1. Are the Business Cycle Risk, Market Skewness Risk and Correlation Risk Priced in Swap Markets? The US Evidence Sohel Azad, Deakin University Jonathan Batten, HKUST Victor Fang, Deakin University 1

2. Objective To examine whether Business Cycle Risk, Market Skewness Risk and Correlation Risk are priced in US swap spreads Paper in early draft 2

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 3

4. Motivation Empirical studies in determinants of swap spreads:  Level  Slope  Curvature/volatility  Default risk  Liquidity risk 4

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. 5

6. Other risk factors Business cycle risk Market skewness risk Correlation risk 6

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. 7

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. 8

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. 9

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 10

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. 11

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 12

13. 3 Hypotheses Business cycle risk: H1: Swap spread is positively associated with the business cycle risk Market skewness risk H2: 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 13

14. Spreads vs BCYC&SKEW 14

15. Spread vs Correlation risk 7-year spread Corr_7yrTB&6mLib 15

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. 16

17. Methodology 17 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. 18

19. Methodology_cont. 19 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. 20

21. Correlation between Swap Spread and its Risk Determinants IRS2IRS3IRS5IRS7IRS10BCYCSKEWTB2_LIBTB3_LIBTB5_LIBTB7_LIBTB10_LIBDEFLIQ IRS2 10.94050.90390.80210.64700.61720.5753-0.0349-0.00090.0574-0.0235-0.01780.45830.7727 IRS3 0.940510.94330.87360.72920.67470.5775-0.04680.00260.0775-0.0385-0.03230.45480.6403 IRS5 0.90390.943310.95060.82830.70800.5256-0.05780.00290.0810-0.0329-0.02610.34280.5825 IRS7 0.80210.87360.950610.84400.62280.4211-0.05430.00340.0892-0.0329-0.02730.16190.4051 IRS10 0.64700.72920.82830.844010.67820.3792-0.05660.00600.0941-0.0316-0.02170.20900.3267 BCYC 0.61720.67470.70800.62280.678210.5445-0.02870.00250.0406-0.0092-0.00420.35780.4307 SKEW 0.57530.57750.52560.42110.37920.54451-0.08090.00680.1346-0.1148-0.11780.54560.5804 TB2_LIB -0.0349-0.0468-0.0578-0.0543-0.0566-0.0287-0.08091-0.1472-0.66010.84250.7801-0.0167-0.0110 TB3_LIB -0.00090.00260.00290.00340.00600.00250.0068-0.147210.0839-0.2047-0.20960.00240.0066 TB5_LIB 0.05740.07750.08100.08920.09410.04060.1346-0.66010.08391-0.6466-0.60520.07840.0450 TB7_LIB -0.0235-0.0385-0.0329 -0.0316-0.0092-0.11480.8425-0.2047-0.646610.9556-0.0464-0.0348 TB10_LIB -0.0178-0.0323-0.0261-0.0273-0.0217-0.0042-0.11780.7801-0.2096-0.60520.95561-0.0393-0.0346 DEF 0.45830.45480.34280.16190.20900.35780.5456-0.01670.00240.0784-0.0464-0.039310.6365 LIQ 0.77270.64030.58250.40510.32670.43070.5804-0.01100.00660.0450-0.0348-0.03460.63651 21

22. Full sample result 2-year3-year5-year7-year Pred sign MIMIIMIMIIMIMIIMIMII BCYC + +ve and signific +ve and significt SKEW + -ve but insignific +ve but insignific -ve and signific -ve but insignific -ve and signific -ve but insignific CORR -/+ +ve but insignific -ve but insignific +ve but insignific -ve and signific DEF +- +ve and signific +ve but insignific - +ve and signific - -ve but insignific LIQ +- +ve and signific +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) 22

23. Robustness: Sub-samples results 2-year5-year Pred sign12 3 12 3 BCYC + +ve and signific -ve and signific +ve and signific +ve but insignific -ve and signific SKEW + +ve but insignific +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 but insignific LIQ + +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) 23

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 24

25. 2-year TB and 6-M LIBOR 25

26. 3-year TB and 6-M LIBOR 26

27. 5-year TB and 6-M LIBOR 27

28. 7-year TB and 6-M LIBOR 28

29. Descriptive stats Swap Spread BCYCSKEW Correlation Risks DEFLIQ 2-year3-year5-year7-year10-yearTB2_LIBTB3_LIBTB5_LIBTB7_LIBTB10_LIB Mean 0.444 2 0.519 8 0.53750.56930.57680.16290.16280.17980.17370.15890.15140.14320.96430.6023 Max 1.570 0 1.522 5 1.24001.27001.36500.22891.40790.38660.40900.72170.37160.36903.50004.6800 Min 0.105 0 0.137 5 0.1000 - 0.0325 0.07750.10020.0649-0.2251-0.2157-0.2550-0.0604-0.08680.5000-0.0400 Std. Dev 0.214 9 0.216 7 0.23000.23890.23880.03930.09210.01610.02160.09990.01090.01060.41470.5231 Skewnes s 0.969 0 0.630 7 0.42140.24820.6569 - 0.1007 4.3436-4.1294-0.73390.3741-1.0233-1.66953.21562.7060 Kurtosis 4.376 0 3.419 1 2.10652.26763.01421.7432 37.183 4 108.943934.26474.229582.2886106.400016.536215.0504 J-B*1404439374195429403309178278355524148051115506992638219558243371 N5965 5916 5965 29

30. Full sample results 2-year3-year5-year7-year Predicted sign MIMIIMIMIIMIMIIMIMII 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) 30

31. Sub-sample results 2-year5-year Sub-sample123123 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) 31