of liabilities D . If the firm value is a geometric Brownian motion with drift µV and variance σ 2V 2 , the one year default probability π is given by ln V + (µ − σ22 )T D , π = Φ (1) σ T where Φ denotes the cumulative normal distribution and T denotes the length of the period. The risk neutral default probability obtains by replacing the drift rate µ by the instantaneous 4 risk free rate rf . With an assumption about the drift rate µ and the variance rate σ 2 , it is straightforward to derive the risk neutral probability πq from a given default probability π :2 µ − rf πq = Φ Φ−1 (π) + T (2) σ Given the risk neutral default probability πq the credit risky bond can be priced by discounting the expected end of period payoff according to the risk neutral probabilities at the risk free rate of return. Formally, the credit risky bond’s price ν results as (1 − πq ) ⋅ N + πq ⋅ δ ⋅ N ν= , (3) 1 + Rf where Rf = exp rf − 1 is the one-period risk free rate of return. After having described the investment universe, the investors’ preferences, as well as the pricing of the credit risky bond we now turn to the description of the market imperfections. At the beginning of the period, at date t = 0 , the rating agency knows the correct default probability and reports it publicly as its rating. At date t = 0+ , immediately after t = 0 , we assume that new information about the credit risky bond becomes available. The new default probability prevailing from date t = 0+ on is observed by the rating agency. Let p : (0,1] → ¡ + denote the density function of the new default probability. Thus the new 0 default probability is assumed to be a realization in the unit interval according to the probability law represented by the density p . Likewise, the investors receive a perfect signal about the new default probability at date t = 0+ with probability θ . Hence, some investors are privately informed, and information will be asymmetric if the rating agency does not publish the new default probability. Based on the private information, the informed investors may decide to adjust their portfolio at date t = 0+ . If the rating agency announces the new default probability publicly, the uninformed investors may revise their initial portfolio decision, too. Furthermore, we assume that there are no agency conflicts between the rating agency and the investors, and that no subset of investors is favored by the rating agency. Thus, the announcements of the rating agency are credible. We assume that neither trading on private information affects the credit risky bond’s market price nor retrading of the private 2 The derivation of risk-neutral default is described, for example, in Crouhy, Galai and Mark (2000). 5 information is possible.3 Consequently, the market price of the credit risky bond is determined by the uninformed investors which rely on the default probability reported by the rating agency. The following timeline summarizes the model’s structure: t=0 t = 0+ t =1 Investors’ Default Signal on new default Credit risky bond fully information probability probability from repays or defaults agency and/or private information Investors’ Portfolio Portfolio Portfolio action allocation revision liquidation Transaction costs are modeled as a percentage commission on the transaction value that are to be paid when buying or selling risky bonds. Transactions in the riskless bond are presumed to be costless. Our focus is on the analysis of the optimal rating policy of the rating agency, where optimality is defined from the perspective of the investors. A rating policy is referred to as optimal if an investor’s average expected utility at date t = 0+ is maximized. By a rating policy we mean the extent of information which is disclosed at date t = 0+ by the rating agency. We differentiate three potential rating policies which we denote as fully informative, imperfectly informative, or uninformative. In the first case, the rating agency discloses the new default probability at date t = 0+ so that everybody is perfectly informed about the riskiness of the corporate bond. An imperfectly informative rating policy means that there are scenarios in which the agency reports the new default probability, and others in which it does not. An uninformative rating policy is the extreme form of an imperfectly informative rating policy; here the agency never announces new information at date t = 0+ . If ratings do not report the new default probability, uninformed investors – lack of any private information – presume it is still equal to the one from date t = 0 . The aim of the paper is to examine whether there are circumstances in which investors benefit from an imperfectly informative rating policy, or are at least indifferent between fully and imperfectly informative rating policies. Let E π [U (W )] denote an investor’s expected utility in t = 0+ which results for a given new default probability π and from a portfolio allocation that is optimal given the information set 3 Note that we plan to incorporate the price impact via a microstructure analysis á la Glosten and Milgrom (1985). Preliminary analyses in which we made transaction cost dependent on the degree of information 6 of the investor. The information set depends on the rating policy and the availability of private information. We use E fπ [U (W )] to denote the expected utility if investors are fully informed (subscript f ) about the new default probability p; Euπ [U (W )] is the expected utility of investors who are uninformed (subscript u ) about p; E pr [U (W )] denotes the expected utility π of investors with private information (subscript pr) about p. The rating agency has to commit to a rating policy which maximizes the average expected utility of an investor. Pursuing a fully informative rating policy implies an average expected utility of E f 1 ∫ E [U (W )] ⋅ p (π)d π , π Ef = f (4) 0 Given a fully informative rating policy it is irrelevant whether an investor received private information or not since private information is redundant due to the publicly available rating. An uninformative rating policy leaves those investors uninformed who do not possess private information and therefore yields 1 ∫ θ ⋅ E [U (W )] + (1 − θ ) ⋅ E [U (W )] ⋅ p (π)d π π π Eu = pr u (5) 0 as average expected utility. Given the uninformative rating policy the presence of private information on the part of the investor affects the average expected utility. Next, we describe our notion of an imperfectly informative rating policy in detail. A rating agency which implements an imperfectly informative rating policy only provides an update of the rating at date t = 0+ if the corporate bond’s default probability exceeds a lower threshold π l or an upper threshold π u . As long as the default probability is within the thresholds the rating remains unchanged; an investor’s expected utility is then given by Euπ [U (W )] if the investor has no private information and by E pr [U (W )] if the investor is privately informed. π In the case that a threshold is surpassed and an updated rating becomes publicly known each asymmetry θ did not lead to qualitative changes of the results. 7 investor’s expected utility results as E fπ [U (W )] . Hence, an imperfectly informative rating policy generates an average expected utility of πu Eim = ∫ θ ⋅ E pr [U (W )] + (1 − θ ) ⋅ Euπ [U (W )] ⋅ p (π)d π π l π (6) πl 1 +∫ E fπ [U (W )] ⋅ p (π)d π + ∫ E fπ [U (W )] ⋅ p (π)d π . 0 πu The rating agency’s decision problem of choosing an optimal rating policy from the investor’s perspective amounts to determining average expected utilities E f , Eu , and Eim and choosing the policy that leads to maximum average utility. Among other parameters, the optimal policy will depend on the degree of asymmetric information among investors and the magnitude of transaction cost. For ease of exposition, we have not shown the impact of transaction costs explicitly in the formulae. Trading costs make portfolio revisions costly, and thus reduce expected utility differences between situations where investors are uninformed, and those in which they are informed and revise their portfolios accordingly. 3 Implementation Since the agencies' maximization problem described in the previous section defies a closed- form solution, we suggest an implementation of the model which can be studied numerically. The reference case we study is described by the following parameters (Cf. table 1 for a summary.). The investors’ coefficient of relative risk aversion is γ = 4 . The length of the period T is set to one year. The publicly known one-period default probability at date t = 0 is set to π = 0.25% . We choose this value, which is typical for investment grade bonds with rating BBB (Standard & Poor's) or Baa (Moody's), because investment grade bonds make up the great part of the rated issuer universe.4 To derive risk-neutral default probabilities from the Merton model, we let µ = 0.05 and σ = 0.15 . Furthermore, both the risk-free interest rate and the recovery rate in case of default are set to zero, that is Rf = rf = 0 and δ = 0 . 4 In 2001, for example, 63% of the issuers rated by Standard & Poor's had a rating better than BB (Standard & Poor's, 2002, p. 24). 8 Finally, the bonds’ face values are assumed to be unity, that is N = 1 . The credit risky bond’s price is thus given by ν = 1 − πq , (7) whereas the price of the riskless bond is always one. The distribution of the new default probabilities at t = 0+ is described by a five-point distribution. The new default probability is assumed to realize one out of n = 5 values πi n (i = 1, K, n ) with probability pi , ∑ i =1 pi = 1 . The probabilities pi (i = 1, K, n ) represent the discrete counterpart to the density function p from section 2. The variance of the default probabilities’ distribution is chosen to match the variance of empirical one month changes in default probabilities. As proxies for the default probabilities, we use KMV EDFs from 1982 to 2002. EDFs (expected default frequencies, from the financial software firm KMV) are quantitative estimates of one year default probabilities that are based on the Merton (1974) model of corporate default; key inputs are balance sheet data, equity market valuation and equity volatilities.5 The data set used for the analysis contains EDFs for rated US and non-US corporate issuers.6 Specifically, we examine end of month EDFs for firms whose EDF at the preceding month’s end was between 0.2% and 0.3%; their empirical variance is 0.031%. Apart from matching this variance, we also impose the condition that the mean price effect of the new information is zero, i.e. the mean risk neutral probability at date t = 0+ is equal to that at date t = 0 . The matched five point distribution results as follows (we assume round figures for EDFs and choose probabilities accordingly): i State 1 State 2 State 3 State 4 State 5 πi = default probability 0.05% 0.15% 0.25% 0.50% 1.00% pi = probability of πi 6.20% 38.00% 39.49% 13.31% 3.00% In the reference case, the imperfectly informative rating policy is such that the rating is only changed if the default probability at date t = 0+ equals or exceeds 1%. That is, the thresholds for updating the rating are given by π l = 0 and π u = 0.01 . We study the reference case in 5 EDFs have been advocated as a more accurate and timely alternative to agency ratings (e.g. Kealhofer, 2000); EDFs and EDF-type measures are used in the financial industry as well as in academic studies (e.g. Delianedis and Geske, 1999). 9 four economies which differ with respect to the existence of transaction costs and the presence of private information: No private information Private information No transaction cost Section 4.1 Section 4.3 Transaction cost Section 4.2 Section 4.4 Let π denote the credit risky bond’s publicly known default probability and α0 the optimal fraction of initial wealth invested into the credit risky bond at date t = 0 . That is α0 is the solution to the investor’s initial optimization problem 1−γ 1− π α + (1 − α) π 1−γ α0 = arg max + (1 − α) (8) α 1 − γ ν0 1− γ where ν 0 denotes the price of the credit risky bond at date t = 0 . Since the initial wealth is α unity, ν0 gives the number of credit risky bonds held in the portfolio. The end of period wealth amounts to α ν0 + (1 − α) and 1 − α in the case of non-default and default, respectively. Based on this discrete setting we now provide an investor’s expected utilities which result from the different rating policies. For ease of exposition, we present these expected utilities for the case of zero trading costs. The extension to positive percentage transaction costs is straightforward. Note that, irrespective of the rating policy, α is used to denote the fraction of wealth invested in the credit risky bond at date t = 0+ . If the rating is fully informative, i.e., investors are perfectly informed about the riskiness of the corporate bond at date t = 0+ , the bond price reflects the new information about the new default risk and adjusts from ν 0 to νi . An investor’s expected utility given the new default probability πi results as 6 The data was kindly provided by Moody’s Investors Service. 10 1−γ 1 − πi α α E [U (W )] = max πi 0 νi + (1 − α0 ) + (1 − α) f α 1− γ ν 0 ν i 1−γ (9) π α + i 0 νi + (1 − α0 )(1 − α) 1 − γ ν 0 α0 where the subscript f reminds of the fully informative rating policy. Since ν0 was the optimal number of credit risky bonds at date t = 0 , the portfolio value amounts to νi + (1 − α0 ) at date t = 0+ if πi is the new default probability revealed by the rating α0 ν0 agency. Thus, the release of a new rating affects the value of the bond portfolio. Under an uninformative rating policy, investors who do not possess private information do not know whether new information has arrived. Neither does the market, meaning that the uninformed investors stick to the belief that the default probability still amounts to π – the publicly known default probability at date t = 0 – and that the bond price remains unchanged at ν 0 . Consequently, uninformed investors do not revise their portfolios. Since, the new default probability truly is πi , an investors’ expected utility is given by 1−γ 1 − πi α0 πi E [U (W )] = πi + (1 − α ) 1−γ (1 − α0 ) , ν 0 + (10) u 1− γ 0 1− γ where the subscript u reminds of the uninformative rating policy. If the rating policy is uninformative, an investor who has access to a private signal derives the expected utility 1−γ 1 − πi α πi E [U (W )] = max πi + (1 − α) + 1−γ (1 − α) , (11) pr 1− γ ν 1− γ α 0 where the subscript pr indicates that the investor is privately informed about the new default characteristic of the credit risky bond. If the rating due to an uninformative rating policy remains unchanged, so does the market price of the credit risky bond. However, a privately informed investor adjusts his portfolio at date t = 0+ according to his private information that the new default probability is πi . Thus, the investor revises the portfolio from α0 to α . 11 To summarize, with a fully informative rating policy both the market price changes and the portfolio is revised at date t = 0+ whereas an uninformative rating policy does not affect the market price. Portfolios are only revised if an investor has access to private information. The average expected utility which results from the different potential rating policies among which the rating agency has to choose are characterized similarly to section 2. Under a fully informative rating policy an investor’s average expected utility results as n E f = ∑ pi ⋅ E fπi [U (W )] , (12) i =1 whereas an uninformative rating policy yields n Eu = ∑ pi ⋅ θ ⋅ E pri [U (W )] + (1 − θ ) ⋅ Euπi [U (W )] π (13) i =1 as average expected utility of an investor. With an uninformative rating policy the presence of private information on the part of the investor affects the average expected utility. Finally, under an imperfectly informative rating policy the rating is only updated if the default probability surpasses the 1% threshold, which occurs in state i = 5 . Obeying this imperfectly informative rating policy generates an average expected utility of 4 Eim = ∑ pi ⋅ θ ⋅ E pri [U (W )] + (1 − θ ) ⋅ Euπi [U (W )] + p5 ⋅ E fπi [U (W )] π (14) i =1 4 Numerical analysis and comparative statics 4.1 Neither transaction costs nor private information The economy analyzed in this section serves to clarify the informational value of a rating system within the model although the analysis does not provide an answer to the question underlying the paper. If rating agencies do not publish information at all or reveal their information only imperfectly, investors lack perfect knowledge of the relevant parameters, which reduces the expected utility. The less information is conveyed by the rating agency, the more utility is lost. The following table gives optimal investment decisions and expected 12 utilities for fully informative ratings, uninformative ratings and a rating policy which only reveals the worst state i = 5 : α Average expected Rating policy, j State 1 State 2 State 3 State 4 State 5 utility, E i Fully informative, f 24.7% 22.7% 21.8% 20.4% 18.8% -0.3328003 Only state 5 is revealed, im 21.8% 21.8% 21.8% 21.8% 18.8% -0.3328015 Uninformative, u 21.8% 21.8% 21.8% 21.8% 21.8% -0.3328029 If the rating policy is uninformative or imperfectly informative, investors do not optimally revise their portfolios at date t = 0+ except for state five which is revealed under a imperfectly informative rating policy (upright digits). Both policies reduce the expected utility relative to an fully informative rating system; hence, the more information is revealed, the higher is the expected utility, that is E f > Eim > Eu . Absent any friction, the best rating policy is thus a fully informative one since it provides maximum expected utility (gray-shaded cell). The next sections examine whether this conclusion has to be modified if transaction costs and private information are introduced. 4.2 Transaction costs, no private information We start by examining the case of a fully informative rating system. Once the new default probability is revealed at date t = 0+ the portfolio weight of the credit risky bond may change because the price of the credit risky bond adjusts to the new default information. Thus, actual portfolio weights before portfolio revision differ across states because the publicly known change in default probabilities affects prices. The following table shows actual portfolio weights of the risky bond and, for comparison, optimal ones if transaction costs were zero: Portfolio weights given a fully informative rating State 1 State 2 State 3 State 4 State 5 Actual (not revised) 21.9% 21.8% 21.8% 21.7% 21.5% Optimal (revised) 24.7% 22.7% 21.8% 20.4% 18.8% If portfolio transaction are not costless, but associated with a percentage commission, investors may not find it optimal to (fully) adjust the portfolio from the actual weight to the weights that are optimal under zero trading costs. The following table shows transaction costs that are just large enough to prevent any portfolio adjustment: 13 Critical transaction costs that prevent portfolio adjustment State 1 State 2 State 3 State 4 State 5 0.03% 0.03% - 0.09% 0.34% The table can be interpreted as follows: if transaction costs are 0.09% or higher, investors do not benefit from being able to discriminate between states 1, 2, 3 and 4 because this knowledge would not make them change their portfolio anyway; transactions costs incurred from portfolio adjustment would harm more than the loss of expected utility from having a portfolio that has either too much risk (state 4), or to little (states 1 and 2). If transaction costs are between 0.09% and 0.34%, on the other hand, the investors benefit from knowing whether state 5 prevails or not; the investors would thus be indifferent between a fully informative rating policy and an imperfectly informative one which only reveals state 5. Schultz (2001) estimates round-trip transaction costs for corporate bonds to be 0.26%; using a different methodology and different data, Chen and Wei (2001) arrive at a median of 0.59%. The figures correspond to one-trip transaction cost of 0.13% and 0.28%, respectively. Plugging these empirical estimates in our model thus produces situations in which investors would not object if rating agencies suppress rating changes for small, but significant changes in default probabilities. Note that changes in default probability from 0.25% to 0.5% or 0.1% are large enough to warrant a rating change from BBB to BB+ or A-, respectively, according to historical default rates associated with these rating classes. While the analysis shows that the stickiness of ratings may not harm investors, it does not per se justify why rating agencies should act in such a manner. Investors could decide on their own if a rating change is sufficient to trigger a portfolio revision. One explanation is exogenous investment restrictions. Many financial institutions are restricted to invest in investment-grade bonds. If revelation of the state 4 default probability would correspond to a downgrade to non-investment grade level, investors facing such a restriction would be forced to sell the bond, which would be sub-optimal. Another explanation why investors could benefit from imperfectly informative ratings is private information, whose value is reduced by publicly available rating information. This is examined in the next two sections. 4.3 Private information, no transaction costs In this section, we set transaction costs to zero again, but assume that investors receive with probability θ a signal which perfectly reveals the new default probability. We examine the 14 expected utility of investors for various values of θ in the presence of three different rating policies: fully informative, informative only about state 5, and uninformative. If the investor receives no signal, he would prefer a fully informative rating system (section 4.1); if he is privately informed, the rating information is not only redundant to him but damaging because it makes private information worthless. If ratings are uninformative, market prices do not reflect the new default probabilities at date t = 0+ . An informed investor can buy cheaply in states 1 or 2; in cases 4 and 5 he can benefit from (short-)selling the bond.7 These two opposing effects of having private information suggest that the probability of being informed is decisive. The higher θ , the less likely are cases in which investors benefit from informative ratings, and the more likely are cases in which they benefit from uninformative ratings. The following table gives average investor utility for four different values of θ , separately for the three rating policies outlined above: Average expected utility Ei Rating policy, j θ = 0% θ = 0.5% θ = 1% θ = 2% Fully informative, f -0.3328003 -0.3328003 -0.3328003 -0.0174430 Only state 5 is revealed, im -0.3328015 -0.3328007 -0.3327999 -0.3327982 Uninformative, u -0.3328029 -0.3328017 -0.3328005 -0.3327981 With θ = 0% , there is effectively no private information, and we obtain the same result as in section 4.1.; with θ = 0.5% , the result still holds as the benefits of rating information outweigh its costs. With θ = 1% , however, the rating policy that leads to maximum expected utility is the imperfectly informative rating policy. For even higher values of θ the investors prefer a completely uninformative rating policy. Figure 1 graphs expected utilities for θ ∈ [0, 0.05] and delivers the insight, that for θ ∈ [0.77%,1.87%] the imperfectly revealing policy is superior from the perspective of the investors. The results give an alternative rationale for rating stickiness. Investors may prefer a policy of imperfectly informative ratings because it achieves a good balance between the costs of ratings and their benefits. Costs arise to informed investors because public ratings devalue private information, while benefits accrue to uninformed investors. It seems difficult to derive a value for θ which is empirically plausible. It has to be small because we assume that private information does not affect prices. Thus, the values discussed above could well be those that bring the model close to reality. 7 The results presented obtain under the assumption that short selling is possible; if short sales are impossible, 15 4.4 Private information, transaction costs If the analysis of the previous section is extended by allowing for transaction cost, the main conclusion does not change. Again, there is a trade-off between the benefits and costs of ratings quality. We repeat the analysis from section 4.3 where transaction costs are assumed to amount to a 0.2%. The results are shown in Figure 2, and the following table: Average expected utility Ei Rating policy, j θ = 0% θ = 0.3% θ = 1% θ = 2% Fully informative, f -0.33280265 -0.33280265 -0.33280265 -0.33280265 Only state 5 is revealed, im -0.33280265 -0.33280248 -0.33280209 -0.33280152 Uninformative, u -0.33280286 -0.33280253 -0.33280176 -0.33280067 For θ ∈ (0, 0.39%] , the imperfectly revealing policy is superior. There are thus two main differences to the previous section: First, the imperfectly informative rating policy is better than the fully informative rating policy as soon as there is a positive probability of being informed. Second, the critical probability θ which makes uninformative ratings superior is smaller compared to the case of no transaction costs. The intuition is as follows. With transaction costs, information about small changes in default probability are worthless to investors, because it would not make them change their portfolio anyway. Thus, the advantage of being informed under fully or imperfectly informative policies is reduced in the presence of transaction costs. The higher the transaction costs, the smaller the region in which the imperfectly revealing policy leads to maximum expected utility. With transaction costs of 0.3%, for example, the interval is θ ∈ (0, 0.03%] . Since realistic values for θ should be small, however, this does not greatly affect the generality of the conclusion that there are situations in which imperfectly revealing rating policies are optimal. 4.5 Numerical comparative statics In this section, we explore the effects of parameter changes on the key results presented above. We start by examining how critical transactions costs that prevent portfolio revisions are affected by the following, non-accumulating variations: conclusions do not change (see section 4.5). 16 § γ ∈ {2, 6,10} instead of γ = 4 (Risk aversion) µ − rf 1 § ∈ {0.25, 0.5} in equation (2) instead of (Sharpe ratio) σ 3 § T ∈ {5,10} instead of 1 (Length of period) For the last variation with respect to the length of the period between dates t = 0 and t = 1 we interpret the default probabilities of the reference case as one-year default probabilities and use formulae (1) and (2) to derive the according 5-year and 10-year default probabilities and bond prices. The results of these variations are collected in the following table: Critical transaction costs that prevent portfolio adjustment state 1 state 2 state 3 state 4 state 5 Reference case 0.03% 0.03% - 0.09% 0.34% risk aversion = 3 0.03% 0.03% - 0.09% 0.34% risk aversion = 6 0.03% 0.03% - 0.09% 0.34% risk aversion = 10 0.03% 0.03% - 0.09% 0.34% Sharpe ratio = 0.25 0.02% 0.02% - 0.06% 0.21% Sharpe ratio = 0.5 0.06% 0.06% - 0.20% 0.75% Length of period = 5 years 1.11% 0.46% - 0.82% 1.93% Length of period = 10 years 1.82% 0.68% - 1.09% 2.39% Changing the risk aversion parameter does not affect critical transaction costs. The higher the Sharpe ratio, the more dispersed are bond prices for a given distribution of actual default probabilities; thus, trading on new information is more valuable, and critical transaction costs are higher. The same argument applies to increases in the length of the period. The longer the period, the stronger is the impact of a change in the one-year default probability on bond prices. The critical transaction costs for a holding period of 5 or 10 years are higher than empirical estimates of transaction costs, which could be taken to question the validity of the transaction cost argument for stabilizing ratings. However, price effects are likely to be overstated here, which would make critical transaction costs too high. The shocks to long- term default probabilities at date t = 0+ are derived from the shocks to one-year default probabilities by assuming those shocks to be permanent—contrary to evidence on mean- reverting credit quality.8 Since empirical studies on the behavior of long-term probabilities are not available, it seems difficult to derive a plausible distribution for shocks to long-term default probabilities. 8 Fama and French (2002) document mean-reversion in leverage ratios, while the survey of Graham and Harvey (2001) reveals that firms pursue leverage targets. 17 We proceed by analyzing the effects of exogenous parameter changes on the degree of information asymmetry which renders the imperfectly informative rating policy optimal. We set transaction costs to 0.2% and define the rating policy as in the reference case, i.e., only state 5 is revealed—except for those variations in which transaction costs or the rating policy themselves are varied. In addition to the variations from above, we examine three further variations which were irrelevant for critical transaction costs: § the imperfectly informative rating policy does reveal states 1 and 5, instead of revealing only state 5 as in the reference case § the transaction costs amount to 0.1% or 0.3% instead of 0.2% § short selling is not possible The following table shows the intervals for θ , the probability of being informed, in which the imperfectly informative rating policy is optimal: Lower and upper bound for θ which renders an imperfectly informative rating policy optimal Reference case 0.000% 0.393% risk aversion = 3 0.000% 0.382% risk aversion = 6 0.000% 0.403% risk aversion = 10 0.000% 0.412% Asset Sharpe ratio = 0.25 0.000% 0.001% Asset Sharpe ratio =0.5 0.000% 2.445% Length of period = 5 years 1.980% 3.229% Length of period = 10 years 3.712% 4.492% transaction cost = 0.1% 0.000% 1.043% transaction cost = 0.3% 0.000% 0.031% Short selling prohibited 0.000% 0.398% Imperfectly informative policy 0.000% 0.259% does not reveal states 1 and 5 In each variation, there is a range in which the imperfectly informative rating policy is optimal. The higher the risk aversion, the more important are the information benefits of the rating policy because investors trade less aggressively on private information, and the costs of being uninformed are higher. The interval can be fairly small if transaction costs are high, or the Sharpe ratio is low. In those cases, the value of public information is low because its price impact is low, or the costs of trading on this information are high. Short selling has a very small impact; similarly, a change in the definition of the imperfectly informative rating policy does not affect the bounds substantially. Increasing the length of the period to 5 or 10 years lets the lower boundary of the interval increase to 1.98% or 3.72%, respectively. Due to stronger price effects, critical transaction costs that prevent adjustment are higher (see above), 18 which increases the value of information about states 1 to 4; this information is provided by the fully informative rating policy, but not by the imperfectly informative one. Thus, a higher q is needed to compensate the disadvantage of the imperfectly informative policy relative to the informative one. The variations thus show that the main results reported in the sections 4.2, 4.3, and 4.4 — transaction costs can annihilate the value of new rating information, and an imperfectly informative rating policy is optimal for certain ranges of asymmetric information among investors — are largely robust to exogenous changes of the presumed parameter values. 5 Conclusion We derived two rationales for the rating management practices of rating agencies. If investors are subject to rating-based investment guidelines, dampening rating volatility leads to lower transaction costs, which can outweigh the costs of imperfect information. If there is asymmetric information among investors, a less than fully revealing rating policy can optimally balance the diverging interests of informed and uninformed investors. While the first argument has been put forward by rating agencies, the second is novel, and also more general because it does not require the existence of investment restrictions. The results were derived within an expected-utility framework in which the rating agency maximizes the average expected utility of investors. Our analysis thus abstracts from agency problems and from the role of issuers. Without doubt, agency problems are present in practice, and it would be worthwhile to explore their effects on the optimal information policy of rating agencies. The fact that prior studies show that information intermediaries might choose to publish uninformative signals (Ramakrishnan and Thakor, 1984, and Lizzeri, 1999) suggests that such an analysis could even corroborate our results. As regards issuer interests, it seems that one can establish an argument that is similar to the transaction cost argument from the perspective of investors. Issuers might have a preference for stable ratings because rating changes can entail irreversible costs for issuers even if they do not issue new debt, e.g. because rating triggers make coupon payments dependent on the current rating. A direct extension of our work would be to model the price impact of informed investors, and we aim to do this in the next version. Preliminary analyses in which we made transaction costs dependent on the degree of information asymmetry do not affect conclusions. If the market was fully inefficient, of course, informational asymmetry could not justify an imperfectly revealing rating policy. In other words, we implicitly assume that liquidity trading 19 prevents the market price from being perfectly revealing, and that these liquidity traders do not enter the objective function of the rating agency. While the latter is somewhat debatable, it seems plausible that rating agencies do not weigh all kinds of investors equally. The fact that rating agencies sell detailed rating information, which is likely to be purchased mainly by active investors, is one instance that suggests that potentially informed investors play a larger role in the agencies’ objective function than liquidity traders. 20 References Altman, E.I, Rijken, H., 2004, How rating agencies achieve rating stability. Working Paper. Boom, A., 2001, A monopolistic credit agency. Working Paper. Boot, A., Milbourn, T., Schmeits, A., 2004, Credit ratings as coordination mechanisms. Working Paper. Cantor, R., Packer, F., 1997, Differences of opinion and selection bias in the credit rating industry. Journal of Banking and Finance 21, 1395-1417. Cantor, R., 2001, Moody’s investors service response to the consultative paper issued by the Basel Committee on Banking Supervision and its implications for the rating agency industry. Journal of Banking and Finance 25, 171-186. Cantor, R., Mann, C., 2003, Measuring the performance of corporate bond ratings. Special comment, Moody's Investors Service. Carey, M., Hrycay, M., 2001, Parameterizing credit risk models with rating data. Journal of Banking and Finance 25, 197-270. Chen, L., Wei, J., 2001, An indirect estimate of transaction costs for corporate bonds. Working paper, University of Michigan/Toronto. Crouhy, M., Galai, D., Mark, R., 2000, A comparative analysis of current credit risk models. Journal of Banking and Finance 24, 59-117. Delianedis, G., Geske, R., 1999, Credit risk and risk neutral default probabilities: information about rating migrations and defaults. Working paper, UCLA. Fama, E., French, K., 2002, Testing tradeoff and pecking order predictions about dividends and debt. Review of Financial Studies 15, 1-33. Fons, J., 2002, Understanding Moody’s corporate bond ratings and rating process. Special Comment, Moody’s Investors Service. 21 Glosten, L. R., Milgrom, P. R., 1985, Bid, Ask, and Transaction Prices in a Specialist Market Under Asymmetric Information. Journal of Financial Economics 14, 71-100. Graham, J., Harvey, C., 2001, The theory and practice of corporate finance: Evidence from the field. Journal of Financial Economics 60, 187-243. Kealhofer, S., 2003, Quantifying Credit Risk I: Default Prediction. Financial Analysts Journal 59, 30-44. Lizzeri, A., 1999, Information revelation and certification intermediaries. Rand Journal of Economics 30, 214-231. Löffler, G., 2004, An anatomy of rating through the cycle. Journal of Banking and Finance 28, 695-720. Löffler, G., 2003, Avoiding the rating bounce: Why rating agencies are slow to react to new information. Working paper, University of Frankfurt. Merton, R.C., 1974, On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance 29, 449-470. Ramakrishnan, R., Thakor, A., 1984, Information reliability and a theory of financial intermediation. Review of Economic Studies 51, 415-432. Schultz, P., 2001, Corporate bond trading costs: a peek behind the curtain. Journal of Finance 56, 677-698. 22 Figure 1: Expected utility depending on rating policy and probability θ of being privately informed (no transaction costs) -0.33279 Informative ratings Expected utility Imperfectly informative -0.33280 Uninformative -0.33281 0 0.01 0.02 0.03 0.04 0.05 q Figure 2: Expected utility depending on rating policy and probability θ of being privately informed (0.2% transaction costs) -0.33280 Expected utility Informative ratings Imperfectly informative Uninformative -0.33280 0 0.01 0.02 0.03 0.04 0.05 q 23 Table 1: Parameters Symbol Meaning Value in reference case γ Risk aversion 4 T Length of period 1 year π Default probability Time- and state-dependent πq Risk neutral default probability Time- and state-dependent p Prob. of default prob. at t = 0+ State-dependent ν Risky bond price Function of time, state and information α Investment in risky bond at t = 0+ Function of time, state and information pi Probability of state i at t = 0+ State-dependent θ Probability of being informed Varied µ Drift rate of asset value returns 0.05 σ2 Variance rate of asset value returns 0.15 Rf Riskfree rate of return 0 rf Cont. compounded riskfree rate Rf = exp rf − 1 V Firm value Unspecified D Firm debt Unspecified δ Recovery rate 0 N Face value of credit risky bond 1 24