Realized And 'In Progress' Term Premiums For U.S. Treasury Yields: 7 Years Versus 6 Months

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Our notes for holdings of 10, 20 and 30-year Treasury bonds versus an investment in six-month Treasury bills showed excess returns on bonds were always positive, so far.

In doing the same analysis for seven-year U.S. Treasury bonds, we find that 100% of in progress observations and 99.68% of completed observations had positive excess returns.

We remind readers that this result is an accident of 30 years of declining rates, not a forecast for the future.

This is the fourth in our series of notes on the historical values of the term premium embedded in the U.S. Treasury (TLT) (TBT) yield curve. The magnitude of a “term premium” or risk premium in long term U.S. Treasury yields is a major focus of research by economists in the Federal Reserve System. A recent paper by Canlin Li, Andrew Meldrum, and Marius Rodriguez summarizes two important papers on this topic and reviews their methodologies. Estimates of the term premium are a function of the data used, the modeling approach taken, and market expectations. The focus of this note is a simple one: the calculation of historical realized term premiums and “in progress” term premiums. A historical perspective on actual realized term premiums is an important contributor to market expectations, subject to the caveat stated by Robert A. Jarrow, “History is just one draw from a Monte Carlo simulation.” 1

We seek to answer this question: “Which investment has provided the best total dollar return to investors, a U.S. Treasury bond maturing in X years or a money market fund that invests only in Treasury bills?”

In this brief note, we focus on the seven-year Treasury bond.


We use the time series of U.S. Treasury yields maintained by the U.S. Department of the Treasury and distributed by the Board of Governors of the Federal Reserve. 2

We assume that on each day for which data is available, an investor invests $1000 in the U.S. Treasury bond and $1000 in six-month Treasury bills. Every six months, the investor will receive a coupon on the bond. We assume that cash from the coupon payment is invested in six-month Treasury bills and that this investment is rolled over in new six-month Treasury bills until the underlying bond matures. 3 The investment in the “money fund” starts with an investment in six-month Treasury bills and all cash thrown off is reinvested in new six-month Treasury bills until the underlying investment in the fixed rate bond matures. Interest on the six-month bills is calculated on an actual/365 day basis because the U.S. Treasury data series for short term rates is on an “investment” basis.

The payment dates, six-month bill rates, and the value of the “money fund” are given in this spreadsheet. The total dollar returns on 1, 2, 3, 5, 7, 10, 20, and 30-year Treasury bonds, both realized and “in progress,” are given in a separate spreadsheet. Both the money fund spreadsheet and the total return spreadsheet are also available as supplemental materials on Seeking Alpha.



We discuss the other maturity bond results in separate notes.

Seven-Year Treasury Bond Results:

The Term Premium Has Been Negative on Only 23 Origination Dates

The results of a comparison of the total dollar return on the seven-year Treasury bond and the six-month Treasury bill “money fund” are still surprising even in light of our prior results for 10, 20 and 30-year Treasury bonds. We discuss the results both for completed seven-year horizons and for “in progress” seven-year periods that have not yet been completed. Exhibit 1 shows the evolution of the seven-year bond total dollar return (in red) versus the six-month T-bill money fund total dollar return (in blue) for completed seven-year terms originated on each business day from 1982 through 2010:

Exhibit 1

Interest rates have declined substantially over the seven-year investment periods that have been completed. The graph also includes the evolution of the initial six-month Treasury bill yields (in light blue) and seven-year Treasury bond yields (in pink) on the origination dates. Because the ending dollar value of an investment in seven-year Treasury bonds (red) is almost always above the ending dollar value of an investment in the six-month T-bill money fund (in dark blue), the realized term premium has been positive for 99.68% of the completed origination dates, as summarized in this histogram:

The term premium was negative on 23 origination dates in September and October 1993. The average dollar advantage of the bond investment over the T-bill investment was moderately large: $195.50 for an initial investment of $1,000.00. The standard deviation was $96.67.

We now turn to more recent holding periods that have not yet reached the seven year point. For these incomplete periods, we define the “pending excess return” as the known dollar advantage of the Treasury bond over the six-month T-bill investment as of the observation date. For example, on August 28, 2017, the amount of interest that will be paid on a six-month Treasury bill equivalent that matures in six months (not necessarily 182 days) on February 28, 2018 is known with certainty. We tally all of the pending dollar term premiums, all of which have a differing time to maturity, in this graph:

Surprisingly, the pending dollar term premiums have been positive for 100% of the origination dates (so far). The average pending excess return is $56.85 with a standard deviation of $44.14.

Highest and Lowest Realized Dollar Term Premiums

One of the reasons for these surprising results is the large size of the interest earned on coupon payments, which are assumed to be invested in six-month Treasury bills. The highest total realized dollar return among all of the completed seven-year periods was that for an origination date of February 9, 1982, graphed below:

The ending dollar value was $2,350, which included principal of $1,000, coupon payments of $1,049 and interest on these coupons of $302.

The lowest total realized dollar return among all of the completed seven-year periods was that for an origination date of December 18, 2008, shown here:

The total realized return was $1112, which included principal of $1,000, coupons of $111 and interest on the coupons of less than $1.

How Has Quantitative Easing Impacted the Term Premium?

Readers of our posts for 20 and 30-year maturities have asked “how has the term premium been affected by quantitative easing for those ‘in progress’ holding periods?” This is a complex topic, and it requires a very precise and technical answer. Kamakura Corporation’s Managing Director for Research Prof. Robert A. Jarrow and Hao Li addressed this topic in 2014 in the Review of Derivatives Research. Please note that the article is written for readers with a highly technical background.


The total dollar returns for the seven-year Treasury bond have exceeded the total dollar returns for the six-month T-bill money fund on all but 23 completed seven-year holding periods and every partially completed seven-year holding period for which data is available. This is due in part because interest earned on coupon payments rises when rates rise over the holding period, and, at least so far, this has been enough to generate positive excess returns for almost every origination date for seven-year bonds. Our prior study showed excess returns for every holding period for bond maturities of 10, 20 and 30 years.

As we will see when we study shorter maturities, the probability of positive excess returns becomes lower as the maturity of the Treasury bond analyzed shortens.

It goes without saying that there is no guarantee that the future will be like the past. At the same time, expectations for the future should be set with the past in mind.

Appendix: Data for Other Points on the U.S. Treasury Yield Curve

10 Years versus 6 Months

20 Years versus 6 Months

30 Years versus 6 Months


Li, Canlin, Andrew Meldrum, and Marius Rodriguez (2017). "Robustness of long-maturity term premium estimates," FEDS Notes. Washington: Board of Governors of the Federal Reserve System, April 3, 2017, here.

Heath, David, Robert A. Jarrow and Andrew Morton, ”Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claim Valuation,” Econometrica, 60(1),1992, pp. 77-105.

Jarrow, Robert A. and Hao Li, “ The Impact of Quantitative Easing on the U.S. Term Structure of Interest Rates,” Review of Derivatives Research 17(3), 2014.

  1. Conversation with the author, 2015.
  2. This is a different data series than was used by the papers reviewed by Li, Meldrum, and Rodriguez. The selection of the U.S. Department of the Treasury series was intentional, because of quality differences that we will discuss in a separate note.
  3. The “use of proceeds” of cash thrown off from coupon payments was chosen for two important reasons. First, the typical academic assumption that cash generated is reinvested in the same security is an investment strategy that is difficult, if not impossible, to execute in the U.S. Treasury market due to lack of liquidity in “off the run” issues. Second, such an approach preserves the valuation of the Treasury bond when using the risk neutral discounting methodology of Heath, Jarrow and Morton [1992].

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

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