Predicting Agency Rating Migrations with Spread Implied Ratings

Jianming Kou Simone Varotto† ISMA Centre

University of Reading, UK ISMA Centre

University of Reading, UK

Abstract

Rating agencies are known to be prudent in their approach to rating revisions, which

results in delayed ratings adjustments. For a large set of eurobonds we derive credit

spread implied ratings and compare them with agency ratings. Our results indicate that

spread implied ratings often anticipate the future movement of agency ratings and hence

could help track credit risk in a more timely manner. This finding has important

implications for risk managers in banks who, under the new Basel 2 regulations, have to

rely more on credit ratings for capital allocation purposes, and for portfolio managers

who face rating-related investment restrictions.

JEL Classification: C20, G11, G23, G33

Keywords: Credit rating, Spread implied rating, Credit risk

† Corresponding author. Address: ISMA Centre, University of Reading, Whiteknights Park, PO Box 242, Reading RG6 6BA, UK. Tel.: +44(0)118 378 6655. Fax: +44(0)118 931 4741. Email: s.varotto@ismacentre.rdg.ac.uk. We are grateful to Frank Skinner for valuable comments. We would also like to thank Jean-Martin Aussant, Emese Lazar and Naoufel El-Bachir for helpful discussions. All errors remain our own.

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1. Introduction

Against the tenets of (semi-strong) market efficiency, researchers have found that

market prices react to credit rating changes. 1 Several studies have also shown that the

market can anticipate credit rating changes. 2 This suggests that market prices can be

employed to predict credit rating movements. In this study, we focus on the period before

the date of a rating change announcement. Through a simple procedure, we convert bond

spreads into “implied ratings” and study the behaviour of the implied ratings in relation to

the bonds’ actual ratings. If bond spreads anticipate agency rating changes, then implied

ratings extracted from bond spreads should exhibit similar predictive properties.

The advantage of using spread implied ratings instead of bond spreads has to do

with ease of interpretation. The under-performance of a bond relative to other bonds with

same rating and maturity may or may not indicate that the bond’s rating is inaccurate, as

bond spreads within the same rating category and same maturity tend to vary

considerably. Therefore, it is important to employ a criterion that can signal when the

under-performance (out-performance) is strong enough as to justify a downgrade

(upgrade).

Moreover, the general public, institutional investors, banks and regulators are

increasingly more used to thinking in terms of ratings when assessing default risk. Hence,

deriving implied ratings from bond spreads has clear practical advantages. As a result,

implied ratings obtained from market instruments (Breger 2003, Cantor et al 2005 and

Kealhofer 2003), accounting information (Cantor et al 2005) or both (Altman and Rijken

2004) have become common in the market place. Regular publications report implied

ratings alongside agency ratings.3

1 Stock price reactions after the announcement of rating revisions are reported in Ederington and Goh (1998), Matolcsy and Lianto (1995) and Holthausen and Leftwich (1986). Bond price reactions are observed by Grier and Katz (1976) and possibly Hite and Warga (1997) as they report abnormal price adjustments in the month of the rating change, but due to the monthly frequency of their data can not determine to what extent the price correction takes place before or after the change. 2 For price anticipation in the stock market see Ederington and Goh (1998) and Matolcsy and Lianto (1995), and in the bond market see Hite and Warga (1997), Weinstein (1977) and Grier and Katz (1976). 3 For example, Moody’s have recently started a monthly publication titled “Market Implied Rating Strategies”.

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As far as we know, this is the first study that (1) investigates the ability of spread

implied ratings to predict the behaviour of the two leading rating agencies’ ratings,

Moody’s and S&P’s (2) that employs a statistically rigorous approach to measure the

significance of the implied ratings’ predictive power and (3) that analyses the convergent

and divergent behaviour of implied ratings and agency ratings before an agency rating

change.

Our findings suggests that (a) spread implied ratings can predict agency ratings up

to six months before the announcement date; (b) that such predictions are statistically

significant for both downgrades and upgrades; this is surprising given that recent studies

commonly find no or mild bond spread anticipation of rating upgrades; (c) that rating

agencies are more likely to act against the market when downgrading, (d) that implied

ratings would help correct for the asymmetry between downward and upward revisions of

agency ratings,4 (e) that the timeliness of Moody’s and S&P’s ratings changes is similar.

The rest of the paper is organised as follows. Section 2 is a review of the relevant

literature. Section 3 describes the data. In Section 4 we explain how spread implied

ratings are derived. Section 5 investigates the lead-lag relationship between spread

implied ratings and agency ratings. Section 6 concludes the paper.

2. Background and literature review

Credit ratings are widely regarded as an important indicator of creditworthiness by

investors in credit markets. They are also an essential input to many credit risk models,

such as the pricing model proposed by Jarrow et al. (1997) and CreditMetricsTM, the

portfolio credit risk model introduced by JP Morgan (see Gupton et al., 1997). Under US

regulation, the ratings of recognised rating agencies (NRSRO5) are used to assess the

value of securities held by securities firms and the amount of capital they must hold.

Many institutional investors, such as pension funds, have restrictions on the proportion of

their holdings that can be allocated to investment grade and speculative grade securities.

4 See for example, Altman and Kao (1992). 5 NRSRO stands for “Nationally Recognized Statistical Rating Organization”. There are four NRSROs in the US. The SEC initially granted this status to Standard & Poor’s, Moody’s and Fitch in 1975. Later on, Dominion Rating Services was also added to the list. See Beaver et al. (2004) for details.

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More recently, the New Basel Accord (see Basel Committee on Banking Supervision

2004) incorporates credit ratings to determine the adequacy of banks’ capital. Finally,

changes in rating have important implications for investors, since they can affect the price

of stocks, bonds and associated derivative securities.

Despite their vast popularity, credit ratings have some weaknesses. One of the

major criticisms often being raised is their “stickiness”, that is their inability to adjust

promptly to changes in risk. For example, when the South-East Asian crisis hit in 1997

rating agencies were under the spotlight for misrepresenting the financial strength of the

countries involved, as sovereign ratings were downgraded only after the onset of the

crisis (Ferri et al., 1999). Several recent high profile corporate defaults also highlight this

problem.

In answer to this criticism, rating agencies argue that their objective is to produce

stable credit ratings. Since rating changes can have substantial economic consequences

for a wide variety of market participants, a rating is altered only when the issuer’s

creditworthiness has changed and the change is unlikely to be reversed in the near future

(see Altman and Rijken, 2004 and 2005). Inevitably, there is a trade-off between

accuracy and stability. And, according to rating agencies, some short-term accuracy, the

so-called “early warning power”, may be sacrificed for stability (see Moody’s, 2003).

Nevertheless, investors need an indicator that can provide a timely assessment of

default risk. Therefore, practitioners have started to look at alternative ways to measure

credit risk. Implied ratings, for instance, have become increasingly popular in the industry.

Implied ratings can be obtained from the market price of various traded instruments.

Moody’s KMV for example, following Merton (1974), produce expected default

frequencies (EDFs) by modelling the equity price of a firm as a call option on the firm’s

assets. The estimated EDF can then be matched to historical default frequencies of

agency ratings to generate stock price-implied ratings. Alternative indicators are bond

spread-implied ratings recently introduced by Barra and Moody’s6. The idea is to derive

implied ratings by mapping individual bond spreads to the prevailing spread levels of

various rating categories.

6 See, Breger et al. 2002, Moody’s 2003, Cantor et al 2005 and Munves and Jiang 2005a,b,c.

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In this work, we derive yield spread implied ratings for a large sample of eurobonds

and study the relationship between spread implied ratings (SIR) and agency ratings

(AR).7 Kealhofer (2003) and Breger et al. (2002) have also looked at the relationship of

agency ratings and market implied measures. However, they limit their analysis to

individual event studies. Munves and Jiang (2005a,b,c), on the other hand, compare

implied ratings with a large sample of Moody’s ratings. This paper differs from Munves

and Jiang’s studies in several respects: (a) we investigate the performance of implied

ratings in relation to Moody’s as well as S&P’s ratings, which allows us to make an

assessment of the relative timeliness of the two major rating agencies, (b) we look at an

11-year sample period which is more than twice as long as in Munves and Jiang and

includes more and diverse credit cycles, (c) we calculate the statistical significance of the

leading behaviour of spread implied ratings, and (d) explore the diverse behaviour of

implied ratings while approaching the announcement of agency rating revisions.

Our findings confirm recent research by Hite and Warga (1997) who report that a

credit rating migration is anticipated by significant bond abnormal returns up to six

months prior to rating downgrades. Similarly, Hull et al. (2004) examine the relationship

between Credit Default Swap (CDS) spreads and Moody’s rating events and find that

changes in CDS spreads tend to anticipate negative rating announcements. However, both

studies do not find convincing evidence that upgrades can be predicted. In contrast, our

study suggests that spread implied ratings also significantly lead agency ratings upgrades.

3. The Data

The data used in this study are 4,183 bond issues (79% of which are eurobonds)

extracted from the Reuters 3,000 Fixed Income Service. The data span 11 years from

January 1988 to March 1998. These bonds are selected using the following criteria: fixed

coupon rate and repaid at par, no option or convertibility features and no sinking fund.

The information contained in the database includes issue date, dated date,8 maturity date,

coupon rate, seniority, currency, industry, daily price history and rating history. The price

7 Throughout the paper the abbreviations SIR and AR will be used for both their singular and plural variants: spread implied rating and spread implied ratings, agency rating and agency ratings. 8 The dated date is the date from which a bond begins to accrue interest.

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data are daily “Reuters composite” bid prices that correspond to the best bid reported at

the close of trading by a market maker from which Reuters have a data feed.

{Graph 1 Graph 2 here}

Eurobonds usually carry high credit ratings.9 Issues rated A and above account for

over 90% of the total. Graph 1 is a plot of the credit rating distribution of issues over the

sample period. The average maturity of these bonds is 6.4 years. As shown in Graph 2,

the majority of the bonds have a maturity between 2 and 10 years, while issues with time

to maturity longer than 10 years only account for 3% of the total.

{Table 1 here}

Eurobonds are typically unsecured instruments. As shown in Table 1, among the

4,183 bonds we used for the analysis, 57.4% are unsecured and 10.2% are senior

unsecured. The dataset consists of bonds denominated in 9 major currencies, among

which 33% are US dollar-denominated. Issuers of these bonds come from 46 countries,

72.7% of them are banks or other financial institutions.

4. Spread implied ratings

The first difficulty that one faces when deriving spread implied ratings is to define

the spread range that identifies each SIR. Once spread boundaries are in place at a

particular point in time, a specific SIR would be assigned to all bonds whose spread is

within the given boundaries at that time. The simplest solution would be to create equal

width spread ranges. So, for example, bonds with a spread from 0 to 45 basis points (b.p.)

would be assigned to the first SIR class, bonds with a spread from 45 to 90 b.p. to the

second and so on. However, this solution would make it difficult to compare AR and SIR

and study their lead-lag relationship because the spread distribution of bonds with a

particular AR varies considerably among rating categories. This is the reason that we take

“typical” AR spread ranges to define SIR ranges. For example, if we observe that over

the last two-months AAA bonds typically have a spread of 0~45 basis points and AA

bonds usually have a spread of 45~75 b.p., any bonds whose spread is less than 45 b.p.

9 High-yield eurobonds started to appear only in the late ‘90s. The first benchmark was issued in 1997 (see Munves 2003).

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could be assigned an implied-rating of AAA, and those with spread between 45 b.p. and

75 b.p. could be given an implied-rating of AA. However, the difficulty with this

approach is that the yield spreads of bonds in different rating categories often overlap.10

For example, single-A issues may trade at a higher spread than BBB issues, and it is not

uncommon for the spread of some junk bonds to be lower than that of investment-grade

issues. To overcome this difficulty, a criterion is needed to set an appropriate boundary

between say, AAA bond spreads and AA bond spreads. Moody’s and Barra use different

methods to deal with this point.11

To estimate spread implied ratings we adopt the method introduced by Barra as

described in Breger et al. (2002). For each rating category, we create a penalty function

that depends on the position of spread boundaries. The penalty value will increase when a

bond’s yield spread is outside the upper or lower boundaries corresponding to its credit

rating (i.e. when the bond’s implied rating is different from its agency rating). The

penalty function for the boundary between any two adjacent rating categories, say A and

BBB, is defined as follows:

( ) ( ) ( )∑ ∑= =

−+−=m

i

n

jBBBjAi sb

nbs

mbP

1 1,, 0,max10,max1

Where refers to the spread of bond i with a single-A agency rating, m is the total

number of bonds currently rated single-A, s refers to the spread of a bond with a

BBB agency rating, n is the total number of bonds currently rated BBB, and b is the

spread boundary between A and BBB. The optimum boundaries will be the ones that

minimize the penalty function for each rating class. Appendix I provides an example of

how this optimisation works.

Ais ,

BBBj ,

After obtaining the optimum spread boundaries, a mapping procedure can be

employed to derive implied ratings. Issues within the estimated spread region for a

certain agency rating will be given an implied rating equal to that agency rating. In other

words, an issue traded at a spread level typical for A-rated issues will have an implied- 10 This overlapping behaviour is documented, for example, in Perraudin and Taylor (2004). 11 To derive bond market implied ratings, Moody’s (2003) use end-of-month bid price and spread data. They relate option-adjusted spreads to option-adjusted durations on a single day for all straight and callable coupon bonds in their sample and derive a pricing “matrix” which maps the median credit spread by rating category to different option adjusted spreads. A table then allows them to infer the bond market’s implied credit rating for any individual bond.

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rating of A, even if its actual agency rating is different. Indeed, often there are

inconsistencies between a bond’s agency rating (which reflects rating agencies’

judgement of risk) and its market price, in which case the implied and agency rating will

differ. This is the case especially in the period immediately before a bond’s rating

migration, when the bond’s spread may already have crossed the boundary of another,

more appropriate, spread implied rating.

4.1 Liquidity, market premium and spread boundaries

A firm’s credit rating varies in relation to the firm’s perceived risk of default. Hence,

when comparing agency ratings and spread implied ratings we need to ensure that

changes in spread implied ratings are only due to default risk fluctuations. However, bond

yields, from which spread implied ratings are calculated, are influenced by default risk as

well as several other factors. As pointed out by Elton et al (2001) bond spreads are the

result of a default premium, a tax premium and a market risk premium. Also, Warga

(1992) , Clare et al (2000), Janosi et al (2002), Perraudin and Taylor (2003), Houweling

et al (2003) and Longstaff et al (2004) show that another important component of bond

spreads is a liquidity premium.

The tax premium in our sample should be negligible since our data almost entirely

consist of bearer securities.12 We control for the effect of systematic changes in market-

wide liquidity and risk premium by allowing spread boundaries to be time varying. For

example, in periods of high market illiquidity spreads become larger and so do our

estimated spread boundaries. Similarly, if investors’ risk aversion decreases, spreads and

our estimated boundaries shrink. As noted by Elton et al (2001) the required

compensation for market risk, which reflects the predominant risk aversion in the market,

is the main factor that determines the risk premium in bond spreads. Therefore, on

average, spreads cross our time varying boundaries not because of market-wide liquidity

12 Eurobonds are usually issued as bearer securities, that is, they are not registered in a way that makes ownership known to national tax authorities. Interest on Eurobonds during the sample period was paid gross, without any deduction of withholding tax by the issuer. And it is up to the recipient to report the income earned to the authorities. See Munves (2004) for a detailed introduction to the Eurobond market.

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or systematic market risk, whose combined influence determines the position of the

boundaries, but because of changes in default risk.

However, for a given level or market wide liquidity the liquidity of individual bonds

may differ. A common indicator of liquidity is the bid-ask spread13. Our database only

includes bid prices which makes the use of the bid-ask spread unfeasible. There is not

agreement in the literature about the relative importance of other liquidity proxies.

However, price frequency appears to be one of the most obvious choices. So, we address

issue-specific liquidity by simply eliminating bonds with infrequent prices. In the next

section, we explain how the data have been pre-processed before being used for our

analysis.

4.2 Data filtering

To obtain SIR, we first calculate the yield spread between corporate and treasury

bonds and then filter out noisy data. To start with, daily yields to maturity for all the

bonds in our sample are extracted from price and cash flow information. Then, we

calculate the yield spread between our corporate bonds and government bonds. Our

approach is the same as that in Diaz and Navarro (2002). For each corporate bond and

each trading day, we create a hypothetical treasury bond that has the same cash flow

structure and maturity date as the corporate bond under consideration. We then price the

hypothetical treasury using treasury zero-coupon curves for the same day. The calculated

price and future cash flows are employed to work out the yield to maturity of the

hypothetical treasury. The yield spread will be the difference in yield to maturity of the

corporate bond and the hypothetical treasury bond. The major advantage of this approach

is that it matches the duration and convexity of our corporates, thereby avoiding the so-

called coupon bias in spread calculation (see Duffee, 1998). The treasury zero-coupon

rates used to price the hypothetical treasuries are obtained from JP Morgan and

Bloomberg. These are rates for nine currencies and maturities from 1 to 30 years. For the

non-integer maturities we use linear interpolation of spot rates.

As is well known, bonds tend to become illiquid when they approach maturity.

13 See, Amihud and Mendelson (1986,1991).

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Therefore, we eliminate prices when the time to maturity is less than one year. In addition,

the following criteria are used to filter out possible errors and outliers. Yield spread

observations are ignored whenever (a) the yield spread is negative, (b) the issue is illiquid,

that is, there is no price within seven days before and after the current date, (c) outliers

occur in the spread time series14 and (d) when we encounter incorrect entries in credit

rating history, that is, the rating changes but reverts back to its previous level within 5

trading days. After the filtering process, we are left with around 3 million spread

observations. In Graph 3, we take a sample of bonds with maturity between 2 to 10 years

from January 1994 to April 1994 and illustrate the distribution of spreads across agency

ratings.

{Graph 3 here}

As one may expect, average spreads increase as credit quality declines. In this

sample, the mean yield spreads for AAA, AA, A, BBB and junk (BB and below) ratings

are 44, 63, 84, 128 and 236 basis points respectively. Unsurprisingly, spreads of lower

rating categories exhibit higher volatility. Another important feature of the data is that

spreads of different rating groups are clearly overlapping. For example, the spread of

some AAA issues are higher than that of BBB issues, and quite a few junk issues trade

with a spread lower than that of investment grade bonds.

4.3 Boundary setting

There are two practical issues related to the choice of boundaries. First, empirical

evidence indicates that market spread levels fluctuate with the business cycle (see, for

example, Van Horne 1998 and Huang and Kong 2003). During times of recession, credit

spreads are expected to increase as firms’ profitability declines and investors become

more risk averse. This pattern is confirmed by our data, as shown in Graph 4. For

example, a 100 b.p. spread is equivalent to AAA rating in 1991, while in 1995 this is

closer to a BBB.

{Graph 4 here}

14 We eliminate large blips in the spread series, that is, one-off deviations from the prevailing spread level by more than 2 standard deviations.

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In Graph 5 we show the term structure of credit spreads.15 As one may expect, the

spread of a 2-year BBB issue can substantially differ from the spread of a 10-year BBB

issue, even though they have the same agency rating. The Graph also allows us to

appreciate how the term structure of credit spreads varies over time. For instance, in June

1992, spreads of BBB and junk issues are strongly downward sloping as maturity

increases, while in April 1997 their slope is positive.

{Graph 5 here}

We estimate spread boundaries by taking these observations into account. For all

available bonds in each trading day, we collect yield spreads over the previous two

months. We then divide the sample into 5 maturity bands, 1 to 2 years, 2 to 3 years, 3 to 5

years, 5 to 10 years, and 10 to 30 years. Within each maturity band, we pool the spread

data into different categories according to their agency ratings. We solve equation (1) to

find the boundaries between adjacent rating categories within each maturity band.16

Finally, from the estimated spread boundaries, spread implied ratings are inferred.

Boundaries are derived daily from January 1989 to April 1998. In Graph 6, we

report the term structure of the boundaries between 1993 and 1998. The term structures of

the boundaries between the four investment grade categories are generally upward

sloping, while the slope of the boundary between BBB and junk often changes sign. From

spread boundaries, we can infer implied ratings. Graph 7 shows typical time series of the

agency rating and spread implied rating that refer to the same bond.

{Graph 6 here}

{Graph 7 here}

In many cases, we observe that the SIR of a bond is persistently different from its

AR. Then, it may be interesting to investigate whether differences between SIR and AR

are random or whether one type of rating systematically anticipates changes in the other.

In the next section, we use our data to test these hypotheses.

15 Studies on the term structure of credit spreads are Longstaff and Schwartz (1995), He et al. (2002), Duffie and Singleton (1999). 16 As we have very few observations for ratings below BBB, the convergence of the optimisation procedure is difficult and very unstable. For this reason, we combine all the categories below BBB together and create a junk category.

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5. Lead-lag relationship between SIR and AR

Having the history of agency ratings for each bond issue in the sample and having

derived the bonds’ spread-implied ratings, we are able to compare the behaviour of the

two types of ratings over time. In a market with perfect information, agency ratings and

spread implied ratings should be consistent with each other. Any inconsistency would

suggest that the market and rating agencies have different opinions about the future

performance of individual firms. To test this, whenever we observe a change in agency

rating, we look at the history of the associated spread implied rating and check whether it

anticipates the agency rating change. For this exercise we transform letter ratings into

numerical values, AAA rated issues are given a value of 1, AA, A and BBB are 2, 3 and 4

respectively and BB and below are assigned a value of 5. For each agency rating change,

we calculate the average difference between the SIR and AR for various time intervals

prior to the AR change and check whether the mean of the average differences is

significantly different from zero. In case of AR downgrades, if the difference is

significantly greater than zero, we can conclude that the SIR leads the agency rating

migration. Similarly, SIR lead agency rating upgrades if the SIR-AR difference is

significantly negative. We do this test when agency ratings change by one category only

(say from AA to A) as changes by two categories or more are rare in our sample. We can

test the significance of the average SIR-AR difference in any sub-sample of our data with

the standard t-statistic σµ n=t , where µ is the sub-sample mean, σ the sub-sample

standard deviation and n denotes the number of sub-sample observations. However, if the

sample size is small, the distribution of the t statistic is not known. To solve the problem,

we use the bootstrap technique described in Hull et al. (2004) which allows us to

determine the empirical distribution of the t-statistic. The null hypothesis of our test is

that the mean of the average SIR-AR difference is zero. For the sub-sample of, say, n

downgrades, we compute SIR-AR average differences , … over a given period,

and their average

1X 2X nX

X , and form a group of n adjusted observations X−X , which by

construction have a zero mean. We then sample n times with replacement from the group

of adjusted observations and calculate the t-statistic of the sample mean. By repeating the

i

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above procedure 20,000 times we can obtain an empirical distribution for the t-statistic

under the null hypothesis that the mean of the average SIR-AR difference is zero. If the t-

statistic for the original (i.e. unadjusted) sample mean exceeds a given quantile of this

empirical distribution, we reject the null hypothesis.

In our dataset, 2,850 bonds have S&P’s rating histories and 4,005 have Moody’s

rating histories. To estimate the spread boundaries we have kept all bonds in our sample,

including multiple issues from the same issuer. This was necessary because distinct

spread boundaries are estimated for different maturity bands, so issues with different

maturity from the same issuer are used for this purpose. However, spread implied ratings

of multiple issues from the same issuer would not be statistically independent. Therefore,

in the remainder of the paper, whenever more than one bond has been issued by the same

obligor we only consider the average numerical agency rating and average numerical

spread implied rating across all the bonds issued by that obligor.

We carry out the analysis using S&P and Moody’s data separately and then test

whether the two sets of results for the two agencies are significantly different from one

another. The results are presented in Table 2.

Table 2 here

The columns in the Table show the average difference between spread implied

ratings and agency ratings during various time intervals prior to the agency rating

adjustment. As we have transformed the letter ratings into numerical values, with higher

values for lower ratings, negative (positive) SIR-AR differences imply that the average

spread implied rating is better (worse) than the agency rating. Panel A of the Table

reports results for the whole Moody’s and S&P’s samples. It is clear from the Table that

agency rating adjustments are anticipated by spread implied ratings. The signs of the

mean difference between SIR and AR are all consistent with a SIR-lead pattern. For AR

upgrades, the mean differences are negative for all time intervals up to 126 trading days

(half a calendar year) prior to the rating event, which means that spread implied ratings

get better than agency ratings well before the AR upgrade. For AR downgrades, the mean

differences between SIR and AR are positive for all time intervals prior to it, which

means that spread implied ratings get worse than agency ratings well ahead of AR

downgrades. For downgrades, the magnitude of SIR-AR mean differences increases

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when the announcement date of the AR adjustment is approaching, which may indicate

that rating agencies feel market pressure and tend to adjust their ratings when market

spreads are clearly out of line with current agency ratings. The same applies to upgrades

but only for the last two months before the AR change. All the above mean differences

are statistically significant at 1% confidence level.

Interestingly, the size of Moody’s SIR-AR differences is always smaller than S&P’s.

Since a SIR-AR difference of zero indicates perfect synchronism between agency ratings

and spread implied ratings, the above suggests that Moody’s rating revisions are more

timely, that is, more in line with market expectations, than S&P’s. We have used a

standard statistic to test if the differences between pairs of results referring to the two

agencies in Table 2 are statistically significant. The statistic is,

( ) SSMMSM NNz 22 σσµµ +−= , where Mµ and Sµ are two of the results in Table 2

from the Moody’s and S&P’s samples respectively, and are the sample standard

deviations and N and are the sample sizes. As before, since we do not know the

distribution of z for small samples we have derived its empirical distribution through a

bootstrapping technique similar to the one just described for the t-statistic. These tests

reveal that Moody’s timeliness is not statistically significantly different from that of

S&P’s.

2Mσ 2

Sσ

M SN

Since many fund managers can only commit part of their holdings to speculative

grade securities, it is also important to look at the agency ratings’ behaviour around the

boundary between investment-grade and speculative-grade. We use the popular definition

of “fallen angels” (issues whose ratings fall from investment grade to speculative-grade)

and “rising stars” (issues whose ratings rise from speculative grade to investment grade)

and examine the relationship between SIR and AR prior to their “rising” or “falling”. As

shown in Panel B of Table 2, the results are qualitatively the same as those in Panel A.

For “rising stars”, the mean differences are negative for all time intervals and are

significant at 1% confidence level. For “fallen angels”, mean differences are significantly

positive for all intervals up to 44 days (2 calendar months) ahead of the AR downgrade,

but are generally not significant. Again, tests of the difference between Moody’s and

S&P’s timeliness show that for rising stars the two agencies’ behaviours are not

14

significantly different. For fallen angels for time intervals above 2 calendar months the

two agencies are significantly different from one another (figures in bold) but the small

number of fallen angel observations and low significance of their SIR-AR differences

does not allow us to draw any firm conclusion.

Overall, the results of our analysis show that SIR can predict the future movements

of AR. The leading effect is highly significant. The results for various intervals show that

SIR can provide early warnings up to six months before an AR change. In addition, it

appears that SIR are able to predict rating agencies’ actions around the boundary between

the investment-grade and speculative-grade, especially for “rising stars”.

5.1. Convergence analysis

The above analysis reveals that SIR provide information about future AR

movements. However, it does not explain how the SIR changes before the AR migration.

Are the two ratings converging or diverging? In fact, we can observe several patterns in

the run up to an agency rating adjustment: (1) SIR leading behaviour, when the AR

moves towards the SIR, (2) Convergence, when the AR and SIR move towards each

other, (3) Divergence, if the AR moves away from the SIR, and (4) AR overreaction that

occurs when the AR and SIR move in the same direction but the AR overshoots.

These patterns can be identified by using a simple regression. For every AR change,

we collect SIR for n consecutive days before the change and estimate the following

model,

tt et b a SIR +⋅+=

where is the numerical value corresponding to the SIR at time t, t indicates time in

days, a and b are two regression parameters and e is the error term. The interaction of

SIR and AR can then be studied by examining the intercept a, the slope coefficient b and

the position of the AR before and after the migration. Appendix II illustrates all possible

interactions. We run this regression for all bond issues whose AR has changed. Our

findings are reported in Table 3 and 4.

SIRt

t

Tables 3 and 4 here

15

The general trend is that SIR leading behaviour becomes increasingly more

prominent while approaching the announcement date. This indicates that rating agencies

respond to market pressure, the higher the pressure, the more likely the rating will move

in the direction indicated by the market. Interestingly, although six months prior to the

announcement date none of the alternative patterns to SIR leading clearly stands out as

the second most important, as time goes by the market appears to polarize around SIR

leading and divergence. Convergence, which occurs when the market and rating agencies

appear to influence each other, subsides as we approach the announcement date. The

implication is that, either agencies follow the market (SIR leading), or they do not

(divergence), but there is not indication that the market follows the agencies. Also the

fact that AR overreaction declines as we get closer to the agency rating change suggests

that agencies, although influenced by the market, are not over-sensitive to its signals and

yield to market pressure only gradually.

Table 4 Panel A shows that in general, differences between results for Moody’s and

S&P’s are not statistically significant. 17 Hence, the timeliness of rating revisions

measured in terms of the ratings’ responsiveness to market indications, is broadly

consistent between the two main rating agencies, which is consistent with the findings in

the previous section.

The results also reveal that the SIR leading behaviour is stronger for upgrades than

for downgrades shortly before the agency rating change. The difference between

upgrades and downgrades when the SIR leads is statistically significant for both agencies

up to two month before the AR rating change. This suggests that rating agencies act more

promptly when downgrading, thus pre-empting, to a degree, the SIR leading behaviour.

Consistently with this pattern, divergence is stronger for downgrades than for upgrades at

short horizons which shows that rating agencies act “against” the market more often

17 To test the statistical significance of the difference between pairs of percentages in Table 3 referring to the two rating agencies for a given SIR behaviour and time horizon we use chi-square statistic with one

degree of freedom defined as ( ) ( )( ) ( ) ( )( )θθθθθθχ ˆ1ˆˆˆ1ˆˆ 2221 −−+−−= SSSMMM NNxNNx

M N where and

are the number of observations in the specific sub-samples considered, N and are the sub-

sample sizes and

Mx

Sx S

( ) ( )SMS NNx +Mx +=θ̂ , see Miller and Miller (2004) for more details. Pairs of percentages that are statistically significantly different at 10% confidence level are reported in bold in Table 4.

16

when their private information indicates bad news.18 The above indirectly confirms the

well known fact that downgrades are more likely than upgrades, which reflects the

tendency of rating agencies to be more prudent when upgrading. It also provides evidence

that such asymmetry in rating revisions may not be consistent with information available

in bond spreads. Hence, spread implied ratings should naturally be shielded against this

asymmetric effect.19

6. Conclusion

We compare the behaviour of spread implied ratings and agency ratings and find

that spread implied ratings are good predictors of agency ratings movements. The pattern

is confirmed for both upgrades and downgrades. We also show that spread-implied

ratings have predicting power for agencies’ actions around the boundary between the

investment and speculative grade, which is useful information for portfolio managers

subject to rating based investment constraints. We find that the two major rating agencies

respond to market pressure in a similar way. The leading effect of spread implied ratings

gathers momentum while approaching the announcement date and rating agencies

respond more quickly when credit quality deteriorates than when it improves. Also,

agencies act “against” the market more often when downgrading.

18 This result is statistically significant for Moody’s two months prior to the rating change and marginally significant (p-value 0.119) one month before the change. For S&P’s the difference in divergence frequencies between downgrade and upgrade supports our conclusion but are not statistically significant. 19 Of course, the frequencies of spread implied rating upgrades and downgrades would still be unequal when, in the observation period, the number and depth of credit cycle troughs and peaks are not perfectly balanced.

17

Appendix I. Optimisation of the penalty function

To illustrate how the penalty function and the optimisation procedure work, we

randomly generate two groups of yield spreads as shown in the following table. One is

AAA yield spreads with mean of 50 b.p. and standard deviation of 30 b.p.. The other is

AA yield spreads with mean of 90 b.p. and standard deviation of 45 b.p.. Each group has

30 observations. The penalty function is calculated using the formula

( ) ( ) (

−+−= ∑ ∑= =

−−−

30

1

30

1,, 0,max0,max

301

i iAAiAAAAAAAAAAAAAiAAAAA sbbsbP )

As shown in the table and graph, by varying the boundary, the value of the penalty

changes accordingly. The optimum boundary between AAA and AA is the point where

the penalty function is minimized, at around 75 b.p..

AAA

spreads AA

spreads Spread

boundary Penalty value Shape of the penalty function

59.86 145.64 5 43.12 112.54 151.44 10 38.67 19.12 154.98 15 34.50 46.97 115.31 20 30.67 5.41 54.44 25 27.32 21.77 104.12 30 24.18 107.98 106.33 35 21.47 23.23 78.89 40 18.84 72.47 92.93 45 16.64 82.99 141.23 50 14.97 99.49 75.92 55 13.67 52.86 106.83 60 12.73 102.95 119.71 65 12.25 47.15 86.58 70 12.08 20.63 90.92 75 11.99 41.93 80.57 80 12.26 38.64 42.31 85 12.98 5.50 92.11 90 14.05 7.73 86.30 95 15.69 63.71 111.59 100 17.85 14.39 92.34 105 20.45 30.02 0.14 110 23.58 10.65 96.72 115 27.11 45.99 29.14 120 30.94 41.95 125.76 125 34.94

18

Appendix II. Implementation of convergence analysis Consider the regression,

tt et b a SIR +⋅+= where SIRt is the time series of spread implied ratings for a period of n days before an AR change, and t denotes time in days (t=1 is the first day of the n-day period before the AR change and t=n is the last day of the period). We can describe how AR and SIR interact with each other by looking at the intercept a and slope coefficient b. We shall illustrate all possible patterns for AR upgrades. Those for AR downgrades can be derived by symmetry. Consider the case when AR is upgraded from AR1 to AR2. In the following graphs, the bold line denotes the movement in AR, the thin line denotes the movement in SIR. When the estimated coefficient b is negative and statistically significant at 5% confidence level, we can identify the following three cases:

ˆ

①

②

③

Case 1. Convergence. . 2ˆˆ ARnba ≥+

Case 2. Convergence with AR overreaction.

21ˆˆ ARnbaAR <+<

Case 3. Divergence. 1

ˆˆ ARnba ≤+

When the estimated coefficient b is not statistically significant at 5% confidence level, the following three patterns emerge:

ˆ

Case 4. SIR leading. 2ˆ ARa ≥

④

⑤

⑥

Case 5. SIR leading with an AR overreaction.

21 ˆ ARaAR << Case 6. Divergence. 1ˆ ARa ≤

Finally, when the estimated coefficient is positive and statistically significant at 5% confidence level, the following three scenarios result:

b̂

19

Case 7. SIR leading. 2

ˆˆ ARnba ≥+

⑦

⑧

⑨

Case 8. SIR leading with an AR overreaction.

21ˆˆ ARnbaAR <+<

Case 9. AR overreaction. 1

ˆˆ ARnba ≤+

In Table 3 and 4 “SIR leading” and “SIR leading with AR overreaction” are combined together. The same applies to “Convergence” and “Convergence with AR overreaction”.

20

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21

Ederington, H. Louis and Jeremy C. Goh (1998) "Bond Rating Agencies and Stock Analysts: Who Knows What When?" Journal of Financial Quantitative Analysis, Vol. 33, No. 4, pp. 569-585. Elton, Edwin J., Martin J. Gruber, Deepak Agrawal and Christopher Mann (2001) “Explaining the Rate of Spread on Corporate Bonds," Journal of Finance, v.56(1,Feb), pp. 247-277. Ericsson, Jan and Olivier Renault (2002) "Liquidity and Credit Risk," SSRN working paper. Ferri, G., L. Liu, and J. E. Stiglitz (1999) “The Procyclical Role of Rating Agencies: Evidence from the East Asian Crisis,” Economic Notes 28, no. 3, pp. 335–355. Grier, Paul and Steven Katz (1976) “The Differential Effects of Bond Rating Changes Among Industrial and Public Utility Bonds by Maturity,” Journal of Business, v.49(2), pp. 226-239. Gupton, G.M., C.C. Finger and M. Bhatia (1997) “CreditMetricsTM – Technical Document,” JP Morgan. He, Jia., Wenwei Hu and Larry H. P. Lang (2000) “Credit Spread Curves and Credit Ratings,” Working paper, Chinese University of Hong Kong. Hite, Gailen and Arthur Warga (1997) "The Effect of Bond-Rating Changes on Bond Price Performance", Financial Analysts Journal, May/June, pp. 35-51. Holthausen, R. and R. Leftwich (1986) "The Effect of Bond Rating Changes on Common Stock Prices", Journal of Financial Economics, 17, pp. 57-89. Houweling, Patrick, Albert Mentink and Ton Vorst (2003) “How to Measure Corporate Bond Liquidity" Tinbergen Institute Discussion Papers 03-030/2, Tinbergen Institute. Huang, Jingzhi and Weipeng Kong (2003) “Explaining Credit Spread Changes: Some New Evidence from Option-Adjusted Spreads of Bond Indexes,” Penn State University working paper. Hull, J., Predescu, M., and White, A. (2004) "The Relationship between Credit Default Swap Spreads, Bond Yields, and Credit Rating Announcements," Journal of Banking and Finance 28, pp. 2789-2811. Janosi, T., R. Jarrow and Y. Yildirim (2002) “Estimating Expected Losses and Liquidity Discounts Implicit in Debt Prices,” Journal of Risk, 5(1), pp. 1-39.

22

Jarrow, Robert A., David Lando and Stuart M. Turnbull (1997) “A Markov Model for the Term Structure of Credit Risk Spreads,” The Review of Financial Studies, Vol. 10, No. 2, pp. 481-523. Jarrow, Robert (2001) "Default Parameter Estimation Using Market Prices," Financial Analysts Journal, v.57(5,Sep/Oct), pp. 75-92. Kealhofer, S. (2003) “Quantifying Credit Risk I: Default Prediction,” Financial Analysts Journal, January/February, pp. 30-44. Longstaff, Francis A. and E.S. Schwartz (1995) “A Simple Approach to Valuing Risky Fixed and Floating Rate Debt,” Journal of Finance, 50, pp. 789-819 Longstaff, Francis A., Sanjay Mithal and Eric Neis (2004) “Corporate Yield Spreads: Default Risk or Liquidity? New Evidence from the Credit Default Swap Market,” UCLA working paper. Matolcsy, Z. P. and T. Lianto (1995) "The Incremental Information Content of Bond Rating Revisions: The Australian Evidence." Journal of Banking and Finance, 19, pp. 891-902 Merton, Robert C. (1974) “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,” Journal of Finance 29, pp. 449-470 Miller, Irwin and Marylees Miller (2004) “John E. Freund’s Mathematical Statistics with Applications, seventh edition”, Pearson Education International. Moody’s (2003) “Measuring The Performance of Corporate Bond Ratings.” Moody’s Investor Service, April. Munves, David (2004) “The Eurobond Market," in The Handbook of European Fixed Income Securities, edited by Frank J. Fabozzi and Moorad Choudhry, Chapter 6, Wiley. Munves, David and Shi Jiang (2005a) “Closing the Gap: Issuers’ Moody’s Ratings and their Bond Market Levels,” Market Implied Rating Strategies, March, Moody’s Investors Service. Munves, David and Shi Jiang (2005b) “Credit Default Swap- and Bond-Implied Ratings Compared; An Opportunity Analysis,” Market Implied Rating Strategies, April, Moody’s Investors Service. Munves, David and Shi Jiang (2005c) “Sharpening the Signals from Market Implied Ratings,” Market Implied Rating Strategies, May , Moody’s Investors Service. Perraudin, William and Alex P. Taylor (2003) “Liquidity and Bond Market Spreads,” SSRN working paper.

23

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24

Table 1. Summary statistics of the bond data

Panel A. Seniority of bond issues

Seniority type No. % Unsecured 2399 57.4 Guaranteed 1021 24.4

Senior unsecured 425 10.2 Other 338 8.1

Panel B. Currency of bond issues Currency No. % Currency No. % US Dollar 1390 33.2 French Franc 305 7.3

German Mark 463 11.1 Japanese Yen 276 6.6 Canadian Dollar 456 10.9 Australian Dollar 274 6.6

Swiss Franc 418 10.0 Netherlands Guilder 210 5.0 UK Pound 391 9.3

Panel C. Domicile of bond issues Country No. % Country No. %

United States 1020 24.4 Australia 241 5.8 Netherlands 504 12.0 Canada 213 5.1 France 429 10.3 Netherlands Antilles 164 3.9 United Kingdom 348 8.3 Austria 98 2.3 Japan 314 7.5 Cayman Islands 65 1.6 Germany 290 6.9 Other 497 11.9

Panel D. Industry classification of bond issues Industry No. % Industry No. %

Financial Services 1671 39.9 Business & Public Services 66 1.6 Banking 1367 32.7 Beverages & Tobacco 59 1.4 Utilities, Electrical & Gas 217 5.2 Merchandising 48 1.1 Energy Sources 105 2.5 Food & Household Products 43 1.0 Telecommunications 103 2.5 Wholesale & International Trade 37 0.9 Transportation, Road & Rail 75 1.8 Other 392 9.4

25

Table 2. Mean differences between SIR and AR prior to an AR change

Panel A. Whole sample Time intervals before AR change (days) N [-1,-22] [-23,-44] [-45,-66] [-67,-126]

Moody's downgrades 0.60** 0.50** 0.47** 0.38** 247 S&P's downgrades 0.66** 0.58** 0.54** 0.40** 129 Moody's upgrades -0.61** -0.59** -0.60** -0.54** 95 S&P's upgrades -0.79** -0.75** -0.60** -0.62** 55 Panel B. Rating changes around the BB-BBB boundary Moody's rising stars -0.86** -0.76** -0.64** -0.46** 18 S&P's rising stars -1.04** -1.11** -0.90** -0.76** 12 Moody's fallen angels 0.11 0.05 -0.25 -0.38 13 S&P's fallen angels 0.71 0.79* 0.75* 0.55 9

Notes: 1. The time intervals denote the various periods (in trading days) before an agency rating change. For

example, [-23, -44] refers to the period from 44 days before the agency rating change to 23 days before the agency rating change.

2. In the main body of the table are the mean difference between SIR and AR for different time intervals prior to an AR change, negative values mean that SIR are better than AR, and positive values mean that SIR are worse than AR.

3. “*” indicates that the SIR-AR difference is significant at 5% confidence level, “**” indicates significance at 1% confidence level.

4. N is the number of AR changes. 5. Results that are statistically significantly different between the two rating agencies at 10%

confidence level are indicated in bold.

26

Table 3. Convergence Analysis

Panel A. Downgrades Moody's (N = 247) [-1,-22] [-23,-44] [-45,-66] [-67,-126]Convergence 8.1 12.6 13.4 19.8 Divergence 24.7 26.3 19.4 15.0 SIR leading 64.8 53.8 51.0 47.0 AR overreaction 2.4 7.3 16.2 18.2 S&P's (N = 129) Convergence 9.3 7.8 9.3 18.6 Divergence 26.4 25.6 17.8 16.3 SIR leading 62.8 55.8 58.9 46.5 AR overreaction 1.6 10.9 14.0 18.6 Panel B. Upgrades Moody's (N = 95) Convergence 7.4 10.5 7.4 18.9 Divergence 16.8 16.8 16.8 12.6 SIR leading 74.7 70.5 74.7 65.3 AR overreaction 1.1 2.1 1.1 3.2 S&P's (N = 55) Convergence 5.5 9.1 10.9 21.8 Divergence 16.4 20.0 23.6 23.6 SIR leading 76.4 69.1 61.8 50.9 AR overreaction 1.8 1.8 3.6 3.6

Note: The table reports the behaviour of the SIR before an AR revision. We have a SIR leading pattern when the AR migrates towards the current estimated SIR level. Convergence occurs when the two ratings move towards each other. We have divergence when the AR moves away from the SIR. Finally, the AR overreacts when both ratings move in the same direction but the AR jumps away from the current estimated SIR level. For a graphical illustration of all the cases we refer the reader to Appendix II. N is the number of AR changes.

27

Table 4. Convergence Analysis Tests

Panel A. Moody's - S&P's differences

Downgrades [-1,-22] [-23,-44] [-45,-66] [-67,-126]

Convergence 0.691 0.156 0.250 0.774 Divergence 0.725 0.878 0.706 0.741 SIR leading 0.703 0.716 0.145 0.934 AR overreaction 0.575 0.240 0.568 0.927

Upgrades Convergence 0.651 0.778 0.458 0.672 Divergence 0.940 0.628 0.310 0.081 SIR leading 0.824 0.853 0.096 0.084 AR overreaction 0.694 0.904 0.276 0.875 Panel B. Downgrades - Upgrades differences

Moody’s Convergence 0.823 0.606 0.122 0.853 Divergence 0.119 0.065 0.582 0.579 SIR leading 0.078 0.005 0.000 0.002 AR overreaction 0.421 0.067 0.000 0.000

S&P's Convergence 0.383 0.761 0.737 0.615 Divergence 0.143 0.416 0.363 0.239 SIR leading 0.073 0.093 0.713 0.585 AR overreaction 0.896 0.040 0.040 0.008

Note: The table reports the p-values of a test for the hypothesis that the difference between pairs of percentages reported in Table 3 is statistically significant at 10% confidence level. Statistically significant differences are in bold font. The test statistic is a chi-square with one degree of freedom defined as

( ) ( )( ) ( ) ( )( )θθθθθθχ ˆ1ˆˆˆ1ˆˆ 2221 −−+−−= SSSMMM NNxNNx

( ) ( )

where and are the number of agency rating changes in the specific sub-samples considered, N and are the sub-sample sizes and

Mx

SNSx

M

SMSM NNxx ++=θ̂ .

28

Graph 1. Bond sample breakdown by agency rating

29

Graph 2. Bond sample breakdown by maturity

30

Graph 3. Distribution of yield spreads for different agency ratings

Graph 4. Time series of median spread by agency rating

31

Graph 5. Term structure of median yield spread by rating

32

Graph 6. Term structure of spread boundaries, 1993-1998

Panel A. Boundaries shown separately

Panel B. All boundaries

33

Graph 7. Yield spreads, spread implied rating and agency rating histories

Note: In the scale for rating, 1 stands for AAA, 2 for AA, 3 for A, 4 for BBB, and 5 for BB and below.

34