An Updated Pictorial History of Realized and In-Progress Term Premiums for U.S. Treasury Yields: January 4, 1982 through December 31, 2017

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1 An Updated Pictorial History of Realized and In-Progress Term Premiums for U.S. Treasury Yields: January 4, 1982 through December 31, 2017 Donald R. van Deventer February 26, 2018 In this note we update our October 4, 2017 analysis of realized and in progress term premiums in the U.S. Treasury market through December 31, 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. Adrian, Crump, Mills and Moench (2014) summarize their term premium findings as follows: The evolution of term premia has been of particular interest since the Federal Reserve began largescale 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. 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. From the perspective of prudential regulation of financial institutions, Ramaswamy and Turner [2018] argue that interest rate risk may well be the trigger for the next financial crisis. The magnitude of the term premium, both current and future, is an important element in assessing the interest rate risk of financial institutions. A historical perspective on actual realized term premiums is also a potentially 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? We address the answer to that question with respect to U.S. Treasury fixed rate bonds with maturities of 1, 2, 3, 5, 7, 10, 20 and 30 1 Conversation with the author,

2 years. We remind readers that what follows is an analysis of history, not a forecast for the future. Methodology 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 6-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 6-month Treasury bills and that this investment is rolled over in new 6-month Treasury bills until the underlying bond matures. 3 The investment in the money fund starts with an investment in 6-month Treasury bills and all cash thrown off is reinvested in new 6-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, 6-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. Summary Results The results of the term premium analysis are summarized in the following table: The results show that realized total dollar excess returns have never been negative for maturities of 10, 20, and 30 years. Moreover, pending in progress excess returns 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]. 2

3 have never been negative (so far) for maturities of 5, 7, 10, 20 and 30 years. At the shorter maturities, results are mixed. For 1 year, 73.63% of realized dollar excess returns have been positive but only 6.40% of pending dollar excess returns are positive at this point in time. For the 2-year maturity, the same probabilities of positive excess dollar returns are 82.09% (realized) and 66.05% (pending). At three years, the results are 84.26% (realized) and 97.15% (pending). The statistics for other maturities are shown in the chart. Graphical Analysis Appendix A shows the evolution of total dollar return (in red) versus the 6-month T-bill money fund total dollar return (in blue) for completed 1, 2, 3, 5, 7, 10, 20 and 30-year terms beginning January 4, For most holding periods, interest rates have declined substantially over the investment periods that have been completed. The graphs in Appendix A also include the evolution of the initial six-month Treasury bill yields (in light blue) and the relevant fixed rate Treasury bond yields (in pink) on the origination dates. Appendix B shows the histogram of realized dollar excess returns for each of the 8 fixed rate maturities. Appendix C reports on the histograms of in progress pending dollar excess returns for each maturity. For these incomplete periods, we define the pending excess return as the known dollar advantage of the fixed-rate Treasury bond over the 6-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 6-month Treasury bill equivalent that matures in 6 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 the histograms in Appendix C. One of the reasons for these surprisingly positive term premium results is the large size of the interest earned on coupon payments, which are assumed to be invested in 6-month Treasury bills. The highest total realized dollar return for all of the completed fixed-rate periods are shown in Appendix D. The lowest total realized dollar returns for each of the fixed-rate holding periods are shown in Appendix E. Conclusions The total dollar returns for the 10, 20 and 30-year Treasury bond have exceeded the total dollar returns for the 6-month T-bill money fund on every completed and every partially completed 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. Even at maturities of 5 and 7 years, 100% of pending excess dollar returns are positive as of today. 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. References 3

4 Adrian, T., R. K. Crump, B. Mills and E. Moench (2014), 'Treasury Term Premia: 1961-Present', Liberty Street Economics, available at: present.html. Adrian, T., R. K. Crump and E. Moench (2013), 'Pricing the Term Structure with Linear Regressions', Journal of Financial Economics 110(1), pp Li, Canlin, Andrew Meldrum, and Marius Rodriguez (2017). "Robustness of longmaturity term premium estimates," FEDS Notes. Washington: Board of Governors of the Federal Reserve System, April 3, 2017, Heath, David, Robert A. Jarrow and Andrew Morton (1992), Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claim Valuation, Econometrica, 60(1), pp Kim, D. H. and J. H. Wright (2005), 'An Arbitrage-Free Three-Factor Term Structure Model and the Recent Behavior of Long-Term Yields and Distant-Horizon Forward Rates', Federal Reserve Board Finance and Economics Discussion Series Ramaswamy, Srichander and Philip Turner, A dangerous unknown: interest rate risk in the financial system, Central Banking, February 7,

5 Appendix A: Time Series of Period End Bond and Money Market Values 5

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9 Appendix B: Histogram of Historical Realized Excess Returns 9

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13 Appendix C: Histogram of Pending Realized Excess Returns 13

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17 Appendix D: Highest Realized Total Dollar Returns 17

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21 Appendix E: Lowest Realized Total Dollar Return 21

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