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 30-year Treasury bond.
We assume that on each day for which data is available, an investor invests $1,000 in the U.S. Treasury bond and $1,000 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 spreadsheets are also available here as supplemental materials on Seeking Alpha:
We discuss the other maturity bond results in separate notes.
30-Year Treasury Bond Results: The Term Premium Has Never Been Negative
The results of a comparison of the total dollar return on the 30-year Treasury bond and the six-month Treasury bill “money fund” are surprising. We discuss the results both for completed 30-year horizons and for “in progress” 30-year periods that have not yet been completed. Exhibit 1 shows the evolution of the 30-year bond total dollar return (in red) versus the six-month T-bill money fund total dollar return (in blue) for completed 30-year terms originated on each business day from 1982 (4) through 1987:
Interest rates have declined substantially over the 30-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 30-year Treasury bond yields (in pink) on the origination dates. Because the ending dollar value of an investment in 30-year Treasury bonds (red) is always above the ending dollar value of an investment in the six-month T-bill money fund, the realized term premium has been positive for all of the completed origination dates, as summarized in this histogram:
The average dollar advantage of the bond investment over the T-bill investment was massive: $2,768.29 for an initial investment of $1,000.00. The standard deviation was $887.72.
We now turn to more recent holding periods that have not yet reached the 30-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:
Again, we find the surprising result that the pending dollar term premiums have been positive for 100% of the origination dates. The average pending excess return is $798.09 with a standard deviation of $637.38.
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 30-year periods was that for an origination date of February 9, 1982, graphed below:
The ending dollar value was $9,129, which included principal of $1,000, coupon payments of $4,440 and interest on these coupons of $3,689
The lowest total realized dollar return among all of the completed 30-year periods was that for an origination date of July 15, 1986, shown here:
The total realized return was $4,146, which included coupons of $2,136 and interest on the coupons of $1,010.
The total dollar returns for the 30-year Treasury bond have exceeded the total dollar returns for the six-month T-bill money fund on every completed and every partially completed 30-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 strictly positive excess returns for 30-year bonds.
As we will see when we study other maturities, this is less and less true as the maturity 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.
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.
- Conversation with the author, 2015.
- 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.
- 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).
- January 4, 1982 is the first date that the U.S. Department of the Treasury began publishing three-month and six-month Treasury bill rates.
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