1

Are the Business Cycle Risk, Market Skewness Risk and Correlation Risk Priced

in Swap Markets? The US Evidence

Sohel Azad, Deakin UniversityJonathan Batten, HKUST

Victor Fang, Deakin University

2

Objective

• To examine whether Business Cycle Risk, Market Skewness Risk and Correlation Risk are

priced in US swap spreads• Paper in early draft

3

Motivation

• swap spread>> the difference between swap rate and treasury bond rate of equivalent maturity

• This spread represents the relative price of risk that compensates for– Default risk – Liquidity risk

4

Motivation

Empirical studies in determinants of swap spreads:

Level Slope Curvature/volatility Default risk Liquidity risk

5

Motivation

• But…• Findings are mixed– Some support for default risk as sole dominant– Others support liquidity risk

• Puzzle remains• Motivates to examine other risk factors that

may explain the dynamics of swap prices.

6

Other risk factors

• Business cycle risk• Market skewness risk• Correlation risk

7

Why these risk factors

• Business cycle risk– Uncertainty in business environment– Lang et al (1998) show that swap spreads follow

the business cycle (proxy by unemployment rate)– This implies business cycle risk increases swap

spreads. Why?– Because business cycle risk increases the

probability of default which in turn increases the credit risk of the counterparties.

8

Business cycle risk

• High business cycle risk increases preferences for fixed income assets which motivates derivative activities [see Loey & panigirtzoglou (2005), Cailleteau & Mali (2007)]

• Similarly if a particular swap maturity has a higher exposure to business cycle risk, then swap makers would demand extra premium to cover the risk.

9

Market skewness risk• Due to heterogeneity in firm’s access to funding and

borrowing restrictions that caused asset returns non-normal • Due to the credit risk premium differential across domestic

and overseas markets (Batten and Covrig (2004) and Nishioka and Baba (2004))

• Andrian & Rosenberg (2008) show that market skewness risk (financial constraint risk) is priced in asset return. Why?

• Because the time variation of volatility of asset returns drives the time variation in skewness.

• Similarly if there is a significantly high skewness risk in swap, then swap spread should contain risk premium related to this risk.

10

Correlation Risk• Different interpretation of correlation risk in different

markets• In stock & bond markets- if a market-wide increase in

correlations will affect portfolio diversification• In swap, the correlation is between the underlying

interest rates ie fixed rate and floating rate• Why there is a correlation risk between the underlying

interest rates?• Because of the time varying correlation in interest rates

across the term structure

11

Correlation risk

• How this correlation risk affect swap pricing?• Highly correlated underlying interest rates, reduces swap

spreads. Why– Reduces uncertainty about the future movements of interest

rates, hence reduces hedging cost and mark-to-market risk of IR swap

• If the time varying correlation between the fixed and floating rate is low, it poses uncertainty to pricing and hedgingcost.

12

Contribution

• First study to extensively examine the influences of business cycle risk, market skewness risk and correlation risk in swaps

• First study to use the FS-GARCH approach to extract business cycle risk and market skewness risk from the stock market

13

3 Hypotheses• Business cycle risk:

H1: Swap spread is positively associated with the business cycle risk

• Market skewness riskH2: Swap spread is positively associated with the market skewness risk

• Correlation risk– H3: The swap spread is negatively (positively)

associated with the correlation risk at times of high (low) correlation between underlying interest rates

14

Spreads vs BCYC&SKEW

4/1/1987

1/1/1988

10/1/1988

7/1/1989

4/1/1990

1/1/1991

10/1/1991

7/1/1992

4/1/1993

1/1/1994

10/1/1994

7/1/1995

4/1/1996

1/1/1997

10/1/1997

7/1/1998

4/1/1999

1/1/2000

10/1/2000

7/1/2001

4/1/2002

1/1/2003

10/1/2003

7/1/2004

4/1/2005

1/1/2006

10/1/2006

7/1/2007

4/1/2008

1/1/2009

10/1/2009

7/1/2010-20

020406080

100120140160180

2yr 5yr 7yr

12/1/1987

8/1/1988

4/1/1989

12/1/1989

8/1/1990

4/1/1991

12/1/1991

8/1/1992

4/1/1993

12/1/1993

8/1/1994

4/1/1995

12/1/1995

8/1/1996

4/1/1997

12/1/1997

8/1/1998

4/1/1999

12/1/1999

8/1/2000

4/1/2001

12/1/2001

8/1/2002

4/1/2003

12/1/2003

8/1/2004

4/1/2005

12/1/2005

8/1/2006

4/1/2007

12/1/2007

8/1/2008

4/1/2009

12/1/2009

8/1/2010

00.10.20.30.40.50.60.70.80.9

Bcycle Skewness

15

Spread vs Correlation risk• 7-year spread

• Corr_7yrTB&6mLib4/1

/1987

12/1/1987

8/1/1988

4/1/1989

12/1/1989

8/1/1990

4/1/1991

12/1/1991

8/1/1992

4/1/1993

12/1/1993

8/1/1994

4/1/1995

12/1/1995

8/1/1996

4/1/1997

12/1/1997

8/1/1998

4/1/1999

12/1/1999

8/1/2000

4/1/2001

12/1/2001

8/1/2002

4/1/2003

12/1/2003

8/1/2004

4/1/2005

12/1/2005

8/1/2006

4/1/2007

12/1/2007

8/1/2008

4/1/2009

12/1/2009

8/1/2010-0.2

00.20.40.60.8

11.21.4

4/1/1987

12/1/1987

8/1/1988

4/1/1989

12/1/1989

8/1/1990

4/1/1991

12/1/1991

8/1/1992

4/1/1993

12/1/1993

8/1/1994

4/1/1995

12/1/1995

8/1/1996

4/1/1997

12/1/1997

8/1/1998

4/1/1999

12/1/1999

8/1/2000

4/1/2001

12/1/2001

8/1/2002

4/1/2003

12/1/2003

8/1/2004

4/1/2005

12/1/2005

8/1/2006

4/1/2007

12/1/2007

8/1/2008

4/1/2009

12/1/2009

8/1/2010

0

0.05

0.1

0.15

0.2

0.25

0.3

16

Data• Daily IRS spread data for Five swaps: 2yr, 3yr, 5yr, 7yr and

10yr• S&P 500 index data• Sample coverage: 1989-2011, • Data from DataStream, Bloomberg, Federal Reserve System• Sub-samples:

– 1) AFC, LTCM, RGBD, LTCB and NCB spanning daily data from June 1997 to November 1998

– 2) Normal period covering the daily data from January 1999 to June 2007

– 3) GFC period spanning the daily data from July 2007 to December 2009.

17

Methodology

Business cycle risk (BCYC) and skewness risk (SKEW) are calculated from the S&P 500 using FS-GARCH model of Rangel and Engle (2012), JBES

18

Methodology_cont.

• Correlation risk between TB and 6-Month dollar-LIBOR is estimated using the DCC approach of Engle (2002)

• Default risk (DEF) is calculated as the yield spread between 10-year BBB and AAA corporate bond reported by Bloomberg

• Liquidity risk (LIQ) is calculated as the difference between 6-month Eurodollar rate and 6-month T-bill.

19

Methodology_cont.

Regression Estimation (GMM)

20

Findings summary

• Result are consistent with the theory with few exceptions

• Full sample:– Spread is associated

• Positively with the business cycle risk• Negatively (but mostly insignificant) with the market skewness risk • Negatively (most cases) with the correlation risk

• Sub-samples:– Spread is associated

• Positively with the business cycle risk, negatively during the GFC• Positively with market skewness risk across the sub-samples• Negatively (most cases) with correlation risk for longer maturities but

positively with shorter maturities.

21

Correlation between Swap Spread and its Risk Determinants

IRS2 IRS3 IRS5 IRS7 IRS10 BCYC SKEW TB2_LIB TB3_LIB TB5_LIB TB7_LIB TB10_LIB DEF LIQ

IRS2 1 0.9405 0.9039 0.8021 0.6470 0.6172 0.5753 -0.0349 -0.0009 0.0574 -0.0235 -0.0178 0.4583 0.7727

IRS3 0.9405 1 0.9433 0.8736 0.7292 0.6747 0.5775 -0.0468 0.0026 0.0775 -0.0385 -0.0323 0.4548 0.6403

IRS5 0.9039 0.9433 1 0.9506 0.8283 0.7080 0.5256 -0.0578 0.0029 0.0810 -0.0329 -0.0261 0.3428 0.5825

IRS7 0.8021 0.8736 0.9506 1 0.8440 0.6228 0.4211 -0.0543 0.0034 0.0892 -0.0329 -0.0273 0.1619 0.4051

IRS10 0.6470 0.7292 0.8283 0.8440 1 0.6782 0.3792 -0.0566 0.0060 0.0941 -0.0316 -0.0217 0.2090 0.3267

BCYC 0.6172 0.6747 0.7080 0.6228 0.6782 1 0.5445 -0.0287 0.0025 0.0406 -0.0092 -0.0042 0.3578 0.4307

SKEW 0.5753 0.5775 0.5256 0.4211 0.3792 0.5445 1 -0.0809 0.0068 0.1346 -0.1148 -0.1178 0.5456 0.5804

TB2_LIB-0.0349 -0.0468 -0.0578 -0.0543 -0.0566 -0.0287 -0.0809 1 -0.1472 -0.6601 0.8425 0.7801 -0.0167 -0.0110

TB3_LIB-0.0009 0.0026 0.0029 0.0034 0.0060 0.0025 0.0068 -0.1472 1 0.0839 -0.2047 -0.2096 0.0024 0.0066

TB5_LIB 0.0574 0.0775 0.0810 0.0892 0.0941 0.0406 0.1346 -0.6601 0.0839 1 -0.6466 -0.6052 0.0784 0.0450

TB7_LIB-0.0235 -0.0385 -0.0329 -0.0329 -0.0316 -0.0092 -0.1148 0.8425 -0.2047 -0.6466 1 0.9556 -0.0464 -0.0348

TB10_LIB-0.0178 -0.0323 -0.0261 -0.0273 -0.0217 -0.0042 -0.1178 0.7801 -0.2096 -0.6052 0.9556 1 -0.0393 -0.0346

DEF 0.4583 0.4548 0.3428 0.1619 0.2090 0.3578 0.5456 -0.0167 0.0024 0.0784 -0.0464 -0.0393 1 0.6365

LIQ 0.7727 0.6403 0.5825 0.4051 0.3267 0.4307 0.5804 -0.0110 0.0066 0.0450 -0.0348 -0.0346 0.6365 1

22

Full sample result

2-year 3-year 5-year 7-year

Pred sign

MI MII MI MII MI MII MI MII

BCYC+ +ve and

signific+ve and signific

+ve and signific

+ve and signific

+ve and signific

+ve and signific

+ve and signific

+ve and significt

SKEW+ -ve but

insignific+ve but

insignific-ve and signific

-ve and signific

-ve but insignific

-ve but insignific

-ve and signific

-ve but insignific

CORR-/+ +ve but

insignific-ve but

insignific-ve but

insignific+ve but

insignific+ve but

insignific-ve and signific

-ve and signific

DEF+ - +ve and

signific+ve but

insignific - +ve and signific - -ve but

insignific

LIQ+ - +ve and

signific+ve but

insignific - +ve but insignific - +ve but

insignific

J-stat(p-val)

14.8758(0.1883)

13.2772(0.7174)

14.3504(0.4239)

10.9909(0.8100)

15.3044(0.3577)

12.0353(0.4428)

28.1242(0.1367)

23

Robustness: Sub-samples results

2-year 5-year

Pred sign 1 2 3 1 2 3

BCYC+ +ve and

signific+ve and signific

-ve and signific

+ve and signific

+ve but insignific

-ve and signific

SKEW+ +ve but

insignific+ve but

insignific+ve and signific

+ve and signific

+ve but insignific

-ve but insignific

CORR-/+ +ve and

signific+ve but

insignific+ve and signific

-ve and signific

+ve and signific

-ve and signific

DEF+ +ve but

insignific-ve but

insignific+ve and signific

+ve and signific

+ve and signific

-ve but insignific

LIQ+ +ve and

signific+ve and signific

+ve and signific

+ve and signific

+ve and signific

+ve and signific

J-stat(p-val)

9.7563(0.4621)

4.3302(0.8884)

14.0614(0.6627)

3.2751(0.9742)

11.3932(0.4109)

5.8961(0.8802)

24

Conclusion

• Swap spread contains risk premia from business cycle risk, market skewness risk and correlation risk

• In terms of the magnitude, shorter maturity swap is more sensitive to the correlation risk than the longer maturity swap, however, in terms of the statistical and economic significance, longer maturity swap is more sensitive to the correlation changes

• The inclusion of frequently used risk factors like default risk and liquidity risk does not erode the significance of the above risk factors

• Results are robust across the sub-samples

25

2-year TB and 6-M LIBOR

26

3-year TB and 6-M LIBOR

27

5-year TB and 6-M LIBOR

28

7-year TB and 6-M LIBOR

29

Descriptive stats

Swap Spread

BCYC SKEWCorrelation Risks

DEF LIQ2-year 3-year 5-year 7-year 10-year TB2_LIB TB3_LIB TB5_LIB TB7_LIB TB10_LIB

Mean 0.4442

0.5198 0.5375 0.5693 0.5768 0.1629 0.1628 0.1798 0.1737 0.1589 0.1514 0.1432 0.9643 0.6023

Max 1.5700

1.5225 1.2400 1.2700 1.3650 0.2289 1.4079 0.3866 0.4090 0.7217 0.3716 0.3690 3.5000 4.6800

Min 0.1050

0.1375 0.1000 -0.0325 0.0775 0.1002 0.0649 -0.2251 -0.2157 -0.2550 -0.0604 -0.0868 0.5000 -0.0400

Std. Dev 0.2149

0.2167 0.2300 0.2389 0.2388 0.0393 0.0921 0.0161 0.0216 0.0999 0.0109 0.0106 0.4147 0.5231

Skewness

0.9690

0.6307 0.4214 0.2482 0.6569 -0.1007 4.3436 -4.1294 -0.7339 0.3741 -1.0233 -1.6695 3.2156 2.7060

Kurtosis 4.3760

3.4191 2.1065 2.2676 3.0142 1.7432 37.183

4 108.9439 34.2647 4.2295 82.2886 106.4000 16.5362 15.0504

J-B* 1404 439 374 195 429 403 309178 2783555 241480 511 1550699 2638219 5582 43371

N 5965 5965 5965 5965 5965 5965 5965 5916 5916 5916 5916 5916 5965 5965

30

Full sample results

2-year 3-year 5-year 7-year Predicted

signMI MII MI MII MI MII MI MII

Intercept(t-stat)

-0.0011(-0.1048)

-0.0410**(-2.4080) -0.0027

(-1.2705)0.0025

(0.5821)-0.0007

(-1.0319)-0.0410***(-3.6863)

0.0113**(2.5159)

0.0180**(2.0801)

SS(-1)(t-stat)

0.9911***(503.6692)

0.9159***(92.1187) 0.9923***

(534.2113)0.9913***(523.5697)

0.9951***(845.7269)

0.9503***(109.9740)

0.9967***(1023.748)

0.9958***(1021.559)

BCYC(t-stat) + 0.0322***

(4.9639)0.1178***(2.5829) 0.0377***

(4.4667)0.0509***(5.3065)

0.0185***(2.7012)

0.2451***(3.1698)

0.0236***(3.8556)

0.0166**(2.5386)

SKEW(t-stat) + -0.0047

(-1.5371)0.0123

(0.7852) -0.0134***(-4.4546)

-0.0209***(-2.8865)

-0.0009(-0.2641)

-0.0056(-0.5903)

-0.0092***(-4.1647)

-0.0020(-0.7323)

CORR(t-stat) /+ 0.0030

(0.0539)-0.0094

(-0.1180) 0.0145(1.2942)

-0.0216(-0.8934)

0.0026(1.3208)

0.0120(1.3629)

-0.0780***(-2.6098)

-0.1148**(-2.0198)

DEF(t-stat) + - 0.0590***

(6.6657) - 0.0006(0.5586) - 0.0301***

(4.5920) - -0.0011(-1.5398)

LIQ(t-stat) + - 0.0196***

(4.1078) - 0.0003(0.4348) - 0.0026

(0.9708) - 0.0007(1.4201)

J-statistics(p-value)

14.8758(0.1883) 13.2772

(0.7174)5.0447

(0.8304) 14.3504(0.4239)

10.9909(0.8100)

15.3044(0.3577)

12.0353(0.4428)

28.1242(0.1367)

31

Sub-sample results

2-year 5-yearSub-sample 1 2 3 1 2 3

Intercept(t-stat) -0.1342***

(-4.3149)-0.0214

(-0.7489)-0.0128

(-0.6961)-0.1669***(-8.8548)

-0.0340***(-1.7986)

0.3690**(2.0616)

SS(-1)(t-stat) 0.8659***

(25.2170)0.9788***(172.4797)

0.9707***(112.8295)

0.8824***(76.6226)

0.9938***(109.9046)

0.9324***(38.7219)

BCYC(t-stat) 0.4648***

(4.0384)0.0258**(2.0482)

-0.3296***(-4.0955)

0.6666***(8.4734)

0.0416(1.2696)

-1.6492*(-1.8405)

SKEW(t-stat) 0.0117

(0.8925)0.0069

(0.8117)0.0414***(6.0017)

0.0603***(5.7945)

0.0033(0.1946)

-0.0364(-0.6080)

CORR(t-stat) 0.3082***

(4.2312)0.1532

(1.1200)0.2948***(8.1038)

-0.0489***(-7.5902)

0.0110*(1.7988)

-0.1060**(-2.4180)

DEF(t-stat) 0.0291

(1.1468)-0.0044

(-1.5166)0.0140***(4.3742)

0.0985***(5.5803)

0.0261*(1.8815)

-0.0071(-1.0546)

LIQ(t-stat) 0.0370***

(3.5840)0.0054***(2.8871)

0.0151***(3.4675)

0.0493***(3.4609)

0.0122**(2.1013)

0.0288**(2.0599)

J-statistics(p-value)

9.7563(0.4621) 4.3302

(0.8884)

14.0614(0.6627) 3.2751

(0.9742)11.3932(0.4109)

5.8961(0.8802)