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An Introduction to Derivative Securities, Financial Markets, and Risk ManagementAdvanced Financial Risk Management, 2nd ed.

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Feb 17

Written by: Donald van Deventer
2/17/2012 3:33 AM 

Today’s forecast for U.S. Treasury yields is based on the February 16, 2012 constant maturity Treasury yields that were reported by the Board of Governors of the Federal Reserve System in its H15 Statistical Release at 4:15 p.m. Eastern Standard Time February 17, 2012. The “forecast” is the implied future coupon bearing U.S. Treasury yields derived using the maximum smoothness forward rate smoothing approach developed by Adams and van Deventer (Journal of Fixed Income, 1994) and corrected in van Deventer and Imai, Financial Risk Analytics (1996). For an electronic delivery of this interest rate data in Kamakura Risk Manager table format, please subscribe via info@kamakuraco.com.

The “forecast” for future U.S. dollar interest rate swap rates is derived from the maximum smoothness forward rate approach, but it is applied to the forward credit spread between the libor-swap curve (also reported in the H15 release) and U.S. Treasury curve instead of to the absolute level of forward rates for the libor-swap curve.

This week’s projections for the 1 month Treasury bill rate (investment basis) reflect a smoother curve in the intermediate to long term compared to the previous week. From 2013 to 2015, bill rates increase up to 9 basis points from last week’s projections. After, bill rates decrease up to 16 basis points throughout the rest of the curve. Bill rates are projected to rise to 3.586% in January 2022, down 16.3 basis points from last week. The 10 year U.S. Treasury yield is projected to rise steadily to reach 3.875% on January 31, 2022, 6.1 basis points lower than projected last week.



U.S. dollar swap spreads this week were a negative 35 basis points at 30 years, 4 basis points more negative than last week. Today’s forecast continues to imply a rise and fall of spreads between the libor-swap curve and U.S. Treasuries, with a local peak in the 1 month spread of 84.4 basis points in June 2012, down 0.8 basis points from the previous forecast. Thereafter, swap spreads drop to a negative spread of 32.7 basis points in January 2013. This extreme gyration is generated by the difference in credit risk on the libor curve (used for 1 month, 3 months, and 6 months) and the interest rate swap curve (used for one year and beyond).  Buyers of Eurodollar deposits run the risk of 100% loss of principal, but swap market participants stand to lose only the present value of the difference in original swap cash flows versus current market rates if the swap counterparty defaults with no collateral. Kamakura’s analysis ignores this credit differential, consistent with common market practice. One month spreads to US Treasuries turn positive thereafter but they turn negative again from 2017 to 2022. The libor-swap curve itself shows a peak in 1 month libor at 99.3 basis points in June 2012 and a fall to negative 4.2 basis points in January 2013.  These gyrations too are caused by the differential in credit risk between the first six months of the curve and longer maturities.

These negative spreads between U.S. dollar interest rate swaps and U.S. Treasury yields reflect the blurring of credit quality between these two yield curves.  The U.S. government has not been seen as risk free for some time by market participants. Eurodollar rates used here are collected by the U.S. Federal Reserve and are different from the “official” libor rates collected by Thomson Reuters on behalf of the British Bankers Association. As reported in other blogs on this website, there is increasing evidence that the BBA Libor figures have been consistently set at below actual funding costs during the credit crisis that started in 2007. The U.S. dollar libor panel was revised in an announcement on December 1, 2011 effective December 5, 2011. Bank of Nova Scotia was removed, leaving 18 banks remaining on the panel. Now 4 of the 18 panel banks that determine U.S. dollar libor have received significant government assistance and are, in effect, sovereign credits. The following banks make up the current U.S. dollar libor panel:

  • Bank of America
  • Bank of Tokyo-Mitsubishi UFJ
  • Barclays Bank PLC
  • BNP Paribas
  • Citibank NA
  • Credit Agricole Corporate Investment Bank
  • Credit Suisse
  • Deutsche Bank AG
  • HSBC
  • JP Morgan Chase
  • Lloyds Banking Group
  • Norinchukin Bank
  • Rabobank
  • Royal Bank of Canada
  • Royal Bank of Scotland Group
  • Societe Generale
  • Sumitomo Mitsui Banking Corporation
  • UBS AG

For more on the panel members, see www.bbalibor.com. Please note that there are periods of dramatic differences between the libor rates reported by the British Bankers Association, using the panel above, and the Eurodollar rates reflected in the H15 statistical release.  Those differences are summarized in this blog entry on www.kamakuraco.com:

van Deventer, Donald R. “Kamakura Blog: Default Probabilities and Libor,” Kamakura blog, www.kamakuraco.com, June 7, 2010. Redistributed on www.riskcenter.com on June 8, 2010.

On March 15, 2011, UBS revealed in its 2010 annual report that the company received subpoenas concerning possible manipulation of libor from the U.S. Securities and Exchange Commission, the U.S. Commodity Futures Trading Commission and the U.S. Department of Justice. On August 23, 2011, Charles Schwab filed two lawsuits against 11 major banks, including Bank of America, JP Morgan Chase, and Citigroup, claiming they had conspired to manipulate libor. It is too early to determine how much of the difference between the H15 Eurodollar figures and libor could be due to manipulation of libor. The public evidence of possible libor manipulation is summarized in this blog:

van Deventer, Donald R. “Public Information and Libor Manipulation,” Kamakura blog, www.kamakuraco.com, December 13, 2011.

Background Information on Input Data and Smoothing

The Federal Reserve H15 statistical release is available here:
http://www.federalreserve.gov/Releases/H15/Update/

The maximum smoothness forward rate approach to yield curve smoothing was described in this blog entry:

van Deventer, Donald R. “Basic Building Blocks of Yield Curve Smoothing, Part 10: Maximum Smoothness Forward Rates and Related Yields versus Nelson-Siegel,” Kamakura blog, www.kamakuraco.com, January 5, 2010.  Redistributed on www.riskcenter.com on January 7, 2010.

The use of the maximum smoothness forward rate approach for bond data is discussed in this blog entry:

van Deventer, Donald R. “Basic Building Blocks of Yield Curve Smoothing, Part 12: Smoothing with Bond Prices as Inputs,” Kamakura blog, www.kamakuraco.com, January 20, 2010. Redistributed on www.riskcenter.com on January 21, 2010.

For a pictorial history of daily U.S. Treasury forward rates since January 2, 1962, see

Dickler, Daniel T., Robert A. Jarrow and Donald R. van Deventer, “Inside the Kamakura Book of Yields: A Pictorial History of 50 Years of Daily U.S. Treasury Forward Rates,” Kamakura Corporation memorandum, September 13, 2011.

For a quantitative summary of forward rate curve shapes that have prevailed since January 2, 1962, see

Dickler, Daniel T. and Donald R. van Deventer, “Inside the Kamakura Book of Yields: An Analysis of 50 Years of Daily U.S. Treasury Forward Rates,” Kamakura blog, www.kamakuraco.com, September 14, 2011.

The reasons for smoothing forward credit spreads instead of the absolute level of the libor-swap curve were discussed in this blog entry:

van Deventer, Donald R. “Basic Building Blocks of Yield Curve Smoothing, Part 13: Smoothing Credit Spreads,” Kamakura blog, www.kamakuraco.com, April 7, 2010. Redistributed on www.riskcenter.com, April 14, 2010.

The Kamakura approach to interest rate forecasting was introduced in this blog entry:

van Deventer, Donald R. “The Kamakura Corporation Monthly Forecast of U.S. Treasury Yields,” Kamakura blog, www.kamakuraco.com, March 31, 2010. Redistributed on www.riskcenter.com on April 1, 2010.

Today’s Kamakura U.S. Treasury Yield Forecast

The Kamakura 10 year monthly forecast of U.S. Treasury yields is based on this data from the Federal Reserve H15 statistical release:



The graph below shows in 3 dimensions the movement of the U.S. Treasury yield curve 120 months into the future at each month end:



These yield curve movements are consistent with the continuous forward rates and zero coupon yields implied by the U.S. Treasury coupon bearing yields above:



In numerical terms, forecasts for the first 60 months of U.S. Treasury yield curves are as follows:



The forecasted yields for months 61 to 120 are given here:



Today’s Kamakura Forecast for U.S. Dollar Interest Rate Swap Yields and Spreads

Today’s forecast for U.S. Dollar interest rate swap yields is based on the following data from the H15 Statistical Release published by the Board of Governors of the Federal Reserve System:



Applying the maximum smoothness forward rate smoothing approach to the forward credit spreads between the libor-swap curve and the U.S. Treasury curve results in the following zero coupon bond yields:



The forward rates for the libor-swap curve and U.S. Treasury curve are shown here:



The 10 year forecast for U.S. dollar interest rate swap yields is shown in the following graph:



The 10 year forecast for U.S. dollar interest rate swap spreads to U.S. Treasury yields is given in the following graph:



The numerical values for the implied future U.S. dollar interest rate swap spreads to U.S. Treasury yields are given here for 60 months forward:



The numerical values for the implied future U.S. dollar interest rate swap spreads to U.S. Treasury yields are given here for 61-120 months forward:



For more information about the yield curve smoothing and simulation capabilities in Kamakura Risk Manager, please contact us at info@kamakuraco.com.  Kamakura interest rate forecasts are available in pre-formatted Kamakura Risk Manager data base format.

Andrew Sheahan, Donald R. van Deventer and Martin Zorn
Kamakura Corporation
Honolulu, February 17, 2012

Copyright © Kamakura Corporation, 2012.  All Rights Reserved.

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