THE PREDICTION OF CORPORATE B O N D RATINGS: T H E C A N A D I A N CASE BARNES & BYNG

The Prediction of Corporate Bond Ratings: The Canadian Case

Tom Barnes Brock University

Tom Byng Union Gas Ltd.

Abstract Statistical models that can be used to assign a bond

rating to a given company are very useful in financial research. Surprisingly, there is no published work in which the prediction of Canadian corporate bond ratings has been considered. This paper is a first step to remedy that situation.

Financial statement variables obtained from samples of industrial companies over three different time intervals are used with the multiple discriminant analysis procedure to predict the ratings of the Canadian Bond Rating Service. The jackknife procedure is used to measure classification accuracy,

Risumi Des modPles statistiques que nous pouvons utiliser

pour attribuer une evaluation de bons a une telle sociPtP sont trPs utiles 2 la recherche financikre. I1 est etonnant de constater qu i’l n ’existe pas d’oeuvres publikes ou l’on traite la prediction des evaluations de bons canadiens. Ce document est la premiPre Ptape vers la resolution de cette situation.

Nous utilisons les variables d’ktats financiers obtenues d’une enquzte de societts industrielles au cours de trois intervalles dfferents, ainsi que le prockdi ctanalyse discriminante multipleo afin de pridire les evaluations de la Sociitk canadienne d’kvaluation du credit. Nous utilisons le procddt! tqackknifen pour determiner la prkcision de la classification.

INTRODUCTION

A bond rating provided by a rating agency measures the risk of default on a bond issue. Both in theory and in practice there is a need for a statistical model which can be used to predict bond ratings. In the investment area predicted ratings are useful to portfolio managers who seek mispriced issues. Ratings are also important to financial managers because they affect the interest that is paid on new debt. If a model can be used to categorize a new issue and its coupon rate then it can be of value to the issuing company, the underwriter and even to the government agency that regulates security distribution. An added dimension that may assume importance is that there are some bonds for which no agency rating exists, i.e. unrated.

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Most important work concerning bond ratings has been done with American corporate issues where the procedure has been to examine the relationship between bond ratings supplied by either Moody’s or Standard and Poor’s and financial statement data that are available on the Compustat Tapes. The first studies used regression, then discriminant analysis, and more recently, probit analysis and logit have been used. Surprisingly, there is no published research where the prediction of Canadian bond ratings has been consi- dered. One reason for this void is that prior to 1972 there was no service that provided bond ratings on a wide spectrum of Canadian bonds (even though selected issues that were of interest to American buyers were rated by both Moody’s and Standard and Poor’s). The Canadian Bond Rating Service (CBRS) in 1972 and the

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T H E PREDICTION OF CORPORATE B O N D RATINGS: THE C A N A D I A N C A S E BARNES & BYNG

Dominion Bond Rating Service (DBRS) in 1976 began to supply ratings on Canadian issues and to provide similar services to those of Moody’s and Standard and Poor’s. These two rating agencies are acknowledged to have had a growing influence on the Canadian bond scene.

The twofold purpose of this research is to provide some insight into the bond rating process in Canada and to suggest a framework that can be used to predict Canadian corporate ratings. There are two reasons why, in this paper, we concentrate on the multiple discriminant analysis (MDA) procedure.’ First, most recent work in the bond rating area has been with MDA. Since this is the initial study of its type involving Canadian bond ratings the direct comparisons that can be made with the previous research will be more valid if the same statistical procedure is used. Second, the main focus of this paper is classification accuracy for which MDA (of all the statistical procedures) is the best. In the future, after this initial research is complete, other techniques will be considered.

Researchers should be aware that there are features of the Canadian corporate bond market that make it distinct from its American counterpart. For example, the smaller average issue size results in a thinner secondary market, there are far fewer outstanding issues, publicly owned utilities are less dominant, there are few issues with an initial maturity greater than 20 years, there is more foreign control of domestic industry, tax laws are different and there is no legal definition of “investment grade”. These market differences, alone, are a sufficient reason to merit this study.

LITERATURE REVIEW

Initially, ordinary least squares (OLS) regression analysis was used to explain the relationship between bond ratings and financial and/ or accounting variables. Horrigan (1966) and West (1970) both developed specific models that were used to predict bond ratings. One major problem never solved in the regression studies dealt with the coding of dependent variable, the bond rating. Both Horrigan and West use a 0 to 9 scale to represent rating class. Kaplan and Urwitz (1979) point out that this presumes an interval scale on bond ratings that is ordinal. This leads to a bias in bond predictions because the range of default risk is not the same within each rating class.

Pinches and Mingo (1973) were the first t o use multiple discriminant analysis (MDA) to classify bonds into rating class. Most of the subsequent works related to bond rating including those of Belkaoui (1980) and Peavy and Edgar ( 1982) have used the M D A procedure because it is particularly suited to this type of problem. Detractors of MDA argue that the important assumption of multivariate normality of the data is rarely met, the ordinal information contained in bond ratings is not

considered, and there are no standard significance tests for the discriminating coefficients.

Kaplan and Urwitz (1979) have suggested an N- chotomous probit model and Ederington (1985) a multinomial logit model as alternative classification techniques to handle the theoretical difficulties just mentioned. Both procedures require less stringent assumptions of the data (than MDA) and they allow fo r hypothesis testing of a models coefficients. Ederington was the first to analyse the comparative performance of these four classification techniques (i.e. OLS regression, MDA, probit and logit). He did not find any one model t o be consistently superior to the other three in terms of predictive capability.

An examination of the previous research in the prediction of bond ratings results in some observations that are worth noting. First, each empirical study is based on a different time period, uses a different sample of bonds and employs a unique set of variables to predict bond ratings. This makes it more difficult to make comparisons and to draw conclusions. Second, the traditional set of financial ratios and accounting variables that were used as explanatory variables in the first studies has not changed much over time. Gentry, Whitford and Newbold (1985) have used funds flow variables but they d o not report superior results. Third, across all statistical procedures moderate success of accurately predicting approximately two out of three bond ratings from a holdout sample is the norm. It is generally concluded that the subjective aspect of the bond rating process can’t entirely be captured by a statistical model, i.e. a rating depends, in part, on the rater’s judgement about the firm’s ability to meet its principal and interest payments.

DATA

Non-overlapping data sets were developed for each of the years 1972, 1978 and 1983. The bonds that were chosen each year were the publicly traded non- subordinated industrial corporates that were rated by the Canadian Bond Rating Service (CBRS) for which financial statement data were available. The use of three separate data sets allows for an examination of two inter- temporal issues; first, the stationarity of the explanatory variables in the best M D A models and second, the consistency of classification success.

The relevant rating classes are A++, A+, A, B++ and B+. Because of a paucity of bonds in the top two rating classes it was decided to combine them and to form one class with the A+ label. This assumes the dispersion matrices in the two former classes are the same. The other prospect of excluding these bonds from the study is rejected. The importance and size of these companies requires they be included. The total number of bonds in each rating class for each of the three data sets is given in Table 1.

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Rating

A+ A B++ B+

BARNES & BYNG

Year 1972 1978 1983

13 13 17 14 17 23 25 27 18 34 37 26

TABLE 1

7 Sample Sizes bv Year I

These small sample sizes were unavoidable. They are the result of the small number of Canadian bonds professionally rated. For instance, in 1978 there were approximately 130 industrial bonds rated by CBRS, before missing data and qualifying under the criteria reduced this number to 94.

Financial statement data for the fiscal year-end are taken from the Canadian file of the Compustat Tapes and from information cards supplied by the Financial Post. This latter source of data was important because some firms that were rated by CBRS were not available on Compustat.

For each data set, specific ratios and accounting numbers were gathered for the most recent year. Also to capture time series information, averages and coefficients of variation using five years of data were used. This list of 27 explanatory variables shown in Table 2 is obtained from Peavy and Edgar (1982) and is a subset of the original group used by Pinches and Mingo (1973). The economic rationale for using these is that they do represent the important groups of ratios and variables that are typically used in this type of analysis. These important groups are size, financial leverage, long term capital intensiveness, return on investment, short term capital intensiveness, earnings stability and interest coverage. They also provide for some continuity across studies.

Many rated companies are subsidiaries of large British and American corporations.. For instance, 18 companies in the 1983 sample were controlled by foreign firms. This raises the possibility that the parent company would act as a guarantor with regards to principal and /o r interest of a specific issue. If this were the case then the financial variables and ratios used in a bond rating model should be those of the parent company. But it happens that no adjustment t o the data was necessary. Although explicit guarantor arrangements are quite common in an industry such as banking, they are almost non existant between industrial companies.*

The samples described above are composed mainly of seasoned issues. The usual procedure is t o use new issues to build a bond rating model because these ratings are supposed to be more accurate.3 However, the usual procedure could not be followed here because of the

small size of the new issue market in Canada. Incidently, the problem is avoided in 1972 because the seasoned issues were all being rated for the first time.

TABLE 2

Financial Variables Variable Class* Size

Financial Leverage

Long Term Capital Intensiveness

Return on Investment

Short Term Capital Intensiveness

Earnings Stability

Debt and Debt Coverage Stabilitj

Variable Name 1. Total Assets 2. Net Working Capital 3. Sales 4. Common Shares Outstanding 5. Total Assets (5 year mean) 6. Net Income (5 year mean)

7. Long Term Debt/Total Assets 8. Common Stock at Market/

9. Long Term Debt/ Net Worth 10. Long Term Debt/Total Assets

1 1 . Common Stock at Market/

12. Sales/Net Worth 13. Sales/Total Assets 14. Sales/Total Assets

(5 year mean)

15. Net Income/ Sales 16. Net Income/Net Worth 17. Net Income/Total Assets 18. Net Income/Total Assets

19. Net Working Capital/Sales 20. Net Worth/Total Assets

Long Term Debt

(5 year mean)

Long Term Debt (5 year mean)

(5 year mean)

21 . Price/ Earnings Ratio 22. Earnings Per Share 23. Net Income/Total Assets

24. Net Income (co. of var.)

25. Net Income Plus Interest/ Interest (5 year mean)

16. Net Income Plus Interest/ Interest (co. of var.)

(co. of var.)

27. Long Term DebtlTotal Assets (co. of var.)

METHODOLOGY

There are a great many unresolved issues that are related to the use of discriminant analysis. For excellent summaries and appropriate references see Pinches (1980)

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and Altman et a1 (198 I ) . This section is a brief description of the methodology used here. 1 . The stepwise method is the statistical procedure we

use to reduce a large set of explanatory variables to a more manageable number. The stepwise MDA programs of both SPSS and BMDP are used because each package has specific options not carried by the other. The F-to-enter was set at a level of 2.0, up from the default level of 1 .O. Another approach initially considered was to develop a specific model that was based on an economic rationale. But, this idea was rejected because there does not exist any normative theory to explain bond ratings. Belkaoui ( I 980) does provide an economic rationale for a set of eight variables before stepwise procedures were used.

2. For proper use of MDA the explanatory variables should be multivariate normally distributed. Usually data sets of the type in this research don’t meet this condition. Two tests were used. The Kolgomorov- Smirnov (KS) goodness-of-fit test was used to measure univariate normality ( .I0 level) and a computer algorithm developed by Mardia and Zemroch (1975) was used to test various data sets for multivariate normality. In order to simplify this explanation, consider only the second (i.e. 1978) data set. On a univariate basis none of the 27 variables were normally distributed. Log and square root transformations were used and in all cases the distributions i m p r ~ v e d . ~ For example, the KS test shows that with 7 of 27 variables the null hypothesis of a normal distribution could not be rejected. Because of these results the variables of all three data sets were arranged with the specific transformations that were best. The importance of these transformations was measured by comparing classification accuracy for each data set, before and after. None of the three original 27 variable data sets (before or after transformations) were multivariate normally distributed; nor were any of the reduced data sets obtained after using the stepwise procedure.

3. There are two reasons why linear as opposed to quadratic classification rules were used. First, linear rules are favored if the covariance matrices of the different groups are from the same population. An F test associated with Box’s M statistic was calculated to determine if the covariance matrices of the four rating groups were equal. For each transformed data set there was a positive probability of this equality. For example, with the 1978 data set the null hypothesis of equality could not be rejected at the .05 level. Second, the relatively small sample sizes support the use of linear MDA (See Pinches 1980,

When the same F statistic was calculated for the approporate untransformed data sets, it was always significant at the .001 level resulting in aclear rejection of the null hypothesis of equal covariance matrices.

p. 443).

4. The a priori probabilities to be used in the MDA model are based on the number of the bonds in each rating class divided by the number in the sample. These probabilities are more realistic than equal probabilities because there is a disproportionate number of bonds in each rating class.

5. The Lachenbruch U or jackknife method is used to classify bonds into rating classes. This procedure holds out one observation, de’velops a model and classifies the holdout observation, sequentially, until all observations are classified.

In summary, stepwise MDA that begins with an initial set of 27 explanatory variables is used to categorize samples of industrial bonds into their respective rating classes. The data is transformed to make it more closely conform to the normal distribution and linear classi- fication rules with sample probabilities are used. But there are a variety of results that are available from the authors not reported in this paper. These unreported results relate to the adding of utility bonds to samples, quadratic classification rules, equal probabilities, replications (where possible) of existing studies and inclusion of omitted variables (i.e. subordination). The number of options, above, relates more to the exploratory nature of this work and certainly not to any expectations of improved performance.

RESULTS

Wilks’ lambda and the multivariate F-test are used to test the overall discriminating power of each model. The null hypothesis that the differences in the group centroids are zero was clearly rejected for each of the final three stepwise models (p < .01).

It has been well established in the literature that success percentages determined by classifying the same bonds that were initially used to develop the models are biased. This upward bias in the estimation sample results in classification tables that are of very little practical value. Therefore, the results that are reported and discussed, below, refer to the jackknife procedure.

Table 3 (a) shows the average classification accuracy and the number of bonds correctly rated for each rating class of each of the transformed data sets. The average percentages from the transformed data sets of 71, 63 and 77 are consistently high and compare favorably with the results reported for American corporates. As with previous studies even these results may be biased downwards because it is naturally assumed in all cases that the agency rating is correct.5 Most of the misclassified bonds are within one rating class of the actual rating.

The effect of transformations on this data can be seen by examining the classification results when the explanatory variables were left in their natural form (Table 3 (b)). On average, the classification accuracy is 15% lower when the data is left untransformed. It would be a convenient solution if these transformations

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THE PREDICTION OF CORPORATE B O N D RATINGS: T H E C A N A D I A N CASE BARNES & BYNG

TABLE 3 (a)

Classification Matrix - Jackknife Procedure Transformed Data

Part A - 1972

TABLE 3 (b)

Classification Matrix - Jackknife Procedure Untransformed Data

Part A - 1972

Predicted Rating Actual Percent Rating Correct A+ A B++ B+

Predicted Rating Actual Percent Rating Correct A+ A B++ B+

A+ 85. 1 1 2 0 0 A 29. 2 4 7 1 B++ 68. 2 2 17 4 B+ 85. 0 0 5 29

A+ 69. 9 0 4 0 A 14. 0 2 7 5 B++ 40. 0 3 10 12 B+ 88. 0 1 3 30

Total 71. 15 8 29 34

Part B - 1978 Predicted Rating

Actual Percent Rating Correct A+ A B++ B+

A+ 62. 8 5 0 0 A 53. 3 9 5 0 B++ 48. 0 5 13 9 B+ 78. 0 0 8 29

Total 59. 9 6 24 47

Part B - 1978 Predicted Rating

Actual Percent Rating Correct A+ A B++ B+

A+ 54. 7 2 2 2 A 12. 3 2 3 9 B++ 4. 1 I 1 24 B+ 89. 0 0 4 33

Total 63. 1 1 19 26 38 Total 46. 11 5 10 68

Part C - 1983 Part C - 1983

Predicted Rating Actual Percent Rating Correct A+ A B++ B+

Predicted Rating Actual Percent Rating Correct A+ A B++ B+

A+ 77. 13 4 0 0 A 65. 3 15 3 2 B++ 78. 0 2 14 2 B+ 89. 0 2 I 23

A+ 65. 11 2 0 4 A 48. 2 1 1 3 7 B++ 50. 0 6 9 3 B+ 81. I 3 1 21

Total 77. 16 23 18 27 Total 62. 14 22 13 35

always led to such improvements in success. Of course, this is not the case and the specific results reported in Table 3 are, in part, due to chance. But, an examination of the complete set of results (available from the authors) does reveal that, generally, there was greater accuracy when transformed data sets were used, ceteris paribus.

Table 4 is the list of variables in the final model of each estimation sample and the order in which they were selected by the stepwise procedure. There is almost a complete change in the variables selected across time, i.e. no one variable is in all three models and only two repeat. A more satisfactory result, however, is that there is some stationarity with regards to variable class. Size, financial leverage and return on investment are represented in each year. One finding similar to that reported in studies with American corporates is the relative unimportance of interest coverage which is included only in 1983 (V25).

One important result was the consistency of the models that were developed from modified versions of the data sets. Holdout groups of 20 bonds were randomly selected from the three data sets (1972 = 1, 1978 = 5, 1983 = 1 ) and in each case they were classified by models developed from the remaining bonds. The final estimation sample models were virtually the same as those reported in Table 4. Since five replications were made with 1978 data we will concentrate on these results. Two of these models had only the same four variables reported in part B of Table 4; the other three models were only slightly different (i.e. having either two or three of the same variables). Incidently, the classification accuracy for the holdout groups was 40%, 50%, 55%, 65% and 70%, respectively for an average of 56%. This compares to 63% for the total sample reported in Table 3(a).

The stepwise procedure leads to a different model in each time period; but, each works well in that period

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T H E PREDICTION OF C O R P O R A T E BOND RATINGS: T H E CANADIAN CASE

.3 - .4 Total

BARNES & BYNG

1 0 0 0 0 0 61 59 65 25 35 19

TABLE 4

The Set of Discriminating Variables

Number 7.

23. 4.

22.

Number 6.

11.

16. 10.

Number 17. 11 .

16. 23.

I . 20. 19. 13. 25.

14.

Part A - 1972 Variable

Long Term Debt/ Total Assets Net Income/Total Assets (co. of var.) Common Shares Outstanding Earnings Per Share

Part B - 1978 Variable

Net Income (5 yr. mean) Common Stock at Market/ Long Term Debt (5 yr. mean) Net Income/Net Worth Long Term Debt/Total Assets ( 5 yr. mean)

Part C - 1983 Variable

Net Income/Total Assets Common Stock at Market/ Long Term Debt (5 yr. mean) Net IncomelNet Worth Net Income/Total Assets (co. of var.) Total Assets Net Worth/Total Assets Net Working Capital/Sales Sales/Total Assets Net Income Plus Interest/ Interest (5 yr. mean) Sales/Total Assets (5 yr. mean)

for which it was developed. This raises two important questions. First, how well does a specific MDA model perform over time? Second, how successful is the MDA procedure if the discriminating variables are held constant and the coefficients are updated through time? The answer to the first question was found by taking the 1972 model and using it to classify the 1978 and then 1983 samples and repeating this experiment with the 1978 model and the 1983 sample. The classification accuracy of the jackknife procedure dropped to 45%, 38% for the 1972 model and to 46% for the 1978 model. These are not surprising results. But they do emphasis the fact that the greater the distance between when a model is estimated and when it is used, the less useful it is. The second question was answered by taking the specific variables of the 1972 set and using direct MDA (with the jackknife procedure) on the 1978 and 1983 samples; similarly the variables obtained in 1978 were used with the 1983 data. The average classification rates were 53%, 50% for the 1972 variables and 68% for the 1978 variables. These results are more variable and contrary to the spirit of those reported by Peavy and Edgar (1982). They had shown that a specific set of six discrimianting variables continued to be capable of replicating bond ratings.

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Kaplan and Urwitz (1979) suggest an analysis of misclassifications to determine how many are “near misses”. The predicted discriminant scores are used to calculate posterior probabilities that a bond will fall into each possible rating class. Misclassifications occur when the predicted rating class (highest posterior probability) differs from the actual rating class. The reliability of a model would be enhanced if high probabilities were associated with correct classifications; similarly, most misclassifications should occur when probabilities are low because this usually means that the specific discriminant score is close to the boundary of another rating group. The results of this type of analysis are presented in Table 5. Most of the probabilities greater than .8 result in correct classifications but the number of exceptions is troublesome. It is hard to come to any conclusions for the incorrectly classified firms because the 1983 distribution is skewed the wrong way. Incidently, Table 5 was further broken down to analyse the posterior probabilities by rating class. One interesting result was that when the posterior probability is greater than .8 for A+ or B+ bonds, classification accuracy was 100 percent (76/76 over the three data sets).

TABLE 5

Distribution of Classification Results Based on Posterior Probabilities

I-- I Correctly I Incorrectly I Classified I

I I 1 3 1 1 0 1 2 1

1 2 1 1 2 1 3 1

There is one final note on misclassifications. There was a tendency for the MDA procedure to misclassify a firm a second time. For example, consider the 1972 data set where the use of the specific model resulted in 25 incorrect ratings. An average of 20 of these firms that were incorrectly rated in 1972 were still in the 78 and 83 samples. Of these 20 firms, 10 were again misclassified in 78 and 4 in 83. One firm was misclassified in the same wrong direction for all three sets.

These findings like those of many previous studies show that the MDA classification effectiveness is fairly

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THE PREDICTION OF C O R P O R A T E B O N D RATINGS: T H E C A N A D I A N C A S E BARNES & BYNG

robust to the assumption of multivariate normality (MVN). But, it may be that there would have been better results if this assumption had been met. Recall that none of the final data sets were MVN. An effort was made to build MVN data sets from the original list of 27 variables. The variables that were univariate normal were combined by trial and error to reveal several 3 and 4 variable sets (nothing larger found) that were MVN. The classification accuracy that resulted from the use of MDA was in all cases disappointing. Our procedure was not exhaustive and neither were any new transfor- mations nor other discriminating variables used. One finding was that these small da ta groupings that were MVN in one period tended to remain so in the next.

CONCLUSION

The methodology and observations of this research should be of value to academic researchers and to practitioners who use bond ratings. In particular, the high classification rates obtained by using the M D A procedure on different transformed da ta sets are impressive.

Intertemporally, the variables in final MDA models are not stationary even though the variables classes are. One consequence of this is that models that are best in one period d o not work as well later. Cross sectionally, there is an essential consistency in the variables of final models when holdout groups are used. These two results place an added importance on the data that are used to develop an MDA rating model. This data must be the most recent and be updated each year.

The multinoniial logit procedure, used by Ederington (1985) to predict bond ratings, should be the next step in this research. It may be that this technique will give some insights into variable selection and answer why final models are sample dependent.

FOOTNOTES

* The ideas and suggestions of L. Keirer, M. Ragab, D. Burnie and P. Vandal1 were important to this research. The data collection assistance provided by Andy Ng and the comments of two anonymous referees were also appreciated.

I The choice of which statistical procedure to use is an issue because each has certain advantages (disadvantages) compared to another. Multiple discriminant analyhis has specific shortcomings (to be mentioned later) but we don’t think they affect the quality of our results.

2 In the absence of formal explicit guarantor arrangements we guess that in some cases there are implicit or informal guarantees between pairs of companies. There are two reasons why we d o not attempt to measure the impact of an informal guarantor. First, t o measure the effect of an informal agreement on a bond rating is difficult in itself, and partly subjective. Second. even though it is casual evidence, bond raters at both CBRS and DBRS have expressed the opinion that “in general, Canadian subsidiaries stand on their own”. There is no evidence to indicate that the ratings of seasoned issues are out of date. On the contrary, CBRS monitor their ratings closely. All issues are reviewed at least once a year and some more frequently as conditions warrant.

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4 For log transformations negative values of any variable were set to + I .OO. For square root transformations, negative signs were reversed, square roots taken and signs reversed back.

5 One advisement for future research is that more effort should be made to build a model that satisfactorily assesses bond risk rather than to deduce one that compares with a bond rating service.

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* Cet article a ttt stlectionni par le professeur Ronald J . Burke This article was selected by Professor Ronald J . Burke.

S E P T E M BR E / S E PTEM BE R I988