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Som e F actors A ffectin g L ong-term
Yield Spreads in R ecen t Years
E dge C orporations: A M icrocosm of
International Banking T rends

■ ■

Volume 59
Number 9



Some Factors Affecting Long-term
Yield Spreads in Recent Years

T h e past d eca d e has been a p eriod

between the corporate bond rate and the short-term

of unprecedented movement in interest rates. Chart 1

Treasury bill rate m oved from a low of 24 basis

shows the m ovem ent over this period in five co m ­

points in January 1966 to a high o f 401 basis points
in M arch 1971.

m only cited interest rates series. T w o observations
can be made from Chart 1 about the behavior of the
interest rate series in the period shown.

T he first is

that the rates generally m ove in the same direction
over time.

A ll five of the series shown rose greatly

T his characterization o f interest rate movement
differs substantially from the standard m acroeco­
nom ic textbook treatment in which “ the” interest
rate is determined by an appropriately specified

in the late 1960’s, and all reached a peak in the first
half of 1970.
T he second observation is that the


differentials am ong the interest rate series changed
substantially over the 10-year period. T his observa­

rate spreads displayed little variation— then it would

If the relationships am ong the interest rates

were fairly constant over time— that is, if interest

tion is true not only for long-term rates relative to
the short-term rate, but it is also true of the long-term

be o f little concern that there are many interest rates,
since an appropriate explanation of the movement in
any one of the interest rates w ould suffice as an

rates relative to each other. T o take one example, at
the beginning of the period in February 1964, the

explanation for the m ovem ent in all other rates.

corporate bond rate was only 25 basis points higher
than the long-term United States governm ent bond
T he differential or spread between the tw o
rates rose to 135 basis points in September 1966, fell
to 88 basis points in February 1967, increased to 273
basis points in N ovem ber 1970, and fell to 153 basis
points in February 1973.
T he lack of stability that characterizes the spread
between the corporate bond and U . S. governm ent
bond interest rate series extends to the other interest
rates as well, as shown in Table I, where all four of
the other rates are com pared to the corporate bond
rate. T he spreads between the corporate bond rate
and the other rates varied 180 basis points or m ore in
all four cases. In the most extreme case, the spread
Table I



Nov. 1970


types o f real investment. State and local bonds fi­
nance state and local construction, hom e m ortgages
finance residential construction, corporate bonds p ri­
marily finance the construction o f plant and equip­
ment, and long-term U . S. bonds finance part o f the

activity the form er finances becom es relatively m ore
T o the extent

F e b .1964

ing interest rates when making decisions on real

J a n . 1966

to another can thereby affect the pattern of capital
allocation in the econom y. Therefore, a change in a

investment activity, a rise in one interest rate relative

M inus Treasury

M arch 1971


Corporate Bond Rate

particular spread is a matter o f concern not only for

M inus

June 1970

-1 .4 1

F e b .1964

Corporate Bond Rate

the sectors supplying the securities but also for p oli­
cymakers whose decisions can influence interest rate

M inu s State and
Local Bond Rate

Second, what

causes this variation? T he answer to the first ques­
tion is related to the fact that securities are issued to
finance a variety o f activities. In particular, different
long-term securities are issued to finance different

that the various econom ic sectors respond to chang­

Corporate Bond Rate

M o rtga ge Rate

First, of what concern is it that the

spreads vary substantially over tim e?

expensive, at least at first glance.

M inu s U.S.

Bill Rate


series for another of the securities, the cost o f the

Corporate Bond Rate
Bond Rate

Security characteristics T h e size and v a ria b ility
of spreads am ong interest rates raise tw o im portant

of these securities rises relative to the interest rate


over time, particularly in a period o f large interest
rate movements, such as the late 1960’s.

Federal deficit. W h en an interest rate series for one



Unfortunately, as shown in Chart 1, the relationships
am ong the various levels show substantial variation



A u g . 1970


Jan. 1966

T he second question— what causes m ovem ent in


the spreads— is extrem ely com p lex.1 T he five inter­

curities by these sectors is a w hole set of factors,

est rate series shown in Chart 1 represent only a
small fraction of the total number o f available interest

sometimes called “ fundamental” influences on inter­
est rate movements. T h ey include the savings be­
havior of the various sectors and the real invest­
ment expenditures o f these sectors. A ls o included are
certain policy variables o f the Federal Government
that influence econom ic activity by directly affecting
security supply or demand in a particular market.

rate series. Salom on B rothers’ invaluable publication,
A n Analytical R ecord of Yields and Yield Spreads,
alone contains 111 different interest rate or yield
series, which implies the existence of literally thou­
sands of spreads.2 These yield series can best be
classified according to the characteristics o f the se­
curity or securities they represent. F or the purposes

Attem pts to determine the effects o f these factors on
interest rate spreads are greatly com plicated because

of this article, these characteristics will be classified

a given factor, such as household saving, has simul­

into three groups.
T he first relevant characteristic of the security is

taneous effects in many security markets.

the length of its term to maturity.

of a security relevant to a discussion of yield series is
the special features it has with respect to the taxa­
bility, timing, and certainty o f the returns associated
with holding it. T here are four such features that
vary am ong securities.3 T he first is whether the

The F ederal R e ­

serve Bulletin, for example, provides yield series for
U . S. governm ent securities maturing in three
months, six months, one year, three to five years,
and over ten years. T he spread between any pair of
these series changes dramatically over time, as can be
seen in Chart 1.
Securities can also be characterized by the particu­
lar sectors of the econom y that issue and purchase
them. U nderlying the supply of and demand for se­

T he third characteristic, or group o f characteristics,

interest earned on the security is subject to Federal
incom e tax. T he second is whether the security earns
income in the form o f capital gains (o r capital losses),
which are subject to low er tax rates than interest in­

T he third feature is whether the issuer o f the

security has the option of repaying the principal
1 For an excellent discussion of many of these causes, see James C.
Van Horne, Function and Analysis of Capital Market Rates (Engle­
wood Cliffs, New Jersey: Prentice-Hall, Inc., 1970).
2 The terms “ interest rate” and “ yield” will be used interchangeably
in the remainder of the article.

3 The feature of convertibility of a bond into a common stock is not
considered, since the article is concerned exclusively with bond yield

Chart 1


M ortgage
■ Corporate Bond

9.0 -


Long-term U.S. Bond

..... 1-year Treasury Bill

— — State and Local Bond

7.0 -











/V '





Note: The corporate bond rate is for new callable corporate bonds rated A a by M o o d y 's Investor Service. The state
and local bond rate is the Securities Industry A ssociation's series for new issue A a 20-year general obligations.
The m ortgage rate is the FHA series for conventional new home loans. The two U. S. governm ent security rates
are the 1-year Treasury bill rate and the seasoned long-term bond rate series.
All are monthly averages of
daily or weekly series, except for the m ortgage rate which is the rate as of the first day of the succeeding

I _______ I
________ I
________ I
________ I _______ I
________ 1
________ I _______ I




Sources: Treasury Bulletin and Federal Reserve Bulletin.







( “ calling” the security) at a time before it matures.
A n d the fourth feature is the degree to which the
income prom ised on a security is subject to uncer­
tainty or risk of default on the part of the borrow er.

O n new issue securities, bonds typically sell at (o r
near) par, which in this case is $1000. A djustm ents

Each of the three security characteristics mentioned

in yield are brought about by changes in C, the
coupon. F or securities that are not new, but “ sea­
soned,” P will deviate from $1000 in order to keep

is related to both the level and movement o f interest
rate spreads over time. T he ideal procedure to use in

the yield o f the security in line with current market
interest rates. F or example, suppose a new 20-year

attempting to explain the movement in spreads is to
isolate one security characteristic at a time and study

security is issued at a yield to maturity o f 5 percent,
with P = $1000 and C = $50. F ive years later, the

yield series for securities that are alike in all respects

security, now seasoned, is resold when the yield to
maturity on com parable new securities has risen to

but that one characteristic. T he problem then is to
determine the factors underlying the spreads associ­

7 percent. Because the $50 annual coupon on the

ated with that one characteristic (e.g. m aturity).
Unfortunately, finding interest rate series that isolate

seasoned security is low er than the $70 annual co u ­
pon on the new security, investors will only purchase

a given security characteristic is sometimes difficult,
if not impossible. Nevertheless, this article w ill at­

the seasoned security at a reduced price.

tempt to use that procedure in illustrating the effects

(w here N now equals 15) w ould have to d rop to
$817 in order fo r the yield to maturity to equal 7

that the four special features indicated above have
had on observed yield spreads in the past ten years.
T he article will not attempt to explain the elements of
observed yield spreads related to differences in m a­
turity or to the behavior o f the various econom ic

A ssum ing

the absence o f all taxes, the price o f the security

percent. T he buyer o f the security w ould realize a
capital gain at the end o f 15 years of $183.
T here are tw o features o f the yield form ula that,
when com bined with the four special features, ac­

sectors, but it will be argued that any attempt to

count for a large part of the variation in the yield

explain those spreads requires an understanding of

spreads in Chart 1 and Table I. First, it should be
noted that the form ula com putes the b efore-ta x yield

the impact on yield spreads of the special features.
Assumptions underlying the computation of yield
series O b s e rv e d spread s b e tw e e n in terest rate
series, such as those in Chart 1, contain an important
element that results from inherent shortcom ings in
the form ula em ployed in calculating yields.


between yield series for securities that differ only
with respect to one of the fou r special features dis­
cussed above are related in that they all result from
these shortcom ings. T h e yield of a security is the
discount rate, r, which equates the price, P, o f a
security to the present value of the future cash flow s
associated with holding i t :

(') p = ( T^ + < 1 T ^ +
where Q

+ (T+Tj" '

to maturity, when clearly the after-tax yield is the
relevant consideration for the buyer o f a security.
Therefore, the yield form ula (w hich is used to co m ­
pute the interest rate series in Chart 1) cannot
differentiate between securities that provide interest
income that is or is not subject to personal and c o r ­
porate incom e tax. N or does it differentiate between
securities that yield or do not yield a return in the
form o f capital gains that are taxed at a low er rate
than interest income.
In the second place, implicit in the form ula is the
assumption that the timing and amounts of the
returns associated with holding a security are known

is the prom ised return in the ith time

with certainty.
Therefore, the form ula cannot be
used to calculate, with precision, the yield on securi­

In com puting the yield, the assumption is

ties that are callable, either immediately or after a

usually made that the security is held to maturity, so

deferred period.

M oreover, it cannot take into

F or sim­

account the varying degrees of certainty felt by in­

plicity, the remainder o f the article w ill assume that

vestors that the issuer of the security will not default.

that r becom es the “ yield to maturity.”

we are dealing with a bond that pays a constant re­

T he rest o f this article will look at and attempt to

turn, C, each year until it matures in period N , at

explain spreads am ong long-term interest rates aris­

which time it pays the holder o f the security its face

ing prim arily out o f the failure of the yield to m a­

value of $1000.

T he yield to maturity is then com ­

turity form ula to take account o f the effects on

puted by finding the value o f r that satisfies the

com puted interest rate series of incom e tax rates,

eq u a tion :

capital gains tax rates, call provisions, and default
Income tax rates and yield spreads T h e a fter-ta x
yield to maturity of a security for a particular in­

4 An explanation of this formula can be found in any introductory
finance book.


vestor is the discount rate, r*, which equates the


price of the security to the present value of the
future after-tax prom ised retu rn s:
(2 )

P =


C ( l - t )
— --------- - +
(l + r*)“ ^

( 1 0 0 0 - P) ( l - e g )
----------------- —--------- —
(1 — r * ) N

(1 + r * ) N

where t is the marginal income tax bracket of the
investor and eg is the tax rate on long-term capital

T he interest income, C, is taxed at the rele­

vant personal or corporate income tax rate, while
the capital gains ($1000 — P ) are taxed at the capital

from the preceding discussion that all the change in
the spread cannot be attributed to the tax factor,
since the effects of the tax factor have not been
isolated from those of the other factors discussed.
F or the period 1966-1968, it appears that a m ajor
part of the movement in the spread can be explained
by the differential tax status.
In that period, the
spread rose and fell with interest rate levels, keeping
the relationship between the after-tax yields on the
two securities relatively constant.

In 1969, however,

gains tax rate. O ver much of the past 10 years, eg
was equal to one-half of t, up to a maxim um tax of

interest rates rose sharply, while the spread opened
only moderately.

25 percent of total capital gains.5
By using Formulas ( 1 ) and ( 2 ) and by specifying

It should be noted that since the yield series in
Chart 2 are for new securities selling at par, the

an income tax rate, a capital gains tax rate, a matur­

equal-after-tax relationship between the state and

ity date, and a coupon value, it is possible to deter­

local rate ( r si) and the corporate bond rate ( r cor)
series can be expressed simply as

mine, for any security, a before-tax yield that is con ­
sistent with any after-tax yield.6 The effects of vary­

(3 )

ing income tax rates, capital gains tax rates, maturi­
ties, and coupons on the relationship between beforeand after-tax yields to maturity, and consequently on
yield spreads, can then be isolated.

rsi = (1

t ) r cor •

A lthough t varies am ong individuals, it has been
fairly constant for corporations, about 50 percent,
over the period shown in Chart 2.

Form ula ( 3 ) can

A n example of this procedure is reported in Table
II. T he relevant marginal income tax rate is shown

be used to determine a marginal tax rate at which
investors w ould be indifferent in choosing between

for values of 30 percent and 40 percent, and the

new state and local bonds and new corporate bonds

capital gains tax rate is assumed to be one-half the

o f the same quality.

income tax rate. T he hypothetical securities are new
issues sold at par. It is assumed that one security
yields interest income that is tax-free, while the other
yields interest income taxable at the indicated m ar­
ginal tax rates. It is also assumed that investors
demand equal after-tax rates.
T w o points, which
are evident from examination of the table, are rele­
vant to the discussion o f the relationship between

That tax rate w ould be

(3' )

t* =


1 -

1 cor


A n investor in a marginal tax bracket greater than t*
would prefer state and local bonds to corporates. The
t* series is shown in Chart 3.

T he series averages

about 32 percent over the period and never reaches
40 percent. A s w ould be expected, these values o f t*

the yield to maturity form ula and yield spreads.

lead to a situation in which the market for state and

First, in a period of rising interest rates, spreads
between yield series for securities that yield taxable
interest versus those that yield tax-free interest
should rise. A n d second, increases in income tax

local securities is com pletely dominated by financial
institutions subject to corporate income tax rates—

Table II

rates should also increase those spreads.


A s is well known, interest income on state and
local securities is generally tax-free.

Chart 2 com ­

pares the movement of the corporate bond rate with

Spread Between Before-tax Yield of a N ew Issue Security

the movement o f the spread between the corporate

Providing Taxable Interest Income (rj) and Before-tax Yield

bond rate and the state and local bond rate.
rates are for new issues.7


of a New Issue Security Providing Non-taxable Interest
Income (r2) Assum ing Equal After-tax Yields

There is clear evidence

that the spread rises as interest rates rise, as was
predicted in Table II, although it should be clear

t=4 0 %

t= 3 0 %

6 This fact was pointed out in an article by J. W . Colin and Richard
S. Bayer, “ Calculation of Tax Effective Yields for Discount Instru­
ments,” Journal of Financial and Quantitative Analysis, 5 (June
1970), 265-73.
7 Unless otherwise stated, the interest rate series referred to are
those in Chart 1.


3 The relationship of t to eg became somewhat more complex in 1970
after maximum capital gains tax rates were increased.















































com m ercial banks and casualty insurance companies—
and by high incom e individuals.8
Capital gains tax rates and yield spreads

C hart 4

com pares the movement of the corporate bond yield
series with the spread between the corporate bond
yield series and the long-term U . S. governm ent bond
yield series.

T he yield series and the spread m ove

very closely together indicating that, during the years
shown, the spread increased when interest rates rose
8 Of the total $166.47 billion outstanding in state and local securities
at the end of 1971, the household sector held 31.41 percent, casualty
and fire insurance companies held 11.59 percent, and commercial
banks held 49.78 percent. A factor contributing to the failure of the
spread between the corporate and state and local bond rates in
Chart 2 to rise in 1969 was undoubtedly the behavior of the com­
mercial bank sector, which virtually withdrew from the state and
local market, thereby creating upward pressure on the state and
local bond rate relative to other long-term rates.

and decreased when interest rates fell. T his section
and the follow in g will deal with tw o o f the m ajor
factors causing this relationship.
T he corporate bond yield series in Chart 1 is for
new issue bonds selling at or near par, while the
long-term U . S. governm ent bond yield series is for
seasoned bonds. T here is no yield series fo r new
issue long-term U . S. bonds since none were issued
over most of the period under consideration because
the m axim um legal coupon was 4.25 percent until
1971. Thus, the long-term U . S. bond yield series
over m ost of the period is fo r a group o f securities
having coupons of 4.25 percent or less. T he average
coupon rate on the bonds making up the yield series
in June 1970, when interest rates were at their peak,
was only 3.64 percent.

Chart 3

4 0 f—

Chart 4




Note: Yield series are those described in Chart 1.

Table II I shows the spreads between the before­
tax yields on a new security selling at par and a

most one-half the movement of the spread in Chart 4.9
Table I V recomputes the spreads with a coupon o f

seasoned security with a $40 coupon, for equal-after­
tax yields. T he income tax rate of the investor is

$30, and the other assumptions unchanged.

assumed to be 40 percent, the capital gains tax rate,
20 percent, and N , 20 years. A s interest rates rise,
the price of the seasoned bond falls, increasing the

security, the greater the discount and, consequently,
the greater the amount of the return of the security
in the form o f capital gains. T his results in an in­

amount of income that is received in the form o f

crease in the spread for any specific after-tax yield.

capital gains.

Chart 5 com pares tw o yield series from Salom on
Brothers that are for tw o sets o f securities which are

Since capital gains are subject to a

substantially low er tax rate than interest income, a
low er before-tax yield on the seasoned bond is re­
quired to provide an after-tax return equal to that
o f the new bond. U nder the assumptions made in
Table III, this “ capital gains” effect on the seasoned
long-term U . S. bond yield series would explain alTable III

N e w vs. $40 Coupon Seasoned Security

ostensibly alike in all respects except that one is new
and the other is seasoned with a 4 ^ - 4 ^ percent

T he yield series are both for deferred call­

able A a public utility bonds.10 T he spread between
the tw o yield series is similar to that indicated under
the assumptions made in Table II I and corroborates
the capital gains tax effect on yield series between
yields for new and seasoned discount bonds. Chart 5
indicates an apparent change in the relationship be­
tween the spread and interest rate levels beginning in

Spread Between Before-tax Yield of N e w Security (r^) and
Before-tax Yield of $40 Coupon Seasoned Security (r2)


One explanation for this change is that the

T a x R eform A ct of 1969 increased maxim um capital

Assum ing Equal After-tax Yields (r*)
N = 20 t = 4 0 %

A s the

table indicates, the low er the coupon on the seasoned

gains tax rates from 25 percent to 32.5 percent for

eg = 2 0 %

individuals and to 30 percent for corporations.




































A s­

suming an equal-after-tax yield of 4 percent and a
9 Of course, over the period, the average term to maturity of the $40
coupon securities would decline; however, at large values of N,
this would have a very small effect on the spreads in Table III.
10 The word “ ostensibly” is used because a high coupon deferred
callable bond is more likely to be called than a low coupon deferred
callable bond.



Table IV

A a deferred callable, new, utility bond yield series
with the spread between it and the yield series for a


similar bond that differs only in that it is seasoned
with an 8 - 8 ^ percent coupon.
T he chart clearly
indicates that when market rates fell below the

N e w vs. $30 Coupon Seasoned Security
Spread Between Before-tax Yield of a N ew Security (r^) and
Before-tax Yield of a $30 Coupon Seasoned Security (r.,)

coupon (8 p ercen t), the observed yield on the sea­

Assum ing Equal After-tax Yields (r*)

soned bond became larger than the new issue bond

N = 20 t = 4 0 % eg = 2 0 %



Table V shows the before-tax yields on a






hypothetical premium seasoned bond with an $80
coupon necessary to give after-tax yields equal to







those on new issues in a period when interest rates













are below 8 percent. T he results are similar to the
actual spread in Chart 6.


















Recently, new long-term U . S. bonds at current
coupons have been issued. A t the present time, three

marginal income tax bracket of 50 percent, the effect

of the ten bonds in the sample used to com pute the

of an increase in the capital gains tax from 25 percent

long-term U . S. bond series are high coupon (o v e r 6

to 30 percent w ould be to decrease the spread be­

percent) bonds.

tween the before-tax yields of a new security selling
at par and a seasoned one bearing a $40 coupon from

bonds in the sample should affect the relationship

T he presence of the high coupon

between the U . S. governm ent bond yield series and
the other series. Chart 4 provides some support for

114 to 104 basis points. Thus, the increase in capital
gains tax rates would explain some, but apparently
not all, of the change in the relationship in 1970 be­

this expectation in that it appears that in 1973 the

tween the tw o curves shown in Chart 5.

smaller than it has been at similar interest rate levels
in the past.

spread between the corporate and U . S. bond rates is

W h en interest rates have fallen from past levels,
seasoned securities with coupons higher than pre­
vailing market interest rates will sell at a premium

Call provisions and yield spreads A th ird elem en t

( P > $1000) and, consequently, will yield a capital

entering into observed yield spreads results from the

loss at maturity.

inability of the yield to maturity form ula to account

U nder these circumstances, in­

vestors would be expected to demand a higher before­

for differences in call provisions.

tax yield to maturity on the seasoned bond. Chart 6
demonstrates this effect by com paring the yield of the

give the issuer of the security the option o f prepaying
the face value before the stated time of maturity.

Chart 5



Note: Yield series are for A a deferred callable utility bonds.
Source: Salom on Brothers, A n Analytical Record of Yields and Yield Spreads.

Call provisions

Table V

N e w vs. $80 Coupon Seasoned Security
Spread Between Before-tax Yield of a N ew Security (rj) and
Before-tax Yield of A n $80 Coupon Seasoned Security (r.,)
A ssum ing Equal After-tax Yields (r*) and N o Tax Break
O n Capital Losses11


N = 20

t= 40%






w illing to pay for the security will clearly be influ­
enced by the amount o f call protection he gets— in
terms o f the period of deferment and the call price—
and by his expectations of the degree and timing of
future interest rate movements.
A reasonable be­
havioral assumption is that a price will be determined
at which the marginal investor will be indifferent
between purchasing the security with a call provision
versus one that is noncallable.

That is, a price (o r

cou p on ) will be determined such that r ', the expected
holding period yield (w hich depends on m, C P , and















-.3 1






-.5 2

bond with a maturity of N years com puted by fo r ­






-.7 2

mula ( I ) . 33

-.1 1

V irtually all corporate bonds and m ortgages have
some kind of call provision, while state and local
bonds do not. Som e U . S. governm ent bonds are
callable, but the long-term U . S. bond yield series
shown in Chart 1 excludes bonds callable in less
than 10 years. Call provisions for corporate bonds
for which yield series are available specify that the
bond is callable either immediately or after a deferred
period of five years. Typically, if the bond is called,
a penalty is paid by the issuer, which varies directly
with the remaining years to maturity. A com m on
penalty for a corporate bond called after five years
w ould be one year’s coupon.

i ) , will equal r, the yield to maturity o f a noncallable

T he general implications for yield spreads of the
difference between form ulas ( 1 ) and ( 4 ) are fairly
straightforward. First, if interest rates are not e x ­
pected to drop enough to justify the issuer of the
security to prepay the face value of the security
(given the presence of the call penalty and refinan­
cing co sts), then expectations will be that the security
will not be called. Investors will not be willing to pay
a premium (accept a low er yield ) for call deferment
provisions, and the yield to maturity form ula ( 1 )
will give com parable yields for securities with differ­
ent call provisions.

If interest rates are expected to

fall enough that the security will be called and if the
subsequent expected holding period yield, as indi­

Y ields on bonds with call features are calculated,
like yields on bonds without call features, by the yield
to maturity form ula ( 1 ) . T he resulting effects on

cated by form ula ( 4 ) , becom es smaller than r, the
yield to maturity of a noncallable security, then the

observed yield spreads can be seen by considering
the case of an investor with m oney to invest for N
years w ho buys a N -year bond subject to call any­
time after it is issued.

If the bond is called, the in­

vestor reinvests the call price (the face value plus
the call pen alty), C P , immediately at the current
market rate of interest, i, until the end o f the original
N years. H is expected (h olding p eriod ) yield over
the N years is the discount rate, r ' , which equates
the price of the security with the discounted value of

1 This assumption implies, contrary to currently accepted theory,
that investors do not demand a higher expected (than certain)
return in exchange for the uncertainty associated with buying the
security with the call provision. The same simplifying assumption
is made in the next section with respect to another type of uncer­
tainty. The assumption does not affect any of the general conclu­

Chart 6



the ex p ected future incom e flow s :12
(4 )




- —

“ x (i +




(l)C P - +

J r + 1 (1 +

r') '1

.O +



T he call date, m, and the market interest rate at the
date of call, i, are clearly matters of uncertainty,
unless there is a deferred call provision, in which
case it is at least known that the bond cannot be
prepaid before the end of the period o f deferment.
T he attitude of the investor towards the price he is
11 In fact, part of the capital loss is deductible against current in­
come. Introduction of this factor would make the spreads in Table
V smaller.
12 In order to keep the discussion manageable, taxes will be ignored
in both this section and the next. Doing so does not affect any of
the basic conclusions.

Note: Yield series are for A a deferred callable utility bonds.
Source: Salom on Brothers, A n Analytical Record of Yields
and Yield Spreads.



coupons on the callable security will have to rise (o r
in the case of a seasoned security, the price will have
to fa ll) in order to equate r and r ' . U nder these
circumstances spreads will be created between calcu­
lated yield series for securities with different periods
of call deferm ent.14
Salom on

Brothers has calculated yield


w illing to accept a low er yield in return for five years
of call deferment. T he chart shows positive values
both in the early and late 1960’s. T h e chart also
demonstrates that, over the period shown, expecta­
tions of future interest rate changes m oved inversely
with respect to interest rate levels.

m a­

A n alternative way of illustrating the effect of the

turity series up to 1969 for securities that are identi­

call feature on yields is to com pute the yield to call

cal in all respects except that one set is immediately

(b y assuming the call price is paid at the end o f the

callable, while the other has a deferred call period of

period o f deferm ent) and com pare it to the yield to
maturity for a given security. A s indicated by fo r ­

five years.15

Therefore, the spread between these

tw o series, shown in Chart 7, isolates the effect of
five years call deferment. Given the above discussion,
investor expectation has to be that interest rates will
fall in the five years follow in g any period when the

mula ( 4 ) , a low value of expected future interest
rates com pared to current interest rates will raise
coupons (o r low er prices) on securities with a call
provision, so that the higher yield on the security
for the period until it is called will compensate for

immediately callable rate rises above the deferred

the low er expected yield thereafter. Chart 8 shows

callable rate.

the spread between the yield to call and yield to m a­

Otherwise, investors w ould not be

turity of 8 ^ 2 -9 ^ percent coupon A a utility bonds
14 By imposing the condition that r in formula (1) equals r ' in
formula ( 4 ) , and by specifying values for CP, i, m, and N, specific
spreads between calculated yields to maturity on bonds with differ­
ent call provisions are implied. For instance, suppose a noncallable
20-year bond, selling at par, has a $60 coupon and, consequently, a
yield to maturity of 6 percent. Let CP = $1000
C and assume
that interest rates are expected to fall to a “ normal” level, i, in
three years and remain at that level. If i equals 5.50 percent, then
no premium will be demanded on bonds with less than 20 years call
protection. However, if i is equal to 5.25 percent, the coupon on an
immediately callable security will be $65.70 and the coupon on a
security with five years of call protection will be $62.61. The cal­
culated yields to maturity will be 6.57 percent and 6.26 percent,
respectively, implying that investors demand a premium of 57 basis
points to buy the immediately callable security and 26 basis points
to buy the deferred callable security. The value of five years call
protection would be 31 basis points.
15 The series for immediately callable issues was discontinued in 1969
because of the absence of any new callable issues.

with a five-year deferment period issued in 1970, at
a time when long-term
record high.

interest rates were at a

T he chart supports the evidence from

Chart 7 that when interest rates are high, purchasers
o f securities with call provisions demand to be co m ­
pensated for the expected low er yields follow in g the
end of the deferment period.

T he differential in the

tw o yields was wiped out before the end of the d efer­
ment period, however, when long-term rates fell at

the end of 1970 and the beginning o f 1971.16
Chart 7 shows the value o f five years call defer­
ment at different points in time arrived at by isolat­
ing that particular special feature.
A n important
question posed by Chart 7 is what is the value and
what is the effect on yield spreads o f longer periods
of call deferment ? In particular, what is the value
o f call deferment until maturity (fo r 20 or 30 years)

Chart 8



that characterizes state and local and most U . S.
governm ent bonds ? T he specific answer to that ques­
tion is unknown, since there are no yield series that
isolate longer periods of call deferment.17

One can

only speculate that in periods o f high interest rates,
such as 1969-1970, calculated yield series for securi­
ties with call provisions w ou ld

rise significantly

relative to long-term yield series for securities with

Note: Yield series are for A a seasoned utility bonds.

complete call protection. It seems likely, for example,

Source: Salom on Brothers, An Analytical Record of Yields
and Yield Spreads.

that part of the unexplained increase in the spread
between the corporate bond and U . S. governm ent
bond rates in the late 1960’s resulted because the
latter series excluded bonds callable in less than 10
years. In any case, the point is that call provisions
will not only affect the spreads between various co r­
porate bond rates, but they will also affect spreads
between yield series for corporate bonds and other
types of long-term securities with longer periods of

substantial effect on the calculated yield series. Chart
9 shows the usual F H A -in su red yield series com pared
to a recomputed one18 in which the call date assump­
tion is changed from 15 to 10 years.

T he latter rate

shows almost as much movement in the last 10 years

call deferment.
Y ield series for m ortgages, unlike those fo r the
other long-term securities, are com puted by assuming
that the mortgage is called ( “ prepaid” ) at a date
before maturity.

m ortgage. W h en the assumed prepayment date is
changed for such discount m ortgages, it can have a

A lthough there are often “ prepay­

as the corporate bond yield series in Chart 1.




m ortgage


shown in Chart 1, and the corporate bond rate, h ow ­
ever, fell considerably during the same p eriod.19

ment penalties,” they do not enter into the com puta­

Default risk and yield spreads

tion of com m only used yield series. F or the yield
series on conventional m ortgages shown in Chart 1,

last element in yield spreads to be considered results

T h e fou rth and

the calculated yield series. F or yield series on F H A -

from the fact that the yield to maturity form ula im ­
plicitly assumes that the prom ised returns associated
with holding a particular security are know n with

insured m ortgages, however, the prepayment assump­
tion can substantially affect the yield series, because
F H A -in su red m ortgages sell at a discount when

certainty and that there is no risk o f delay or failure
in making those returns. In fact, there is default risk
associated with holding m ost securities, and the

market yields are greater than the m axim um perm is­
sible “ interest rate” on the mortgages. In order to
raise the effective yield of the m ortgage, the p u r­

amount o f this risk as perceived by investors varies
from security to security.

the prepayment date assumption has little effect on

chaser adjusts the actual amount o f the loan rather
than the m onthly payments. In the context o f fo r ­

Consider, as an example, the situation of an in­
vestor faced with the option of buying one of tw o
T he first one is, say, a U nited States

mula ( 1 ) , when C is at the legal m axim um , the

governm ent bond, which is assumed to be completely

yield, r, is adjusted by changes in P , the price of the

free of default risk. T he yield to maturity, ri, will be

1 After setting values for CP, i, m, and N, and imposing the condi­
tion that r in formula (1) equals r ' in formula (4 ), the yield to
maturity and yield to call on a deferred callable security can be
calculated and compared. Because of the call penalty, a yield to
call greater than yield to maturity does not necessarily imply an
expectation of falling interest rates. However, given fixed interest
rate expectations, a fall in interest rates from a level at which a
deferred callable security has a higher yield to maturity than a
noncallable security will decrease the spread between the yield to
call and yield to maturity of the deferred callable security.

18 The series was recomputed through 1967 in an extremely interest­
ing book by Jack M. Guttentag and Morris Beck, New Series on
Home Mortgage Yields Since 1951 (New York: National Bureau of
Economic Research, 1970), p. 184. The series was recomputed from
1968 to the present by making the assumption that the relationship
between the changes in the two series was the same as in the earlier
period. If anything, the difference between the two series is under­
estimated in the latter period, since FHA-insured mortgages had
even greater discounts in that period.

17 One estimate is that the value of a 30-year call deferment in a
period of high interest rates is 70 basis points. See Gordon Pye,
“ The Value of Call Deferment on a Bond: Some Empirical Results,”
The Journal of Finance, 22 (December 1967), 623-36.

1 Guttentag and Beck, op. cit., pp. 63-70, provide a reasonable
explanation, based on the behavior of the different sectoral partici­
pants in the two markets, for the greater movement of the F H A insured mortgage rate series than the conventional mortgage rate
series in the period under consideration.



will default, either by nonpayment or delayed pay­

securities is apparently determined largely by quality
ratings made by investment agencies such as M o o d y ’s
Investors Service. T he market risk premium o f a
security wih a given rating is the spread between the
yield series for that rating and that of a U . S. govern ­

ment of the coupons or face value of the bond.

ment security of comparable maturity.

accurately determined by form ula ( 1 ) and will be
known with certainty. The second security is a co r ­
porate bond for which the investor definitely feels
there is some possibility that the issuing corporation

will foresee a number of possible streams o f returns
associated with holding the bond, only one of which

corporate bonds rated by M o o d y ’ s. T he highest, Aaa,

corresponds to the full promised amounts at the

is for “ bonds with the smallest degree o f investment

prom ised time periods.

r is k ; interest payments are protected by a large or by
an exceptionally stable margin and principal is se­

B y em ploying form ula ( 1 )

each possible stream of returns implies a different
yield to maturity for the bond. T he investor’s e x ­
pected yield to maturity on the second bond, r2e, can
be thought of as the average of all the possible yields

Chart 10 shows yield series for four categories of


T he lowest rating shown, Baa, is for bonds

whose “ interest payments and principal appear ade­

to maturity com puted in this fashion. Clearly, if ri,
the prom ised yield to maturity on the risk-free bond,

quate for the present but certain protective elements
may be lacking or may be characteristically unreliable
over any great length of time.”
Since none o f the

is equal to r2, the prom ised yield to maturity on the
bond subject to default risk, then r x will be greater

four yield series ever intersects, the opinions o f in­

than r 2e, the expected yield to maturity on the risky

T he investor, that is to say the market, will

prefer the default-free bond to the one perceived to
have default risk. T his preference will drive up the
price of the default-free security relative to the price
o f the risky security to the point where ri = r2e.
H ence r2, the calculated yield series on the risky
security, will be greater than rt.

T he difference be­

tween r2 and ri is generally called the “ market risk

vestors, in general, correspond with those of M o o d y ’s.
A com m only asked question is what determines the
quality rating of a particular security?20


that have been cited in response to that question fall
into tw o predictable classes. T he first set o f vari­
ables is related to the balance sheet o f the issuer of
the security, and the second set to the size and sta­
bility of the issuer’s net incom e flow s.

F o r example,

balance sheet variables that have been determined to

In the w orld de­

be related to the quality ratings o f corporate bonds
are ( 1 ) the ratio o f long-term debt to total capitali­

scribed above, it would equal r2 — r2e, the “ expected

zation, a measure of leverage, and ( 2 ) the market

prem ium ” for the risky security.

default loss” (difference between the prom ised and
expected yields to m aturity) on the risky security.
In the real w orld the perceived quality, or relative
lack o f default risk, on state and local and corporate

Digitized for12

20 Recent articles that have dealt with this question are Thomas F.
Pogue and Robert M. Soldofsky, “ W hat’s in a (Corporate) Bond
Rating?” Journal of Financial and Quantitative Analysis, 4 (June
1969), 201-28, and Williard T. Carleton and Eugene M. Lerner,
“ Statistical Credit Scoring on Municipal Bonds,” Journal of Money,
Credit and Banking, 1 (November 1969), 750-62.


Chart 10


value of all publicly traded bonds of the com pany, a

larly in the fourth quarter, which was the worst.

measure of marketability. Incom e variables that have
been related to corporate bond ratings are the earn­
ings variability of the com pany and the ratio o f after­

D uring the rest of the period, however, the spread
did not m ove closely with changes in real G N P . T he
same general observation may be made for state and

tax net income plus interest charges to interest

local rates over the period.
Table I shows that the spread between the c o r ­

charges, a measure of earnings coverage.
A second question is whether the yield spreads
embodied in market risk premium s respond inversely

porate bond rate series and the long-term U .


T he

governm ent bond rate series shown in Chart 1
reached its peak in the fourth quarter of 1970. In

spread between M o o d y ’s Baa and A aa corporate bond

view of the previous discussion and Chart 11, it

yield series is shown in Chart 11. Clearly, the spread
rose substantially in the recession of 1970, particu­

appears likely that the m ovem ent in the spread be­

to cyclical movement in econom ic activity.

tween the tw o interest rate series was affected not

Chart 11




only by the capital gains tax effect and call risk but
also by a cyclical movement in default risk premiums.
The relationship of the special features to the
other security characteristics T h e d iscu ssio n at
the beginning o f this article centered around the
notion that yield spreads could be neatly divided into
three classes related to characteristics o f marketable
securities. T he three classes of spreads w e r e : ( 1 )
those associated with differences in maturity, ( 2 )
those associated with differences in econom ic sectors
that issue and purchase various securities, and ( 3 )
those associated with differences in the four special
features discussed in this article.
In reality, however, it is extremely difficult to
isolate the part of an observed yield spread related
to each of these characteristics, as has been shown
with respect to the special features. It is useful to
consider briefly the difficulties the presence of the
special features can pose in attempting to isolate and
explain the amount of an observed spread between
security yields that is related to differences in m a­
turity or to the behavior of the particular econom ic
sectors that participate in the market for the securi­
ties. T w o exam ples should suffice.
First, in discussing the movement in yield spreads
over time related to different maturities (the term
stru ctu re), U . S. securities are generally used. T he

U . S. security yield curve fo r maturities greater
than five years. This bias increases as the difference
between the coupon and current market rates increase
and as taxes increase.21
A ttem pts to isolate movements in yield spreads
associated with the activity o f different econom ic
sectors are also difficult. F o r example, consider the
case of an increase in U . S. governm ent debt financed
by long-term bonds.

A n interesting question is how

will this action affect the long-term U . S. bond inter­
est rate relative to other rates, such as the corporate
bond rate. T o attempt to answer this question, it is
clearly desirable to have a corporate bond rate and a
long-term U . S. bond rate for securities that are
identical in all respects, in order to isolate the m ove­
ment (if an y) in the spread associated with the
governm ent debt financing operation. T he relation­
ship between the tw o interest rates in Chart 1, h o w ­
ever, is also affected by capital gains tax treatment,
by call risk, and by default risk.22 Furtherm ore, in
the period under consideration, there is no pair o f
long-term corporate and U . S. bond rates series that
are not influenced by these factors.

B y fo c u s in g on the m o v e m e n t o f

interest rate series over the past 10 years, this article
has attempted to demonstrate how the inability o f the
yield to maturity form ula to deal with taxes and

implicit assumption is that these securities are alike

uncertainty in calculating yield series contributes to

in all respects except maturity.
Table V I shows,
however, that this was not the case in the period

the creation

under consideration, since the long-term U . S. se­
curity yield series was for discount bonds. A s the
table indicates, a situation was created in which
the securities also differed with respect to their tax
treatment, im plying upward bias, albeit small, in the






am ong various long-term interest rates. In particular,
the article has shown that both incom e tax and capital
gains tax rates have effects on observed yield spreads
that vary with interest rate movements. T he article
also has illustrated the effect o f call provisions on
observed yield spreads and has shown how default
risk influences yield spreads.
T he article has made no attempt to explain ele­
ments o f observed yield spreads associated with

Table V I


differences in maturity or associated with the be­

Effect of Taxes On The Term Structure of Before-tax Seasoned

has pointed out, however, that these questions, par­

Security Yields (r) A ssum ing Equal After-tax Yields (r*)

ticularly the latter, are greatly com plicated by the

havior of different econom ic sectors.

C = 40 eg = Vit

effect on the level and m ovem ent of yield spreads o f
the four special features discussed.

t= 50%

t= 40%


















T im othy Q. C ook




















T he article

2 The effect of taxes on the term structure of U. S. security yields
was discussed by Alexander A . Robichek and W . David Niebuhr in
“ Tax-Induced Bias in Reported Treasury Yields,” Journal of Fi­
nance, 25 (December 1970), 1081-90.
22 Of course, an even greater problem is that there are other eco­
nomic sectors that are simultaneously acting in the securities mar­
kets, thereby influencing the relative yields.



A Microcosm of

International Banking Trends
T he grow in g and changing role of U . S. banks in
international finance is closely reflected in the recent
proliferation of E dge A ct C orporations and their
activities abroad.

A n E dge A ct C orporation is a

banking subsidiary organized under Section 2 5 (a ) of
the Federal R eserve A ct to conduct international

E dge Corporation.

A second and m ore serious e ro ­

sion occurred with the 1970 amendments to the Bank
H old in g Company A ct of 1956, as implemented by
Regulation Y

o f the B oard o f Governors.


amendment permitted bank holding com panies to
invest in any com pany in which an E dge Corporation

banking and financing operations.
T he styling is
derived from the name of Senator W alter E dge of

may invest other than one that accepts deposits in the

N ew Jersey, the sponsor of the 1919 legislation au­

panies were permitted investments previously denied

United States.

In other w ords, bank holding com ­

thorizing the Federal chartering of these institutions,

to com m ercial banks but permitted to their E dge sub­

largely by way of im proving the com petitive position
of U . S. banking institutions in international markets.

sidiaries. W ith the adoption o f these tw o amend­
ments, either banks or bank holding com panies could

Earlier legislation in 1916 had permitted the state

acquire, foreign equity interests form erly limited to

chartering of such institutions, which have since com e

E dge Corporations.

to be known as A greem ent C orporations because they

W ith perhaps the m ost im portant advantage of
E dge subsidiaries virtually eliminated, bankers were

must agree to observe the same limitations and re­
strictions as those applicable to Federally chartered
Edge A ct subsidiaries.

T he prim ary restriction on

forced to reevaluate the role of such subsidiaries to
determine whether the remaining advantages w a r­

both types of E dge subsidiaries is that their business

ranted their cost— the m ajor cost being a minimum

must be confined to international banking and finance.

capitalization requirement o f $2 million.

Early H istory1 D u rin g the 1920’s th ere w e re 18
Agreem ent and E dge A ct C orporations in the United
States, but this number diminished sharply during
the depression of the 1930’s, falling to only three at
one point.

B y the beginning o f W o rld W a r II six

T he m ajor

advantage remaining was the ability to use E dge
subsidiaries to conduct a banking business in d o ­
mestic financial centers across state boundaries from
the parent.
Out-of-State Edges

T h e a d v a n ta g es o f o u t-o f-

were in operation, the same number that existed as

state E dge subsidiaries have apparently been suffi­

late as 1959.

cient to warrant continued expansion.

F ollow in g this long period o f eclipse,

O f the 97

however, E dge subsidiaries reemerged in the 1960’s

E dge C orporations authorized as of June 30, 1973,

to play a prominent role in the present international

42 were w holly-ow ned banking type subsidiaries of

banking boom . B y June*30, 1973, there were 97 such
organizations, 91 of which were E dge A ct C orpora­

out-of-state banks. Furtherm ore, there has been an
increasing tendency fo r the larger U . S. banks to

tions and 6 of which were Agreem ent Corporations.

operate more than one E dge subsidiary in financial
centers in different parts of the country. A large

Primary Advantages

E d g e C o rp o ra tio n s have

traditionally enjoyed tw o main advantages over other
form s of international b an k in g : the ability to conduct
an international banking business in a different loca­
tion from the parent bank, even across state lines
and the ability to acquire and hold equity interests in


United States.


in business within


C orresponding to these tw o principal

advantages, tw o kinds of Edges have e v o lv e d : an
in-house holding com pany type and an out-of-state
banking type. In 1966, however, the Federal R eserve
A ct was amended to permit national banks to invest
directly in foreign banks. T his change represented a
m ajor erosion in the traditional advantage o f the
1 For a more complete account of the history of international
banking in the United States see “ U. S. Banking Abroad” in this
Bank’s 1970 Annual Report.

international bank, for example, may have E dges in
N ew Y ork , Chicago, M iam i, San Francisco, or L os
A ngeles, and perhaps H ouston.
T he proliferation of multiple E dges by the larger
banks has disturbed at least one member o f the Board
o f G overnors o f the Federal R eserve System. G over­
nor A ndrew F. Brim m er was quoted in the M arch 9,
1972, A m erican B anker as fo llo w s : “ I look at inter­
national financial centers as w indow s on the w orld,
but a bank doesn’t need an office in every such w in ­
d o w .”

G overnor Brim m er went on to indicate that

he saw no need fo r limits on the number o f banks
having E dge subsidiaries, particularly if the banks
were regional banks operating a unit in N ew Y o rk

H e apparently believes that every bank is en­

titled to a N ew Y o r k presence; but elsewhere, he



w ould limit banks to one E dge per region.

U nder

dom iciled within this District, tw o in V irginia and

G overnor


one in N orth Carolina.

B rim m er’s proposal, the United

O ne of the V irginia E dge

could be split into four re g io n s: the Eastern Sea­

C orporations is operated by its parent bank prim arily

board, the W est Coast, the Gulf Coast, and the
M iddle W est. U nder this regional concept, banks

as a representative in the V irginia ports area; the
other V irginia E dge subsidiary operates generally as

w ould be limited to the form ation of only one E dge

the international department for its parent holding

tffeit, on the East Coast, with the exception o f N ew

com pany and the subsidiary banks that share in its

l$5rk City.


G overnor Brimmer believes that this

T he N orth Carolina E dge C orporation

plari'Wcmld' help to avoid regional concentrations as

is engaged in foreign lending and investing as a

well as i^ew Y o rk concentrations o f international

supplement to the parent bank’s international activity.

b u siA e^ % fth in a select group of large banks.

T w o other Fifth District banks ow n m inority inter­

G overn or B rim m er’s personal proposal points out

ests, with 16 other banks, in A llied Bank Interna­

the dilemma raised by the ability of banks to estab­

tional, an E dge unit in N ew Y ork .

lish E dge A ct subsidiaries across state lines.
the one hand, this ability has enabled the larger re­

Fifth D istrict banks in the use o f the E dge vehicle

gional banks to establish a N ew

to provide an out-of-state presence.

Y o rk


thereby helping to broaden the base of this cou ntry’s
international banking structure. O n the other hand,
this ability has enabled the huge N ew Y o rk banks to
establish E dge units in other areas in order to co m ­
pete with the regional banks on their home ground
for their local international customers.
W hether
greater concentration or decentralization o f the inter­
national financial business has resulted is not known
at this time. It does appear, however, that the estab­

T his year has witnessed an increased interest by
In the early

part of this year a Fifth District bank, presently
having an E dge unit, opened a second E dge C or­
poration in N ew Y o rk C ity ; another bank has re­
ceived permission to do so. Both of these subsidiaries
will conduct a general international business.
W h ile Fifth District banks are showing an interest
in N ew Y ork-based E dge units, there have also been
indications by m ajor m oney-center banks o f an inter­
est in a Fifth District presence. N ew Y o rk banks

lishment of E dge subsidiaries in regional centers,

have investigated the ports of Baltimore and H am p­

such as H ouston, for example, has increased com p e­

ton R oads as possible sites fo r the establishment of

tition am ong banks in those locations.

E dge C orporations.

A fter the

Fifth District banks active in

initial shock, local bankers have realized that d o ­

the international market should be aware of the possi­

mestically their national divisions had long been

bility of this new com petitive force.

com peting with the N ew Y o rk banks for accounts

In conclusion, it is fair to say that there is the

and that this new entry into the local market for

beginning of an awareness by Fifth District banks o f

international banking services should make them look
to im proving their ow n operations.

the need to serve large clients on a national and inter­
national scale through E dge A ct Corporations in

F ifth

D istrict

P a rticip a tio n

W ith in

th e

F ifth

Federal R eserve District, the E dge A ct rush has not
yet occurred on a large scale, but there are indica­
tions of increased interest in the use of this vehicle.
A t present only three E dge A ct


financial centers other than the parents’ prim ary
market areas.

It also appears that m ajor interna­

tional banks have shown some interest in the Fifth
District as a potential market area.

subsidiaries are

D ouglas H . Lem m onds

Federal Reserve Bank of St. Louis, One Federal Reserve Bank Plaza, St. Louis, MO 63102