According to standard economic theory, the yield on a ten-year Treasury bond is composed of the expected path of short-term Treasury yields over the next ten years and the Treasury term premium. The term premium is the compensation demanded by investors for bearing interest rate risk, which is the risk that interest rates will change over the life of the bond. Here, we use a statistical model to describe the joint evolution of Treasury yields and term premia across time and maturities see Adrian, Crump, and Moench [] for more details.

The term premium is the compensation that investors require for bearing the risk that short-term Treasury yields do not evolve as they expected.

Studying the term premium over a long time period allows us to investigate what has historically driven changes in Treasury yields. In this blog post, we estimate and analyze the Treasury term premium from to the present, and make these estimates available for download here.

The term premium estimates that we present are obtained from a five-factor, no-arbitrage term structure model. The model setup and estimation procedure are described in detail in Adrian, Crump and Moench Our model belongs to the affine class of term structure models which characterize yields as linear functions of a set of pricing factors.

The model imposes no-arbitrage restrictions which ensure that the time series and cross section of bond yields are consistent with one another. We estimate the model using zero-coupon yield data described by Gurkaynak, Sack, and Wrightwhich are available at a daily frequency from the Board of Governors here.

Fitting the full sample of yields allows us to estimate the term premium on a daily basis going back to June 14, The ACM model fits the data extremely well, allowing us to decompose yields without concerns about measurement error. In a previous postwe compared our estimated term premium to a number of observable variables.

We showed that the term premium is a countercyclical variable which tends to move with measures of uncertainty and disagreement about the future level of yields. An alternative approach to estimating the ten-year term premium is to subtract the expected average level of short-term interest rates over the next ten years obtained from surveys of professional forecasters from the current ten-year Treasury yield.

Unfortunately, longer-term survey forecasts are only available at a biannual frequency and only since the early s using the Blue Chip Financial Forecasts survey see these three posts for further information. However, by projecting this series onto the principal components of Treasury yields, we can construct an extrapolated monthly series that goes back to The latter estimates the term premium incorporating some survey forecasts into a three-factor affine model.

The chart shows that the different term premium estimates co-move at low frequencies but may differ markedly in certain periods.

In particular, our estimate of the term premium has been considerably higher since the onset of the financial crisis than the other two series.

That means that our model has implied a lower future path of short-term interest rates than those based on survey data.

In fact, we can demonstrate the role of survey data in an even more transparent way by comparing KW to the simple average between our estimate and that purely based on surveys. The following chart shows that the KW term premium and this composite series are very similar.

The evolution of term premia has been of particular interest since the Federal Reserve began large-scale asset purchases. Over this time, short-term interest rates have been close to zero, and our estimates show that the term premium has been compressed and has at times even been negative.

An advantage of our estimate is that it is available back to Hence, we can study the term premium at another time when short-term interest rates were close to zero. By comparing the ten-year ACM term premium of the past decade to that of the s in the first chart, we find that the ten-year term premium was negative at times in the s, but reverted back to positive.

Similarly, our estimate of the term premium has risen above zero recently. The data are updated weekly and include estimates of the term premium for yearly Treasury maturities from one to ten years, as well as fitted yields and the expected average level of short-term interest rates. Any errors or omissions are the responsibility of the authors.

Richard Crump is a research officer in the Group. Benjamin Mills is a senior research analyst in the Group. Emanuel Moench is a research officer in the Group. Posted by Blog Author at Open Document.

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We show how to price the time series and cross section of the term structure of interest rates using a three-step linear regression approach. Our method allows computationally fast estimation of term structure models with a large number of pricing factors. Tobias Adrian, Richard Crump, and Emanuel Moench Some commentators have expressed concern that Treasury yields might rise sharply once the Federal Open Market Committee (FOMC) begins to raise the federal funds rate (FFR), worrying, in particular, about a sudden increase in Treasury term premia.

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