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Do yield curves normally slope up?The term structure of interest
rates, 1862-1982
John H. Wood
The downward-sloping yield curves of recentyears have been
called perverse, but an examina-tion of the history of American
interest ratesreveals that, at least since the Civil War,
fallingyield curves have been nearly as common asthose with upward
slopes. This article summar-izes yield curve patterns since 1862
and suggeststhat (1) the traditional expectations theoryremains a
viable explanation of observed yieldcurves and (2) yield curves
since the abandon-ment of the gold standard in 1971 have much
incommon with those of the greenback era of1862-78 but are distinct
from those of the goldstandard years of 1879-1970. The slopes of
yieldcurves appear to depend upon expectations offuture yields as
determined by expectations ofinflation, which, in turn, depend upon
the pre-vailing monetary standard.
U.S. yield curves in the 20th century
Yield curves for high-grade corporate bondsfrom 1900 to 1982 are
shown in the two panelsof Figure 1.' Each curve shows the term
struc-ture of yields in a particular year, i.e., the rela-tionship
between bond yields and terms tomaturity at a point in time. Panel
A shows yieldcurves for the period prior to 1930. Yield curves
John H. Wood is a Professor of Finance at NorthwesternUniversity
and is currently on leave at the Federal ReserveBank of Dallas.
This paper was written while the author was aconsultant for the
Federal Reserve Bank of Chicago and ispart of a larger study being
conducted with Scott Ulman.
'Data are David Durand's "basic yields on high-gradecorporate
bonds," first published in 1942, updated byDurand and Winn to 1959,
and updated since 1959 byScudder, Stevens and Clark. Selected data
are available for1900-1970 in the U.S. Department of Commerce,
HistoricalStatistics of the United States, Vol. 2, p. 1004, and
morerecently in the annual Statistical Abstract of the
UnitedStates. Ruth Heisler of Scudder, Stevens and Clark has
kindlysupplied data for 1982. A detailed account of the method
bywhich the yield curves in Figure 1 were constructed is givenin
Durand [1942].
Federal Reserve Bank of Chicago
for 1930 through 1982 are shown in Panel B.Curves since 1966
have been identified by yearof occurrence.
A striking feature of the yield curves in Fig-ure 1 is their
tendency to be positively slopedwhen yields are "low" and to be
negativelysloped when yields are "high." Suppose, forexample, that
between 1900 and 1970 one-yearbond yields above 4.40 percent were
consideredhigh and yields below 3.25 percent were thoughtto be low.
The upper portion of Table 1 showsthat if "high" and "low" are
distinguished in thismanner all yield curves had negative
slopeswhen short-term yields were high and all yieldcurves had
positive slopes when short-termyields were low.
This observation applies throughout the1900-1970 period, but
breaks down after 1970.In order to understand yield patterns since
1970,it is first necessary to examine a popular andpersuasive
explanation of the shapes of observedyield curves.
An explanation: the traditionalexpectations theory with
regressiveexpectations2
Any theory of equilibrium relations amongbond yields must
specify (1) the criteria bywhich investors select bonds given their
expec-tations of future yields and (2) how thoseexpectations are
formed. With regard to (1), thetraditional expectations theory of
the term struc-ture of interest rates asserts that
bond-marketequilibrium requires equal expected returns on
2The "traditional" and other expectations theories,most notably
the "modern" expectations theory, are com-pared in Cox, Ingersoll,
and Ross [1981]. An early statementof the traditional expectations
theory with regressive expec-tations was that of Lutz [1937].
17
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14
13
12
a—
7 —
6 —
5 --
4 —
3 —
—
1 —
11
10 F-
6
5
4
3
2
0
bonds of all maturities.' For the simple case ofpure discount
(zero-coupon) bonds, this implieslong-term yields that are averages
of current andexpected short-term yields (see Box).
To convert the expectations theory into anoperational
explanation of the term structure, amechanism for determining
expected short-term yields must be specified. Only two of
thesimplest and most common types of expectations—extrapolative and
regressive—are consideredhere.3 This statement may be illustrated
as follows for 1- and2-period bonds and a 1-period holding period.
The 1-periodrate-of-return on a 2-period zero-coupon bond worth 81
atmaturity is 31 Si
- per 1 1 r ,4171 11 +f4,1 2 11+ 9212
51 I1 s F./1
,•
where p 2 is the current price of the 2-period bond and 1 P
e1isthe price currently expected to prevail next period on
a1-period bond. If the expectations theory holds, (see equa-tion
(1) in Box) this rate-of-return equals R 1 —i.e., theexpected
1-period returns on 1- and 2-period bonds areequal. As indicated in
the Box, these results hold preciselyonly under conditions of
certainty.
FigurePanel k yield curves for high-gradecorporate bonds,
1900-1929
yields-to-maturity (percent)
Figure 1
Panel B: yield curves for high-gradecorporate bonds,
1930-1982
yields to maturity (percent)
15
1981
1980
1979
9
1981
I I I I 1 I I 0 I I I I I I I II 5 10 15 20 25 30 1 5 10 15 20
25 30
years to maturity years to maturitySOURCE Durand 11942 1958,
Durand and Winn ( 947) and Scudder Stevens and Clark,
18 Economic Perspectives
-
"The traditional expectations theoryof the term structure
The equilibrium term structure is
(1) (1+Fi n ) n = (1+R1)(11-1R7)(1+2R7)
• • (1+n-1 i),
where R 1 and 120 are the yields-to-maturitycurrently prevailing
on bonds maturing after oneand n periods, respectively, and
R e are the one-periodRev 2 RI' ' ' ' 'yields currently expected
by investors to prevailone, two, . . , and ( n-11 periods in thr
future.
A convenient linear approximation of theequilibrium term
structure describes long-termyields as arithmetic averages, instead
of geometricaverages as in equation ( ), of current and
expectedshort-term yields:
R 1 + 1 Re1 2R1 " . 11-1131(2) R =n
This approximation deteriorates as short and long
(
yields diverge. For example, let % be the approxi-mate
two-period yield given by equation ( 2 ). Then
Extrapolative expectations mean that inves-tors expect
short-term yields to continue tomove in the same direction as
recent yieldmovements. If yields have been rising, they areexpected
to continue to rise in the future. Ifyields have been falling, they
are expected to fallfurther.
Regressive expectations imply just the op-posite of
extrapolative expectations. If yieldshave been rising, they are
expected to reversecourse, or regress, towards what are
considered"normal" levels. If yields are below "normal,"they are
expected to rise.
Now, suppose that yields have fallen to lowlevels such that the
current short-term yieldis R1 = .02 and, because investors
extrapolaterecent events into the future, the short-termyield
expected to prevail in the next periodis / n 1 = .01. Using the
approximation pro-vided by equation (2) in the Box, this means
atwo-period yield of R2 = (.02 + .01)/2 = .015,and the yield curve
has a negative slope.
Federal Reserve Bank of Chicago
comparing R e2 with R2 from equation (I).
R2 = R 2 = .10 if R 1 = 1 R ei = .10;
= .10 and R 2 = .0997 if R i = .075 and
Re = .125; and R a = .10 and R 2 = .09891 2if R = .05 1 and Fri
.15.
Equation (1) is itself an approximation ofobserved yield curves
even if all the usual assump-tions of the traditional expectations
theory aresatisfied. One reason is that equation (1)
neglectsuncertainty and is therefore valid only under con-ditions
of perfect foresight. (This point has beenmade in different ways by
Nelson [1972, pp. 21-281and Cox, Ingersoll, and Ross [19811.)
Second,equation (1) strictly applies only to
zero-couponbonds—whereas most yield curves, including thosein Chart
1, are for coupon bonds. Garbade 11982,pp. 293-991 and others have
shown that the effectof coupons is to moderate the slopes of
yieldcurves implied by equation (I).
Although it would be difficult to assess theempirical importance
of these deficiencies, it isshown in the text that the traditional
expectationstheory with regressive expectations is at leastroughly
consistent with observed yield curves. j
Considering another example, suppose yieldshave risen to high
levels such that R 1 = .20. Ifexpectations are formed
extrapolatively, so that,perhaps, 1 R i = .21, we have R2 = .205
and theyield curve is rising. Thus, the traditional expec-tations
theory with extrapolative expectationssuggests that yield curves
will tend to have posi-tive slopes when yields are high and
negativeslopes when yields are low. This is inconsistentwith the
data in Figure 1 and Table 1, at least for1900-1970.
On the other hand, suppose short-termyields are expected to
regress toward some"normal" value denoted by R *, . Assume R .1*
=.06 and that the change in each later period isexpected to be
one-half the difference betweenthe normal yield and the short-term
yield prevail-ing in the preceding period. Given R 1 = .02 andR.T =
.06, these assumptions imply that
= R i s(R ;R 1 ) =
.02 + .5(.06 — .02) = .04,
19
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where s = .5 is the expected speed of adjustment.The resulting
yield curve has a positive slopebecause R2 = ( .02 + .04 )/2 = .03.
Following thesame procedure and letting R1 = .20, we obtain
Re1 =13 and-.
R2 = .165, so that the yield curve has a negativeslope when R 1
= .20. These examples supportthe view that the traditional
expectations theorysupplemented by regressive expectations is
con-sistent with observed yield curves, at least
during1900-1970.4
An upward revision of expectationsin the 1970s?
The upper portion of Table 1 suggests thatyield curves between
1900 and 1970 were con-sistent with the traditionalexpectations
theory with re-gressive expectations, if thenormal one-year,
high-gradecorporate bond yield wasthought by investors to bebetween
3.25 and 4.40 per-cent. But notice the high andrising yield curves
for1978 and 1982 in Figure 1.Either (1) the explanationthat is so
effective for 1900-1970 has failed in recentyears because investors
nolonger behave according tothe tenets of the
traditionalexpectations theory and/orthey no longer form
expec-tations regressively, or (2 )they have revised their
esti-mates of the normal rate.
The extrapolative expectations version ofthe traditional
expectations theory appears
'Both extrapolative and regressive expectations may berational
in an economy in which yields fluctuate cyclicallyabout "normal"
levels, with short-term expectations beingformed extrapolatively
and lung-term expectations beingformed regressively. Possible
examples of the interaction ofextrapolative and regressive
expectations are the hump-hacked yield curves that are common when
yields are high.These humps tend to occur at maturities of 3 to 6
months andthus do not appear in the yield curves of Figure 1, in
whichthe shortest maturity is one year.
broadly consistent with the generally risingyields and
positively sloped yield curves of 1971-78. But it does not look as
promising in light ofthe yield curves of 1979-81, which had
negativeslopes during a period of rapidly rising yields. Avariety
of other explanations of the events of1971-82 might be worth
pursuing, but the analy-sis of this paper will remain with the
explanationemphasized thus far—the traditional expecta-tions theory
with regressive expectations. Thatis, we will examine the extent to
which alterna-tive (2) in the preceding paragraph is capable
ofexplaining yield curves since 1971. But thisapproach requires an
additional hypothesis, onethat supplies a rule by which investors
revisetheir estimates of the normal rate. However,such a rule,
whatever it is, cannot be subjected to
Slope of yield curvePositive Flat Negative
1900 - 1970
0 0 20
10 10 5
26 0 0
1971 - 1982
1 0 3
8 a o
any kind of test on the basis of data considered sofar because
the only unambiguous 20th centuryrevision or revisions have
occurred since about1970. For other possible revisions we must go
tothe 19th century.
The 19th and 20th centuries compared
No complete yield curves such as those inFigure 1 are available
for the 19th century. How-ever, the slopes of yield curves may be
inferred
Table 1
Frequencies of rising, flat, and fallingyield curves.
1900.1992
One-year corporate bond yield(percent per annum)
Above 4.40
3.25 - 4.40
Below 3 25
Above 8.00
Below 8.00
SOURCES: Durand, Durand and Winn, and Scudder, Stevens and
Clark.
20 Perspectives
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10
9
8
7
6
5
4
3
2
Figure 2Long and short rates, 1862-1929percent
1862 1872 1882 1892 1902 1912 1922 1929SOURCE Macaulay (1938),
Table 10
from data on the prime commercial paper rate(the short-term
yield ) and Frederick Macaulay'srailroad bond yield index ( the
long-term yield ).5Annual averages of commercial paper and
rail-road bond yields for 1862-1929 are shown inFigure 2. This
figure tells, in a different way,essentially the same stories as
Figure 1: first, thatyield curves tended to be positively sloped
whenyields were low and negatively sloped whenyields were high and,
second, that there wasapparently a revision of the notions of '
'high"and "low".6 However. instead of an upward revi-
`See Macaulay (1938. Table 10) for data on the unad-justed index
of railroad bond yields. "Choice" and "prime"commercialpaper rates,
reported on a discount basis. havehen converted to bond equivalent
yields. Macaulay tried toconstruct yield curves for railroad bonds
like those laterreported by Durand, but he found the correlation
betweenyield and maturity too small. However, the use of
Macaulay'sdata in Table 2 is consistent with the use of Durand's
yieldcurves in Table 1 because Macaulay found that longer-termbonds
tended to have higher yields when short-term rates(such as the
commercial paper rate) were low and thatshorter-term bonds tended
to have higher yields when short-term rates were high (p. HO).
'During 1900-1929, when Figures 1 and 2 overlap, theyield curves
implied by the latter figure have the same sign asthose in the
former on three-quarters of the occasions onwhich Durand's yield
curves are not flat. Furthermore, theslopes implied by Figure 2
tend to be smaller in absolutevalue when Durand's curves are flat
than when they havenon-zero slopes.
sion, as in the early 1970s, Figure 2 suggests adownward
adjustment of the normal rate in thelate 1870s. Notice, for
example, that the sevenshort-term yields between 5.5S percent and
7.55percent during 1866-1875 were all associatedwith rising yield
curves, while after those yearsall short-term yields above 5.40
percent wereassociated with falling yield curves.
No precise dating of the normal rate's revi-sion, which may have
occurred over severalyears, is immediately obvious from the
data.(This is also true of the shift in the 1970s, orperhaps the
late 1960s.' But suppose, for sim-plicity of exposition. that most
of the adjustmenttook place early in 1879. Using this date to
divide1862-1929 into two periods, Table 2 suggeststhat the normal
rate may have been in the vicinityof 7.50 percent during 1862-1878
and between4 and 5.50 percent during the 1879-1929period.
What events triggered these upward anddownward revisions in
investors' expectationsof normal rates? A look at the histor y of
U.S.monetary standards since 1862 may provide ananswer.
Table 2
Frequencies of rising and fallingyield curves, 1862-1929
Commercial paper yield Slope of yield curve(percent per annum)
Positive Negative
1862 - 1878
Above 7.57 0 5
Below 7.56 12 0
1879 - 1929
Above 5.40 0 16
4.21 - 5.40 4 17
Below 4.21 14 0
SOURCE. Macaulay, Table 10.
The monetary standard and the yield curve
The American monetary standard has under-gone the following
changes since early in the
Federal Reserve Bank of Chic-ago 21
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Civil War. The gold standard was abandonedwhen banks suspended
specie payments onDecember 30, 1861. 7 In February 1862, Con-gress
authorized the first of several issues of legaltender currency (the
famous greenbacks). Aftera period of monetary expansion accompanied
bydepreciation of the dollar, followed by pro-longed monetary
controversy, a bill for theresumption of the gold standard at the
prewarexchange rate was passed in January 1875.Resumption was
achieved on the target date ofJanuary 1, 1879, although success was
notassured until late in 1878.8
The monetary standard remained unchangeduntil banks were legally
prohibited from payingout gold in March 1933. The international
goldstandard was resumed in January 1934, 9 althoughthe gold value
of the dollar was reduced to 59percent of that prevailing between
18'9 and1933. Finally, in August 1971, the United Statessuspended
the international convertibility of thedollar and embarked on a
paper standard identi-cal in all important respects to the
greenback eraof 1862-1878.
The following line of reasoning suggeststhat the monetary
standard should be expectedto be an important, perhaps the
dominant, influ-ence on the normal rate. First, define the
normalrate on securities of a particular risk class as theyield
expected by investors to apply to thosesecurities in long-run
equilibrium ( Referencesfrom this point are to normal rates instead
of toa single normal rate.) Second, the available evi-dence
strongly suggests that interest rates are toa considerable extent
determined by inflationaryexpectations, which in turn depend on
actualinflation.10 Finally, inflation has for centuries
"The official standard was bimetallic, but silver had longceased
to circulate because it had been undervalued by theofficial
gold-silver exchange rate.
8For example, see Dewey (1936) and Friedman andSchwartz (1963)
for histories of American monetary stan-dards.
'The domestic circulation of gold was ended by theGold Reserve
Act.
10Most observers, including Fisher (1930) and Fama(1975), would
agree with this statement. Sec Wood (1981for a review of empirical
work on the connections betweeninterest rates and inflation.
been highly correlated, and generally believedto he highly
correlated, with the choice of mone-tary standard.11
These arguments are supported by the datain Charts 1 and 2 and
Tables 1 and 2, which arcconsistent with a downward revision in
the1870s and an upward revision in the 1970s ofinvestor estimates
of normal rates. The rising1982 yield curve suggests that the
latter revisionmay not yet be complete. It is not clear from
thedata whether another revision occurred in the1930s because the
steeply rising yield curves ofthat decade (and of the 1940s and
1950s) were,in view of the record-low yields prevailing at thetime,
consistent with normal rates based onexperience of both gold and
paper standards."'
The values in Table 2 are not directly com-parable with those in
Table 1, because the yieldsin the two tables apply to different
securities.Nevertheless, these tables and the figures uponwhich
they are based combine to tell a singlestory—that American yield
curves since 1862are at least roughly consistent with the
tradi-tional expectations theory supplemented byregressive
expectations where the normal rate isa function of the monetary
standard. That is thehypothesized rule for revising the normal
ratethat earlier was declared to be required for acomplete
explanation of observed yield curves.
Concluding comment: Inflation and themonetary standard as parts
of the samepolitical decision.
The data presented above suggest thatchanges in inflationary
expectations arc asso-
"See Attwood ( 1819), Lester ( 1939 ), Dewey ( 1936),Friedman
and Schwartz (1963), Barro ( 1980), and Bordo(1981) for discussions
of evidence and attitudes regardinginflation under gold and paper
standards,
12 In annual averages, American commercial paper yieldshave not,
except during 1935-46, been Less than 1 percentand have not, except
during 1931-58, been less than 3 per-cent. They were continuously
less than 1 percent during1935-46 and continuously less than 3
percent during 1931-55. These statements arc based on data
available since 1819in Homer (1977).
22 Economic Perspectives
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dated with, and perhaps influenced by, changesin the monetary
standard. But it is important tostress that the monetary standard
is not imposedupon an economic system from outside. A shiftfrom a
fixed-rate to a flexible-rate system, forexample, may be viewed as
merely one of severalreflections of a decision by one or more
coun-
tries to abandon long-run price stability as a goal.This means
that the data contain no implicationsfor monetary policy. The
monetary authority isnot free to attempt to influence
inflationaryexpectations by manipulating the monetary stan-dard.
Both are chosen and imposed upon thecentral bank by the political
process.
References
Thomas Attwood, A Second Letter to the kart of Liverpool onthe
Bank Reports as Occasioning the National Dangersand Distresses, R.
Wrightson, Birmingham, 1819_
Robert J. Barro, "1 .S. Inflation and the Choice of
MonetaryStandards," NBER Conference on Inflation, Washing-ton,
October 1980.
Michael D. Bordo, "The Classical Gold Standard: Some Les-sons
for Today," Federal Reserve Bank of St. LouisReview, May 1981,
2-17.
John C. Cox, Jonathon E. Ingersoll, and Stephen A. Ross,
"AReexamination of Traditional Hypotheses About theTerm Structure
of Interest Rates,"Journal of Finance,September 1981, 769-99.
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Longmans, Green, and Co., New York, 1936.
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Finance, September 1958, 348-56.
, Basic Yields of Corporate Winds, 1900-1942,National Bureau of
Economic Research, TechnicalPaper 3, 1942.
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F. A. Lutz "The Structure of Interest Rates," Quarterly Jour-nal
of Economics, November 1940. 36-63.
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the Movements of Interest Rates, Bond Yieldsand Stock Price in the
United States Since 1856,National Bureau of Economic Research, New
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Books, New York, 1972.
lohn H. Wood, "Interest Rates and Inflation," Federal
ReserveBank of Chicago Economic Perspectives, May/June1981,
3-12.
Federal Reserve Hank of Chicago 23
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