Cody PhD Conference 2012

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Cody PhD Conference 2012

  1. 1. A New Test of Financial Contagion with Application to the US Banking Sector Cody Yu-Ling Hsiao Centre For Applied Macroeconomic Analysis Australian National University November 2012 Cody Hsiao () Contagion Tests 11/27 1 / 18
  2. 2. Outline Motivations Research questions Contribution Statistics of co-kurtosis and co-volatility Contagion tests (testing for smile e¤ect) Application to the US banking sectors
  3. 3. MotivationsSmile e¤ect through co-kurtosis channel Smile e¤ect is represented as the co-movements between return and return skewness (E (ri1 , rj3 ) and E (ri3 , rj1 )) turning from a negative relation to a positive relation in the crisis period Theoretically speculators invest in securities with a positive asset return and negative skewness in normal periods (Brunnermeier and Pedersen, 2008) Funding constraints lead to higher kurtosis and co-kurtosis risk
  4. 4. MotivationsSmile e¤ect through co-volatility channel Smile e¤ect is represented as the co-movements between return volatility and return volatility turning from a negative relation to a positive relation in the crisis period Co-volatility (E (ri2 , rj2 )) is described as the relationship between return volatility and return volatility
  5. 5. Research questions How to test for …nancial contagion (smile e¤ect) through co-kurtosis or co-volatility channels? Does …nancial contagion (smile e¤ect) through co-kurtosis or co-volatility channels really exist in the …nancial markets during the global …nancial crisis of 2008-2009?
  6. 6. Contributions A new class of tests of …nancial contagion based on increases in co-kurtosis or co-volatility is proposedDe…nition Contagion is de…ned as a signi…cant increase in the fourth order co-moments of two markets between a non-crisis and a crisis period This new approach is applied to test for …nancial contagion (smile e¤ect) in equity markets and banking sectors following the global …nancial crisis of 2008-2009
  7. 7. Statistics of co-kurtosis A non-normal multivariate returns distribution is speci…ed The bivariate generalized exponential family of the distribution with the …rst form of co-kurtosis (Cokurtosis13 ), that is " 1 1 r1,t µ1 2 r2,t µ2 2 f (r1,t , r2,t ) = exp 2 + 2 1 ρ σ1 σ2 r1,t µ1 r2,t µ2 2ρ , σ1 σ2 # 1 3 r1,t µ1 r2,t µ2 +θ 7 η σ1 σ2 The Lagrangian multiplier statistic for co-kurtosis (LM1 ) is used to test for extremal dependence with restriction of θ 7 = 0 T 1 3 2 1 r1,t µ1b r2,t µ2b LM1 = T (18b2 +6 ) ρ ∑ b σ1 b σ2 T (3b) ρ t =1 Statistics of co-volatility is derived based on the LM test either
  8. 8. Contagion TestsExtremal dependence testsCo-kurtosis and co-volatility are used for measuring extremal dependence The …rst type of statistic CK13 is to detect the shocks emanating from the asset returns of a source market i to the cubed returns of asset in a recipient market j. 0 12 B by (r 1 ,r 3 ) ξ b (r 1 ,r 3 ) C ξx i j CK13 (i ! j; ri1 , rj3 ) = @ s i 2j A 18b v +6 y jx i 18b2 +6 ρ Ty + Txx The second type of statistic CK31 is to measure the shocks transmitting from the cubed returns of asset in a source market i to the returns of asset in a recipient market j 0 12 B by (r 3 ,r 1 ) ξ b (r 3 ,r 1 ) C ξx i j CK31 (i ! j; ri3 , rj1 ) = @ s i 2j A 18b v +6 y jx i 18b2 +6 ρ Ty + Txx
  9. 9. Contagion TestsExtremal dependence tests Ty m n b yi ,t µyi b yj ,t µyj b rm, rn = ξy i j 1 ∑ 3by jxi v Ty b σyi b σyj t =1 Tx m b xj ,t µxj n b rm, rn = 1 b xi ,t µxi ξx i j Tx ∑ b σxi b σxj (3bx ) , ρ t =1and by ρ b vy jx = s 2 2 . i sy ,i sx ,i 1+ 2 (1 b2 ) ρy sx ,i b vy jx represents the adjusted correlation coe¢ cient proposed by Forbes i and Rigobon (2002). They consider that estimation of cross-market correlation coe¢ cients is biased due to heteroscedasticity in market returns.
  10. 10. Contagion TestsExtremal dependence tests The third type of statistic CV22 is to detect the shocks transmitting from the volatility of asset returns in a source market i to the volatility of asset returns in a recipient market j. 0 12 B b ( ξy ri2 ,rj2 ) b r 2 ,r 2 ( ξx i j ) C CV22 (i ! j; ri2 , rj2 ) = @ s A 4b4 +16b2 +4 v v y jx i y jx i 4b4 +16b2 +4 ρ ρ Ty + x Tx xwhere Ty 2 2 b yi ,t µyi b yj ,t µyj b (r 2 , r 2 ) = ξy i j 1 ∑ v2 1 + 2by jxi Ty b σyi b σyj t =1 Tx 2 b xj ,t µxj 2 b (r 2 , r 2 ) b xi ,t µxi ξx i j = 1 Tx ∑ b σxi b σxj 1 + 2b2 ρx t =1
  11. 11. Contagion TestsExtremal dependence tests To test that there is a signi…cant change in co-kurtosis or co-volatility between the non-crisis period and the crisis period, the null and alternative hypotheses are Ho : ξ y (rim , rjn ) ξ x (rim , rjn ) H1 : ξ y (rim , rjn ) > ξ x (rim , rjn ) Under the null hypothesis of no contagion, tests of contagion based on changes in co-kurtosis or co-volatility are asymptotically distributed as d CK13 , CK31 , CV22 (i ! j ) ! χ2 . 1
  12. 12. Application to the US banking sector The …nancial crisis of 2008-2009 is escalated into a global phenomenon The tests of contagion are applied to identify transmission channels through changes in extremal dependences during the global …nancial crisis of 2008-2009 Data The daily banking equity indices and equity indices are collected for four regions Asian region (Hong Kong and Korea), European region (France, Germany, the UK), Latin American region (Chile and Mexico), North American region (the US) The non-crisis period is chosen from April 1, 2005 to June 29, 2007 and the crisis period is from March 3, 2008 to August 31, 2009 A Vector Autoregressive (VAR) model is estimated in order to control for market fundamentals and handle the problems of serial correlation
  13. 13. Application to the US banking sectorContagion channel through extremal dependenceTesting for contagion based on changes in extremal dependence during theglobal …nancial crisis of 2008-2009. Source market is the US bankingsector(a) CK 13 : co-kurtosis contagion test with co-kurtosis measured in terms of 1E (r US , r 3 ), (b) CK 31 : co-kurtosis contagion test with co-kurtosis measured in J 3terms of E (r US , r 1 ), (c) CV 22 : co-volatility contagion test with co-volatility J 2measured in terms of E (r US , r 2 ) J
  14. 14. Conclusion A new test of …nancial contagion based on changes in co-kurtosis and co-volatility is proposed This new approach is applied to test for …nancial contagion in equity markets and banking sectors following the global …nancial crisis of 2008-2009 The results of the tests show that signi…cant contagion e¤ects (smile e¤ects) are widespread from the US banking sector to global equity markets and global banking sectors through one of the extremal dependence channels
  15. 15. Any questions?
  16. 16. Further studies A joint test of contagion through the co-skewness channel A joint test of contagion through the co-kurtosis and co-volatility channel Selection of the period of crisis period could a¤ect the results of contagion Sensitivity tests given the di¤erent periods of the crisis period Markov switching model in contagion analysis (the crisis period are endogenously by the MS model)
  17. 17. Finite sample properties Monte Carlo simulations are performed to calculate the critical values due to relative large sample period of the non-crisis period but relative short sample period of the crisis. To generate the asset returns in the simulation, the parameters are chosen for the following non-crisis and crisis variance-covariance matrices of returns in two equity market i and j as 0.557 0.143 29.195 14.350 Vx = , Vy = . 0.143 2.660 14.350 16.430
  18. 18. Finite sample properties The size of non-crisis period is Tx = 585 and the size of crisis period is Ty = 391. α is signi…cant level. Based on 10,000 replications. Test statistics α = 0.025 α = 0.05 α = 0.1 CS 12 5.40 4.02 2.73 CS 21 4.91 3.81 2.70 CK 13 9.33 7.04 4.79 CK 31 9.28 7.00 4.81 CV 22 5.03 3.82 2.73 χ2 1 5.02 3.84 2.71 The statistics for contagion based on co-skewness and co-volatility present a good approximation of the …nite sample distribution The test statistics for contagion based on co-kurtosis tend to be biased The results of contagion tests seem quite robust given relative large sample period of the non-crisis period but relative short sample period of the crisis

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