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Federal Reserve Bank of Richmond

:Jorking
Paper 77-3

THE RISK-FREE U.S. BOND RATE:

ERRORS

IN CONSTRUCTION AND USE IN ECONOMETRIC WORK

Timothy Q. Cook

and Patric H. Hendershott

December 1977

The views expressed here are solely those of
the authors and do not necessarily reflect the
views of the Federal Reserve Bank of Richmond.

THE RISK-FREE U.S. BOND RATE: ERRORS
IN CONSTRUCTION AND USE IN ECONOMETRIC WORK

Timothy Q. Cook* and Patric H. Hendershott**

I.

Introduction
Observed differentials among yield series for different types of

--U.S. government bonds, municipal bonds, corporate
long-term instruments
bonds and residential mortgages--vary considerably over time. Many factors
can contribute to observed long-term yield spreads, the most important of
which are "technical" factors that relate to differences in the particular
characteristics of instruments or in the investors that purchase them.
These include the tax status of various types of income accruing to the
security and the degree or certainty associated with that income. Longterm yield spreads might also be affected by relative security supplies
and relatively exogenous demands, e.g., Federal agency demands for residential mortgages, particularly if institutional constraints on permissible
yields or on the various sectors that purchase the long-term instruments
exist.

Failure to consider the effects of all of these factors has

frequently created misunderstanding both in the financial press and in
academia about the causes of observed yield spreads. For example, attempts
have been made to measure the impact on long-term yield spreads of individual
factors--such as default risk or relative security supplies--by comparing
yield series without proper regard for the concurrent impact of other
technical and/or fundamental factors.
This paper deals exclusively with long-term corporate and U.S.
government bond yields.

The most widely used series are Salomon Brother's

*Economist, Federal Reserve Bank of Richmond.
**Professor of Economics and Finance, Purdue University.

Aa deferred call new issue utility yield and the Federal Reserve Bulletin's
average yield on bonds maturing or callable in 10 years or more.1
spread between these series

The

is shown as the solid line in Chart 1.

(The

dashed line will be discussed later.) The spread has moved over a wide
range, rising sharply from 40 basis points in late 1965 to 235 basis
points in the second quarter of 1970, subsequently falling to 140 basis
points in early 1973, and then rising to almost 300 basis points in the
third quarter of 1974. The central question addressed in this paper is
what have been the relative contributions of taxes, risk, and relative
security supplies as determinants of these movements?
The general procedure used to deal with this question is as follows.
First, direct adjustments are made to the yield series to account for some
factors affecting them differently. These include the unusual tax treatment
of some of the income from U.S. government bonds and the impact of the
failure .of Con Edison to pay a dividend in 1974 on the probability investors
attached to receiving the quoted return on utility bonds.

Second, proxies

are specified to capture the impact of call risk, default risk, and relative
security supplies on the spread between the adjusted yield series. The
adjusted yield spread is then regressed on these proxies and the estimated
coefficients are used to compute the impact of these factors.

Section II

of the paper discusses technical factors that affect the yield spread
through their influence on the U.S. bond yield series and surveys several
studies that have used U.S. bond yield series without proper consideration

lThe yield series used throughout the paper are quarterly averages
of monthly data. Series from the Treasury Bulletin are for the last day
of the month while series from Salomon Brothers' are for the first day of
the following month. The Federal Reserve Bulletin's U.S. yield series is
a monthly average of daily figures.

BASIS POINTS

CHA,RT 1

300

250

200

RAa minus RUS
150

loo

50

RAa” minus RUS”
0

I
1961

1963

I

I
1965

I

I
1967

I

I
1969

I
.1971

I

I

I
1973

I

I
1975

CHART 1. The Spread between Salomon Brothers’ Aa Utility and the Federal Reserve’s Average U. S.

Yield Series and the Spread between the Aa Utility and New Issue Equivalent U. S. Yield Series

-3-

for the possible impact of technical factors on the movement of the series.
Section III constructs a "new issue equivalent" U.S. bond yield series that
attempts to eliminate some of the technical factors that contribute to the
spread between corporate and U.S. bond yield series. Different types of
risk that affect the spread through their impact on the corporate bond
yield series are discussed in Section IV.

Section V presents empirical

results.

II. Technical Factors Influencing U.S. Yield Series
Virtually all observed yield series are before-tax yields-tomaturity (or to the earliest call date in some cases) calculated under the
assumption that the future cash flows associated with owning a security are
known with certainty. In this framework the yield of a security is the
discount rate that equates the price of the security to the present value
of the before-tax future promised cash flows. However, the relevant yield
to investors is, abstracting from risk considerations, the discount rate
that equates the price to the present value of the future after-tax promised
returns. Because income that accrues from long-term securities is alternatively subject to the relevant marginal income tax rate, the capital gains
tax rate or, in some cases, no tax rate, a wide range of observed before-tax
yields can provide the same after-tax yield.
Two major technical factors have influenced the movement of the
average U.S. yield series relative to the movement of new issue yield series.
No new U.S. bonds with a maturity of 20 years or greater were

issued from

May 1963 through January 1973. Consequently, as a result of the rising
interest rate trend over that period, all outstanding U.S. bonds became
discount bonds.

Interest income on discount bonds is taxed at the relevant

marginal income tax rate, while the difference between the purchase Price

-4-

and the redemption value is taxed at the lower long-term capital gains tax
rate. Discount bonds have the secondary advantage that a larger part of
the tax is collected at a later date.2

For these reasons investors are

willing to accept a lower before-tax yield on discount bonds than on newlyissued bonds that are otherwise comparable in all respects.
The second factor is that virtually all U.S. bonds issued prior to
1971 are redeemable at par for estate tax-purposes. U.S. bonds that have
this feature are widely called "flower bonds."

Since these flower bonds are

also discount bonds, they offer the potential of a rapid capital gain.
Furthermore, prior to changes in the tax law made in the Tax Reform Act of
1976, the gain was free from capital gains taxation.3

(The capital gain did,

however, enter into the value of the estate and was therefore subject to
of
estate taxes.) The c'ombination the flower bond stipulation and the tax
treatment associated with the capital gain greatly reduced the before-tax
yield necessary to provide a given after-tax yield to the decedent's estate.
The most sought after flower bonds have been those with the lowest coupons,
selling at the greatest discounts,
A third technical factor that can influence the movement of the U.S.
average yield series relative to other yield series results from the fact
that the U.S. series is an average for bonds with a wide range of maturities,

2Robichek and Niebuhr [19] discuss these two factors,
3The Tax Reform Act of 1976 changed the tax basis for inherited
property to its cost to the decedent. For certain property, such as flower
bonds, beneficiaries may increase the cost basis to the fair market value
of the property on December 31, 1976. Consequently, under the new law, the
difference between the par value of the flower bond used for estate tax
purposes and the original cost or market value at the end of 1976, whichever is greater, is subject to capital gains taxation.

-5-

some as low as 10 years.

If the average maturity of the series changes

substantially over time, as one would expect given the absence of new
issues, it can result in a movement of the series solely due to a movement along the yield curve.

In fact, from January 1964 to January 1974,

for example, the average maturity of the U.S. yield series fell from
24.4 to 18.2 years.4

III. A Survey of Studies Using Observed U.S. Yield Series
In spite of the very significant impact of the technical factors on
observed U.S. ,bondyield series, these series have been widely used in three
types of studies.5 The first are studies of the impact of risk premiums on
yield spreads (or yield ratios).

Because Treasury securities are default

free, the spread between the yield on any other security and the yield on
Treasuries depends on the probability of default on the non-Treasury security.
However, a number of researchers have overemphasized default-risk as a determinant of yield spreads to the exclusion of other factors and in doing so
have drawn some questionable implications from their empirical results.
-Brenner [2], for example, concludes that a main determinant of spreads
between observed before-tax yield series on mortgages and Treasuries,

41t should be noted that Salomon Brothers has yield series that
effectively deal with two of the three problems discussed above. Their yield
series for fixed U.S. maturities (i.e., 10, 20, 30 years) are read from monthly
yield curves. When there is a choice of coupons, the curves follow the yields
of higher coupon issues in the longer maturities. The higher coupon (4 to
4-l/4 percent) bonds were largely unaffected by the estate tax effect in the
period when no new bonds were issued from 1963 through 1973. The Salomon
Brothers' series were, however, heavily influenced by the capital gains tax
effect in.those years.
5The use of U.S. bond yield series involves only minor problems prior
to the mid-1960's, because there was only a small differential between current
yields and coupons on seasoned U.S. bonds. In each of the studies cited, however, the series is used into the late 1960's, or beyond, when the tax-related
problems become severe.

-6-

municipal8 and Treasuries, and corporates and Treasuries is differences in
risk as measured by the differences in the variance of the yields.

An

important factor contributing to both the relatively small variance of the
U.S. rate and the relatively low level of the rate, however, was the dampened
movement of the before-tax rate resulting from the aapital gains tax effect
(Salomon Brothers' 20-year U.S. rate is used, thereby eliminating estate tax
problems). Consequently, a large part of both the movement in the spread
between the yield on an alternative long-term bond and the yield on U.S.
bonds--Brenner's dependent variable--and the difference between the variance
of the two yields--Brenner's independent variable--is due to the same underlying cause.
Bisignano [l] assumes that the spread between the corporate (apparently
Moody's Aaa seasoned series) and the U.S. average series is a measure of the
risk associated with Aaa-rated bonds.6

Because this spread rose sharply in

the late 1960's and remained high in the 1970's, he concludes that the risk
premium between high quality corporates and U.S. governments has risen sharply.
He further concludes that the market has been inefficient in letting this "risk
premium" persist. The increased differential.is, however, largely attributable
to the impact, noted above, of technical factors on the U.S. yield series and,
thus, may not be evidence of inefficient markets.
Perhaps the most interesting risk-related problem resulting from the
usage of observed U.S. yield series is found in Kichline, Laub and Stevens [15],
the study on which the Federal Reserve Board's Aaa newly issued and recently

6The problem with using the spread between Moody's Aaa rate and the
U.S. average rate can be seen immediately by comparing it to the spread
between Salomon Brothers' Aaa new issue industrial yield series and 20-year
high coupon U.S. yield series. The former spread is 185 basis points in 1975,
while the latter is only 66 basis points.

-7-

offered Aaa utility bond yield series is based.

In this case the technical

factors plaguing the U.S. series are built into the Board's utility series
because these series are constructed using estimated historical relationships
that involve the "observed yield on a long-term, risk-free U.S. government
bond."

Richline, Laub and Stevens construct a 20-year Aaa-rated 5-year

call utility yield series for periods when no such bonds are offered by
using data on other (lower-rated, nonutility, etc.) new issues. The
adjustment procedure converts the yield on an A-rated new utility issue,
for example, by using the implicit relationship:

(1)

RA - RAaa = i + c (RAaa - RUS),

where RA is the yield on the A-rated utility, RAaa is the yield on the Aaarated utility, RUS is

the

observed yield on the U.S. government bond, and

"aand ^bare coefficients estimated from data in the January 1960 through
February 1972 period when both A and Aaa utility bonds were issued. RUS
is too low throughout the second half of the period because it is for low
coupon, discount bonds; RAaa, however, is for new issue bonds.

Consequently,

the (RAaa - RUS) spread -is too large and c is biased downward.
Equation (1) can be rewritten as

(1)' RAaa-

>+rU,L
1+;
1+;

As long as the WS

RUS.
1+<

series used in equation (1)' continues to be for low

coupon bonds, the relationship would be roughly accurate because the impact
of the biases of G and RUS on the estimated RAaa would be offsetting. Once
RUS is switched to a high coupon bond, however, the estimated RAaa using
equation (1)' will be too high.

Furthermore, because the weight given RUS

in equation (1)' is biased downward, the error in the estimate will become

-8-

more severe as risk premiums rise.

That is, if RA and RUS are relatively

close, this bias will be less significant than if RA rises relative to RUS.
In the latter case we might expect the error built into the estimated RAaa
series to rise.
Comparison of the Board's Aaa, Ii-yearcall utility yield series and
Salomon Brothers' Aaa, 5-year call utility yield series supports the two
contentions made above. The two series move together very closely through
early 1973, the year when high coupon long-term U.S. bonds were again
issued. Subsequently, the Board series increases relative to the Salomon
Brothers series, rising to 45 basis points in the third quarter of 1974.
Thus, while the average spread between the two series in 1970 through 1972
was only l/3 of a basis point, the average spread from the beginning of 1974
through the third quarter of 1975 was 31 basis points.

In 1975 the Board's

equation was reestimated using data from 1973 through late 1975. Since then
the Board's estimated series and'salomon Brothers' series have been quite
close on average.
The second area in which U.S. yield series have been misused is the
term structure of interest rates. Hambor and Weintraub [ll] and Terre11 and
Frazier [21), for example, both attempt to determine the impact of relative
security supplies on the term structure of Treasury securities by relating
the ratio of the Treasury bill rate and the average long-term U.S. yield
series to relative stocks of short- and long-term U.S. securities. Because
no new U.S. bonds were issued over a large part of the.period studied, however,
the average long-term U.S. yield series is heavily influenced by the yields
on low coupon, discount and flower bonds.

Consequently, the relative supply

of long- to short-term U.S. securities declined at the same time that the
tax factors were exerting downward pressure on the average long-term U.S.

-9-

series. This generates a correlation between relative stocks and observed
relative yields, even if there is none between relative stocks and aftertax relative yields.
Dobson ['A]
uses the expectations hypothesis as embodied in the
observed pattern of (Salomon Brothers) U.S. yields to estimate risk
premiums for various maturities of U.S. bonds.

Over much of the period

he considers (1954-74), however, the slope of the U.S. yield curve was
biased downward due to the impact of the tax factors on the longer-term
yield series. Kichline, Laub and Stevens [IS] use the before-tax U.S.
yield curve and the expectations hypothesis to derive a series of forward
rates. The pattern of forward rates derived using such a procedure will,
during part of the period, be faulty because technical factors are creating
a divergence between the slopes of the before-tax and after-tax yield
curves; consequently, interest rate expectations implied by the beforetax yield curve will not be the same as those implied by the after-tax
yield curve.
A third type of study using the long-term average U.S. yield
series.(or Salomon Brothers' U.S. series) is studies of supply and demand
for financial claims and the impact of relative security supplies on longterm yield spreads. In view of the technical factors influencing beforetax U.S. yields, comparisons of the U.S. yield series (prior to 1973) with
new issue yield series on other instruments can be misleading.

Before-tax

yield differentials might be moving quite differently than after-tax differentials. Pesando [17] and Ostas [16] are examples of studies that use
the average of U.S. yield series, in
to explain financial behavior.

comparison with other yield series,

- 10 -

From the viewpoint of this paper, the most important study is that
They compare the level of the relative stocks of
of Fair and Malkiel .[.9]:.
utilities and U.S. government bonds to the level of the spread between
Salomon Brothers' utility and U.S. bond yield series.

Use of the U.S.

yield series introduces the same bias indicated in the studies cited
above that attempted to measure the impact of the relative stock of shortand long-term U.S. securities on their relative yields.

Over a long

period in which the Fair-Malkiel regressions were estimated (1961 through
mid-1969), the U.S. yield series was low relative to new issue corporate
yield series because of the capital gains tax effect.

During the same

period, due to the lack of new U.S. bond issues, the relative supply of
U.S. bonds was declining. Consequently, at least part of the observed
relation between relative corporate and U.S. supplies and relative corporate
and U.S. yields was due to technical, not fundamental, factors.7 Fair and
Ma$kiel conclude that their results "strongly support the theory that yield
differentials of alternative bond instruments of the same maturity are
influenced by stocks of bonds outstanding. . .I' A major goal of this
paper is to determine whether this conclusion still holds for the spread
between corporate and U.S. bond yields after technical factors are taken
into account.

'Pair and Malkiel [9] deal with this problem in one of their
regressions by using the spread between the U.S. bond rate and a low coupon
corporate bond rate. They also compare the spread between Moody industrial
and utility yields to the relative stocks of industrial and utilities. In
all cases their results support the conclusion that relative security supplies affect relative yields. The measured impact of relative supplies on
the U.S. corporate yield spread when the low coupon bond rate is used,
however, is only about 40 percent of the measured impact when the new
issue corporate rate Is used.

- 11 -

IV.

Construction of a New Issue Equivalent U.S. Bond Yield Series
We have constructed a U.S. bond yield series designed to eliminate,

or at least minimize, the technical factors affecting U.S. bond yield series
that create artificial differences between these yield series and new issue
yield series for other sectors, e.g., the corporate sector.8 The series,
hereafter labeled RUS*, was constructed by choosing selected U.S. bond
issues and converting their yields into "new issue equivalent" yields.
First, after making marginal and capital gains tax rate assumptions to
be discussed below, after-tax yields for these issues were,calculated.
Second, new issue yields that provided equivalent after-tax yields were
computed. The issues selected to construct the new issue equivalent
yield series, RUS*, were chosen according to the following rules:
1.

The maturity of a bond issue used in the series should
be 20 years or more. If the issue is callable and
selling at a premium, then the call date should be 20
years or more.

2.

The highest coupon issue available should be used so
as to eliminate all issues whose yields are affected
by the estate-tax provision from consideration.

The adjustment procedure is designed only to deal with the capital
gains tax effect.

It

will be argued below that at every point in time since

1961 (the beginning of our estimation period) the yields of the highest
coupon issues have been unaffected by the estate tax provision.

Hence, the

second rule effectively eliminates the flower bond tax effect.
The maturity requirement embodied in the first rule is used because
differentials among yields on instruments equal to or greater than 20 years
tend to be small and vary little over time. For instance, when there are

8Robichek and Niebuhr [19, p. 10901 proposed such a calculation
years ago.

- 12 -

current coupon, or close to current coupon, U.S. bonds in existence--and
yields can consequently be reasonably compared across maturities--the differential between 20 and 10 year maturity yields is large and variable,
while the difference between 30 and 20 year maturity yields is much smaller
and more stable. In 1973, 1974 and 1975, for example, the yield spreads
between Salomon Brothers' 20 and 10 year U.S. bond rates were 24, 60 and
62 basis points, respectively, while the differentials between Salomon
Brothers' 30 and 20 year U.S. rates were only 2, 4 and 19 basis points,
respectively.
The U.S. bond issues included in the composition of the Federal
Reserve Bulletin's long-term average U.S. bond yield series since 1961
are shown in an appendix with their coupons, maturities and offering dates.
Each issue is judged with respect to the two rules above and the issues used
to construct RUS* are indicated. The appendix also goes into greater detail
on the construction of our series. Due to the absence of alternative
acceptable choices, the maturity rule was violated, but only slightly, in
late 1972 and in the first part of 1973.
The spread between Salomon Brothers' Aa utility yield series, RAa,
and RUS* is the second series (the dashed one) shown in Chart 1.

The spread

between RAa and RUS* rises to a level of 120 basis points in the first quarter
of 1970, but is still only l/2 the level of the spread between RAa and RUS
at the same time.

Consequently, tax factors accounted for roughly one-half

of the observed rise in the spread bettieennew issue corporate and seasoned
U.S. yields in the second half of the 1960's,g and the unadjusted U.S. yield

gCook [5] suggested this magnitude.

- 13 -

series has, on average, been more than a full percentage point below the
fully-taxed, new issue equivalent yield series in the 1970-75 period.lO
Two important assumptions underlying the construction of the new
issue equivalent U.S. bond yield series should be discussed at this point.
The first is the assumption that the yield of the 4-1/4's of 87-92, which
is used in the construction of the series from August 1962 through January
1973, was not affected by its estate-tax provision over that period.11
This assumption can be defended on two grounds.

First, data on year-end

amounts of flower bonds outstanding from the -Treasury Bulletin indicate
that there was very little demand for the 4-1/4's of 87-92 for estate tax
payment purposes through 1972. The net decline in the amount outstanding
of an issue from year to year is a measure of the amount retired for estate
tax purposes. The decline in the amount outstanding of the 4-1/4's of 87-92
was negligible until 1973. ,For lower coupon bonds such as the 3's of 95
the amount outstanding declined steadily beginning in the mid-1960's.
Further support for the assumption comes from a comparison of the yield of
the 4-141's of 87-92 with the yields of high coupon bonds issued in the
first half of 1973. When the 6-3/4's of 93 were issued in early 1973, the
spread between their yield and that of the 4-1/4's of 87-92 could be completely
explained by the capital gains effect, indicating that the estate tax provision was not putting additional downward pressure on the yield of the 4-1/4's
of 87-92 up to that time.

loBecause the U.S. series has traditionally been the discount rate
used in litigation cases to determine the present value of income lost due
to death or injury, these awards have been significantly overstated.
1'The growing impact of the estate tax provision on low coupon bond
yields in the 1973-76 period is discussed in Cook [4].

- 14 -

The second important assumption underlying the construction of the
new issue equivalent yield series is the appropriate marginal and capital
gains tax rates used to calculate after-tax yields.

The assumption employed

throughout the period examined is that these rates are equal to the prevailing
permanent corporate income and capital gains tax rates.

(The impact of the

imposition and removal of the surcharge on the tax rates was ignored.)
Attempts to justify this assumption can proceed from two directions: ex ante
or ex post. On an ex ante basis it

can be supported through 1969 because

numerous sectors in the market--savings and loan associations, commercial
banks, mutual savings banks--were subject to corporate income and capital
gains tax rates. The Tax Reform Act of 1969 modified the treatment of
capital gains for banks and the thrift institutions, however, by requiring
them to treat gains and losses on securities acquired after July 1969 as
ordinary income. Consequently, it is more difficult to justify the
assumption since then. Table I shows new issue equivalent yields for the
4-1/4's of 87-92 on the basis of three different tax rate assumptions. The
first are the corporate tax rates used in the construction of RUS*, the
second are the rates applicable to an individual in a 40 percent marginal
tax bracket, and the third are the relevant alien tax rates of 30 percent
for current income and 0 for capital gains. The alien tax rates are shown
because foreigners have been a major participant in the U.S. government
security market in the 1970's. The table shows that in the period following
the 1969 Tax Reford Act the two alternative tax rate assumptions would have
lowered the new issue equivalent yield series (prior to February 1973, when
we switch to high coupon issue yields) by 10 to 20 basis points.

Consequently,

while the assumption is somewhat tenuous in later years, other reasonable
assumptions have a fairly moderate, although not inconsequential, effect on
the series.

TABLE I
NEW ISSUE EQUIVALENT YIELDS OF 4-1/4's OF 87-92
USING DIFFERENT TAX RATE ASSUMPTIONS
L

Observed
Yield

Marginal and capital
gains tax rates
equal prevailing
corporate rates

Marginal tax
rate equals .40;
capital gains tax rate
equals .20

Marginal tax rate
equal .30;
capital gains tax
rate equals 0

4.49
(l/66)

4.56

4.55

4.54

5.57
(l/68)

5.98

5.88

5.87

7.69

7.53

7.50

6.54

6.48

6.47

6.89

(l/70)
6.02
(l/72)

TABLE 11
THE AVERAGE NEW ISSUE EQUIVALENT YIELDS FOR SEVERAL HIGH
COUPON U.S. BONDS (CORPORATE TAX RATES ASSUMED)

6-3/4's of 93
7-1/2's of 88-93
7's of 93-98
8-1/2's of 94-99
'\ 7-7/8'a of 95-00

8.28
8.13
8.16

8.20
8.12
8.21
8.26
8.32

- 15 -

On an ex post basis it is appropriate to ask whether the tax rate
assumption results in equivalent after-tax yield series for different coupon
bonds of similar maturity.

Robichek and Niebuhr [19, p. 1089) looked at

numerous pairs of low coupon bond issues of equal maturity in 1966 and 1969
and concluded that the tax rate assumption that best explained the spreads
between their yields was a 44 percent marginal tax rate assumption (with a
22 percent capital gains tax rate assumption). This assumption would
lower RUS* slightly prior to 1970 and leave it virtually unchanged thereafter,
because the 44/22 assumption results in the same new issue equivalent yield
series as the 48/30 corporate tax rates in force after the Tax Reform Act.
A better basis for judging the tax rate assumptions is to compare
I

the new issue equivalent yield series of high and low coupon bonds of equal
maturity. Unfortunately, due to the growing impact of the estate tax effect
on the low coupon bonds in late 1973 there is only a short period in which
to make this comparison. On average, from February through July 1973 the
new issue equivalent yield of the 4-1/4's of 87-92 was 16 basis points
higher than the new issue equivalent yield of the G-3/4's of 93 providing
some indication that the corporate tax rate assumption might be too high.
Another worthwhile period of comparison is 1975, when there is a wide range
of high coupon (6-3/4 to 8-l/2 percent) bonds.
new issue equivalent yields for five bonds.

Table II shows the average

The table indicates that the

corporate tax rate assumptions are roughly appropriate. For instance, the
new issue equivalent yields of the 7's of 93-98 and the 8-1/2's of 94-99 are
within five basis points of each other.

v.

Risk Factors Affecting the Corporate-U.S. Yield Spread
We employ Salomon Brothers' Aa deferred-call utility yield series,

RAa, as the corporate rate in our analysis because we believe it is superior

- 16 -

to alternative available corporate yield series.12

The major technical

factors affecting RAa relative to RUS* are call risk and default risk.
Default risk has influenced the spread between RAa and RUS* in three
possible ways, each of which is treated separately below and in the spread
regressions in the following section. First, there was an extraordinary
rise in the impact of risk premiums on utility yield series following
Con Edison's failure to pay a dividend in the second quarter of 1974. The
spread between Salomon Brothers' Aa utility and Aa industrial yield series,
which was stable through the 1970 recession, rose sharply in the second
quarter of 1974 and remained unusually high through 1975.

In this period

the spread between the Aa utility yield series and RUS* can be divided
into two parts:

(Ma-RUS*)

=

(RAa-IAa) +

(IAa-RUS*),

where IAa is the yield on Aa-rated industrial bonds.

These two parts cor-

respond to the notial risk premium for Aa-rated securities observed over
the business cycle and the special risk premium associated with Con Edison
dividend failure. In the empirical work in the following section, rather than
attempting to "explain" the special utility-related risk, the spread between
RAa and RUS* is simply reduced by the amount due to the rise

in the spread

between RAa and IAa.13 The resultant spread RAa* - RUS*, is the truncated

12The Federal Reserve's new issue Aaa yield series is not used for
reasons discussed earlier. Moody's new issue Aaa series is not used because
it is a conglomerate rate for both industrials and utilities and consequently
is affected by the relative mix of new issues; this is a particularly severe
problem in 1974-75 when spreads between Aaa utility and A;iaindustrial yields
are often as high as 60 to 70 basis points.
13Specifically, beginning in the second quarter of 1974 we subtract
(RAa-IAa.22) from the spread. The 22 basis points not subtracted out

- 17 -

dashed series in Chart 1.

As seen in the chart, this episode initially

generated over a 40 basis point risk premium.
Two rationales for cyclical movements in default risk premiums
have been advanced. Jaffee [13, p. 3121 has argued that cyclical movements
in risk premiums "are a technical feature resulting from the fact that
Moody's does not adjust its ratings for short-run business cycle developments." An alternative, or at least contributing, explanation is that
investors' views of risk vary systematically from Moody's over the business
cycle. Kichline, Laub and Stevens [15, p. 121 provide an explanation along
these lines citing Hirshleifer's time and state preference approach, which
implies that the utility of a particular investment depends
not only on the probability distribution of its monetary
returns, but also on the 'state of the world' at the time
those returns are received. A 'depression mentality' about
securities markets may reflect both pessimism about future
monetary returns, and a time in which investors don't think
a given probability distribution on future monetary returns
offers much utility--because of pessimistic beliefs about
the future 'states of the world.'
Either explanation suggests a need to adjust the corporate rate to remove the
impact of default risk or to incorporate variables reflecting cyclical default
risk in a model explaining the spread between risky and non-risky bond yields.
Two proxies are used in the following section to attempt to capture
the cyclical risk premium affecting the spread between Salomon Brothers' Aa
utility yield series and the new issue equivalent U.S. bond yield series.
The first is MOOD, a measure of consumer sentiment constructed by Fair [8]
based on data collected by the University of Michigan Survey Research Center.

represent the average spread between RAa and IAa prior to the Con Edison
dividend failure. The Aa industrial yield series is not used over the
whole period because it is not available prior to 1971.

- 18 -

Jaffee [13] found MOOD to be the most significant uariable in almost all
his risk premium regressions. The second proxy is the employment pressure
index (EPI), a series developed by William Cullison [6] that measures labor
market pressures by dividing actual employment figures by a population
adjusted,trend value.14

The index is designed to measure excess demand or

supply by assuming actual employment as a proxy for labor demand and using
the trend as a measure of long-term labor supply.
The presence of default risk affects the specification of the yield
spread regressions in a third way.

It is not immediately clear whether the

appropriate dependent variable when evaluating risk premiums is the ratio of
yields or the spread between yields.
studies.

Both

measures

have been used in other

The appropriate measure is the one that stays constant, when risk

is constant, as yield levels change. Unfortunately, neither specification
satisfies that requirement. Consider the following example. The after-tax
yield r of a new issue $100 risk-free bond sold at par is Cl(l-t)/lOO, where
t is the appropriate tax rate and Cl is the coupon.

If a risk factor e is

applied to both the coupon and the redemption value of a risky bond, then
the expected after-tax yield r' of the bond is determined by the formula:

100 -

f
n-l

C7(1-e)(l-t)
+-$++
(l+r')"

The promised after-tax yield of the risky bond is r" - C2(1-t)/lOO. Assuming
e is fixed and the expected after-tax yield of the risky bond r' is kept equal
to the after-tax yield of the riskless bond r, what will be the behavior of

140ther risk proxies such as the observed unemployment rate and the
Federal Reserve Board's capacity utilization rate for major materials were
also tested.

- 19 -

(r"-r) and P/r

as yields rise (or fall)?

yields rise, but the ratio r”/r

will fall.

The spread (r"-r) will rise as
However, the rise in the spread

as yields rise is linearly related to the rise in yields.

Consequently, an

appropriate procedure when estimating risk premium regressions is to use the
spread as the dependent variable and the level of rates as an independent
variable to capture the effect on the spread of a constant level of risk
as yields rise. For low levels of risk--for instance e = .02--this effect
is very small, hardly more than a basis point for each percentage point
rise in yields. For high levels of risk, however--such as e = .08--the
effect can be substantial, about 6 basis points for each percentage point
rise in yields. Jaffee 1131, without explanation, uses the level of rates
as an independent variable in his risk-spread regressions and estimates
significant coefficients ranging from 3 basis points to 5 basis points in
equations explaining BAA-AAA corporate, industrial and utility yield spreads.
Because the difference in default risk between Aa utilities and Treasury
securities is less than that between BAA and AAA corporate securities, the
impact of a percentage point increase in the risk-free rate should be even
less than three basis points.
The second risk factor affecting the corporate bond yield series
relative to RUS* is call risk. Jen and Wert [14], Frankena [lo], and Pye 1181
provide ample evidence that differential periods of call protection contribute
to observed yield spreads. Salomon Brothers' Aa utility yield series is for
bonds having 5 years of call protection, while the new issue equivalent U.S.
bond yield series is for bonds that have 20 or more years of call protection.
If rates are expected to fall to a level at the end of 5 years (or more)
that will justify calling the utility bond, then the current utility bond
yield will have to be high enough to compensate investors for the lower yield
they expect to earn in the years following the call.
between current

Consequently, the spread

utility and U.S. bond rates will increase.

- 20 -

An appropriate proxy to capture the impact of call risk on the
corporate bond yield is the spread between two yields whose relative levels
are solely a function of interest rate expectations. Finding two such
yield series is difficult for the very reasons that have been discussed
so far in.this paper.

For instance, Salomon Brothers has five and,ten

year U.S. rates that could be used to derive an explicit measure of the
expected change in interest rates over a five year period.

The ten year

yield series, however, is unquestionably affected by the tax factors
discussed earlier; hence the spread between the ten and five year rates
would be a biased proxy for expectations. Similarly, there are yield series
for long- and intermediate-term corporate (or municipal) bonds of the same
rating category. The spread between the long and intermediate rates, however,
is affected not only by interest-rate expectations but also by the relatively
greater impact of call risk on the long-term rate.
To overcome these difficulties we chose as the interestdrate expectations proxy (EW) the spread between Salomon Brothers 7 and 4 year U.S. rates.
Unlike the ten year maturity bonds, there were new seven year notes issued
during the second half of the 1960's. Consequently, the Salomon Brothers'
seven year series is not significantly affected by tax factors. Furthermore,
the spread between the seven and four year rates is clearly not affected by
default or call risk.

The Salomon Brothers' seven year series starts at the

beginning of 1967. From 1961 through 1966 we use the spread between Salomon
Brothers' five and two year U.S. yield series.
Our final proxy is to reflect the impact of relative security supplies
o=)

l

We define this proxy as the difference between the book value of

corporate bonds, net of the rest of the world, and the level of long-term
Treasury debt, net of holdings of the U.S. government and the Federal Reserve.

- 21 -

The former is from the Flow of Funds Accounts and the latter is from the
Treasury Bulletin. We include all Treasury debt having a maturity of five
years or greater.15 This proxy was tested both in level form--changes in
RSS have a permanent effect on yields a la Fair and Malkiel [9]--and in
first difference form--changes have a temporary impact a la Hendershott
and Kidwell [12]. An increase in RSS or ARSS should raise the rate spread.
Taking all the factors affecting Aa utility and Treasury long-term
yield series into account, we estimate the following equation for the spread
between the adjusted utility and new issue equivalent U.S. yield series:
+
+
+
RAa*-RUS*=f-(MOOD,
EPI, EXP, RUS*, RSS and/or ARSS),

where the signs over the variables denote the expected sign of the estimated
coefficients. The relationship between the dependent and independent variables
is assumed to be linear.16

VI.

Empirical Results
The results of the above yield spread regression estimated from the

beginning of 1961 through the end of 1975 are reported in the Table. The
yields are percentage points, EPI is the Employment Pressure Index ranging
from 98 to 102 over the estimation period, MOOD is the consumer sentiment

15A relative-security-supplies variable was also constructed using
only net U.S. debt having a maturity of 10 years or greater. The variable
is so closely-correlated to the one specified above, however, that it makes
virtually no difference which is included in the regressions.
16Actually, the relationship between JZXPand the spread should not
be linear since EXP, no matter how high, should never have a negative influence
on the spread. That is, at very high levels of EXP, its impact on the spread
should converge to 0. A functional form which has this characteristic is
e-E=.
Some of the equations reported in Section V were rerun using this
form for E2P. The results, however, were extremely close to those reported
assuming a strictly linear relationship between EXP and the yield spread.

- 22 -

index ranging from 58 to 97 , and RSS is largely a trend that rises from
$65 billion to $284 billion.

The equations were estimated using generalized

least squares and assuming a first order autoregressive error.
cedure is similar to the Corchrane-Orcutt procedure.

The pro-

The values of p are

reported in Table III.
The first equation reported in Table III includes all the variables
but RSS.

The coefficients of the cyclical default risk .variables,
MOOD and

EPI, and the call risk variable, EXP, both have the expected signs and are
significant at the 5 percent level. The coefficient of RUS* has the expected
sign and magnitude but is not significant. Equation (2) includes the RSS
variable. The coefficient of RSS has a positive sign and is significant at
the 20 percent level.

Inclusion of the variable, however, has the effect of

sharply lowering the coefficient of RUS*.
variables are highly correlated.
the 15 year period.)

This occurs because the two

(The correlation coefficient is .93 over

Equation (3) is equation (2) with the coefficient of

RUS* constralned to be .0205, its value in equation (1). The coefficient
of RSS in equation (3) would inply that RSS caused 7 basis points of the
rise in the (RAa*-RUS) spread between the beginning of 1962 and the end of
1969 or only 4 percent of the total rise. The change in RSS was substituted
for RSS in equations (2) and (3) but did not have the correct sign in either
equation.,
Additional insight into the difficulties of accurately determining
the impact of RSS on the yield spread is provided by equation (4), which
repeats equation (3) with the dependent variable changed from RAa*-RUS* to
RAa*-RbS (the unadjusted U.S. rate). The coefficient of RSS in equation

(4)

has a magnitude eight times greater than that in equation (3). Furthermore,
it has a highly significant t-statistic of 2.85 compared to the t-statistic

TABLE III

SPREAD REGRESSION RESULTS:

SALOMON BROTHERS' Aa UTILITY YIELD SERIES

LESS THE NEW ISSUE EQUIVALENT U. S. BOND YIELD SERIES

Dependent
Variable

(1) RAa*-RUS*

(2) RAa*-RUS*

(3) RAa*-RUS*

(4) R4a*-RUS

MOOD

EPI

EXP

11.36
(2.23)

-.0116
(2.40)

-.0977
(1.97)

-.6698
(3.32)

-.0109
(2.22)

-.0914
(1.80)

-.7318
(3.54)

10.31
(2.02)

-.OlOO
(2.06)

-.0894
(1.81)

-.6492
(3.40)

.0205

13.76
(2.05)

-.0091
(1.51)

-.1250
(1.92)

-.8334
(3.66)

.r)205

D.W.

.46

.74

2.02

.23

.42

.76

2.06

.0007

C.66)

P

.0020
(1.02)

B.0551
-

E2

.22

.41

.72

1.99

.36

.73

.86

2.33

C.42)

10.88
(2.08)

SE

.23

RUS*

Constant

RSS

.0205

t.65)

.0056
(2.85)

-2

Rote: t-statistics are shown in parentheses. The SR and R (adjusted for degrees of freedom) are for the untransformed observations. The estimation period covers 60 quarters from 1961 I through 1975 IV. The Aa utility
rate is adjusted in 1974-75 as described in the text. The coefficient of RUS* in equations (3) and (4) is
constrained to .0205.

. .

_-

-

..

-

-.

..

.-

-

_~~

._

- 23 -

of .65 for the RSS coefficient in equation (3). These results occur because
the impact of the tax
variable.

effects on RUS as yields rise are captured by the RSS

(The correlation coefficient between RSS and RUS*-RUS is .92.)

Equation (4) suggests that changes in RSS accounted for 61 basis points of
the rise in the spread between the utility and average U.S. bond rate between
the beginning of 1962 and the end of 1969, in contrast to the 7 basis points
implied by equation (3). Failure to account for the tax effects on yields
was apparently the reason Fair and Malkiel [9] obtained results suggesting
the greater importance of relative security supplies.
The coefficient of the call risk proxy in equation (3) implies that
the value of 15 additional years of call protection--that is, the value of
20 years call protection minus the value of 5 years call protection--rose
49 basis points from its lowest level in the first half of 1963 to its
highest level in the second half of 1969. This value appears to be fairly
close (although somewhat smaller) to the value of 15 years of additional
call protection that would be forecast by Pye's model [18, p. 6301 given
the pattern of yield movement in the years prior to 1969.17 The coefficients
of the two default risk variables (MOOD and EPI), in conjunction with the
movement in these variables, suggest that the 1969-70 and 1973-75 recessions
raised the risk premium in the Aa bond rate by about 30 and 40 basis points,
respectively.18

17This conclusion is made on the basis of Tables II and III [18,
p. 630) and a one year Treasury bill rate in 1969 of 6.77 percent. The
Tables can not be used in later years , after rates had remained high for
longer periods of time.
18These estimates seened to us to possibly overstate the impact of
cyclical default risk, especially in the 1969-70 period. On the other hand,
the spread between Salomon Brothers' Aa and Aaa industrial yield series rose
from 10 basis points in 1973 to 30 basis points in the first quarter of 1975.
This increase does not appear inconsistent with our estimate of the rising
impact of cyclical default risk on the spread between RAa* and RUS* over
this period.

- 24 -

Conclusion
VII. -We conclude that technical factors can reasonably explain the
movement in the spread between Salomon Brothers' Aa deferred-call utility
yield series-and the Federal Reserve Board's long-term U.S. bond average
yield series. The most important of these is the more favorable tax
treatment extended seasoned discount bonds, which are heavily used to
construct the average (and all other) U.S. yield series through most of
the period studied. Another important tax-related feature affecting the
yield spread is the provision allowing bonds issued prior to 1971 to be
used for estate-tax purposes at par value.
Two other technical factors having a significant influence on the
spread are call risk and default risk. The former occurs because corporate
bonds underlying the Salomon Brothers' Aa utility yield series have only
five years of call protection, while bonds used in the construction of the
average (and other long-term) U.S. yield series have little or no call risk.
The presence of default risk has influenced the spread in three ways:
1) through a cyclical risk premium, 2) through the impact of rising yields,
given constant default risk, and 3) in 1974 and 1975 following the Con Edison
dividend payment failure, which raised Aa utility rates initially by over
40 basis points.
Perhaps the most striking finding of the study is the lack of support
for the view that relative security supplies are a significant factor contributing to the observed spread between the corporate and U.S. yield series
studied. We do not find this surprising. For relative security supplies to
affect an interest rate spread, there must be an absence of a large quantity
of funds that are indifferent at the margin between the two securities. While
we can imagine securities where this is true, high grade corporate8 and
Treasury bonds are not likely candidates.

- 25 -

Lastly, the results of our analysis point out the extreme difficulties encountered when using a pair of yield series to isolate and
analyze a particular phenomenon, such as the impact on interest rates of
default risk, call risk, interest rate expectations or relative security
suppliesC As a result of these difficulties, great care should be
exercised when making conclusions about any of these phenomenon on the
basis of observed movements in yield spreads.

APPENDIX

The general procedure used to calculate the new issue equivalent
U. S. bond yields is virtually identical to that employed by Robichek
and Niebuhr [19], while the actual calculations follow a procedure suggested by Colin and Bayer (31. We obtained monthly data from the
Treasury Bulletin for each of the issues to be used in the calculation.
Using the actual maturity of each bond over time, assuming semiannual
coupons, and using the prevailing corporate income (tc) and capital gains
(tg) tax rates, an after-tax yield series was calculated via the following
formula:
(1-t&coup

P=

;

n=l

(l+r)"

+

pm
(l+r)' -

Q(PAR-P)
(l+rjN

It was then transformed into a comparable "new issue" before-tax yield
series by dividing it by (l-t=). The actual issues and marginal income/
capital gains tax rates used to conpute the new issue equivalent yields
were:
January 1961 - December 1963:

52/25

January 1964 - December 1964:

50/25

January 1965 - December 1969: 48/25
January 1970 - December 1970: 48/28.7
January.1971 - December 1975:

48/30

Table Al lists the bonds whose yields are included in the longterm average U. S. yield series in or after 1961 and contains comments
on how the various bonds relate to the "rules" specified in the paper.
Two new issue equivalent U. S. yield.series were constructed. The first,
RUS*, used only the new issue yield series of the highest coupon bond

- A2 issue outstanding at any point in time. These issues are shown in Table A2.
The

second series, RUS**, is an average

of the new issue equivalent yields

on those bend issues (shown in Table A3) passing the maturity rule and
judged to be unaffected by the estate tax provision and that had coupons
close to the highest coupon bond outstanding. For instance, whereas RUM
uses only the new issue equivalent yield of the 4 1/4's of 87-92 from
May

1963 through February 1973, RUS** uses an average of the new issue

.equivalentyields of the 4 1/4's of 87-92, the 4's of 88-93, and the 4 1/8's
of 89-94.. There was little difference, however, between RUS* and RUS**,
so RUS* was used in all the empirical work.
The monthly values
Table A4.

of RUS* for the 1361-1375 period are listed in

After early 1973 the difference between RUS& and certain alter-

native U. S. bond yield series--such as Salomon Brothers and the Treasury
Department's constant maturity series--lessens greatly because only the
highest coupon bonds are

used in the construction of these series, and in

this latter period several high coupon non-flower bonds were issued.
Nevertheless, through most of the 1973-75 period, RUS* is higher than these
alternative series because even the high coupon bond issues were generally
selling at discounts, sometimes quite large, in this period.

Table Al
BONDS INCLUDED IN LONG-TERI'f
AVERAGE
U.S. YIELD SERIES IN OR AFTER 1961

Maturity (and call) date

Comment

Offering date_

3 7/8's of 74

pre-1961

Maturity too short.

4's of 80

pre-1961

Maturity too short.

3 1/2's of 80

pre-1961

Maturity too short.

3 1/4's of 78-83

pre-1961

Coupon too low.

3 1/4's of 85

pre-1961

Coupon too low.

4 1/4's of 75-85

pre-1961

Premium bond through 1964;
call period too short.

3 1/2's of 90

pre-1961

OK until 4 1/4's of 87-92.

4 1/4's of 87-92

August 1962

OK until 6 3/4's of 93.

4's of 88-93

February 1963

OK until 6 3/4's of 93.

4 1/8's of 89-94

May 1963

OK until 6 3/4's of 93.

3's of 95

pre-1961

Coupon too low.

3 1/2's of 98

pre-1961

OK

6 3/8's of 84

August 1972

?faturitytoo short.

6 1/8's of 86

November 1971

Maturity too short.

8 1/4's of 90

April 1975

Maturity too short.

6 3/4's of 93

January 1973

Maturity too short, but used
until 7's of 93-98.

7 1/2's of 88-93

September 1973

Premium bond for first 6
months; maturity too short.

7's of 93-98

June 1973

OK.

8 1/2's of 94-99

June 1974

Usually a premium bond; call
period too short.

February 1975

OK.

September 1975

OK,

, 7 7/8's of 95-00
8 3/8's of 95-00

it

8 1/4's of 00-05

June 1975

until 4 1/4's of 87-92.

but disregarded because
has only 4 observations.

OK.

Table A2
BOND ISSUES USED TO CONSTRUCT RUS*
From January 1961:

3 1/2's of 98

From August 1962:

4 1/4's of 87-92

From February 1973:

6 3/4's of 93

From June 1973:

7's of 93-98

From February 1975:

7 7/8's of 00-05

Table A3

BOND ISSUES USED TO CONSTRUCT RUS**

From January 1961:

3 1/2's of 98
3 1/2's of 90

From August 1962:

4 1/4's of 89-92

From February 1963:

4 1/4's of 87-92
4's of 88-93

From May 1963:

4 1/4's of 87-92
4's of 88-93
4 1/8's of 89-94

From February 1973:

6 3/4's of 93

From June 1973:

7's of 93-98

From February 1975:

7's of 93-98
7 7/8's of 95-00

From June 1975:

7's of 93-98
7 7/8's of 95-00
8 1/4's of 00-05

Table A4
NEW ISSUE EQUIVALENT U.S. BOND YIELD SERIES
(End-of-Month Rates)

1961

1962

1963

1964

1965

1966

1967

1968

1969

1900

1971

1972

1973

1974

197!

January

4.15

4.33

3.96

4.18

4.23

4.67

4.58

5.75

6.85

7.79

6.77

6.71

6.88

7.54

7.9(

February

3.94

4.33

3.94

4.18

4.25

4.94

4.81

5.83

6.85

7.23

6.96

6.62

6.94

7.62

7.8:

klarch

3.96

4.19

3.98

'4.25

4.23

4.73

4.65

6.06

6.87

7.38

6.50

6.77

6.92

8.06

8.31

April

3.85

4.08

4.03

4.22

4.23

4.81

4.96

5.88

6.52

7.88

6.83

6.75

6.94

8.37

8.5(

-Y

3.87

4.17

4.03

4*14

4.23

4.88

5.02

5.87

7.10

8.42

6.92

6.54

7.12

8.25

8.2!

June

4.10

4.27

4.04

4.14

4.23

4.96

5.37

5.73

6.92

7.98

7.12

6.67

7.19

8.29

8.1!

JOY

4.12

4.17

4.02

4.20

4.23

5.02

5.33

5.50

6.88

7.73

7.13

6.52

7.79

8.54

8.31

August

4.25

.4.06

4.02

4.22

4.29

5.23

5.44

5.54

7.04

7.85

6.71

6.52

7.40

8.85

8.5(

September

4.27

4.02

4.08

4.21

4.35

5.00

5.50

5;69

7.65

7.69

6.54

6.65

7.04

8.75

8.71

October

4.25

3.96

4.15

4.18

4.37

4.83

5.92

5.85

7.33

7.81

6.40

6.44

7.35

8.27

8.2:

November

4.28

3.96

4.15

4.22

4.46

4.98

6.15

6.17

7.62

7.12

6.54

6.29

7.23

8,04

8.41

December

4.33

3.90

4.18

4.23

4.56

4.65

5.98

6.56

7.69

7.21

6.54

6.58

7.38

7.90

8.1(

REFERENCES

1.

J. Bisignano. "Inflation and the Efficiency of Capital Markets,"
Federal Reserve Bank of San Francisco Economic Rev&,
(summer 1976).

2. M. Brenner. "Determinants of Yield Differentials," forthcoming in
A. Sametz, The Financial Environment, 1976-1985, D.C. Heath & Co.,
(1977).
3.

J. W. Colin and R. S. Bayer. "Calculation of Tax Effective Yields for
Discount Instruments," Journal of Financial and Quantitative Analysis,
(June 1970), pp. 265-73.

4.

T. Q. Cook. "Changing Yield Spreads in the U.S. Government Bond Market,'
Federal Reserve Bank of Richmond Economic Review, (!Iarch/April
1977).
Dp.

3-8.

5.

T. Q. Cook. 'Some Factors Affecting Long-term Yield Spreads in Recent
Years," Federal Reserve Bank of Richmond ?lonthlgReview, (September
1373). no. 2-14.

6.

W. E. Cullison. "An Employment Pressure Index as an Alternative Measure
of Labor !farketConditions," The Review of Economics and Statistics,
(February 1975), pn. 115-21.

-7.

S. W. Dobson. 'U.S. Government Securities Reflect No Increase in Uncertainty," Federal Reserve Bank of Dallas Business Review, (October
1976), pp. 6-11.

8.

R. C. Fair. A Short-run Forecasting ?fodelof the United States Economy,
D. C. Heath &.Co., Lexington, ilassachusetts,(1971).

9.

R. C. Fair and B. C. ?lalkiel,'The Determinants of Yield Differentials
Between Debt Instruments of the Same Maturity," Journal of Plonev,Credit
and Banking, (November 19711, pp. 733-49.

10. PI.W. Frankena. 'The Influence of Call Provisions and Coupon Rate on
the Yields of Corporate Bonds,' in Essays on Interest Rates, Volume II,
National Bureau of Economic Research, New York, (1971).
11.

J. C. Hambor and R. E. Neintraub. 'The Term Structure: Another Look,"
Journal of Money, Credit and Banking, (November 1974), pp* 551-57.

12.

P. H. Hendershott and D. S.Ridwell.. 'The Impact of Relative Security
Supplies: A Test With Data From a Regional Tax-Exempt Bond Market,"
Journal of Money, Credit and Banking, (August 1978).

13.

Variations in the Risk Struature of Interest
D. M. Jaffee. "Cyclical
Rates," Journal of Monetarv Economics, Volume I, Number 2, pp. 309-25.

14.

F. C. Jen and J. E. Wert. 'The Effect of Call Risk on Corporate Bond
Yields," Journal of Finance, (December 19671, pp* 637-51.

15.

J. L. Kichline, P. M. Laub, and G. V. G. Stevens, "Obtaining the Yield
on a Standard Bond from a Sample of Botids
with Heterogeneous Characteristics," Staff Economic Studies '77, Board of Governors of the Federal
Reserve System, (1973).

16.

J. R. Ostas. "Effects of Usury Ceilings in the ?iortgageMarket," -Journal
of Finance, (June 1976), pp. 821-34.

17.

J. E. Pesando. 'The Interest Sensitivity of the Flow of Funds Through
Life Insurance Companies: An Econometric Analysis," Journal of Finance,
(September 1974), pp. 1105-21.

18.

G. Pye. "The Value of Call Deferment on a Bond:
Journal of Finance, (December 1967), pp. 623-36.

19.

A. A. Robichek and GJ.D. Niebuhr. 'Tax-Induced Bias in Reported Treasury
Yields," Journal of Finance, (December 1970), pp. 1081-90.

20,

Salomon Brothers, An Analytical Record of Yields and Yield Spreads, New
York, (1976).

21.

I?,T. Terre11 and I:t. Frazer, .Jr. "Interest Rates, Portfolio Behavior,
J.
and Xarkctable Government Securities," .Journalof Finance, (Ifarch
1972),
pp.

l-33.

Some Empirical Results,'