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