-
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.
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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.
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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).
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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);
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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
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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
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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.
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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”)
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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
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differentials between debt instruments of the same maturity,
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