Reuben A. Kessel

English

Research Papers in Economics

This PDF is a selection from an out-of-print volume from the National
Bureau of Economic Research
Volume Title: The Cyclical Behavior of the Term Structure of Interest
Rates
Volume Author/Editor: Reuben A. Kessel
Volume Publisher: UMI
Volume ISBN: 0-87014-405-7
Volume URL: http://www.nber.org/books/kess65-1
Publication Date: 1965
Chapter Title: CONCLUSIONS AND IMPLICATIONS FOR FURTHER
RESEARCH
Chapter Author: Reuben A. Kessel
Chapter URL: http://www.nber.org/chapters/c1666
Chapter pages in book: (p. 96 - 100)5
CONCLUSIONS AND IMPLICATIONS
FOR FURTHER RESEARCH
THIs INVESTIGATION confirms the principal finding of Meiselman—
that a relationship exists between expectations of future short-term
rates and the term structure of interest rates. The fact that forward
rates incorporate predictions of future short-term rates, with an
appreciable accuracy in a statistical sense, demonstrates, by an a
fortiori argument, that forward rates are a function of expected
future spot rates.
Previous investigators, Hickman and Meiselman, have interpreted
the difference between forward and subsequently observed spot
rates as forecasting errors of the market. (Culbertson found the dif-
ference between holding period yields of different terms to maturity
to be so large that he rejected the view that the market forecasts,
since he found it difficult to believe that the market could forecast
as badly as his interpretation of his findings suggests.) Their inter-
pretations can be questioned because it is unreasonable to expect
the market to err asymmetrically. The mean error in a long series of
observations should be zero. If the work of these investigators is ex-
tended or examined closely, it can be shown that what they re-
garded as forecasting errors were in large part attributable to liquid-
ity premiums, and that the errors of the market were indeed much
smaller.
It is the thesis of this study that a forward rate should be viewed,
not as an expected rate, but as an expected rate plus a liquidity
premium. If forward rates are so interpreted, then the forecasts and
forecasting errors of the market can be detected. These forecasts
are, within the maturity spectrum studied, accurate to a degree
that. cannot be rationalized as the workings of chance. The finding
that forward rates constitute high estimates of future spot rates isfor Further Research
consistent with the Keynesian theory of "normal backwardation'
The implications of this theory for the money and capital markets
have been developed by Hicks in Value and Capital.' Hence these
results support the Hicksian view that forward rates are dqüal w
expected spot rates plus a liquidity premium.
The existence of liquidity premiums indicates that shOrt and
long maturities are not perfect substitutes for one another in the
market as the proponents of the pure expectations hypothesis, sUch
as Lutz and Meiselman, have argued. In particular, short and long
maturities differ with respect to their value as money substitutes;
short maturities are much better money substitutes than long
turities. Consequently, the greater liquidity yield of short maturities
leads to a persistent pecuniary yield differential in favor of long
maturities. This differential offsets the greater liquidity yield of
short maturities. Therefore, the expected value of holding period
yields, (with yield defined as total, as distinguished from pecuniary
only), is equal for all terms to maturity.
The existence of liquidity premiums has been explained as a
consequence of risk avoidance and positive costs for the speculative
services required to convert long- into short-term securities. The
market is willing to take a lower yield in exchange for a lower
variance in the price of governments. The implications of this ra-
tionalization are consistent with the observed behavior of relative
yields of low- and high-grade bonds, both secularly and cyclically.
Liquidity premiums have moved with the cycle in recent years.
Since interest rates also increase during expansions and decrease
during contractions, this raises the question: are liquidity pre-
miums a function of the stage of the cycle or the level of interest
rates? The upward trend in liquidity premiums over the three
latest cycles, when interest rates have also shown an upward trend,
indicates that it is the level of interest rates and not the stage of the
cycle that determines the magnitude of liquidity premiums.
This finding does not support the theory that liquidity premiums
are a development of the Great Depression. It is difficult to under-
stand why evidence of the existence of liquidity premiums was so
sparse before the l93O's and so abundant afterwards. If one argues
I In particular, seep. 147.98 Conclusions and Implications
that the emergence of liquidity premiums was a consequence of risk
aversion caused by the financial losses of the early 1930's, then one
ought to observe that liquidity have been declining
secularly since that time. The foregoing evidence does not support
this view. However, possibly more refined analysis, when the level
of rates is held constant, would show that there a down-
ward trend in liquidity premiums over time.
The joining of liquidity preference to expectations explains the
lack of symmetry in the movement of short- and long-term rates
over the cycle. It explains why short-term rates do not exceed long-
term rates at peaks by as much as they fall below long-term rates
at troughs; why yield curves are positively sloped during most of
the cycle; and why yield curves, when short-term rates are unusually
high, never seem to be negatively slopedthroughout their full
length, but show humps near the short end.
The common belief that short-term rates fluctuate more than
long-term rates is, in general, correct.2 However, this generalization
conceals an important observation—as term to maturity increases,
yield variance first increases, and then decreases. This observation
is inconsistent with a pure expectations hypothesis, but is consistent
with a hypothesis that combines expectations and liquidity forces.
At any instant of time, the power of the market to predict future
spot rates decreases the longer the time span between the moment
a forward rate is inferred from the term structure of interest rates
and the corresponding spot i-ateis observed. Clearly itis more
difficult to see one year than one week into the future. Hence, as
the span of time between the moment a forward rate is inferred and
the relevant spot rate is observed increases, the correlations between
forward andspot rates ought to decrease. The observations for
three- and six-month bills and one- and two-year governments are
consistent with this implication of the expectations hypothesis.
Other tests for this same periodof time, but for different time
spans, between forward and spot rates ought to yield results con-
sistent with the foregoing. Indeed, this argument implies that a
2This -isoniy arithmetic in a world of perfect certainty. Long-term rates can
fluctuate more than short-term rates. The fact that they do not fluctuate as
muchasshort-term rates implies that the market has some powers to recognize
when short-term rates are transitorily high or low.for Further Research 99
correlationbetween forward and two-year spot rates that is greater
than the correlation between forward and one-year spot rates would
contradict the expectations hypothesis.
The data used to show that the expectations hypothesis has pre-
dictive content is primarily drawn from one business cycle, 1.958—61.
Possibly using this particular cycle has produced freakish results
and comparable findings could not be obtained for other cycles.
Clearly much more work can and should be undertaken to find out
just how well the market can predict. In particular, an effort should
be made to determine how much of the market's ability to predict
is attributable to predicting seasonal changes in rates. The results
obtained using one- and two-year maturities indicate that the mar-
ket can do more than predict seasonal changes in rates.3
The explanation of liquidity preference presented here is based
on the postulate that the risk of capital loss associated with holding
short-term securities is smaller than itis for long-term securities.
This implies that in a period free of trends in interest rates, price
variance ought to increase with term to maturity. (It should be
noted that this implicationis not arithmetic. The variance in
prices of three-month bills could, in principle, be greater than
that of six-month bills.) If variance increases with term to maWr-
ity, then mean yields should also increase. Direct evidence of a
relationship between means, price variances, and terms to maturity
should be sought.
Yield curves published in the Treasury Bulletin constitute data
that can be used to determine whether or not these propositions
about variance in yields, at least to the nine-to-twelve-month range,
are correct. These same data can also be used to determin.e what
maturity constitutes the line of demarcation between increasing and
decreasing variances as term to maturity increases. Finally, these
data could reveal how this boundary line changes from cycle to cycle
and whether these changes are correlated with difterences in interest
rate levels.
Although these results support the view that securities of different
3Insofaras the market can predict, one should be able to observe that unclei--
writers' spreads increase during expansions, reach a peak at the business cycle
peak, and decrease (luring contractions.100 Conclusions and Implications
maturities are not perfect substitutes for one another at identical,
pecuniary, holding period yields, they do not support the view that
it is the time span between maturities that explains less than in•
finite cross elasticities. Both liquidity preference and expectations
imply that the cross elasticity of demand between fifteen- and
twenty-year maturities will exceed the corresponding cross elasticity
for five- and ten-year maturities. In addition, the expectations hy-
pothesis implies, for coupon bearing securities with fixed maturi-
ties, the higher the absolute level of rates, the earlier the maturity
at which yield curves will flatten out. This later implication has
not been tested.
Durand's findings show that negatively sloped yield curves oc-
curred more frequently before the decade of the than they
have since. This leads to the questions, do his yield curves correctly
depict what, in fact, was true, and if so, why this change? Further-
more, it appears that before 1914, long-term yields frequently lagged
behind cyclical turns in short-term rates, a result that does not seem
consistent with either the recent behavior of these rates or with the
ipiplications of the expectations-liquidity preference hypothesis.
Tliesc questions deserve a fuller investigation than this study has

The Cyclical Behavior of the Term Structure of Interest Rates

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