Treasury inflation-indexed securities are just like nominal Treasuries, except that their coupon and principal payments are indexed to inflation. The yield spread between the two types of securities should serve as a daily measurement of the market's perception of expected inflation, modified to reflect the cost of inflationary risk. But TIIS yields are about 60 basis points higher than expected. This Commentary examines several factors other than inflation that might raise TIIS yields relative to nominal Treasuries.Inflation-indexed bonds ; Government securities

Ben Craig

English

Research Papers in Economics

except that if the CPI falls, the minimum
nominal amount of principal repaid
equals the security’s original face value.
The coupon payment, on the other hand,
is lower than its face value in a time of
deflation. 
■ Bond Yields and Inflation
Economic theory separates the yield of a
nominal Treasury at its market equilib-
rium into several components: a real
return, the expected rate of inflation, and
an inflation-risk premium (which com-
pensates buyers for the fact that the
inflation rate is uncertain). A TIIS holder
does not have to worry about the infla-
tion component but only about the real
rate. Thus, at first glance, the TIIS yield
should equal the nominal Treasury rate
minus the expected inflation rate and
minus a risk-aversion premium. Put
another way, the yield spread between a
TIIS and a nominal Treasury security of
the same duration and coupon schedule
should represent expected inflation and
the costs of the inflation risk.
March 15, 2003
Federal Reserve Bank of Cleveland
Why Are TIIS Yields So High?  The Case 
of the Missing Inflation-Risk Premium
by Ben Craig
ISSN 0428-1276
Treasury inflation-indexed securities
are just like nominal Treasuries,
except that their coupon and princi-
pal payments are indexed to inflation.
The yield spread between the two
types of securities should serve as a
daily measurement of the market’s
perception of expected inflation, 
modified to reflect the cost of infla-
tionary risk. But TIIS yields are
about 60 basis points higher than
expected. This Commentary examines
several factors other than inflation
that might raise TIIS yields relative 
to nominal Treasuries.
Since 1997, the U.S. Treasury has
been issuing debt with future payments
that depend on the future price level. 
Treasury inflation-indexed securities
(TIIS) guarantee a real return by adjust-
ing the principal and coupon payments
for inflation. In addition to eliminating
default risks, as regular Treasury instru-
ments also do, TIIS eliminate risks asso-
ciated with future price changes. 
The difference between the TIIS yield
and that of nominal Treasury securities
should be a very good measure of
expected inflation: A conventional 
Treasury instrument’s yield should equal
the yield on an otherwise similar TIIS
plus the expected inflation rate and a
premium for inflation risk—the extra
return investors require because inflation
may be higher or lower than expected. 
Surprisingly, the difference in yields
between the two types of securities (their
yield spread) for 10-year instruments is
only about 1.90 percentage points for the
1997–2002 period (see figure 1). Most
estimates suggest that people had
expected inflation to grow about 
2.5 percentage points a year over this
period, and actual inflation as measured
by the Consumer Price Index (CPI)
turned out to be 2.61 percent a year. The
assumption that investors expect the
inflation rate to decline radically over a
10-year period seems far-fetched in light
of historical periods like the 1970s, when
the upside risk of very high inflation
should have more than balanced out the
possibility of a long-term change to very
low inflation. Consequently, not only is
there no allowance for an inflation-risk
premium in the yield spread, there is not
even enough of a difference to allow for
expected inflation. 
Why might the return on TIIS be so per-
plexingly high compared to securities that
pay a nominal yield? In this Commentary,
we consider several possible reasons. 
Keep in mind that as we examine the
behavior of TIIS, we mean only to inves-
tigate an interesting pricing puzzle—
not to assess the success of the TIIS pro-
gram. The period over which we have
TIIS prices is a time during which most
buyers expected only small changes in the
inflation rate. This condition is quite dif-
ferent from that prevailing in the late sev-
enties, when many economists were call-
ing for this form of security. 
■ The Mechanics of TIIS
Payouts
For TIIS—but not for nominal Treasury
securities—coupon payments and prin-
cipal repayments are contingent on the
amount of inflation as measured by the
CPI. As each coupon comes due, the
Treasury adjusts the payment according
to the amount of total inflation since the
security was issued. (For details of the
mechanics of coupon payments for  TIIS
and Treasury bills, see www.public
debt.treas.gov/sec/seciis.htm.) Table 1
compares coupon payments for a 
nominal Treasury security and a TIIS
with a hypothetical inflation outcome. 
The TIIS coupon payments are all
adjusted for the CPI so that if the nomi-
nal coupon payment of the TIIS were
divided by the index ratio, the resulting
real amount would be the same as the
nominal payment of the standard Trea-
sury. The index ratio is calculated by
dividing the level of the CPI announced
just before the coupon payment is made
(adjusted a bit) by the CPI on the date
the bond was issued. The TIIS principal
is repaid according to the same formula,To explore the difference between the
nominal Treasury and TIIS yields, we
can look at the two components that are
not a part of TIIS yields—expected
inflation and the inflation-risk 
premium—over the period for which 
we have data on both securities,
1997–2002. 
Expected inflation is measured in two
ways. One is the telephone survey of
forecasters or consumers. The typical
survey of forecasters calls about 50 pro-
fessionals, asking them to predict the rate
of inflation at various points in the future.
There are also several surveys (the most
widely cited is one conducted at the 
University of Michigan) of consumers’
inflation expectations. The other
approach uses statistical models to pre-
dict inflation. These statistical models,
however, are not completely independent
from surveys of professional forecasters,
most of whom base their views at least
partly on similar statistical models.
These surveys and statistical models
calculate inflation expectations differ-
ently, but they all yield similar estimates
of the rate at which people expect infla-
tion to grow over the next year. Between
1997 and the beginning of 2002, these
different approaches put the estimate at
roughly 2.5 percent on average. The
appropriate figure to use in this analysis
is the rate expected when the TIIS is
purchased. This estimate turns out to be
very close to the average actual rate over
this period. And although other market
inflation measures may give different
figures, only estimates of CPI inflation
matter for TIIS because that is the mea-
sure used to calculate their coupon and
principal payments.
Of all the attempts to measure the cost
of the inflation risk, the most thorough
is reported in a 1996 paper by Campbell
and Shiller (see Recommended Read-
ing). Using a structural model of the
economy to describe investors’behav-
ior, they estimate that the risk-aversion
premium is between 
1/2 percentage point
and 1 percentage point, depending on
the assumptions they impose. If that
estimate is correct, investors should be
willing to pay between 50 and 100 basis
points (a basis point is 1 percentage
point divided by 100) of their yield at
current rates just to know the exact
amount of future inflation. 
These estimates of expected inflation
and the risk-aversion premium suggest
that the difference between comparable
conventional Treasuries and TIIS yields
should be between 3 and 3.5 percentage
points—about 2.5 percentage points
from expected inflation plus 
1/2 to 1 per-
centage point from the risk-aversion 
premium. The actual differences during
this period were much smaller, averaging
only 1.90 percentage points. There is no
risk premium (or indeed a negative risk
“premium”) for inflation. Moreover, the
difference of 1.90 percentage points does
not even cover all of the expected infla-
tion. In short, TIIS yields seem too high.
■ Can Technical Adjustments
Explain High TIIS Yields?
For technical reasons, the simple differ-
ence between the yield for a TIIS and
that of a nominal Treasury of the same
duration does not equal the expected
inflation rate exactly. First, a TIIS must
be compared to a nominal security that is
adjusted slightly for a difference in
coupon payments. For a nominal 
Treasury with a constant coupon rate,
each coupon pays the same amount
throughout the tenure of the bond. 
However, the adjustment for inflation in
a time of rising prices means that more
of the payment for a TIIS with the same
maturity occurs in the latter part of its
payment schedule. Thus, a TIIS is not
entirely comparable to its corresponding
nominal Treasury security. Nonetheless,
an appropriate comparison can be made
by using information contained in the
yield curve to produce a figure that
reflects the difference in payment sched-
ule. This adjustment results in a modest
change—the average difference is only 
3 basis points from the raw difference
reported earlier.
Another adjustment allows for the
wrinkle that a TIIS always pays at least
the nominal value of its principal, even
if there is deflation. Thus, the principal
has an option value because the nomi-
nal value of the principal’s repayment
can be higher than its original nominal
value but can never be lower. However,
the option appears to have had a negli-
gible value in 1997–2000 because there
is only a miniscule possibility of defla-
tion after the long period when the
principal is repaid. 
One last possible technical explanation:
The average of a function is not the same
as the function of an average because of
nonlinearities. That is, an investor who
calculates the possible yields on a TIIS
and then observes their mean will get a
different result than the one who calcu-
lates the mean yield on a nominal secu-
rity and then subtracts from it the average
inflation value. Most researchers estimate
that this “Jensen inequality effect” is only
about 5 basis points over a 10-year matu-
rity. The highest estimate is 11 basis
points and the lowest is 2 basis points. 
Having considered the result of several
technical adjustments, one must con-
clude that whatever their values may be,
they are almost certainly tiny and cannot
by themselves solve the mystery of the
high TIIS yield.
■ Other Possible Explanations
The unexpectedly small difference
between nominal Treasury yields and
TIIS yields may have other causes as
well. TIIS are new, complex securities,
a.  Hypothetical coupon payments on a nominal and a TIIS bond with a 10 percent coupon and $100 face value.
b.  For the sake of clarity, both the nominal and the TIIS bond have the same coupon rate of 10 percent, though normally the
coupon value of the TIIS would be smaller than that of the nominal.
c.  Coupon 3 is paid after a severe deflation.
Nominal
Realized Treasury TIIS
CPI payment payment
Initial issue 200
Coupon 1 220 $ 10 $ 11
Coupon 2 240 $ 10 $ 12
Coupon 3
c 180 $100 $100
Hypothetical principal repayment (deflation) 180 $100 $100
Hypothetical principal repayment (inflation) 240 $100 $120
TABLE 1 PAYMENT SCHEDULES FOR NOMINAL AND INFLATION-
INDEXED SECURITIESa,bso investors may require stronger
inducements to hold them. For exam-
ple, TIIS volatility characteristics may
not be well known because the instru-
ment has no historical price pattern
from which to deduce them. Investors,
who may not know how to fit this novel
security into their portfolios to balance
risk or hedge debt, may also look for a
yield higher than they would usually
demand. However, if newness were
what was keeping the inflation pre-
mium low, its effect should attenuate
over time, as investors learn more about
the security. But in reality, since 1997,
when TIIS were first introduced, the
observed inflation premium has dimin-
ished instead of reaching the level we
would expect.
Another possible reason for higher TIIS
yields is that dealers generally have
nominal debt they must hedge. Because
their debt is not indexed to inflation,
TIIS holders do not rely on these instru-
ments as hedges against specific debt. So
the characteristics that distinguish TIIS
holders from holders of nominal Trea-
sury securities might drive differences in
the securities’yields that have nothing to
do with inflation. Indeed, participation in
the nominal Treasury market is more
weighted toward the primary dealers
than in the TIIS market. A relatively
small set of traders account for the lion’s
share of TIIS transactions, unlike the
trading activity in nominal securities.
Furthermore, primary dealers of
indexed securities tend to roll these
instruments over, whereas they hold
large positions (either long or short) in
nominal Treasuries.
Like the explanations examined earlier,
differences in dealers may account for
some of the higher TIIS yield, but if it
were the main cause of an understated
inflation premium, its effect should have
been attenuated throughout the period
since the introduction of TIIS, as traders
arbitraged away the profit opportunity.
Large institutional investors still predom-
inate as holders of TIIS, and the number
of medium- to large-sized institutions
that include TIIS in their portfolios is
growing. Smaller holders are becoming a
more important source of demand as
well. But once again, although there are
major changes in the characteristics of
those who demand TIIS, there are no
correspondingly large changes in the
inflation premium. Clearly, something
else is happening here.
A final possibility, and perhaps the most
convincing one, involves the characteris-
tics of the markets in which Treasury
securities are sold and traded. For exam-
ple, nominal Treasuries are very liquid
instruments. As a result, the holder of a
nominal Treasury can easily find a buyer
when he wants to readjust his portfolio to
new information quickly. This may give
the nominal Treasury a premium when
liquidity is important to the market. In
other words, the yield on nominal Trea-
suries may be lower than normal in
times when investors see liquidity as an
especially valuable quality. In the fall of
1998, when both the domestic and for-
eign financial markets were particularly
volatile, liquidity was highly valued by
investors who needed an instrument that
could balance their portfolios quickly. In
October 1998, for example, nominal
Treasury yields dropped, and the
implied inflation premium fell with
them, reaching a very low 88 basis
points. Yields on TIIS did not fall as low
because investors perceived that they
could not be sold as promptly as nomi-
nal Treasuries. Little is known about
how to measure liquidity premiums, but
the large premiums that prevailed in the
autumn of 1998 suggest that liquidity
concerns may account for at least part of
the missing inflation premium in the
yield spread between TIIS and nominal
Treasury securities.
However, some researchers feel other-
wise. They point out that while the des-
perate liquidity needs in autumn 1998
did cause the inflation premium to
change considerably, it was only for a
brief time. Indeed, there was not much
trading in TIIS initially, but as investors
began to understand how to use them,
they gradually became more popular
and now trade at a fairly high rate.
Thus, liquidity needs that are especially
well satisfied by the nominal Treasury
market may not explain the small TIIS
inflation premium, which has prevailed
since their introduction.
■ Interpret with Caution
TIIS have enormous potential for guid-
ing policy. By design, this security
removes both inflation’s erosion and its
risk, when compared to a standard nom-
inal Treasury. So the yield spread
between them should serve as a daily
measurement of the market’s perception
of expected inflation, modified to reflect
the cost of inflationary risk. In essence,
it should provide an instant reading of
inflation’s cost to the economy and
could be highly useful in making policy
decisions that may affect inflation.
However, even the adjusted difference
between TIIS and nominal Treasuries
yields is too small to account for both
inflationary expectations and the cost of
risk. Until their relationship is better
understood, the yield spread between
FIGURE 1 YIELD ON TREASURY INFLATION-
INDEXED SECURITIES
0
1
2
3
4
5
1/97 2/98 2/99 2/00 2/01 2/02
Percent
10-year TIIS yield
Yield spread between 10-year Treasury bond and 10-year TIIS
SOURCE:  Bloomberg Financial Information Services.Federal Reserve Bank of Cleveland
Research Department
P.O. Box 6387
Cleveland, OH 44101
Return Service Requested:
Please send corrected mailing label to
the above address.
Material may be reprinted if the source is
credited. Please send copies of reprinted
material to the editor.
Ben Craig is an economic advisor at the
Federal Reserve Bank of Cleveland.
The views expressed here are those of the
author and not necessarily those of the Federal
Reserve Bank of Cleveland, the Board of 
Governors of the Federal Reserve System, or
its staff. 
Economic Commentary is published by the
Research Department of the Federal Reserve
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to 4d.subscriptions@clev.frb.org or fax it to
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We invite comments, questions, and sugges-
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Permit No. 385
TIIS and nominal Treasuries will remain
a statistic that policymakers should han-
dle with caution.
In one sense, the market for TIIS is very
young. The TIIS were designed as a
hedge during periods of high inflation
uncertainty such as the late 1970s, a
market environment that has not pre-
vailed during the five years of the TIIS
market’s existence. Until we see the
market operating during such a period
of high inflation volatility, one cannot
judge the success of the program.
Yet the mystery remains. Apparently,
securities that hedge completely against
the uncertainty created by inflation actu-
ally pay their holders, on average, to
hedge. The excess yield for TIIS over
comparable nominal bonds seems to be
at least 60 basis points, a large number
for bond traders who normally would
arbitrage away profit opportunities much
smaller than this. The extra liquidity risk
of the TIIS may provide the most likely
clue to their excess yield.
■ Recommended Reading
John Y. Campbell and Robert J. Shiller
(1996). “A Scorecard for Indexed Gov-
ernment Debt,” NBER Working Paper
No. 5587.
Brian Sack (2000). “Deriving Inflation
Expectations from Nominal and Infla-
tion-Indexed Treasury Yields,” Journal
of Fixed Income 10, 1–12.

Why are TIIS yields so high? The case of the missing inflation-risk premium

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Why are TIIS yields so high? The case of the missing inflation-risk premium

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