Accounting for the Bond-Yield Conundrum by Tao Wu

Vol. 3, No. 2 FEBRUARY 2008 EconomicLetter

Insights from the Federal Reserve Bank of Dallas

Accounting For the Bond-Yield Conundrum by Tao Wu

Long-term interest rates tend to rise as monetary policymakers increase This conundrum has short-term interest rates. This relationship didn’t hold, however, during the recent prompted a great deal of U.S. monetary policy tightening cycle. Between June 2004 and June 2006, the Fed- discussion regarding both eral Open Market Committee increased the federal funds rate 17 times—going its magnitude and the from 1 percent to 5.25 percent. Yet, long-term interest rates declined or stayed flat factors behind it. However, until early 2006. a compelling and broadly This divergence between short- and long-term interest rates caught many accepted explanation has economists, investors and central bankers by surprise. In his Feb. 16, 2005, con- yet to be reached. gressional testimony, former Federal Reserve Chairman Alan Greenspan charac- terized the behavior of long-term interest rates since June 2004: “For the moment,

the broadly unanticipated behavior of world bond markets remains a conundrum.

Bond price movements may be a short-term aberration, but it will be some time

before we are able to better judge the forces underlying recent experience.” Since then, this conundrum has tinctly different pattern. During the 12 prompted a great deal of discussion months following the initial federal regarding both its magnitude and the funds rate increase, this long-term factors behind it. However, a compel- bond yield declined by about 80 basis ling and broadly accepted explanation points as short-term rates rose rap- has yet to be reached. idly. Based on past performance, the The correct understanding and 10-year bond yield seemed to be off Based on past quantification of the conundrum have track in mid-2005, possibly by 130 direct implications for monetary policy, basis points or more. performance, the which largely impacts economies as Such a decline appeared even long-term interest rates respond to more puzzling in light of other pres- 10-year bond changes in central banks’ target rates. sures in the economy, such as a robust Persistent changes in the relationship expansion, rising energy prices and a yield seemed between short- and long-term interest falling federal fiscal deficit. All had put rates will affect the timing and impact upward pressure on long-term interest to be off track of monetary policy actions. rates in the past. Some analysts have suggested the in mid-2005, The Conundrum Period conundrum occurred because the bond During the previous three mone- market expected very rapid federal possibly by 130 tary policy tightening cycles—1988–89, funds rate increases at the beginning of 1994–95 and 1999–2000—the 10-year the tightening. When the Federal Open basis points or more. Treasury yield responded to increases Market Committee (FOMC) instead in the federal funds rate target by ris- moved in 17 consecutive 25-basis-point ing an average 26 basis points for steps, it surprised the market from the every 100-basis-point increase in the downside and bond yields were adjust- target (Chart 1). ed downward to be consistent. In the tightening episode that This explanation, however, started June 30, 2004, however, the contradicts the general impression 10-year Treasury yield showed a dis- that U.S. monetary policy’s transpar- ency has improved considerably the past two decades. During the most recent monetary policy tightening, the Chart 1 FOMC’s actions were well anticipated. After the first increase, for example, Federal Funds Rate Target and 10-Year Treasury Yield the federal funds futures market and the Eurodollar futures market correctly anticipated almost every quarter-point Percent increase in the federal funds rate for 12 the next 12 to 18 months (Chart 2). Thus, it doesn’t seem plausible that the 10 long-term interest rate declines that fol- lowed the early-stage tightening arose 10-year Treasury rate 8 from a misperception of monetary policy intention.

6 The Usual Suspects

4 In principle, bond yields can be divided into two components. One is Federal funds rate target 2 the long-term real interest rate, which consists of an expected future real interest rate, plus a risk premium to 0 ’86 ’87 ’88 ’89 ’90 ’91 ’92 ’93 ’94 ’95 ’96 ’97 ’98 ’99 ’00 ’01 ’02 ’03 ’04 ’05 ’06 ’07 cover the uncertainties of its future

SOURCE: Haver Analytics. changes. The other is an inflation component, which depends on the

EconomicLetter 2 Federal Reserve Bank of Dallas Federal Reserve Bank of Dallas EconomicLetter trade surpluses, Asian central banks Chart 2 invested many of these reserves in U.S. Treasury bonds, exerting downward Monetary Policy pressure on Treasury yields (Chart 3). Tightening Was Some economists estimate such pres- Well Anticipated sures on the 10-year Treasury yield at 40 to 120 basis points. More generally, a global savings A global savings glut has Percent glut has arisen from surges in revenues 4.5 for oil and commodity exporters, the arisen from surges in 4 Eurodollar futures rapid income growth of high-saving path: June 30, 2004 3.5 East Asian households and the reduc- revenues for oil and tion in fiscal deficits by several Latin 3 American countries. These develop- commodity exporters, 2.5 ments have added to the net supply 2 Actual federal funds of loanable funds to increasingly open the rapid income growth rate target changes 1.5 world financial markets, helping hold down long-term interest rates in the of high-saving East Asian 1 Fed funds futures path: June 30, 2004 U.S. and other advanced nations. .5 Increased demand by pen- households and the 0 sion funds. Some analysts argue that June Sept. Dec. Mar. June Sept. Dec. 2004 2005 declining bond yields may partly owe reduction in fiscal Maturity to higher demand for longer-duration SOURCE: Haver Analytics. Treasury securities as a result of pro- deficits by several Latin posed corporate pension reforms. In particular, U.S. pension funds American countries. expected future inflation rate, plus a might be required to match the maturi- premium compensating investors for ties of their assets and liabilities. This the uncertainties of future inflation. concern may have encouraged them Changes in long-term bond yields to increase their holdings of longer- should reflect variations in long-term real interest rates, long-run inflation expectations or risk premiums.1 Chart 3 With this in mind, it’s worthwhile to review some changes in the econ- Foreign Official Purchases and 10-Year Treasury Yield omy and financial markets that might be relevant to the conundrum. In particular, market participants have cited Ratio Percent 3 10 the following factors as lowering risk premiums, putting downward pressure 2.5 9 on long-term interest rates. 2 8 Foreign official purchases. 10-year Treasury yield Many market participants have sug- 1.5 7 gested that substantial increases in foreign official purchases of U.S. 1 6

Treasury securities in recent years .5 5 have substantially depressed long-term 2 0 4 Treasury yields. In particular, Asian Foreign official purchases/U.S. GDP central banks built up their holdings –.5 3 of foreign reserves and kept their cur- rency values low relative to the dollar –1 2 to boost exports to the U.S. ’90 ’91 ’92 ’93 ’94 ’95 ’96 ’97 ’98 ’99 ’00 ’01 ’02 ’03 ’04 ’05 Faced with a rapid accumula- SOURCES: Haver Analytics; Federal Reserve Board. tion of dollar assets from record-high

EconomicLetter Federal Reserve Bank of Dallas Federal Reserve Bank of Dallas 3 EconomicLetter duration Treasuries ahead of any regu- in the amount of interest rate risks latory changes, suppressing long-term and changes in the pricing of those Treasury yields. Some analysts also risks. It recognizes that reductions in cite U.K. pension reforms, which have risk premiums are likely a part of the been associated with unusually low conundrum. yields on British bonds. In a 2006 article, Glenn Rude- Decreased macroeconomic busch, Eric Swanson and Tao Wu uncertainty. Because long-term bond provide a good example of such yields are closely related to short-term a macro–finance approach.3 The interest rates and other macroeco- analysis is based on two different nomic fundamentals (both present and models. The first is a vector autore- expected), declines in macroeconomic gression-based model developed by uncertainty since the early 1980s may Bernanke, Vincent Reinhart and Brian Foreign official purchases have put downward pressure on long- Sack (BRS) in 2004.4 The second is term interest rates. a New Keynesian-based model that of U.S. Treasury The Great Moderation of the Rudebusch and Wu (RW) developed American business cycle, as described about the same time.5 securities, increased by Fed Chairman Ben Bernanke, has Both models incorporate impor- been linked to decreased uncertainty tant linkages between interest rates demand for Treasury about inflation, real growth and real and macroeconomic fundamentals. interest rates. They also impose the standard no- securities by pension Declines in asset price volatil- arbitrage restriction from financial ity. The deepening global integration analysis to model the variations of funds, decreased of financial markets, coupled with the term premiums across all bond maturi- introduction of new financial instru- ties and over time. However, these macroeconomic ments the past two decades, may have models have technical specifications played a role in reducing the magni- that differ in important ways, such as uncertainty and tude of economic fluctuations and miti- the short-run effect on interest rates gating their effect on long-term inves- and the economy. Analysis drawing declines in asset tors. Consequently, less-volatile asset from both may very well yield more prices—in this case, Treasury bond robust explanations for the conun- price volatility are prices—have ostensibly worked to drum and other aspects of interest rate lower risk premiums and bond yields. behavior. among the reasons Both models account for the gen- A Macro–Finance Analysis erally downward trend in the 10-year long-term Treasury Determining the impact of these bond yield over the past two decades factors on the conundrum requires a (Charts 4A, B). The risk-neutral com- yields have fallen. rigorous framework. Given the vari- ponent—the sum of long-run inflation ous forces at work, a joint macroeco- expectations and the expected real nomic and finance analysis is the most interest rate—falls considerably over desirable. the same period. So does the associ- A macroeconomic perspective ated risk premium in BRS. This is calls for an examination of the rela- consistent with the Great Moderation tionship between current and future interpretation that the U.S. economy economic fundamentals and the Fed’s has become much less volatile and monetary policy. It recognizes that inflation has gradually stabilized at long-term interest rate movements low levels. reflect markets’ expectations of the Nevertheless, the estimations also future federal funds rate, which the yield notable prediction errors in the Fed adjusts to achieve its inflation and most recent monetary tightening cycle economic stabilization goals. (Charts 5A, B). Both models overpre- A finance perspective entails dicted the 10-year Treasury yield by 50 quantifying changing investor percep- to 75 basis points in the second half of tions of risks for bond pricing, both 2004 and almost all of 2005.

EconomicLetter 4 Federal Reserve Bank of Dallas Federal Reserve Bank of Dallas EconomicLetter Chart 4 Models Account For 10-Year Bond-Yield Trend

A. Bernanke–Reinhart–Sack

Percent

14 Model-implied 10-year Treasury yield 10-year Treasury yield 12 Model-implied risk-neutral 10-year yield Model-implied 10-year term premium

10 Both macro–finance 8 models find 6 evidence of a 4 substantial and 2

0 persistent conundrum ’84 ’85 ’86 ’87 ’88 ’89 ’90 ’91 ’92 ’93 ’94 ’95 ’96 ’97 ’98 ’99 ’00 ’01 ’02 ’03 ’04 ’05 ’06 in long-term bond yields B. Rudebusch–Wu in 2004 and 2005 Percent 10 that can’t be accounted Model-implied 10-year Treasury yield 9 10-year Treasury yield Model-implied risk-neutral 10-year yield for by changes in 8 Model-implied 10-year term premium 7 macroeconomic 6

5 fundamentals.

0 ’88 ’89 ’90 ’91 ’92 ’93 ’94 ’95 ’96 ’97 ’98 ’99 ’00 ’01 ’02 ’03 ’04 ’05 ’06

SOURCE: Author’s estimates.

The models failed to closely track substantial and persistent conundrum the 10-year bond yield on a few other in long-term bond yields in 2004 and occasions as well — in 1997–99, for 2005 that can’t be accounted for by instance. But the prediction errors in changes in macroeconomic fundamen- 2004–05 are substantially larger and tals and estimated declines in risk pre- much more persistent than in previous miums implied by such changes. Yet, episodes. the magnitude of the conundrum is In other words, both macro– much smaller than what a simple cor- finance models find evidence of a relation analysis would suggest.

EconomicLetter Federal Reserve Bank of Dallas Federal Reserve Bank of Dallas 5 EconomicLetter market volatility: the implied volatil- Chart 5 ity in the longer-term U.S. Treasury market from the Merrill Lynch MOVE Models Overpredict 10-Year Treasury Yield index; the implied volatility from in Conundrum Period Eurodollar options for uncertainty about the near-term path of monetary policy; and the VIX measure of implied volatility from S&P 500 index options A. Bernanke–Reinhart–Sack for uncertainty in the stock market. Basis points • Two measures of macroeco- 150 nomic volatility: an eight-quarter trailing standard deviation of the real gross 100 domestic product (GDP) growth rate to proxy output uncertainty and a 50 24-month trailing standard deviation of core personal consumption expen-

0 diture (PCE) deflator inflation to proxy inflation uncertainty. A measure of foreign govern- –50 • ment and central bank purchases of U.S. Treasury securities: the 12-month –100 change in custodial holdings by the New York Fed for all foreign official –150 ’84 ’85 ’86 ’87 ’88 ’89 ’90 ’91 ’92 ’93 ’94 ’95 ’96 ’97 ’98 ’99 ’00 ’01 ’02 ’03 ’04 ’05 ’06 institutions, normalized by the total stock of U.S. Treasury debt held by the public. B. Rudebusch–Wu All these series are natural candi-

Basis points dates for omitted variables that could 60 affect long-term bond yields. For instance, less volatility in the longer-

40 term Treasury market tends to make Treasury securities more attractive relative to other assets and drive long-term 20 bond yields down. Similarly, reduced uncertainty about future monetary 0 policy tends to lower the risks of hold- ing long-term bonds and lead to lower –20 risk premiums. Another possibility is that an –40 increase in stock market volatility enhances the safety appeal of Treasury –60 bonds, driving their prices up and their ’88 ’89 ’90 ’91 ’92 ’93 ’94 ’95 ’96 ’97 ’98 ’99 ’00 ’01 ’02 ’03 ’04 ’05 ’06 yields down. Lower macroeconomic

NOTE: Charts depict variations in bond yields not explained by the models. volatility and increased foreign pur- SOURCE: Author’s estimates. chases of U.S. Treasuries also depress the term premium and lower long-term bond yields. Statistical analysis reveals how Both macro–finance models focus which of those factors could have con- these factors differ in their effect on only on macroeconomic fundamentals tributed to the conundrum in 2004–05. long-term bond yields (Table 1). The and their associated risk premiums; To this end, Rudebusch, Swanson most significant factor is the large they don’t examine special factors that and Wu sought to quantify those fac- drop in the implied volatility of lon- might have affected the premiums. A tors by examining: ger-term Treasury securities, with a natural next step involves determining • Three measures of financial 1 point decline in the index reducing

EconomicLetter 6 Federal Reserve Bank of Dallas Federal Reserve Bank of Dallas EconomicLetter the 10-year Treasury yield by 0.5 to To add to the confusion, the rela- substantial part of it stems from model- 1.2 basis points. tionship between foreign official pur- implied term premiums. The RW Increases in stock market vola- chases and Treasury yields hasn’t been model also identifies a decline in the tility also tend to reduce long-term consistent over the past two decades. risk-neutral component of the 10-year Treasury yields, although such effects Controlling for macroeconomic deter- rate, primarily reflecting a decline in aren’t always statistically significant. minants of long-term bond yields long-run inflation expectations. Less uncertainty about real growth and reveals that the correlation is signifi- However, a large portion of the inflation—in particular, uncertainty cantly positive between 1987 and 2000 bond-yield declines remains unex- about inflation—significantly decreases and negative only since 2002.6 plained by macroeconomic funda- long-term Treasury yields. mentals and associated risk premiums. Interestingly, foreign official pur- Dissecting the Conundrum Changes in the model residuals are chases of U.S. Treasuries—the most How much of the conundrum nearly 87 basis points in the BRS important factor many market partici- can these factors explain? One way model and 32 basis points in the RW pants and the financial press cited for to answer this question is to break model. keeping long-term bond yields low down the regression results from the These residuals can be decom- during the conundrum period—don’t declines in 10-year Treasury yields. posed using six measures of volatil- have a significant effect on long-term Focusing on the 12 months following ity and foreign purchases. The fall Treasury yields. the initial monetary tightening in June in implied volatility of longer-term Even the coefficient estimate’s sign 2004 isolates the period when the Treasuries accounts for the greatest is “wrong.” The press had conjectured conundrum was most apparent. fraction of the conundrum, or more a negative correlation between for- The actual decline in 10-year than a third of the unexplained residu- eign official purchases and long-term Treasury yields over those 12 months als from both models. Declines in the Treasury yields, but the data indicate a is approximately 90 basis points uncertainty of real GDP growth also positive relationship. (Table 2).7 Both models suggest that a contribute to the conundrum, accounting for about 10 percent of the model residuals. Table 1 Inflation volatility doesn’t change Regressions of Model Residuals substantially in those 12 months and has essentially no effect. The three remaining factors aren’t statistically significant and account for relatively Bernanke–Reinhart–Sack Rudebusch–Wu small changes in bond yields during Independent variable Coefficient t( stat) Coefficient t( stat) the period. Implied volatility on longer-term Treasury Half or more of the model securities (Merrill Lynch MOVE index) 1.20 (5.47) .49 (4.11) residuals—49 basis points in the BRS model and 23 basis points in the RW Implied volatility on six-month-ahead Eurodollar futures (from options, in model—remain unexplained after the basis points) –.23 (–1.35) –.17 (–1.83) six variables are taken into account. These may be related to such factors Implied volatility on S&P 500 as pension fund reforms or abnormal (VIX index) –.33 (–.63) –.50 (–1.73) changes in risk appetites that aren’t Realized volatility of quarterly GDP growth considered in the analysis. (trailing 8-quarter standard deviation, Despite its incomplete results, the in percent) 15.40 (3.10) 3.90 (1.45) macro–finance approach provides a Realized volatility of monthly core PCE useful perspective for disentangling the price inflation (trailing 24-month conundrum. standard deviation, in percent) 360.00 (2.18) 214.00 (2.39) Two models identify a bond-yield Foreign official purchases of U.S. Treasury conundrum during the most recent securities (trailing 12-month total, monetary tightening cycle, albeit a as percent of U.S. debt in hands of public) 147.00 (.76) 38.00 (.04) smaller one than was presented by R 2 .30 .14 the financial press. The conundrum is heavily related to a substantial decline SOURCES: Haver Analytics; Federal Reserve Board. in the volatility of long-term bond prices. Contrary to many accounts, foreign

EconomicLetter Federal Reserve Bank of Dallas Federal Reserve Bank of Dallas 7 EconomicLetter EconomicLetter is published monthly by the Federal Reserve Bank of Dallas. The views expressed are those of the authors and should not be attributed to the Federal Reserve Bank of Dallas or the Federal Reserve System. Table 2 Articles may be reprinted on the condition that the source is credited and a copy is provided to the Decomposition of Long-Term Bond-Yield Conundrum Research Department of the Federal Reserve Bank of Dallas. Economic Letter is available free of charge by writing the Public Affairs Department, Federal Bernanke–Reinhart– Rudebusch– Reserve Bank of Dallas, P.O. Box 655906, Dallas, TX Independent variable Sack model Wu model 75265-5906; by fax at 214-922-5268; or by telephone at 214-922-5254. This publication is available on the Observed change in 10-year yield (basis points), Dallas Fed website, www.dallasfed.org. June ’04–June ’05, of which: –93.3 –87.0 • Model-implied change in risk-neutral 10-year yield 13.1 –29.6 • Model-implied change in term premium –19.9 –25.2 • Change in model residuals, of which: –86.5 –32.2 Change in implied volatility on longer-term Treasuries –29.9 –12.2 Change in realized volatility of core PCE inflation 1.1 .7 Change in realized volatility of GDP growth –11.6 –2.9 Change in implied volatility of Eurodollar rate 7.0 5.1 Change in implied volatility of S&P 500 1.2 1.7 Change in foreign official purchases –6.0 –1.6 Unexplained by above –48.6 –23.0

SOURCE: Author’s construction.

official purchases of Treasury securities 3 “The Bond Yield ‘Conundrum’ from a Macro– Richard W. Fisher President and Chief Executive Officer apparently play little or no role. Finance Perspective,” by Glenn Rudebusch, Eric The bond-yield conundrum—fall- Swanson and Tao Wu, Monetary and Economic Helen E. Holcomb ing long-term interest rates in the midst Studies, vol. 24, no. S-1, November 2006, pp. First Vice President and Chief Operating Officer of monetary tightening—posed chal- 83–109. Harvey Rosenblum lenges to the Fed’s monetary policy 4 “Monetary Policy Alternatives at the Zero Executive Vice President and Director of Research actions in 2004 and 2005. Will the Bound: An Empirical Assessment,” by Ben opposite of the bond-yield conundrum Bernanke, Vincent Reinhart and Brian Sack, W. Michael Cox Senior Vice President and Chief Economist occur now, with the Fed cutting the Brookings Papers on Economic Activity, Issue 2, federal funds rate at a time of uncer- 2004, pp. 1–78. Robert D. Hankins tainty about rising energy and food 5 “A Macro–Finance Model of the Term Structure, Senior Vice President, Banking Supervision prices and long-run inflation stability? Monetary Policy, and the Economy,” by Glenn This question increases the importance Executive Editor Rudebusch and Tao Wu, Economic Journal, of closely monitoring the relationship W. Michael Cox forthcoming. between long- and short-term rates. 6 “The Long-Term Interest Rate Conundrum: Not Editor Richard Alm Wu is a senior economist in the Unraveled Yet?” by Tao Wu, Federal Reserve Research Department of the Federal Bank of San Francisco FRBSF Economic Letter, Associate Editor Kathy Thacker Reserve Bank of Dallas. April 29, 2005. 7 Actual changes in the 10-year bond yield differ Graphic Designer Notes by a few basis points across the two models. The Ellah Piña 1 “Globalization’s Effect on Interest Rates and the Bernanke–Reinhart–Sack model uses month- Yield Curve,” by Tao Wu, Federal Reserve Bank of average yield data, while the Rudebusch–Wu Dallas Economic Letter, vol. 1, September 2006. model uses end-of-month yields. 2 “International Capital Flows and U.S. Interest Rates,” by Francis Warnock and Veronica Federal Reserve Bank of Dallas Warnock, International Finance Discussion 2200 N. Pearl St. Papers no. 840, Board of Governors of the Dallas, TX 75201 Federal Reserve System, September 2005.