FRBSF Economic Letter
2007-21; July 20, 2007
What We Do and Don't Know about the Term Premium
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From January 2000 through this past June, the 10-year U.S. Treasury bond yield
has moved over a wide range, falling from 6.8% in early 2000 to 3.1% in June 2003
and rising back to over 5% more recently. The interest rate on 30-year fixed-rate
mortgages has similarly varied from a high of 8.6% in 2000 to a low of 5.2% in
June 2003 and back to about 6.75% more recently. These fluctuations translate into
huge variation in the debt financing costs of the U.S. government and in the prospective
monthly mortgage payments of U.S. homebuyers.
What caused these large fluctuations? In July 2005, Alan Greenspan, then Chairman
of the Federal Reserve Board, reported to Congress that "a significant portion of the sharp decline in [long-term interest
rates] over the past year appears to have resulted from a fall in term premiums" (Greenspan
2005). While this is not the only possible explanation for movements in long-term
interest rates, the term premium is nonetheless an important component of these
rates. Thus, understanding long-term interest rate fluctuations requires one to
understand what the term premium is and how it may change over time.
In this Economic Letter, we define the term premium and explain the state
of the art in measuring it. Unfortunately, the term premium turns out to be very
difficult to measure; thus, we conclude with some discussion of the limitations
of our current knowledge.
What is the term premium?
Briefly stated, the term premium is the excess yield that investors require
to commit to holding a long-term bond instead of a series of shorter-term bonds.
For example, suppose that the interest rate on the 10-year U.S. Treasury note is
about 5.5%, and suppose that the interest rate on the 1-year U.S. Treasury bill
is expected to average about 5% over the next 10 years ("note" and "bill" are
the customary names for U.S. Treasury securities of these maturities). Then the term premium on
the 10-year U.S. Treasury note would be about 0.5%, or 50 basis points.
Thus, a key component of the term premium is investor expectations about the future
course of short-term interest rates over the lifetime of the long-term bond. In
the example above, the term premium on the 10-year Treasury note depends crucially
on financial market expectations about the course of shorter-term U.S. interest
rates over the next ten years, a very long horizon. This foreshadows some of the
difficulties of measuring the term premium that we will encounter below.
Note that, while we usually think of the term premium as being positive--that financial
market participants require extra yield to induce them to hold a bond for a longer
period of time--there is nothing in the definition of the term premium that requires
it to be so. For example, if some purchasers of long-term debt, such as pension
funds, are interested in locking in a fixed rate of return for a long period of
time, they could be willing to accept a lower yield on long-term securities
(a negative term premium) in order to avoid the risks associated with rolling over
their investments in a series of shorter-term bonds with uncertain, fluctuating
interest rates. Thus, both the sign and the magnitude of the term premium are ultimately
empirical questions.
Measuring the term premium
In principle, it is easy to measure the term premium using the definition in the
previous section, but this requires us to obtain data on or to estimate financial
markets' expectations about the future course of short-term interest rates over
a fairly long horizon. There are many possible ways one might go about doing this,
of which we now highlight four:
 1. Survey-based measure. One can simply survey financial
market participants regarding their expectations for future
short-term interest rates and plug those forecasts into the
definition of the term premium above. Unfortunately, surveys
of market participants about their interest rate forecasts
over such long horizons are conducted very infrequently and
may suffer from substantial rounding error (since respondents
report only very rough average estimates of future rates) and
other problems. In Figure 1, we make use of what long-term
survey data there are and plot a survey-based measure of the
term premium as the dashed line. The data on market expectations
come from the Blue Chip Survey of forecasters, which asks respondents
for their long-horizon forecasts of the 3-month Treasury bill
rate twice per year, every March and September. We interpolate
between these semiannual survey forecasts to create the monthly
frequency plot in Figure 1.
2. VAR-based measure. Because long-term
survey data are available so infrequently and
because survey responses are sometimes not
very good measures of financial markets' true
expectations as embodied in market prices,
it may make sense to use a macroeconomic forecasting
model such as a vector autoregression (VAR)
to forecast short-term interest rates instead.
Plugging these VAR-based forecasts into the
definition of the term premium then provides
an alternative and more timely measure, which
we depict by the solid thin line in Figure 1.
3. RW model-based measure. Instead
of a VAR, one can forecast interest rates using
a New Keynesian macroeconomic model. For example,
the RW (Rudebusch and Wu 2003) model has some
advantages over a VAR for forecasting long-term
interest rates, such as allowing the market's
long-run expected rate of inflation in the
economy to vary over time, which is likely
to have been a very important factor in the
1980s and which some studies (for example,
Gürkaynak, Sack, and Swanson 2005) have found to be important for
explaining movements in U.S. long-term bond yields even in recent years. (The RW model also satisfies
the "arbitrage-free" conditions mentioned below, which ensure that the
yield curve at any point in time is consistent with its future evolution over time.)
We plot this RW model-based measure of the term premium as the solid thick line
in Figure 1.
4. Cochrane-Piazzesi measure. In contrast to survey-based
or model-based approaches to measuring expectations and the
term premium, Cochrane and Piazzesi (2005) developed a purely
empirical measure of the expected excess total return (yield
plus capital gain) on long-term Treasury securities over the
next year. These expected one-year excess total returns, together with the current
one-year interest rate, can be iterated forward to compute
the expected excess return for each of the next ten years,
thereby producing a measure of the 10-year term premium, which
we plot as the dotted line in Figure 1.
The measures above represent just four out of many possible approaches to measuring
market expectations and the term premium. For example, Cochrane (2007) considers
two different specifications of a VAR and shows that the resulting term premium
estimates are vastly different, even though both measures are derived from a VAR
and thus might be expected to be similar. Rudebusch, Sack, and Swanson (2007) also
compare several of the above measures to "arbitrage-free" term premium
estimates that are standard in the finance literature, such as the Kim-Wright (2005)
measure that is produced by Federal Reserve Board staff and frequently cited in
speeches and testimony by Federal Reserve Board officials.
Limitations to our understanding of the term premium
Despite displaying some basic similarities, the four measures of the term premium
depicted in Figure 1 are strikingly different. First, three of the four measures
show large secular declines over time, while one measure (the one from the Rudebusch-Wu
model) shows a much smaller decrease; that is, the RW model attributes almost all
of the decline in long-term interest rates over the past 20 years to a fall in
market expectations for inflation and the future path of short-term interest rates
rather than to a fall in the term premium.
Second, in June 2007, the most recent month in the figure, the four estimates of
the term premium range from -2% up to 2%--a tremendous difference considering that
the 10-year Treasury yield has been only about 5%. Even the Survey and VAR measures,
which have tracked each other fairly closely since 1993, differ by about 50 basis
points. Thus, we cannot even say with much certainty whether the term premium is
positive or negative at present.
Third, the Survey, VAR, and Cochrane-Piazzesi measures of the term premium all
show substantial short-term fluctuations, while the Rudebusch-Wu measure is much
smoother over time. That is, the RW model is much more likely to attribute fluctuations
in long-term bond yields to changes in market expectations about long-run inflation
and the future path of short-term interest rates, while the other three measures
are much more likely to attribute these movements in long-term bond yields to changes
in the term premium.
Why are these measures of the term premium so different? The answer is that any
estimate of the term premium depends crucially on the markets' expectations of
the future path of short-term interest rates for the next ten years, and these
expectations are very difficult to measure for such long horizons. Our uncertainty
regarding the markets' expectations of inflation and short-term interest rates
in the far-distant future is reflected in our uncertainty regarding the current
level of the term premium.
Summary and conclusions
Long-term interest rates have moved a great deal in recent years as well as over
the past few decades. A key component of long-term interest rates is the term premium,
and many financial market analysts have attributed a substantial fraction of the
changes in long-term interest rates to changes in the term premium. While this
may be true, there are daunting limitations in our ability to measure the term
premium, so it is very difficult to make any such claims with confidence. In the
future, better surveys and research into better econometric techniques will hopefully
improve the accuracy of our measurements of the term premium and improve our understanding
of this important component of long-term interest rates.
Eric Swanson
Research Advisor
References
[URLs accessed July 2007.]
Cochrane, John. 2007. "Commentary on 'Macroeconomic Implications of Changes in the Term Premium.'" FRB
St. Louis Review 89(4) (July/August) pp. 271-282. http://research.stlouisfed.org/publications/review/07/07/Cochrane.pdf
Cochrane, John, and Monika Piazzesi. 2005. "Bond Risk Premia." American Economic Review 95(1)
(March) pp. 138-160.
Greenspan, Alan. 2005. "Federal Reserve Board's Semiannual
Monetary Policy Report to Congress," July
20. http://www.federalreserve.gov/boarddocs/hh/2005/july/testimony.htm
Gürkaynak, Refet, Brian Sack, and Eric Swanson. 2005. "The Sensitivity
of Long-Term Interest Rates to Economic News: Evidence and Implications for Macroeconomic
Models." American Economic
Review 95(1) (March) pp. 425-436.
Kim, Don, and Jonathan Wright. 2005. "An Arbitrage-Free
Three-Factor Term Structure Model and the Recent Behavior of Long-Term Yields and
Distant-Horizon Forward Rates." Federal
Reserve Board Finance and Economics Discussion Series 2005-33. http://www.federalreserve.gov/pubs/feds/2005/200533/200533abs.html
Rudebusch, Glenn, Brian Sack, and Eric Swanson. 2007. "Macroeconomic Implications of Changes in
the Term Premium." FRB St. Louis Review 89(4) (July/August) pp. 241-269.
http://research.stlouisfed.org/publications/review/07/07/Rudebusch.pdf
Rudebusch, Glenn, and Tao Wu. 2003. "A Macro-Finance Model of the Term Structure, Monetary Policy,
and the Economy." FRB San Francisco Working Paper 2003-17, forthcoming in The Economic
Journal. http://www.frbsf.org/publications/economics/papers/2003/wp03-17bk.pdf
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