Inside the Kamakura Book of Yields: A Pictorial History of ... · 9/13/2011 · Heath, Jarrow and Morton (1992) and focus on the monthly forward rate curves constructed from U.S

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Inside the Kamakura Book of Yields: A Pictorial History of 50 Years of U.S. Treasury Forward Rates Daniel T. Dickler, Robert A. Jarrow and Donald R. van Deventer September 13, 2011 Copyright © 2011 by Kamakura Corporation. All Rights Reserved.

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Introduction This pictorial history of the US Treasury forward rate curve is designed to help both academics and financial market participants better understand the evolution of the term structure of interest rates. In what follows, we take the approach of Heath, Jarrow and Morton (1992) and focus on the monthly forward rate curves constructed from U.S. Treasury yields reported by the Federal Reserve beginning January 2, 1962. We analyze the data daily through August 22, 2011. We employ the “maximum smoothness forward rate” smoothing method of Adams and van Deventer (1994) as corrected in van Deventer and Imai (1997) to generate monthly forward rates for this time period, producing 12,395 daily forward rate curves. This document generates a pictorial history of these monthly forward rate curves for each business day, year by year. For visual acuity, every third monthly forward rate is graphed, i.e. month 3, month 6 and so on. A number of conclusions can be drawn after observing the term structure evolution for 50 years. The first is that forward rate curves display a richness of shapes that are not accurately captured by the academic literature on this topic. The second is that the evolution of the term structure of interest rates is driven by a larger number of risk factors than the 1, 2 or 3 factor models commonly employed in the academic literature. The third is that the maximum smoothness forward rate smoothing procedure is robust, generating smooth and stable forward rates even during periods of severe disruption in the financial markets, like the credit crisis of 2007-2008, the Russian debt crisis in 1998, and in the 1980-1982 period when interest rates were at historic highs. Large movements in forward rates appear to be almost exclusively triggered by one of two events: a change in the maturities reported by the Federal Reserve, which adds or subtracts key information used in the smoothing process, or specific financial market events like the September 14, 2008 bankruptcy announcement by Lehman Brothers. The daily monthly U.S. Treasury forward rates were generated using the Federal Reserve H15 statistical release and Kamakura Risk Manager version 7.3. Daily data on monthly forward rates, monthly zero coupon yields, and par coupon yields for each semi-annual maturity are available for purchase from Kamakura Risk Information Services. For more information, please contact Kamakura Corporation at [email protected]. The 12,395 forward rate curves are analyzed in more quantitative fashion in a series of blogs on www.kamakuraco.com beginning September 15, 2011.

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Federal Reserve Data Regimes for U.S. Treasury Yield Curve Data

References Adams, Kenneth J. and Donald R. van Deventer. "Fitting Yield Curves and Forward Rate Curves with Maximum Smoothness.” Journal of Fixed Income, June 1994. Heath, David, Robert A. Jarrow and Andrew Morton, "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, 60(1), January 1992. van Deventer, Donald R. and Kenji Imai, Financial Risk Analytics: A Term Structure Model Approach for Banking, Insurance, and Investment Management, Irwin Professional Publishing, Chicago, 1997. van Deventer, Donald R., Kenji Imai, and Mark Mesler, Advanced Financial Risk Management, John Wiley & Sons, 2004. Translated into modern Chinese and published by China Renmin University Press, Beijing, 2007.

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2011 through August 22, 2011 Data Regime: 1, 3 and 6 months with 1, 2, 3, 5, 7, 10, 20 and 30 years The continuance of near zero short rates created a strongly upward sloping forward rate curve

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2010 Data Regime: 1, 3 and 6 months with 1, 2, 3, 5, 7, 10, 20 and 30 years The Federal Reserve’s near zero short rate policy continued in 2010.

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2009 Data Regime: 1, 3 and 6 months with 1, 2, 3, 5, 7, 10, 20 and 30 years The Federal Reserve’s zero interest rate policy and flight to quality into the 30 year U.S. Treasury bond created a strongly humped forward rate curve

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2008 Data Regime: 1, 3 and 6 months with 1, 2, 3, 5, 7, 10, 20 and 30 years Forward curve volatility dramatically increased after the September 14, 2008 announcement that Lehman Brothers would file for bankruptcy.

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2007 Data Regime: 1, 3 and 6 months with 1, 2, 3, 5, 7, 10, 20 and 30 years The spike in short rates on August 20 was caused by a shift in 1 month rates from 3.03 to 2.47 and then to 3.17 on August 17, 20 and 21 with minimal moves in the 6 month rate, a time when the severity of the 2007-2009 credit crisis was strongly evident to the Federal Reserve

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2006 Data Regime: 1, 3 and 6 months with 1, 2, 3, 5, 7, 10, and 20 years until February 8, 2006; 1, 3 and 6 months with 1, 2, 3, 5, 7, 10, 20 and 30 years thereafter The restoration of 30 year yield data again causes a significant shift in the shape of the forward curve

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2005 Data Regime: 1, 3 and 6 months with 1, 2, 3, 5, 7, 10, and 20 years

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2002 Data Regime: 1, 3 and 6 months with 1, 2, 3, 5, 7, 10, 20 and 30 years until February 15, 2002; 1, 3 and 6 months with 1, 2, 3, 5, 7, 10, and 20 years thereafter The lack of 30 year Treasury yield information causes a significant change in forward curve shapes

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2001 Data Regime: 3 and 6 months with 1, 2, 3, 5, 7, 10, 20 and 30 years until July 30, 2001; 1, 3 and 6 months with 1, 2, 3, 5, 7, 10, 20 and 30 years thereafter Many observers label the year 2001 as the year of the “high technology crash,” but forward rate curve movements were modest

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2000 Data Regime: 3 and 6 months with 1, 2, 3, 5, 7, 10, 20 and 30 years

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1999 Data Regime: 3 and 6 months with 1, 2, 3, 5, 7, 10, 20 and 30 years 1999 shows the impact of a “flight to quality” into the 30 year bond, forcing forward rates down at longer maturities. This is a frequent phenomenon

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1998 Data Regime: 3 and 6 months with 1, 2, 3, 5, 7, 10, 20 and 30 years The default of the Russian Federation in August 1998 triggered a period of dramatic shifts in the forward rate curve

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1997 Data Regime: 3 and 6 months with 1, 2, 3, 5, 7, 10, 20 and 30 years Although many observers date the Asia crisis as beginning July 2, 1997, there was not a dramatic movement in forward rates

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1993 Data Regime: 3 and 6 months with 1, 2, 3, 5, 7, 10 and 30 years until September 30, 1993; 3 and 6 months with 1, 2, 3, 5, 7, 10, 20 and 30 years thereafter Note how the arrival of 20 year data causes a dramatic shift in the smoothed curve given new information

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1992 Data Regime: 3 and 6 months with 1, 2, 3, 5, 7, 10 and 30 years

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1982 Data Regime: 3 and 6 months with 1, 2, 3, 5, 7, 10 and 30 years from January 4, 1982 1982 was another year of volatile, high interest rates with the 30 year yield ranging more than 300 basis points

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1981 Data Regime: 1, 2, 3, 5, 7, 10, and 30 years 30 year yields exceeded 15% in 1981

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1980 Data Regime: 1, 2, 3, 5, 7, 10, and 30 years 30 year yields moved more than 300 basis points in 1980, reaching 12.71% on November 10

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1979 Data Regime: 1, 2, 3, 5, 7, 10, and 30 years

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1978 Data Regime: 1, 2, 3, 5, 7, 10, and 30 years

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1977 Data Regime: 1, 2, 3, 5, 7 and 10 years until February 15, 1977; 1, 2, 3, 5, 7, 10, and 30 years thereafter The 1 day swing in forward rates on December 29 was caused by a 1 day one-time 10 bp swing in the 7 year rate, probably an error in data collection

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1976 Data Regime: 1, 3, 5, 7 and 10 years until May 28, 1976; 1, 2, 3, 5, 7 and 10 years thereafter

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1975 Data Regime: 1, 3, 5, 7 and 10 years The spike in forward rates on March 26 is due to a one day 18 basis point drop in the 7 year rate with no move in 5 and 10 year rates, most likely a data error by the Federal Reserve

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1974 Data Regime: 1, 3, 5, 7 and 10 years By the end of 1974, the period of declining forward rates has come to an end.

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1973 Data Regime: 1, 3, 5, 7 and 10 years 1973 brings a rare display of declining forward rates

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1972 Data Regime: 1, 3, 5, 7 and 10 years The humped forward rate pattern seen often in later years persists for most of 1972

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1971 Data Regime: 1, 3, 5, 7 and 10 years 10 year yield was 6.18% on February 23, 5.38% on March 23, 6.65% on May 18, and 5.89% at year end

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1970 Data Regime: 1, 3, 5, 7 and 10 years V-shaped pattern ends March 10, 1970 when 7 year exceeds 5 year yield level

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1969 Data Regime: 1, 3, 5 and 10 years until June 30, 1969; 1, 3, 5, 7 and 10 years thereafter. V-shaped forwards on December 30 caused by yield inputs: 8.26 (5y), 7.7 (7y), 7.97 (10y)

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1968 Data Regime: 1, 3, 5 and 10 years

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1967 Data Regime: 1, 3, 5 and 10 years The mid-year hump in forward rates caused by 5 year yield 15-25 basis points higher than 3 year and 10 year

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1966 Data Regime: 1, 3, 5 and 10 years Even with only 4 input maturities, the data demonstrate a rich array of forward curve shapes during 1966

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1965 Data Regime: 1, 3, 5 and 10 years Downward sloping forward rates make a rare appearance at the end of the year

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Documents

Inside the Kamakura Book of Yields: A Pictorial History of ... · 9/13/2011 · Heath, Jarrow and Morton (1992) and focus on the monthly forward rate curves constructed from U.S