The Bond Yield “Conundrum” from a Macro-Finance Perspective
Seminar, Bank of EnglandNovember 13, 2006
Eric T. SwansonFederal Reserve Bank of SF
Note: The views expressed in this presentation are the authors’ and do not necessarily reflect the views of the management of the Federal Reserve Bank of San Francisco, the Federal Reserve Bank of Dallas, or any other individuals within the Federal Reserve System.
Glenn D. RudebuschFederal Reserve Bank of SF
Tao WuFederal Reserve Bank of Dallas
The Bond Yield “Conundrum”
[L]ong-term interest rates have trended lower in recent months even as the Federal Reserve has raised the level of the target federal funds rate by 150 basis points. This development contrasts with most experience, which suggests that, other things being equal, increasing short-term interest rates are normally accompanied by a rise in longer-term yields… For the moment, the broadly unanticipated behavior of world bond markets remains a conundrum.
—Testimony of Fed Chairman Alan Greenspanto the U.S. Senate, February 16, 2005
Is There A Bond Yield “Conundrum”?or, Are current long-term interest rates simply an extension of 20 years
of bond market trends?
2
4
6
8
10
12
14
pe
rce
nt
10-year Treasury Yield, 1984–2005
• Estimate historical, dynamic relationships between macroeconomic variables and interest rates
• Provide a rigorous econometric framework with which to analyze bond yields
• Like finance models, recognize that Treasury yields consist of two components:
– “risk-neutral” component: i.e., expected future short rates – “term premium” component (time-varying)
• But macro-finance models recognize that macroeconomic variables and bond yields are determined jointly:
– Interest rates affect output, employment, inflation, etc.– But output, employment, inflation also affect current and future
short-term interest rates (through central bank)– Much theory (and empirical evidence) that macro variables also
affect term premia
Macro-Finance Models of the Term Structure
Macro-Finance Models of the Term Structure
• Price of an n-period zero-coupon bond at time t, from finance:
• Simplifying functional form assumption on m (e.g., Duffie-Kan, 1996, Dai-Singleton, 2000, Ang-Piazzesi, 2003):
• Where λt is an affine function of the state of the economy Xt:
Bernanke-Reinhart-Sack Model
• Five variables in Xt:
– employment (HP-filtered)– core PCE deflator inflation (trailing 12-month)– federal funds rate– one-year inflation expectations from Blue Chip (inflation outlook)– four-quarter-ahead Eurodollar futures rate (policy outlook)
• State variables Xt are observable macro variables, follow a VAR:
Rudebusch-Wu Model
• State variables Xt are divided into two groups:
– three observed macro variables– two unobserved (latent) variables, Lt and St
• Bond risk premia are assumed to depend only on Lt and St
• Model dynamics are governed by a structural hybrid New Keynesian model, with macroeconomic interpretations placed on Lt and St
– Lt denotes medium- to long-run inflation level
– St denotes a cyclical indicator, the term structure slope
• Three macroeconomic variables:
– capacity utilization– core PCE deflator inflation (trailing 12-month)– federal funds rate
Rudebusch-Wu Model
• Dynamics of Lt and St:
Differences Between BRS and RW Models
BRS RW
Model dynamics
Parameterization: model dynamics risk pricing
Estimation sample
Bond yield data
reduced-form VAR more structural NK model
10025
134
Jan 1984 – Dec 2005 Jan 1988 – Dec 2000
month-average end-of-month
Latent factors? No Yes – 2
Estimation technique two-step one-step
Model EstimationModel Estimation
• Estimate BRS model over 1984–2005 period (1988–2000 for RW)– begin estimation after Volcker disinflation
monetary policy may have changed since Volcker inflation expectations may have become more stable
– update original BRS sample through end of 2005– try to fit the “conundrum” in-sample as opposed to out-of-sample
(gives model the best possible chance to fit the conundrum)
• Models are fairly simple: linear, only a few state variables
• Nonetheless, estimation of the models is nonlinear in the parameters, can be tricky
– dozens of local minima
BRS Model Decomposition of 10-year Yield
0
2
4
6
8
10
12
14
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
per
cen
t
10-year Treasury yield
model-implied risk-neutral 10-yr yld
model-implied 10-yr term premium
model-implied 10-yr Treasury yield
-100
-50
0
50
100
15019
84
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
bas
is p
oin
ts
50-75 bpconundrum
BRS Model Residuals
RW Model Decomposition of 10-year Yield
0
1
2
3
4
5
6
7
8
9
10
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
per
cen
t
10-year Treasury yield
model-implied risk-neutral 10-yr yld
model-implied 10-yr term premium
model-implied 10-yr Treasury yield
-60
-40
-20
0
20
40
60
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
bas
is p
oin
tsRW Model Residuals
20-50 bpconundrum
Summary of Macro-Finance Model Analysis
• Simple Macro-Finance models explain behavior of Treasury yields from 1984-2005 remarkably well
• Neither model fits the 10-year yield perfectly: there are model residuals
• The recent episode of low long-term rates is one that the models fail to fit– i.e., there is a bond yield conundrum
• Magnitude of the conundrum is in the range of 25-75 bp
What Factors Could Explain the Conundrum?
Story: term premium may be lower than models predict because one (or more) omitted factors is lower than in the past
Some candidate variables that are not in the BRS and RW models:– time-varying interest rate uncertainty– time-varying inflation uncertainty– time-varying output uncertainty– foreign central bank purchases of U.S. Treasuries
• Low term premium?No – accounted for by the model already
• Low inflation/low inflation risk?No – accounted for by the model already
• Irrational pricing or an interest rate “bubble”?Unsatisfying
• Model specification error?Maybe (but why now, and why so large?)
• Omitted variable?Most promising explanation
What Factors Could Explain the Conundrum?
What Factors Could Explain the Conundrum?
We consider:
Three measures of financial market uncertainty:
• Implied volatility on long-term Treasuries (Merrill-Lynch MOVE index)
• Implied volatility on eurodollar rate (from options)
• Implied volatility on S&P 500 (VIX index)
Two measures of macroeconomic uncertainty:
• 8-quarter trailing standard deviation of GDP growth
• 24-month trailing standard deviation of core PCE deflator inflation
One measure of foreign official purchases of U.S. Treasuries:
• 12-month change in custodial holdings at the Federal Reserve Bank of New York
What Factors Could Explain the Conundrum?Implied Volatility on Long-Term Treasuries (MOVE index)
60
80
100
120
140
160
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
Implied Volatility on Eurodollar Rate (from options)
25
50
75
100
125
150
175
200
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
Implied Volatility on S&P 500 (VIX)
10
15
20
25
30
35
40
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
What Factors Could Explain the Conundrum?GDP Growth Realized Volatility (trailing 8 quarters)
0
1
2
3
4
5
6
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
Core PCE Inflation Realized Volatility (trailing 24 months)
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
Foreign Official Purchases of U.S. Treasuries (% of Debt)
-4.0%
-2.0%
0.0%
2.0%
4.0%
6.0%
8.0%
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
-100
-50
0
50
100
15019
84
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
bas
is p
oin
tsBRS Model Residuals
What Factors Could Explain the Conundrum?
What Factors Could Explain the Conundrum?
What Factors Could Explain the Conundrum?
Foreign Official Purchases of U.S. Treasuries (% of Debt)
-4.0%
-2.0%
0.0%
2.0%
4.0%
6.0%
8.0%
Foreign Official Purchases
Conclusions
• A rigorous, macro-finance econometric analysis documents that there is a bond yield conundrum in the 2004–2005 period
• The magnitude of the conundrum is in the range 25–75 bp
• Low volatility of long-term Treasuries appears to have played a role
• Foreign official purchases of long-term Treasuries appear to have played little or no role
Foreign Holdings of U.S. Treasuries
0%
5%
10%
15%
20%
25%
30%
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
as p
erce
nt o
f U
.S.
Deb
t in
Han
ds o
f P
ublic
Foreign Official Holdings (FRBNY)
Total Foreign Holdings (TIC)
Foreign Official Holdings/Purchases
Foreign Purchases of U.S. Treasuries (trailing 12-mo)
-3%
-2%
-1%
0%
1%
2%
3%
4%
5%
6%
7%
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
as p
erce
nt o
f U
.S.
Deb
t in
Han
ds o
f P
ublic
Foreign Official Purchases (FRBNY)
Total Foreign Purchases (TIC)
Foreign Official Holdings/Purchases
Foreign Purchases of U.S. Treasuries (trailing 12-mo)
-10%
-5%
0%
5%
10%
15%
20%
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
as p
erce
nt o
f U
.S.
Deb
t in
Han
ds o
f P
ublic
Foreign Official Purchases (FRBNY)
Total Issuance of U.S. Treasuries to the Public
Total Issuance of U.S. Debt Net of Foreign
U.S. Treasury Issuance (Gross and Net)
-100
-50
0
50
100
15019
84
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
bas
is p
oin
tsBRS Model Residuals
-60
-40
-20
0
20
40
60
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
bas
is p
oin
tsRW Model Residuals