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How to calculate the term premium

Measuring Treasuries to track yield curve inversions

The term premium is the amount by which the yield on a long-term bond is greater than the yield on shorter-term bonds. This premium reflects the amount investors expect to be compensated for lending for longer periods. Because U.S. Treasuries come in a variety of maturities, we can take the differences between the various yields to measure the term premium. Above is a FRED graph with the 10-year Treasury yield less the 2-year Treasury yield and less the 3-month Treasury yield. The 10-year yield is often greater than the 2-year or 3-month yields, usually with a drop preceding recessions. A drop into negative territory, when the 10-year yield is lower than the 2-year or 3-month yields, is often called a “yield curve inversion.” (See, for example, this Economic Synopses essay.)

With FRED’s international data, we can repeat this exercise for other countries. For instance, we can measure the term premium in the United Kingdom by comparing yields on 10-year U.K. government bonds and 3-month U.K. Treasury securities. We see a similar trend, with an increase in the term premium during and after recessions and a fall in the term premium before recessions.

How these graphs were created: For the first graph, search for and select “10-Year Treasury Constant Maturity Rate” and click “Add to Graph.” From the “Edit Graph” panel, use the “Customize data” tool to search for and add “2-Year Treasury Constant Maturity Rate” and then enter a-b in the “Formula” box. Repeat this with “3-Month Treasury Constant Maturity Rate.” For the second graph, repeat the steps above but instead search for “10-Year (Medium-Term) government bond in the United Kingdom.” With the “Customize data” tool, search for and add “3-Month Treasury United Kingdom” and enter a-b in the “Formula” box.

Suggested by Mahdi Ebsim and Julian Kozlowski.

View on FRED, series used in this post: DGS10, DGS2, DGS3MO, IR3TTS01GBM156N, MTGB10UKM

Long-run inflation expectations

The Federal Reserve Bank of St. Louis recently held its 25th annual Homer Jones Memorial Lecture. This year’s Lecture was given by University of Chicago Professor Robert E. Lucas, recipient of the 1995 Nobel Prize in Economics. Professor Lucas emphasized that, over long periods of time, inflation depends importantly on money growth. Countries with high inflation have invariably experienced rapid rates of money growth. So, some economic analysts, financial market participants, and ordinary citizens are worried that the more than fourfold increase in the monetary base since October 2008 (from $895 billion to $3,885 billion) will lead to much higher rates of inflation. At this point, though, key measures of inflation—as measured by the year-to-year percent change in the CPI and PCE price indexes—continue to track below the Fed’s 2 percent inflation target. However, since the Fed’s actions tend to affect the economy with a lag, expectations about future inflation are important in setting prices today: If the public expects higher inflation in the future, then it’s more likely inflation will begin to rise in the present. There are many ways to measure inflation expectations, including forecasts from economic models and surveys of consumers and businesses. One well-known measure of inflation expectations is the simple difference between yields on nominal Treasury securities and yields on inflation-adjusted Treasury securities. These series are available in FRED. This chart plots the difference between yields on 10-year Treasury securities and 10-year inflation-protected securities (TIPS); this difference provides a measure of the financial market’s expected average inflation rate over the next 10 years. A few observations from the chart are worth noting. First, relative to the period from 2004 to mid-2008, long-run inflation expectations have been more volatile since the onset of the financial crisis in August 2008. Second, inflation expectations fell sharply during the financial crisis and shortly thereafter but quickly rebounded. Finally, while more volatile, long-run inflation expectations, on average, have been slightly lower after the financial crisis than before the crisis. Bottom line: Financial markets believe that the Federal Reserve will not allow inflation to accelerate, despite the huge increase in the monetary base.

How this graph was created: First, plot the 10-Year Treasury Constant Maturity Index, daily. Second, adjust the sample to 2004-01-02. Third, click the “Add Data Series” arrow. In the search box, search for “10-Year Treasury Inflation Indexed Security.” Choose the daily series. Next, click the “Modify existing series” button and then click on “Add Series.” Finally, to plot the difference between the two series, click on the “Edit Data Series” button. Next click on “Create your own data transformation.” In the formula box, type “a-b” and then click “Apply.”

Suggested by Kevin Kliesen

View on FRED, series used in this post: DFII10, DGS10

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