Journal of Monetary Economics 1 (1975) 309-325. Q North-Holland Publishir g Company

CYCLICAL VARIATIONS IN THE RISK STRUCTURE OF INTEREST RATES

Dwight M. JAFFEE”

Pritrcetow Utticersity, Princeton, N.J. 08540, IJ.S.A.

1. Introduction

The risk structure of interest rates may be defined as the interest rate differen- tials that exist between securities that are identical in all relevant aspects except for the likelihood of default on the pa,yment of interest or principal. The risk structure of interest rates is thus directly analogous to the term structure of interest rates, in which term to maturity is the differentiating characteristic. In particular, macroeconomic results on the risk structure of interest rates, like term structure relationships, have a wide range of applications, as illustrated below. To date, however, most studies on the risk structure have been primarily concerned with explainin, 0 the risk of individual firms and bond issues on a microeconomic basis.l The present effort builds on these previous studies in terms .>f making use of risk category aggregates, and then investigates the cyclical variations in the interest rate differentials (hereafter, risk spreac~~) between the various risk categories.2

The study consists of three main parts. In section 2, we face immediately the key problem with risk structure work, namely that the distinguishing character- istic - risk - is not directly and objectively measurable. This situation contrasts strongly, for example, with term structure work, where the distinguishing feature - term to maturity - is explicit and well-defined. Our solution to this risk structure problem is to make use of the available bond ratings in the United States3 - in particular Moody’s AAA to BAA ratings - and the associated

*Associate Professor, ECollomics Depa~ tmwt, Princeton University. The present study is a revised and shortened version of An Empirical Study of the Risk Stnccturi :)f Interest Rates, [see Jaffee (197311. Financial support for the project has been provided by the American Life Insurance Association through the Financial Research Center of Princeton University.

‘For cx,rmplcs, see Fisher (1959), Johnson (1967), Sloane (1963). a11J tlw survey of Coh‘m (1973). Also. Mcrton (1974) provides a unique attempt to develop a ri$~rous theoretical fwndation for the risk structure.

‘An aggregate orientation is also present in Silvers .,1’)73) Silvc~s, in fact, does discuss the variation in risk spreads over time, but his emphasis is on the measurement rather than the explanation of the variations.

3Pogue and Soldofsky (1969) and !hcir cited references provide a survey description of thtic rating :.ystems.

310 D.M. Jaffie, Risk structure of inretest rates

aggregate risk spread indexes. We assume that Moady’s classifications are accurate in the sense that that at any moment in time they accurately separate bonds into diRerentia1 risk categories. We do not assume, however, that the risk associated with any given category remains constant over the business cycle. Indeed, as developed in section 2, a main point of the study concerns the extent to which cyclical variations in Moody’s risk spread indexes can be attributed simply to cyclical variations in the risk associated with the specific risk categories.

In section 3, we consider more fundamental explanations for the cyclical variations in risk spreads. The dimensions of the problem are illustr.lted in table I. which shows the risk spread and the standard deviation of the risk spread between BAA and AAA bonds for various issuer groups. The mear Eexrel of the risk spread is relatively large, ranging between approximately 50 r,n,S 75 basis points dependin g on the issuer group. We find these large magnitudes quite surprising given that there has been only a single default - Penn-Central - of bonds rated BAA and higher in the postwar period. These magnitudes, of course, could still be ths direct result of high risk aversion and continuir g es ante anticipation of default. Alternatiliely, regulated and institutional invcrstors may find highly rated bonds a simple way of protecting themselves agains!. claims of ‘imprudent’ investment policies. Also, along similar lines, highly r.lted bonds may be more attractive investments, since they tend to b’s large issues \vith thick secondary markets. In any case, it is beyond the scope or the present study. and particularly of the methods used, to explain the levels oft ne risk spreads.

Instead, the material of section 3 is basically conl:er:lcd with explaining the cyclical variations of the risk spreads, the magnitude:: of’ which are indicated by the standard deviations of table 1. Three theories for *he cyclical variations arc considered in analogy with term struaure theory: seginentation, pcricct sub- stitutes, and habitat. Under the segmentation theory, lhe market for each risk category is isolated: and thus each risk spread is determined by its own exo- genous factors crf demand and supply. Under the perfect substitutes theory, in cor,trast, given some appropriate risk premium, the risk spreads should be ccnstant, and, in particular, independent of demand and sui~ply factors. Finally, the habitat theory is essentially eclectic and wouId alla\v elements of both segmentation and perfect substitutes.4 Regression lests of the model dc~clop~d in section 3 indicate essentially a perfect substitutes characicr for risk catcgorics.

In section 4, we conclude the study w811 discussion of an applic;ltion of the results and an outline of possible topics for further study. The applic:ltion con- cerns the Penn-Central default, for which we are able to indicate the magnitudes and time-phasing of changes in risk spreads due to the default. The topics for further study include the implications of the risk structure for the operation of monetary policy and for the time-phasing of rational investment strategies. It should also be noted that the present study is necessarily specific to the United

4See FLlalb.iel (19~56), and Modgliani and Sutch (1966. 19671, for further discusskn of thex theoric\ in ;i tc: m structure context.

D.M. Jaffee, Risk structure of interest mres 311

States because of the existence of the bond ratings as well as other features of the capital markets. Some implications of risk structure for monetary policy in the context of Western European capital markets are outlined, however, in section 4.

Table 1

The level and variability of risk spreads. - --.- -.--. _

Total corporates Industrials fJtilities Rails

- _~ .._-.. _ _._ _. .- ..- ----- --_ -

Mean of BAA 5.15 5.12 3.02 5.31 Mean of AAA 4.50 4.41 4.55 4.61 Mean spread: BAA-AAA 0.65 0.71 0.48 0.70 Standard deviation

of spread 0.18 0.21 0.16 0.36 ~. _ _.~___ __ ___ ..-

Sortrce.~ Moody’s Investor’s Service. Snny~le: 1954 to 1969, quarterly observations.

hlunicipals ._

4.05 3.29 0.76

0.93

2. Cycilical variations in Moody’s risk categories

2. I. Buckgrourtd

The basic data used in the regression analysis of this study are the interest rate time series tabulated by Moody’s Investor’s Services for the bond issues of categories of corporate and municipal issuers. The time series are particularly useful because they are available for each of Moody’s risk rating categories BAA to AA.4, and because they are reasonably consistent over time. There has been continuing concern over these data, however, on the grounds that it has not been clear uhnt is being measured by the ratings.’ Recently though, this problem appears to have been clarified. On a general level, the previous studies cited in footnote 1 have verilied that there is a strong correlation between the quality of a firm, 3s measured by various income and balance sheet variables, and the risk premium its debt issues must provide. This would suggest, therefore, that it is plausible that a rating service could usefully summarize the riskiness of a firm’s debt Lsuc in terms of a single grade. Then, more concretely, a series of studies h;ive provided evidence that Moody’s ratings, in particular, do correlate at a I@ level ivith similar income and balance sheet variables.6 Moreover, although the correlations of course are not perfect, these authors do not rule out the possibility that Moody’s may have taken into account other reasonable data,

-‘There has also been concern \vith the technical and statistical properties of the time series interest rate indexes. These issues are diy.:usscd in Jaffee (1973, especially pp. 4-6).

?jee Hickman (1958), Katz (1973), Pinches and Mingo (1973), and Pogue and Soldofsky (1969).

312 D.M. Jaffee, Rid stnrcture of irfferest rules

albeit on a quali:ative basis. It thus seems fair to assume that any moment in time ~oody’s ratings do contain useful information on the riskiness of the cross sec- tion of issuing firms.

A second, and less easily solved problem, concerns whether the amount of risk associated with a particular rating class, say BAA, remains constant over time. Cohan (1973), in particular, has stressed that the relative infrequency of changes in ratings for a particular company jindicates that the risk associated with a given rating must vary over the business cycle. In other words, a firm’s risk is pre- sumably varying over the business cycle, while its rating is fixed, and therefore the risk associated with the rating must be changing.

Moreover, as a hypothesis, there may be systematic variations in the relative risk of rating classes in comparison with one another. At one extreme, for example, one might expect BAA bond quality to deteriorate significantly during business cycle recessions. While, at the other extreme, the top quality A/IA bonds might be truly risk-free regardless of the business cycle phase. The effect, there- fore, would be for the relative riskiness of BAA bonds to rise in recessions and to fall in booms. Or, translated into risk spreads between BAA and AAA bonds, one would expect the BAA-AAA different’al (which is positive) to gt ?w larger in recessions and to shrink back in booms. And more generally, this sane effect would occur for the risk spreads, BAA-AAA and BAA-A, though in a smaller absolute amount.

It should be stressed that these changes in risk spreads are not th,? result of economic behavior in the sense either of changing risk aversion by individuals or of a changing flow of funds to different investors over the business cycle. Rather, the changes are a technical feature resulting from the f;rct that Moody”s does not adjust its ratings for short-run business cycle developments. Still, the magnitude of the variations could be large, and thus it is necessar)? to purge the ;isk spread indexes of these effects before turning to ahe more behavr(aral material of section

2.2. Empisical tests

To proceed, therefore, we first need a set of variables that will proxy as in- dicators of the level of confidence m economic activity and of the position of the economy in the business cycle. The following variables, with a self-evident rationale as cyclical measures, were used :

JlOOD A measure of consumer sentiment tabulated by Professor Ray C. Fair (1971) based on data collected by the University of Michigan Survey Research Center;

u The unemployment rate, Bureau of Labor Statistics; G,:( The growth rate of retained earnings of corporations, National Income

Accounts (NLA);

D.M. Jaffce, Risk strnctwe of iufrrcst rates 313

GI The growth rate of fixed capital investment, NIA ; GP The growth rate oi’the output price 1$ex, NIA ; BAA Interest rate on Moody’s BAA rated hondj of indicated issuer.

The use of these variables presumes that the risk of firms generally moves in a contracyclical fashion (i.e., risk is high in recessions). The specific timing of risk variations, however, is more difficult to set. For example, it appears in many cases that the financial position of firms begins to deteriorate in the final phases of the boom, even though employment and output continue at high levels. It is for this reason, in fact, that we specify CR in the equation. And more generally, we have included a number of cyclical variables so that a variety of timing patterns would be covered by the specification.’

The test then consists, for each risk spread, of regressing the risk spread LLgainst a constant to account for the average level, and against the list of business cycle variables to account for the c]c!ical variations. In each case t!le dependent variable is the risk spread between the BAA rate and one of the three higher quality rates (A, AA, and AAA). The tests were done separately for Moody’s total corporate category, and for each of its three subdivisions - industrials, utilities, and rails. Thus, in itiLl, iweive regressions are involved. In addition, similar results for municipal bonds are reported below.

The tests were carried out on a quarterly time series basis with a sample beginning in 1954-I (the .irst quarter of 1954) and ending in 1969-4. The beginning point was chosen to avoid t!le unusual capitai market conditions following World War II and the Korean War. The end point was made necessary by the Penn-Central default, which occurred in late June of 1970. Preliminary testing indicated that the risk differentials were dramatically increased upon the Penn-Central default, and that the return to more normal difYerentia!s then occurred very slowly. While it would have been possible to attempt to ‘dummy out’ this period, a safer and more interesting approach is to end the estimation sample at this point; below, we extrapolate the estimated equations through the Penn-Central period to obtain direc,t estimates of the eirect of the default.

The results of these tests are presented in table 2. Sets of equations correspond- ing to the three risk spreads are shown for each of the four corporate issuer categories. It is useful to focus first on the total corporate sector, since these equations illustrate the mail1 points and the other sets all have the same basic form. The first three variables in the equations - nlOQD (consumer sentiment), GR (grov.th of retained earnings) and GZ (gro\cth of investmel:t) - all have negative 4gns. This is correct since these variables corrclale with optimism or peaks in business activity, and therefore ullelk they are high, risk spreads should

‘Tests were also carried out with a number of other cyclicnl rnxrocconornic variables. 4 nl:ljnr problem, of course, was the multicollinearit~ of the variables. The omittcct variables were statistic:~ll~ signifknt by thcnxelves, but not significn;lt ~vhen testccl together \vlth the abow list.

ISSu

cr/c

icpe

l~~l

clll

\~3r

iab

lc”

~iw

pcw

rrti

otr

s

BA

A-A

AA

BA

A-A

A

BA

A-A

Itlc

lust

riu

ls

BA

A-A

A.4

BA

A

-AA

BA

A--

A

Uii

liti

rs

BA

A-A

A

A

BA

A-A

A

BA

A-A

Rai

ls

BA

A-A

4A

BA

A-A

A

BA

A-A

-.

-.

_ In

dcpc

nden

t va

riabl

es”

-_

- -..

-

.----.

_-

..- -

- -

---

-___

__

_--.-

-- -

.- Su

mm

ary

StiL

tiSt

ic‘S

cuus

tall

t G

i V

G

P

BA

A

U.W

. S.

E.

- _

. ._

A

lOO

l) C

R

1.88

-0

.17

- 0.

34

- 0.

95

0.31

0.

79

0.03

1.

21

0.09

(5

.X)

(6.1

) (3

.2)

(2.3

) (1

.7)

(1.5

) (2

.4)

1.43

-0

.13

- 0.

25

- 0.

68

0.44

I .

32

0.01

1.

14

0.08

(5

.0)

(5.6

) (3

.0)

(1.8

) (2

.7)

(2.9

) (1

.1)

I.18

-

0.09

-

0.20

-0

.50

0.15

0.

76

-0.0

01

1.36

0.

06

(5.5

) (5

.2)

(2.9

) (2

.0)

(1.2

) (2

.2)

(0.5

0)

I .43

-0

.14

- 0.

55

- 1.

12

0.68

1.

17

1.48

0.

13

(3.7

) (3

.7)

(3.7

) 0.

0)

(2.7

) (1

.6)

(Y::

0.78

-

0.08

-0

.52

-0.9

5 0.

67

1.40

0.

05

1.12

0.

12

(1.9

) (2

.4)

(3.X

) (1

.8)

(2.8

) (2

.1)

(2.8

) 0.

65

- 0.

06

- 0.

43

- 0.

96

1.25

0.

02

0.98

0.

10

(1.8

) (2

.0)

(3.5

) (2

.1)

,::a;

(2

.1)

(1.4

)

2.18

-0

.18

0.00

1 -0

.56

- 0.

43

-0.1

3 0.

05

1.58

G

.08

(7.9

) (7

.9)

(0.0

3)

(1.6

) (2

.7)

(0.2

9)

(4.5

) 1.

87

-0.1

~ -

0.00

1 0.

31

-0.3

5 -0

.19

0.02

1.

83

0.07

(7

.4)

(7.0

) (O

M)

(1.3

) (2

.4)

(0.4

6)

(2.1

) I .

05

- 0.

06

C!.

c)h

-0.3

1 -

0.53

-0

.81

0.02

1.

55

0.08

(3

.9)

(2.8

) (0

.66)

(0

.94)

(3

.5)

(1.9

) (1

.7)

0.73

-

0.08

-

0.72

-1

50

-

0.09

-

0.05

1.

24

0.24

(0

.86)

(1

.1)

(2.5

) (1

.4)

Z)

(0.0

6)

(1.4

) 1.

53

-0.1

6 -0

.31

- 0.

60

1.06

2.

24

-0.0

01

0.85

0.

14

(3.2

1 (4

.1)

(1.9

) tiL

9s;

(3 S

) (2

.9)

(0.2

4)

1.72

-0

.16

- 0.

27

- 0.

32

0.55

1.

60

- 0.

04

0.82

0.

13

(3.9

) (4

.2)

(1.8

) (0

.57)

(2

.2)

(2.2

) (1

.9)

aOrd

inar

y le

ast

squa

rese

stim

ates

fo

r th

e sa

mpl

e 19

54-I

to

19

69-4

; t-

qtat

istic

s ar

c sh

own

in p

aren

thes

es.

bBA

A-A

AA

in

dica

tes

the

risk

spr

ead

betw

een

BA

A

and

AA

A

secu

ritie

s of

the

ind

icat

ed

issu

er

cate

gory

, an

d si

mila

rly

for

A a

nd

AA

. ‘D

efin

ition

of

the

qsc s

ymbo

ls

is g

iven

ab

ove

in t

ext.

C’o

rpor

atc

rcgr

cssi

on

resu

lts:

Con

fide

nce

and

busi

ness

cy

cle

vari

able

s.”

R’

0.75

0.72

0.60

0.61

0.50

D.M. Jaffee, Risk structure of interest rates 31.5

be low. The next two variables - U (unemployment rate) and GP (growth of prices) - have positive signs. Since both these variables correlate with low levels of business activity or uncertainty, as they rise spreads should rise, and thus the positive signs are correct here. The last variable (&IA) (the BAA bond rate) is included to test for any Ze~el of interest rate effects on the structure of interest rates. It can be seen that the estimated coefficients for &I,4 are very small, indicating that a 100 basis point change in the level of rates will change spreads by at most 3 basis points.

Another interesting feature of the results is that the size of coefficients, the significance (as measured by the T-statistics), and the goodness of fit (as measured by the I?‘) all tend to fall as one moves from the BAA-AAA equation through to the BAA-A equation. This is reasonable since the absolute risk differentials fall as we move in this direction, and thus one would anticipate that the power of an explanation based on tt.e same independent variables should also fall.

Special note should be taken of the importance of the MOOD variable. 46000 is by far the most significant variable fn almost all the regression equations shown. This is interesting because the same MOOD variable has an important role in other recent studies of financial and consumption markets. Fair (1971), for one, finds that the MOOD variable is the single most important determinant of consumption expenditures in his forecasting model. Modigliani (1971), on the other hand, has found that A4000 has a smaller effect than stock market profits on consumption expenditures, and, in the Federal Reserve-M.I.T. econometric model, the stock market profits rather than MOOD are used as the driving variable for consumption expenditures. Modigliani’s argument is that the stock market influences MOOD and that a relationship between consumption and lzZOOD is only the result of this more basic correspondence. Without entering in:o the details of this discussion, howelTer, it is clear that the three variables - MOOD, stock market level, and consumption - are all closely interrelated variables. and the main issue is the direction of causation between expectational variables and expenditure decisions.

These studies kvith MOOD are important in the present context for two reasons. First, the studies provide confirmation that the expectational content of MOOD is of ;i useful form, making our significant results with regard to risk structure more compelling. Second, an implication of the studies is that MOOD can be cxpl:lincd as a function of other economic variables. This is important if the equations for rclte sprc;lds are to be used to forecast into future periods.

Only brief comments are now necessary with regard to the results of table 2 for the three components of the corporate sector - industrials, utilities, and rails. Overall, it can be seen that the significance: of the results and, in particular, the strong negative effect of AfOOD is apparent in almost every cast. tine exception, howe\(er, should be noted. For utilities, the variables GR, GI, U, and GP give rather mixed results with many incorrect signs and generally a low level of significance. The MOOD variable, on the other hand, retains its high level of

316 D. M. Jafee, Risk structure of interest ra tcs

significance for utilities. There are a number of possible explanations for this. Perhaps the main point is that the revenue flow of utilities is less dependent on the general state of the economy and more dependent on the lags in regulatory price-setting than for most industrial firms. *

-*. Behavioral sources of cyclical variations

The results of the previous section provide estimates of the amount of cyclical variat:ion in risk spreads that should be attributed to cyclical variations in the risk associated with a given rating class. In this section we consider the beLaviora1 sources of cyclical variations in risk spreads. The approach is first to set up a behavioral model of risk spread determination, and then to test regressions including both the behavioral variables and the business cycle variables of the previous section. Both sets of variables must be included, of course, since the observed variations in the risk spreads are presumably the outcome of the two sets of factors working together.

3.1. AI model

Consider a specific issuer category of bonds - say utility bonds - for which there exists a number of different risk ratings. Denote the investor demand for bonds of risk category i as Di, the issuing firm supply oj‘bonds of risk category i as Si, and the interest rate on the bonds as li. We can assume II different risk categories, i = 2, . . ., II, noting that we have really fo:lr categories (BAA to AAA). The investor demand function can b,., specified in tht general form

The own rate Yi should have a positive effect on investor demand, while the other rates (rj,i # i) would generally have negative effects. The symbol Xid denotes the variable or vector of variables that have exogenous influences on the demand for bonds of risk category i.

The supply function of issuing firms can be specified as

Si = Sj('i ) xf)) i = I, 2, . . . , H. (2)

Here, the oivn rate ri should have a negative effect on the supply of such bonds, and X: denotes the exogenous forces influencing bond supply. There is an impor- tant asy’mmetry between the demand and supply functions in that the other risk rates (rj,i + i) do not enter the supply function. This occurs because issuing

The numerous recent reclassifications of utility companics are interesting in this regard. In particular the reclassifications may indicnte that the rating services are prompt in adjusting ratings for changes in regulatory conditions.

D.M. Jafee, Risk structure of itrterert rates 317

firms cannot arbitrage between risk categories. On the other hand, issuing firms can substitute toward other means of financing, and thus the interest costs of these other instruments are important elements in the X/variable.

Now assume equilibrium in each risk market such that

Di=Si, i= 1,2,...,!2. (3)

Using this condition to set (1) equal to (2), the reduced form solution for ri can be obtained as

ri = gi(r: . . . ri-l,rifl . . .r,, Xt, Xf), i= I,2 ,..., n. (4)

This indicates that the interest rate for any risk category will depend on the speci- fic elements affecting demand and supply in that market and on the rates for the other risk categories. Moreover, by substitution of the equations for rj(j # i) in the ith equation, the rates of interest on other rusk categories can also be elimin- ated from the equation. Thus, for example, from (4) there is an equation r, = g,( l ), and this can be substituted into the equation for ri of (4) to yield

i= I,2 ,..., n. (5)

This process can then be continued until only the rate r 1 is left,

ri = ki(r 1, Xi . . . Xnj, Xi . . . Xi), i = 1, 2, . . . , II. (6)

The usefulness of this formulation is seen most clearly if we now interpret the risk category 1 as the most risk-free category (that is, AAA bonds), and assume the other risk-categories have been arranged in ascending order of risk with respect to the index i. The general formulation of (6) then indicates that the rate ri will be a function of the risk-free rate r 1 and of the various exogenous demand and supply factors affi:cting the risk markets. Moreover, on the basis of (6), the distinguishing characteristics of the three market structures - market segmenta- tion, perfect substitutes, and habitat theory - can be made clear. Specifically, if market segmentation is valid then the demand and supply in other markets have no influence, and (6) reduces to: Market segmentatior.,

ri = kf(Xf, Xf), i = 1, 2, . . . , n. (6’)

If perfect substitutes hold, then the risk structure will be fixed over time and (6) can be written in terms of the risk-free rate alone: Perfect substitutes,

ri =tq(r,), I= 1,2 ,..., n. (6”)

318 D.M. Jafee, Risk struciure of Meres: rates

Finally, the habitat theory, which includes both the element; of (6’) and (6”), has the general form of (6). The implication, therefore, is that one can test the general form of eq: (6)? and verify whether either of the more polar cases of (6’) or (6”) are valid.

3.2, Empirical tests for corporate issuers

Empirical tests of eq. (6) were carried out using the format and variables already discussed in table 2, together with specified sets of variables for the Xf and A’: of (6). The results were distinctive in that we could find no case in which the A’; demand variables - in the form of the specific flow of funds in the ef?onomy __ or in which the Xf supply variables - in the form of various investment variables or the amount of financing actually undertaken - had a statistically significant effect on the risk structure. ’ In other words, from these results, the only factors that move the risk structures are the business cycle and confidence variables that, as already indicated, are more properly interpreted as risk measure adjustmtnts than as behavioral determinants. Consequently, ou. results are closely analogous to the-e of Modigliani and Sutch (1966, 1967), wh’o found no effect for supply factors on the term structure of interest rates, but they differ from the results 4 Fair and Malkiel (1971), who found supply effects for the ‘issuer structure’ of interest rates.

3.3. The results fos mrrrticipal bonds

The rest&s for municipal bonds are based on the Sam\: model as the corporate bonds, but the type of variables used and the nature of t?e results are ARerent. The definitions of variables and the estimated coefficients are given in table 3.

The first three variables in the estimated equation cotrespond to the same factors of confidence already discussed for the corporate bonds. The MOOD variable obtains a negative coeficient, and the GP and BAA variables obtain positive coefficients as expected. We have also carried out tests for other business cycle effects on municipal risk structure, but obtained no significant results. This is not surprising since municipal bonds, like the utility bonds already discussed, should not be appreciably affected by normal business cycle fluctuations. The fourth variable in the equation, RAT, is a measure olr credit rationing by com- merical banks, and thus also serves as a measure of confidence. One would expect that with high credit rationing, credit markets would be uncertain, and thus risk spreads should increase. The positive coefficient on RAT confirms this rssult. The same variable was also tested for the corporate bondsj, but it did not obtain a significant effect in those equations.

The last tivo variables in the equation correspond to demand factors. One important factor influencing municipal bond demand is that commercia: banks

9See Jaffee (1973) for more details on these tests.

D.M. Jufie, Risk structure of interest rates 319

buy primarily top quality municipals on national markets to compensate for the lower quality issues that they are under pressure to buy from their own state and local community. Consequently, high loan to deposit ratios (LD) should imply sales of top quality municipals, and therefore a decrease in risk spreads. The negative coefficient of LD confirms this. A second factor influencing municipal bond demand is that the higher the income tax rate structure, the lower the income level at which it becomes profitable for an individual to purchase tax exempt securities. Furthermore, it is plausible that the lower the income level of the individual the more risk averse he will be, and thus the greater the likeli-

Table 3

Municipal regression results. - -_ _. -_ _-______ -__---_--. .__.~_ ___ _

Definition of Variables

I?A,4-AAA Spread between the BAA and A4A municipal bond rates (dependent variabIe) MOOD Consumer sentiment variable (see above) GP Growth rate of prices (see above) LD Loan/deposit ratio of commercial banks, Federal Reserve RAT Proxy variable for credit rationing by commercia! banks, from Jaffee (1971) TAX The effective tax rate for federal income tax from the Federal Reserve-M.I.T.

econometric model BAA The level of the BAA mur;icipal bond rate

Regression rwtlr

B,4,4-A.lA = ~.3-O.O’~.~?i)OD+l.lSGPS-0.11BA.~i0.09RAT-O.S3I~D+0.1ST~4~~, (-1.0) (2.7) (1.9) (2.4) (3.1 (S.1) (1.6)

D.W. = 0.90, S.E. = 0.11, R’ = 0.80.

.Yorc: Ordinary least squares estimates over the sample 195’1-1 to 19694. t-statistics are s,hc~ xn in parentheses.

hood high quality bonds will be demanded. Putting these two pieces together, therefore, the implication is that high tax rates should imply more demand for relatively risk-free municipals or, equivalently, high LIX rates should imply high risk spreads, This is consistent with the positive c.)efficient obtained for the larinblc T.4 X. ’ ’

The important finding \vith respect to municipal bonds is that demand factors in terms of commercial b:rnk loan-deposit ratios and household personal income tax rates do have an effect on the risk structure. This, then, should provide encouragement that there also exists issuer supply effects for the municipal bond risk structure. Unfortunately, however, the data on issuer supply of municipal bonds by rating class is diAcult to obtain because of the very large number of

‘Vhis analysis, ofcourse, greatly simplifies the rather cornplicatcd rcl~?ionshipbetM’ccnyiclds and tax rates, The questions of capital gain taxes and security prices not at par have been studied by Pye (1969).

320 D.M. Jafee, Risk stvuctwe of interest vdes

individual bond z’ssues involved. Hempel (1972) h: ; provided some nleasures, however, and this has been analyzed in a study coordinated with the present study by Dill (1973). Surprisingly, Dill i’ands no significant :,upply effects. 1 *

4.1. Tile Penn-Central barlkruptcy

We indicated above that the sample for estimation was ended in 1969-4 in order tlo avoid the effects of the Penn-Central bankruptcy in June 1970. This allows the opportunity, therefore, to extrapolate the results of the regressions through the period of the bankruptcy a3d the time following it. The results of this exercise are shown in table 4. The data are tabulated for the BAA- IAA rate spread for each of the 5 issuer categories, The results for the other risk structure spreads are in the same direction as the BAA-AAA spread, but they are not as large since the original spreads are smaller. The period of extrapolation is 1970-I (the first quarter beyond the sample) to 1972-4 (the last quarter for which a complete set of data were available). In addition, the fitted values for the four quarters of 1969 are shown as an indication of how well the eqk Ation was fitting during the last part of the estimation period.

In table 4, for each issuer category, the first column shows the actual Ieve’ of the BAA-AAA rate spread. The second column gives the value of this spread predicted by the estimated equation. The third column gives the residual calculated as the actual value minus the predicted value. One can see irrmediately from the array of positive residuals after 1970-2 that the actual values for rate spreads were significantly exceeding the p,redic:ed ‘L.&U::; of the estimated equation during and following the Penn-Central pcnod. In oll;er words, these data are consistant ivith the hypothesis that the F:;nn-Central b&nkruptcy by itself led to a significant increase in risk spreads.

It is also interesting to examine the timing of this increase in risk spreads, and of the relative effects across different issuer categories. First, however, it is important to note how the equation was fitting in the last quarters of the sample (1969) and in the exrrapolation quarters before the Penn-Central bankruptcy (1970-l and part of 1970-2). It can be seen, using the total corporate issuer class ai the example, that during the first three quarters of 1969, the equations were estimating quite well, and without any obvious positive or negative bias to the residuals. Beginning in ?969-4, and accelerating with 1970-l and 1970-2, how- ever, there is a sequence of large negative residuals in al! categories. Then, in 1970-3, the first full ‘Penn-Central’ quar.ter, the residual becomes positive and

“It should also be noted that Dill has tested, with varying success, R number of variables not reported here. In particular, he has tested for an eflect on municipal bond risk spreads of the sporadic Congressional discussions to eliminate or modify the tax-exemption of municipal securities.

D. . Jaflee, Risk structure of interest rates

Table 4

The elfects of the Penn-Central bankruptcy (BAA-AAA risk spicds: (1) actual, (7) predicted, (3) residual = actual-predicted).

321

1. Corporate (total) (1) (2) (3)

6901 6902 6903 6934 7001 7002 7003 7004 7101 7102 7103 7101 7’01 7’0’ 7% 7203

-iI. IndustriaI --_ -__-. -_

6901 6902 6903 6904 7GOl 7002 7003 7001 7101 7102 7103 710-I 7201 7?0? _ _ 7’03 720-t

III. Uti!itics ~__ ----

6901 6902 6903 690-I 7001 7002 7003 7w4 7101 7102 7103 7101 7201 7402 7203 7’04

0.66 0.64 0.02 0.72 0.83 -0.11 0.91 0.92 -0.01 0.93 1 .O? -0.15 0.79 1.03 -0.24 0.77 i.11 -0.37 1.30 1.10 0 20 1 A8 1.30 Cl.18 I.3 0.99 0.26 1.11 1 .OO 0.11 1.15 1 .oo 0.15 1.13 0.95 (‘.1X 0.99 0.87 0 13 0.97 0.81 0.16 0.87 0.75 :,.I3 0.85 0.76 0.09

0.71 0.77 0.9s 1 .oo 0.96 0.89 1.50 1.61 1.38 I .-I3 1.29 1.1s 1.1-l 1.08 0.92 0.90

_ .-. .__~ (1)

0.61 0 h9 0.87 1.03 0.74 0.73 0.93 I .0-Y I .Ol 0.78 0.85 U ‘IO 0.72 0.78 0.60 0.52

(2)

0.69 0.90 0.99 1.1.: 1 .OY I.20 1.17 1 .-xl 1.01 1.09 1.10 1.01 0.9s 0.W O.SS 0.83

(2) --

0.59 0.71 0.79 0.9s: 0.94 1.03 0.97 0.97 0.90 O.SZ 0.8 1 o.sI! 0.07 0.65 0.59 0.63

(3)

0.02 --0.13 -0.01 -0.13 -0.12 -0.31

0.33 0.15 0.37 0.33 0.19 0.17 0.16 0.1’) 0.07 0.07

._ .~~ -. (3)

0.05 - 0.02

0.08 0.05

-0.X -0.30 -0.W

0.10 0.11

- 0.05 0.05 0.0s 0 05 oh0 0.01

-0.09

322 D.M. Jaffee, Risk swcture of interest rates

Table 4 (conk.)

Iv. .-

l&ails (1) (2) (3)

6901 6902 6903 6904 7001 7002 7003 7004 7101 7102 7103 7104 7’01 7202 7203 7204

__ -.. v. Muilicipals

0.44 0.19 0.25 0.13 0.37 -0.24 0.25 0.44 -0.19

- 0.07 0.50 -0.57 0.32 0.49 -0.17 0.18 0.69 -0.51 0.54 0.67 -0.13 1.32 1.04 0.28 1.31 0.64 0.67 0.61 0.76 -0.15 1.37 0.86 0.51 1.42 0.83 0.59 1.38 0.70 0.68 1.28 0.70 0.58 1.21 0.67 0.44 1.21 0.58 0.63

(1) (2) (3)

6901 6902 6903 6904 7001 7OQ2 7003 7001 7101 7102 7103 710-l 7’01 7’OY A _ 7203 7’01

0.64 0.70 - 0.06 0.43 0.75 -0.32 0.75 0.77 -0.02 0.73 0.86 -0.13 0.59 0.82 -0.23 0.60 Cl.94 -0.34 0.59 0.85 - 0.26 0.59 0.93 -0.35 0.56 0.93 -0.37 0.71 1 .O’ -0.31 0.77 0.91 -0.15 0.M O.h5 -0.29 O.h2 0.90 -o.?s 0.65 0.;3 -0.1s 0.57 0. ‘;o -0.23 0.48 0 x0 -0.32

positive residuals continue through to the end. This same pattern is evident, to a greater or lesser extent, in all the issuer categories. It is thus clear that the three quarters prior to ‘Penn-Central’ (1969-4 to 1970-2) were quarters in which the equations were generally owrpredicthg the risk spreads. The cnilct \ve are interested in during the Penn-Central peri,Dd, !lo\vever, is an ur~ck~~p~rtii~tiorl of the spread. The implication, therefore, is that our results for the etl’ccts of the Penn-Central on risk spreads may actually be too small, since just previous to the default period, the estimated equations had residuals in the opposite direction.

Turning now to the timing of the effect of Penn-Central on risk spreads, the total corporate sector provides the clearest example. From table 4-1, it is seen that the residual for 1970-3, the first complete ‘Penn-Central’ quarter, is 20 basis pGnts. In view of the above discussion about the fit in the previous quarters, 20

D.&i. Jaffee, Risk structure of interest rates 323

basis points would then appear a minimum estimate of the effect, and an amount of possibly 50 basis points is conceivable. It is then seen, going down the residual column of table 4-1, that the residual varies, but with a distinct trend toward smaller values. In particular, in 1972-4, the last quarter in the sample, we observe the smallest residual (9 basis points) since before the Penn-Central period. While more data would be necessary to conclude that by the end of 1972 the effects of Penn-Central had worn off, it is apparent that the impact evident in late 1970 has become certainly much less by the end of 1972.

Finally, it is interesting to consider how the effect of Penn-Central varies by issuer categories. It can be seen that rails and industrial bonds (along with the total corporate se&or) are significantly affected, while the utility and municipal bonds show relatively little effect. 1 ’ This can be understood in terns of the type of risk associated with the specific issuer categories. For the rails and industrials (particularly in view of the difficulties of Chrysler at the time of the Penn-Central default), the Penn-Central episode would have create

324 D.M. Jaffee, Risk structure of interest rates

spreads, and thereby to determine the investment timing. I3 Also alternative investment strategies could be compared.

The speed artd incidence of U.S. monetary policy. A full array of results on the risk structure and ‘issuer structure’ of interest rates could also be used to simulate the speed and direction of monetary policy. For such purposes, the logical next ste;, for empirical work concerns the rate spreads that exist between different issuer categories - that is, the issuer structure. Fair an? Malkic 1(1971), in fact, have already provided ec:>nometric evidence on Is bei--‘een industrial and utility bonds. The additional empirical studies can interpreted as the generalization of the Fair-Malkiel study to the full range o1 A: >Jer categr)ries.

With this completed, the system of interrelated bond markets could be inter- preted as a tableau with, say, issuer categories corresponding to the columns and risk categories corresponding to the rows. In this setting, monetary policy is to be thought of as the control by the monetary authority of one cell in the Tableau - namely the risk-free government bond interest rate. Changes in this rate, for example by open market operations, would then spread throughout t’;e capital markets, both by being transferred to different issuer categories and by being transferred to different risk classifications. By simulating such a syhtem, one could then determine both the magnitude and the speed of the effect of monetary rsslicy on the ultimate financial markets to Lvhich its in1 ,,ict is directed.

Risk 3 tixctwe effects with rcghtcd cqi ril t?ldiCl.c. A> rioted above, this stud> has been developed in the context of the I_J.S. capital markets in which, at least over some range. risk categories are distinguished and risk spreads develop. In many Western European countries, in contrast, explicit risk spreads are not observed, presumably due to policies that regulate rl,te long-term interest rate and the issue of new private debt. One lvould anticipate, however, that, subject to these constraints, the capital markets would still adjust 10 diKercntial risk. Specifically, mith risk spreads fixed (or zero), the rationin of credit to risky firms v:ould become an obvious solution. Such rationing, in fact, could be one of the major costs of regulating capital markets in this manner. Conscqucntly, ii is useful to develop measures of the magnitude and variation of such rationing, and to evaluate its allocative cost. Similar considerations apply, ofcoursc, to the most risky segments of the U.S. capital markets where ratioping also might occur.

D.M. JaBpe, Risk structure of interest rates 325

Cohan, A.B., 1973, The risk structure of interest rates (General Learning Press, Morristown, N.J.).

Dill, D.A., 1973, Interest rate determinants in the municipal bond market: 1954-1969, submitted senior thesis (Economics Department, Princeton University, Princeton).

F&ir, R.C., 1971, A short-run forecasting model of the United States economy (Heath, Lexington, Mass.).

Fair, R.C. and B.G. Malkiel, 1971, The determinants of yield differentials between debt instruments of the same maturity, Journal of Money, Credit and Banking, Nov.

Fisher, L., 1959, Determinants of risk premium on corporate bonds, Journal of Political Economy, June.

Hempel, G.. 1972, The post-war quality of state and local debt (N.B.E.R., New York). Hickman, W.B., 1958, Corporate bond quality and investor experience (N.B.E.R., New York). Homa. K. and D. Jaffee, 19711 The supply of money and common stock prices, Journal of

Finance, Dec. Jaffce, D., 1971, Credit rationing and the commercial loan market (Wiley, New York). Jaffee, D.. 1973, An empirical study of the risk structure of interest rates, research memorandum

no. 16 (Financial Research Center, Economics Department, Princeton University, Princeton).

Johnson, R.E.. 1967, Term structures of corporate bond yic!.is as a function of risk of default, Journal of Finance XXIJ, hlay, 313-345.

Katz. S.. 1974, The price adjustment process of bonds to rating reclassifications: A test of bond market efficiency, Journal of Finance XXIX, May, 55 I-559.

Mall\icl, B.G., 1966, Thr: term structure of interest rates: Expectations and behavior patterns (Princeton University Press, Princeton).

hlcrton. R.C., 1974. 01 the pricing of corporate debt: The risk structure of interest ratc5, Journal of Finance XXIX, slay. 449-370.

hlodigliani, F., 197!,1Llonctary policy and consumption, in: Consumer spending and monc‘tary policy. conference series no. _ 5 (Federal Reserve Bank of Boston, Barton).

hlodigliani. F. am1 R. Sutch, 1966. Innovations in intcrcbt rate policy. American Esonomic Rev&v, May.

hlodigliani, F. and R. Sutch, 1967, Debt management and the term structure of interest rates: An empirical study, Journal of Political Economy, Aug., supplement.

Pinches, G.E. and K.A. Mingo, 1973, A multivariate anul\,cis of industrial bond ratings, Journal of Finance MX\‘lll. March, I-IS.

Poguc. T.G.. and R.M. Soldof&y, IOhY, What’s in a bond rating, Journal of Financial anti Quantitative Analyses, June, ?OI-228.

1’1~. (;.. 1969, On the tax st:ucturc of intcrcst r.ltcs, Quarterly Journal of Economic% Nov. Sil\cr\, J.B., 197.1. An altcrnntivc to the yield as a nlc;~surc of risk, Journal of F’iriancc: XXVlii.

scpt,. 033--955.