7 Year Treasury Note Rate – This is the fourth in our series of notes on historical values of the term premium placed on the US Treasury ( NASDAQ:TLT ) ( NYSEARCA:TBT ). The size of the “term premium,” or risk premium, in long-term U.S. Treasury yields is a major focus of research by Federal Reserve economists. Kanlin Lee A recent paper by Andrew Meldrum and Marius Rodríguez summarizes two important papers on this topic and reviews their methodology. Estimates of the term premium are a function of the data used; Adopted modeling approach and market expectations. The focus of this note is simple: calculating historically realized term premiums and “in-progress” term premiums. As cautioned by Robert A, historical view of actual realized premiums is important for market expectations. Jarrow, “History drawn from a Monte Carlo simulation”. 1
We seek to answer this question: “Which investment provides the best total dollar return for investors, a US Treasury bond maturing in X years or a money market fund that invests only in Treasuries?”
7 Year Treasury Note Rate
We use time series of US Treasury yields maintained by the US Treasury and distributed by the Board of Governors of the Federal Reserve. 2
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We assume that an investor invests $1000 in US Treasury Bonds and $1000 in six-month Treasury bills on each day for which data are available. Every six months the investor will receive a coupon on the bond. We assume that the proceeds from the coupon payments are invested in six-month T-bills and that this investment is rolled into new six-month T-bills until the underlying bonds mature. 3 An investment in a “money fund” begins by investing in six-month Treasury bills and any money disposed of is reinvested in the six-month Treasury bills until the underlying investment in the fixed-rate bond is exhausted. Because the US Treasury’s short-term rate data series is an “investment” basis, the interest rate on the six-month note is calculated on a real/365-day basis.
Payment dates; The six-month rates of accounts and the value of the “money fund” are given in this table. 1-, 2-, 3-, 5-, 7-, 10-, 20-, and total dollar returns over a 30-year fiscal year are provided in a separate table. Both the money fund spreadsheet and the total return spreadsheet are available as supplemental materials in Request Alpha.
The results comparing the total dollar return on the seven-year Treasury note and six-month Treasury bills were 10-; Even on top of our past results for 20- and 30-year fiscal years, it’s still surprising. We discuss the results for the completed seven-year period and the seven-year period that has not yet completed. Exhibit 1 shows the evolution of the six-month Treasury dollar total return (in blue) and the seven-year bond total return (in red) for seven-year maturities starting on each business day from 1982 to 2010:
Interest rates have fallen significantly over the past seven years of investment periods. The chart also includes initial six-month Treasury yields (light blue) and seven-year Treasury bond yields (pink) at the start dates. Because the terminal dollar value is the seven-year Treasury bond investment (red).
Year Treasury Rate
As summarized in this histogram, the term permanent premium over the closing dollar value of the investment in the six-month Treasury bill (dark blue) is positive.
The term premium is negative in September and October 23, 1993. The standard deviation is $96.67.
We now turn to the more recent periods, which have not yet reached the seven-year period. For these imperfect times, We define “pending excess” as the dollar preference of Treasury bonds known to invest six months from the observation date. for example, February 28, 2017 August 28, 2018, the amount of interest payable for six months equivalent to T-bills maturing within six months. In 2018, I know for sure. We calculate all expected dollar-term premiums in this table; All have different times until maturity;
Surprisingly, Dollar deferred premiums are positive for 100% of origination dates (so far). The mean excess deferred return is $56.85 with a standard deviation of $44.14.
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One reason for these surprising results is the large interest earned on the coupon payments, which are assumed to be invested in six-month Treasury bills. February 9, 1982, the highest total dollar refund received in the last seven years. Shown graphically below:
A closing dollar value of $2,350 and a principal of $1,000; Includes $1,049 in coupon payments and $302 in interest on those coupons.
The lowest total dollar return received in the last seven years was in 2008. December 18 Shown here:
The total refund was $1,112 with a principal of $1,000. Includes $111 in coupons and less than $1 in coupon interest.
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Readers of our 20- and 30-year-old posts have been asking, “How quantitative easing affects the term premium for those ‘in-progress’ holding periods.” Research scholars Prof. Robert A. Jarrow and Hao Li, managing director of Kamakura Corporation, addressed this topic in Derivatives Research Review in 2014. The article is written for a highly technical readership. Be careful.
The total dollar return on the seven-year Treasury note exceeded the total dollar return on the six-month Treasury bill, but for 23 seven-year holding periods and every partially completed seven-year holding period for which data are available. This is partly because interest rates earned on coupon payments have risen over the holding period, at least so far. That’s because it’s enough to generate positive excess returns for nearly every strike date of the seven-year bond. In our previous study, 10-, Excess returns were shown for each holding period for 20- and 30-year bond maturities.
As we see when we study short maturity. As the duration of the analyzed government bonds shortens, the probability of positive surpluses decreases.
It goes without saying that there is no guarantee that the future will be like the past. At the same time, hopes for the future should be placed in the past.
Us Treasury Yield Curve
Lee, Kanlin, Andrew Meldrum and Marius Rodriguez (2017). “Robustness of Long-Term Maturity Premium Estimates,” notes the FEDS. Washington: Board of Governors of the Federal Reserve System; 3 April 2017; Here.
Heath, David, Robert A. Jarrow and Andrew Morton; “The Maturity Determination of Bond Prices and Interest Rates: A New Approach to Relative Acceptance Valuation.”
Jarrow, Robert A. Hao Li. “The Impact of Quantitative Easing on the Structure of US Term Interest Rates”, Review of Derivatives Research 17(3); 2014.
Donald R. van Deventer is the Managing Director of the Applied Quantitative Finance Center at SAS Institute, Inc. Corporation. Kamakura Corporation was established in April 1990. His second book, Advanced Financial Risk Management (Kenji Imai and Mark Messler), was published in 2013. Dr. van Deventer was a senior vice president in the investment banking division of Lehman Brothers from 1987 to 1990. From 1982 to 1987; Dr. van Deventer is treasurer of First Interstate Bancorp in Los Angeles. In this capacity, bond financing requirements; He was responsible for the company’s commercial paper program and the company’s multi-billion dollar derivatives hedging program. From 1977 to 1982, Dr. Van Devanter was Vice President of the Risk Management Division of Security Pacific National Bank. Dr. Van Deventer is a Ph.D. Business Economics A joint degree from Harvard University’s Department of Economics and the Harvard School of Business Administration. In 1999, he was appointed to the Harvard University Graduate School Alumni Association Council, serving until 2021. Dr. Van Devanter was Council President for four years from 2012 to 2016. From 2005 to 2009, he was one of two directors of the Harvard Alumni Association, representing the Faculty of Arts and Sciences. Dr. van Deventer also holds a BA in Mathematics and Economics from Occidental College, where he graduated second in his class.
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