kenneth singleton: risk premiums in sovereign debt markets

Unspanned Macro Risks Financial Frictions Early Warning System References

Risk Premiums in Sovereign Debt Markets2012 Barcelona Lecture

Kenneth J. Singleton

Graduate School of BusinessStanford University

Based on joint research with Anh Le, Scott Joslin,Francis Longstaff, Jun Pan, and Lasse Pedersen

May 10, 2012


“In-2-For-1” Year Forward Term PremiumsJoslin, Priebsch, and Singleton (2011)

‐2%

0%

2%

4%

6%

8%

10%

12%

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

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2007

Forward Rate

Expected Yield

Forward Term Premium


The Ingredients of Risk Premiumsin Sovereign Bond Markets

1 Which risks are priced in sovereign bond markets?

Macro-finance models used at many central bank explicitlyinclude macro risks factors as determinants of bond yields.

Most models used by financial institutions focus on factorsthat capture the changing shapes of yield curves.






2 Measuring the compensation that investors require for bearingthese risks?

The role of the macroeconomy?

The role of indigenous yield-curve factors?






2 Measuring the compensation that investors require for bearingthese risks?

The role of the macroeconomy?

The role of indigenous yield-curve factors?

3 How do financial “frictions,” limits to arbitrage, liquidity, etc.affect the quantities of risk and their market prices?



ert(n): the expected return over one period on a bond with

initial maturity n, over and above the riskfree yield rft .

ert(n) =(−Et

[(n− 1)yn−1

t+1

]+ nynt

)︸︷︷︸expected return

− rft︸︷︷︸riskfree rate

≈ B(n)︸︷︷︸Factor Loadings

· Σt︸︷︷︸Quantities of Risk

· Λt︸︷︷︸“Prices” of Risks

What are the sources of risks in sovereign bond markets, andhow are they “priced”?


Parsimony in Modeling Sovereign Risks I

Looking inside financial institutions, bond yields are assumedto follow a low-dimensional factor structure:

ynt ≈ an + bnLLevelt + bnSSlopet + bnCCurvaturet,

where the sources of risk are:

Level: y10yrt (1st PC of yields)

Slope: (y10yrt − y1yrt ) (2nd PC of yields)

Curvature: (0.5y10yrt + 0.5y1yrt − y5yrt ) (3rd PC of yields)

These three principal components (PCs) are “portfolios” ofyields that explain over 95% of the variation in bond yields.


Loadings on PCs of US Bond Yields: 1961-2010European Central Bank Research WP1276

21ECB

Working Paper Series No 1276December 2010

of the zero-coupon yields – with respect to this issue, it should be stressed that the

methods used in computing the zero-coupon yields are consistent across the countries

considered in this paper.

!"#$%&'()'*+,-".#/'+0' !" 1' !# ',.-' !$ 1'2)3)'4564768(9497('

!

!"#

!"$

!"%

!"&

'

' ( ) '* '+ #' #( #) ** *+ $' $( $) (* (+ %' %( %) +* ++ &' &( &) )* )+ '!' '!( '!) ''* ''+ '#'

,-./0123 4565,

,-./0123 7,-85

,-./01239:;6.<:;5

Note: The figure shows the loading of each latent factor at each maturity, expressed in months.

The estimates of the mean values of the three latent factors are reasonable and fairly

precise (see Annex 1). The negative mean values estimated for !# and !$ imply the

typical shape of the yield curve as an ascending and concave curve, as expected.

Moreover, all three latent factors follow highly persistent autoregressive processes, but,

as usual in the literature, !" is more persistent than !# which, in turn, is more persistent

than !$ . Our estimates indicate that the lagged value of the curvature, 1!$ , significantly

drives the dynamics of the level, !" (with a decrease in the degree of concavity

associated with an increase in the level) and that the lagged value of the level, 1!" ,

significantly drives the dynamics of the slope, !# (with an increase in the level

associated with an increase in the slope).

In addition, the innovations to the curvature, !$ , have a larger variance than those

to the slope, !# , which in turn have a higher variance than the innovations to the level,

!" . Such a result is consistent with the literature and with our %&'()*()& ideas. Overall,


Where’s the Macro?

How can we understand risk premiums in bond marketswithout any reference to the macroeconomy?

True, this approach prices bonds almost perfectly!

However, the compensations that investors require for bearingthese risks depend on global macroeconomic conditions.

These macro links are missing, so this “internal” approachdoes a poor job of capturing investors’ risk premiums.


“In-2-For-1” Year Forward Term PremiumsFitting with the Yield Curve (SP)

‐2%

‐1%

0%

1%

2%

3%

4%

5%

6%

7%

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

FTP2,1x

SP

OM

FTP

SP

OM

2,1


Macro-Finance Approach toModeling Risk in Bond Markets

Start with the recognition that the policy rate rt is set by amonetary authority according to a Taylor-style rule

rt = ρ0 + ρπ πt︸︷︷︸inflation

+ ρg gt︸︷︷︸output gap

+ρ` `t︸︷︷︸policy surprise

.

Price bonds of all maturities using a term structure modelthat rules out arbitrage opportunities.

Now the factors are directly linked to macroeconomic activity!

However, does this model accurately price bonds?


Actual Minus Model-Implied Yieldsfrom Macro-Finance Model

1970 1975 1980 1985 1990 1995 2000 2005−150

−100

−50

0

50

100

150

200

Basis

poin

ts

1−yr

5−yr

10−yr


Why Do Macro-Finance Models Fail to Price Bonds?

An implication of including macro variables as risk factors,

rt = ρ0 + ρπ πt︸︷︷︸inflation

+ ρg gt︸︷︷︸output gap

+ρ` `t︸︷︷︸policy surprise

,

is that output growth and inflation are perfectly predictablegiven information in the current yield curve.

Why? Because bond yields are linearly related to (πt, gt) and,therefore, we can invert these relationships to express (πt, gt)in terms of bond yields.

(A weaker version: some models used by the FRB and ECBreplace (gt, πt) with survey forecasts.)


How Large Are Unspanned Macro Risks?

Real economic activity (GRO) and inflation (INF ):

INF is the expected one-year expected inflation rate asmeasured by Blue Chip Economics.

GRO is the Chicago Fed National Activity Index (GRO), ameasure of current real economic conditions.

There is substantial variation in (GRO, INF ) that isunrelated to sovereign yields.

15% (85%) of the variation in GRO (INF ) is explained bychanges in Level, Slope, and Curvature.

The part of (g, π) that is uncorrelated with bond yields hassubstantial predictive power for risk premiums!

Explained variation in realized excess returns increases from28% to 46% when unspanned macro information is added!


Forward Term Premiums WithSpanned Macro Risks (CMM)

‐1%

0%

1%

2%

3%

4%

5%

6%

7%

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

JPS CME0

JPS spanned

CM KW

S-CM 0 E

CM 0 E

CM M


Bringing Policy Analysis and Market Pricing Together

If we focus on bond-market factors, we miss the impact of themacroeconomy of risk premiums in financial markets.

If we introduce macroeconomic variables (output, inflation) asrisk factors, we fail to accurately price bonds.

Can we build an economic framework for pricing bonds andmeasuring risk premiums in which:

Bond yields follow a low-dimensional factor model (say withlevel, slope, and curvature as risk factors);

Profitable riskless arbitrage opportunities are ruled out;

Macroeconomic information influences investors’ attitudestowards risks


Risk Premium Accounting with Unspanned Macro RisksJoslin, Priebsch, and Singleton (2011)

Bond yields have a low dimensional factor structure:summarize underlying risks as (Level, Slope, Curvature):

ynt ≈ an + bnLLevelt + bnSSlopet + bnCCurvaturet,

Risk premiums (expected excess returns) also depend on thestate of the macroeconomy– GRO and INF .

Intuitively, there are a small number or risks underlying eachbond market, but investors’ attitudes towards these risksdepend on the state of the global economy.


Forward Term Premiums in the US

‐1%

0%

1%

2%

3%

4%

5%

6%

7%1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

JPS CME0

JPS spanned

CM KW

S-CM 0 E

CM 0 E

CM M


Forward Term Premiums Versus FRB Fed Funds Target

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

‐1%

0%

1%

2%

3%

4%

5%

6%

7%1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

‐2%

3%

8%

13%

18%

‐1%

0%

1%

2%

3%

4%

5%

6%

7%1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

JPS CME0

JPS spanned

FF Target

S-CM 0 E

CM 0 E

rFF (right)


Do Financial Frictions Matter for Risk Premiums?[With hindsight!] What should we look for?

1 Liquidity and the balance sheets of financial institutions: Shin(2008), Adrian and Shin (2009).

2 Funding and Hedging pressures from GSEs: slope of the termstructure of GSE spreads, GSE2.

Massive growth in balance sheets of GSEs, indicative offunding conditions.

GSEs hedge the interest rate risk of their mortgage positionswith swaps.

3 Conditions in bank-loan market: senior loan officer survey ofdemand for C&I loans by large and medium size companies.


Repo Positions and Mean Leverage of Primary Dealers

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

Ann

ual G

row

th R

ate

GRepo

91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08

16

17

18

19

20

21

22

23

24

Leve

rage

Rat

io

LevPD


Senior Loan Officer Survey And BBB Corporate Spreads

-0.01

-0.005

0

0.005

0.01

0.015

-0.2

0

0.2

0.4

0.6Survey Strong C&I Demand

--Survey Tighter C&I Terms

BBB PC1

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6Survey Strong C&I Demand

--Survey Tighter C&I Terms

BBB PC1


Projections of xrLevelt+1yr and xrSlopet+1yr

Excess Returns on U.S. Dollar Swap Portfolios

PPPPPPPPRHSLHS

xrPC1t+1yr xrPC2t+1yr

PC1 −.441∗ .309�

PC2 .997∗ −.353�

PC3 −.957 1.06∗

INF −5.89∗ 2.60 .101 1.97� −2.12 −.020GIP 1.65∗ 2.13∗ 2.82� −.868� −1.16† −1.59�

GPay −9.48� −9.66� −9.96� 1.35∗ −1.88 .945MbsED .003 .016� .016� −.013�

GSE2 −.0004� −.0003� −.0001 −.0002�

C&ILT .002 .038� −.010∗ −.003GRepo .034 .043∗ −.010∗ −.013R2 0.75 0.47 0.70 0.91 0.52 0.86

Significance: � 1%; ∗ 5%; † 10%.


Forward Term Premiums in the US

‐1%

0%

1%

2%

3%

4%

5%

6%

7%1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

JPS CME0

JPS spanned

CM KW

S-CM 0 E

CM 0 E

CM M


Risk Premiums as Early Warning SignalsSingleton and Tamarisa (2012)

Is there information in sovereign bond markets about“abnormal” conditions that regulators should be monitoring?

Did investors fail to adequately price sovereign risks in Europe?

Or where risk premiums the natural outcome of economic andregulatory policies?

Will risk premiums signal the next financial crisis?


Early Warning: Risk Premiums for US Market

‐0.5

0

0.5

1

1.5

2

United States

-2.5

-2

-1.5

-1

9/29

/198

93/

30/1

990

9/28

/199

03/

29/1

991

9/30

/199

13/

31/1

992

9/30

/199

23/

31/1

993

9/30

/199

33/

31/1

994

9/30

/199

43/

31/1

995

9/29

/199

53/

29/1

996

9/30

/199

63/

31/1

997

9/30

/199

73/

31/1

998

9/30

/199

83/

31/1

999

9/30

/199

93/

31/2

000

9/29

/200

03/

30/2

001

9/28

/200

13/

29/2

002

9/30

/200

23/

31/2

003

9/30

/200

33/

31/2

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9/30

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9/29

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9/28

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73/

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83/

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9/30

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93/

31/2

010

9/30

/201

03/

31/2

011

9/30

/201

1

Data ending in 2006

Data ending in 2011


Early Warning: Risk Premiums for Greek Market

2.5

3

GreeceData ending in 2007

Data ending in 2009

1 5

2

1

1.5

0

0.5

-0.5

-1.5

-1

-2

1/1/

2001

5/1/

2001

9/1/

2001

1/1/

2002

5/1/

2002

9/1/

2002

1/1/

2003

5/1/

2003

9/1/

2003

1/1/

2004

5/1/

2004

9/1/

2004

1/1/

2005

5/1/

2005

9/1/

2005

1/1/

2006

5/1/

2006

9/1/

2006

1/1/

2007

5/1/

2007

9/1/

2007

1/1/

2008

5/1/

2008

9/1/

2008

1/1/

2009

5/1/

2009

9/1/

2009

1/1/

2010

5/1/

2010

9/1/

2010

1/1/

2011

5/1/

2011

9/1/

2011


Adrian, T., and H. Shin, 2009, “Liquidity and Leverage,” Journalof Financial Intermediation, 17, 315–329.

Joslin, S., M. Priebsch, and K. Singleton, 2011, “Risk Premiums inDynamic Term Structure Models with Unspanned Macro Risks,”working paper, Stanford University.

Kim, D., and J. Wright, 2005, “An Arbitrage-Free Three-FactorTerm Structure Model and the Recent Behavior of Long-termYields and Distant-Horizon Forward Rates,” working paper,Discussion Series 2005-33, Federal Reserve Board.

Shin, H., 2008, “Risk and Liquidity in a System Context,” Journalof Financial Intermediation, 17, 315–329.

kenneth singleton: risk premiums in sovereign debt markets

Economy & Finance