Rationalizing the Policy of Credit Rating Agencies by eld18221


									                   Rationalizing the Policy of Credit Rating Agencies²

           Karl L. Keiber, WHU Otto Beisheim Graduate School of Management
                             Gunter Löffler, University of Ulm*

           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

 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.

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

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

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

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

    The derivation of risk-neutral default is described, for example, in Crouhy, Galai and Mark (2000).

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

    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

  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

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

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


        ∫ E [U (W )] ⋅ p (π)d π ,
Ef =         f                                                                                           (4)

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


        ∫ θ ⋅ E [U (W )] + (1 − θ ) ⋅ E [U (W )] ⋅ p (π)d π
                  π                           π
Eu =              pr                          u                                                          (5)

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.

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.
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
         l
           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 .

 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).

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

(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

 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).

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− 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
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,


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

    The data was kindly provided by Moody’s Investors Service.

                 1 − πi            α                α        
E [U (W )] = max
                                   0 νi + (1 − α0 ) + (1 − α)
                                                             
              α  1− γ              ν
                                    0
                                                      ν
                                                            i
                                               π  α                     
                                            + i  0 νi + (1 − α0 )(1 − α)
                                                                 
                                                                          
                                             1 − γ  ν
                                                                 0
                                                                          

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

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 − πi      α0                        πi
E [U (W )] =
     πi                  + (1 − α )                             1−γ
                                                         (1 − α0 ) ,
                        ν        0 
                                               +                                             (10)
             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 − πi   α                          πi
E [U (W )] = max
     πi                            + (1 − α)
                                                        +
                                                                   (1 − α) ,                   (11)
                         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 .

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

E f = ∑ pi ⋅ E fπi [U (W )] ,                                                                 (12)
       i =1

whereas an uninformative rating policy yields

Eu = ∑ pi ⋅ θ ⋅ E pri [U (W )] + (1 − θ ) ⋅ Euπi [U (W )]
       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

Eim = ∑ pi ⋅ θ ⋅ E pri [U (W )] + (1 − θ ) ⋅ Euπi [U (W )] + p5 ⋅ E fπi [U (W )]
        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

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

                                         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:

                        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

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.

    The results presented obtain under the assumption that short selling is possible; if short sales are impossible,

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).
§      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.

  Fama and French (2002) document mean-reversion in leverage ratios, while the survey of Graham and Harvey
(2001) reveals that firms pursue leverage targets.

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),

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

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.


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Figure 1: Expected utility depending on rating policy and probability θ of being privately
informed (no transaction costs)


                                                                                       Informative ratings
     Expected utility

                                                                                       Imperfectly informative

                                         0   0.01   0.02       0.03    0.04    0.05

Figure 2: Expected utility depending on rating policy and probability θ of being privately
informed (0.2% transaction costs)

           Expected utility

                                                                                        Informative ratings

                                                                                        Imperfectly informative


                                         0   0.01   0.02        0.03    0.04    0.05

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


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