南華大學數位論文

Transcription

1 A THESIS FOR THE DEGREE OF MASTER OF BUSINESS ADMINISTRATION INSTITUTE OF FINANCIAL MANAGEMENT NAN HUA UNIVERSITY A STUDY OF THE RELATIONSHIPS BETWEEN SHORT INTEREST FUTURES AND SPOTS OF THE THREE-MONTH U.S. TREASURY BILLS AND EURODOLLARS ADVISOR PH.D.CHING-JUN HSU GRADUATE STUDENT YI-CHAIN TSAI

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3 ADF PP Johansen ECM Granger Granger (ECM) i

4 Tile of Thesis A STUDY OF THE RELATIONSHIPS BETWEEN SHORT INTEREST FUTURES AND SPOTS OF THE THREE-MONTH U.S. TREASURY BILLS AND EURODOLLARS Name of Insiue Insiue of Financial Managemen, Nan Hua Universiy Graduae dae June 003 Name of suden Yi-Chain Tsai Degree Conferred M.B.A. Advisor Ph.D. Ching-Jun Hsu Absrac From he financial heories and previous empirical sudies, mos of he people will foresee ha he fuures marke is more sensiive han he spo marke, and he fuures marke may promoe he spo marke as well. In oher words, i implies a significan lead-lag relaionship. The purpose of his sudy is o discuss he relaionships beween he U.S. shor ineres fuures marke and he spo marke based on he closing price from 994 o 00 of he hree-monh Treasury bills and Eurodollars. On he relaionship beween prices of fuures and spo, his research will apply Johansen co-inegraion mehod o evaluae he long-run equilibrium relaionship. Our resuls indicae ha boh he fuures and spo of hree-monh Treasury bills and hree-monh Eurodollars exis he long-run equilibrium relaionship. Moreover, we employ he ECM o confirm ha here is a shor-erm imbalance on he marke, and he hree-monh Treasury bills and hree-monh Eurodollars will exercise fuures o do he adjusmen, bu he Treasury bills fuures and Eurodollars fuures will reach he equilibrium simulaneously. By Granger causaliy model, we disinguish ha here exiss a unidirecional relaionship on reasury bills and Eurodollars and he spo akes he lead. However, here exiss a feedback relaionship beween Treasury bills fuures and Eurodollars fuures. Keywords Shor Ineres Fuures, Granger causaliy, Error correcion model(ecm). ii

5 i ii iii iv v vi vii viii ix x Granger 3 38 ARCH GARCH iii

6 ECM AIC 55 ECM AIC 56 ECM AIC GARCH(,) 68 - GARCH(,) 69 - GARCH(,) 69 iv

7 v

8 ( ) ( ) 5.98 ( - ) ( ) 3.0% 9.88% ( - )

9 - ( ) % % % % % % % IOMA daa 00 - Conrac Exchange Y.T.D. 00 Y.T.D. 000 Change (%) U.S. T-Bonds CBOT 4,84,93 38,34,67 9.8% 3-Monh Eurodollar CME 35,600,663 3,83, % BUND EUREX 6,03,307 4,755,33 5.3% Euro-BUND EUREX 4,35,463,004,34 0.4% KOSPI00 Opions KSE 4,046,684 7,668, % CAC 40 Index Opions MONEP,409,947 8,567,94 5.3% U.S.T-Bond Opions CBOT 5,593,573 6,40,03 (5.3%) Crude Oil NYMEX 5,037,488,73,843 8.% Ten Year T-Noes CBOT,487,04,053,79 (4.7%) 3-Monh Serling LIFFE,38,74 0,837,95 3.7% Fuures Indusry June/July 00

10 : (Ineres Rae Forward Conrac) (Ineres Rae Swap) Caps Floors 3

11 (CP) ( -) 4

12 (move ogeher) (coinegraion) (Error Correcion Model ECM) Granger GARCH

13 Granger GARCH - 6

14 Granger GARCH 7

15

16 975 9 (GNMA) 80 (LIFFE) (SIMEX) (TIFFE) (SFE) (TFE) (COMEX) 4 Fuures Indusry 00 (CBOT) ( (CME) 3 (T-Bills) (Eurodollar CD) 5 9

17 () () (3) (4) (5) 976 / 98 / CME/IMM 90 (3 ) / 0

18 (IMM index) 00% I ( ) Kuprianov(986) (LIBOR) % $,000, =$985,500 { ( )}

19 / ( ) ( ) ( ) ( )

20 (The Normal Backwardaion Theory) Keynes(964).. 3. (The Theory of he Price of Sorage) 3

21 Working(949) Brennan(958) Working ( X ) F S = f (-) T F S X Brennan m(x ) o(x ) r(x ) c(x ) m ( X ) o( X ) + r( X ) c( X ) = (-) (Cos of Carry Theory) Brenner and Menachem(989) (Basis) (carry reurn) (convenience reurn) 4

22 F, T S + CC, T CR, T CY, T = (-3) CC,T T CR,T T CY,T T (long arbirage) (shor arbirage). ( ) 5

23 . (daiy selemen) (iming opion) 6

24 Hendersho(967), Kwack(97), Argy and Hodiera(973) Levin(974) Hendersho(967), Kwack(97), Argy and Hodiera(973) (T-Bill Rae) (Eurodollar-rae Fuures Conrac) 973 (Feedback Effec) Giddy, Dufey and Min(979)

25 Marikainen(995) Granger causaliy Swanson(987) Granger Causaliy (Lead-Lag) () () (3) Kean and Hachey(983) Granger Causaliy Edgar and Swanson(984) Granger Causaliy

26 Swanson(988a) (Lead-Lag) Granger Causaliy (l) (Feedback effec) () ( ) ( ) Swanson(988b) Granger Causaliy Swanson(988a) (99) Li(99) (ARIMA) (Transfer Funcion) Fung and Leung(993) () () (3) 9

27 Fung and Lo(993) Tradiional and Modified rescaled range mehods (Long-erm Relaion) (Incremen of ineres rae) Krehbiel and Adkins(994) Fama and French (987) Johansen(988) (000) (00) ( ) ( Engle and Granger(987) (coinegraion) 0

28 Granger(988) (ECM) Nelson(99) EGARCH Engle and Granger EGARCH (ECM) 987 (Feedback) Granger -3

29 -3 Kean and Hachey (983) 974~98 Granger Causaliy.. Edgar and Swanson (984) 973/07/0 ~983//30 Granger Causaliy Swanson (987) 973/0/0 ~983//3 Granger Causaliy.. : 3. Swanson (988a) 973/07/0 ~984/04/30 Granger Causaliy.. (99) 98~ 99 (ECM) Li (99) 983 ~ 989 ARIMA Li (994) 983 ~989 (000) 98~998 EGARCH.. (00) 985~99 EGARCH

30 ( -) Granger GARCH Granger GARCH Granger GARCH 3

31 (ECM) AR() ( ) ( ) ( ) ( ) 4

32 (OLS) (GLS) Granger and Newbold(974) Mone Carlo F (spurious regression) R D.W. (cu-off) Granger and Newbold(974) (Difference) Engle and Granger(987) X d ARMA d (inegraed of order d) X ~ I d I() I(0) ( ) 5

33 Dickey-Fuller (DF ) Augmened Dickey-Fuller (ADF ) Phillips and Perron (PP ) Augmened Dickey-Fuller(ADF) Dickey-Fuller (ime-dependen heeroskedasiciy) ADF(AugmenedDickey-Fuller) PP(Phillips Perron) Pagan & Wickens(989) ADF DF ADF (Serial correlaion) Schwar(987) Mone Carlo ADF PP ADF PP Augmened Dickey-Fuller Υ Υ Υ p = β Υ + ρ Υ + ε (3-) = = α + βυ + ρ Υ + ε p (3-) = p + ρ Υ + ε = = α + γτ+ βυ (3-3) p Y (deerminisic rend) 6

34 (whie noise) e ~N(0,s ) Y ß=0 Y ß?0 H 0 ß = 0 ( ) H ß? 0 ( ) a 0 H 0 ß=0 H 0 ADF AIC Engle and Yoo AIC(Akaike Informaion Crieria) SBC SC(Schwarz Crieria) d Dickey-Fuller ADF Phillips and Perron(PP) Phillips and Perron(988) ADF ( α 0) 7

35 ) S ) ) ) ( ) = ( ) ( ) N Z τ µ ) τ µ SNm S N S Nm Y Y S (3-4) n= Nm N ) N Y = ( N ) = Yn s ) s Nm n (a =0) = ~ Nm Nm xx Nm s ( ) ( ~ ~ 3 ) s s ) N ( 4s ( 3D ) ) Z τ τ ~ τ τ s (3-5) s~ Nm ) Nm ) s~ s s of he regressor cross-produc marix) D xx (deerminan (coinegraion) (long-run equilibrium) (common facor) (co-movemen) X =ßX X X (saionary process) f(x,x )=0 e =f(x,x ) e X X (error) X X 8

36 Johansen 988 Engle & Granger (maximum likelihood raio es) n (vecor auoregressive model) X = A X + Κ + AK X k + µ + ΨD + ε, =,,T (3-6) X n X -k+,,x 0 e,,e niid(0,s) (Gaussian errors) µ D (seasonal dummies) (3-6) X = Γ X + Κ + Γk X k+ + ΠX k + µ + ΨD + ε, =,,T (3-7) X k = Γ X i + ΠX µ + Ψ k + D + ε, =,,T (3-8) = = L L (lag operaor) Γ = ( I A Λ ) i A i Π =, i=,,k- ( I A Λ ) A k (3-8) (error-correcion model)? X -k (error correcion erm)? n n (long run impac marix)?x -k VAR Γ k = X 9

37 ?? ()rank(?)=n ()rank(?)=0 (3)0<rank(? )<n () X I(0) ()? I(0) (3-8) VAR (3) n r a ß?=aß a (adjusmen vecor) ß n r Johansen(988) (likelihood raio saisic) H rank(?)=r (r<n) (race saisic) (maximum eigenvalue saisic). (race es) H 0 rank(?) r H rank(?)> r λ race n ) n ) = ln Tλ ( Q) = T ln ( λ ) = r+ = r+, r=0,,n- (3-9). (maximal eigenvalue es): H 0 rank(?)= r H rank(?)= r+ 30

38 ( Q) = ln ( Q: r ) λ max = ln r + (3-0) (Brownian Moion) EViews Oserwald-Lenum(99) Cas Johansen and Nielson(993) Johansen Coinegraion Tes Likelihood Raio 5% criical value min(aic) min(schwarz crierion) (Error-correcion model ECM) Granger Granger 60 Sargan Hendry(964) Engle and Granger(987) 3

39 Granger(980) Engle and Granger(987) ( ) X = x x,, x X CI( d, b) ~, Κ n. X d ( ). β = β, β, Κ, β n β X = βx + β x + Κ + βnxn (d-b) b>0 ß e = βx e (equilibrium error) e. ßx =0 e =ßx e ~N(0,s ) 3

40 ~ I( 0) e x ß ( ) e =ßx. I() ~ I 0 e Engle and Granger(987) I() y z P P + α y α i= i= ( y βz ) + α( i) y i + ( i) z i+ y = α (3-) q q + α z α i= i= ( y βz ) + α( i) y i + ( i) z i+ z = α (3-) α α α y z α α ( i) α ( i) α ( i) α ( i) q y = y y z = z z p p q e ) (-) y z α α 0 a y a z 0 Engle-Granger y + z { } e ) y β z y z = α = α ) P P + α ye + α α i= i= ) ( i) y i + ( i) z i + y q q + α ze + α α i= i= ( i) y i + ( i) z i+ z (3-3) (3-4) 33

41 (3-3) (3-4) y y z z ECM y z Granger. H0 α =0? H 0 z y z y. H0 α =0? H 0 y z y z 3. () () y z 4. H0 a y =0? H 0 y 5. H0 a z =0? H 0 z α =0 α =0 F-es ( ) ( ) (residual sum of squares) F F = ( SSEr SSEu )/ m [ N ( m + ) ] SSE u (3-5) SSE r (resriced) SSE u (unresriced) N M H0 F 0 F 34

42 y z (a y a z ) -es a y a z y z y z a y >a z y z X Y X X Y X Y X (Y causes X) Y Y X Y X Y (feedback effec) Granger(969) Granger X Y X X X X Y Y Y Y 35

43 σ () ( x X, Y ) σ ( x X ) σ < (3-6) Y X Y () ( X X, Y ) σ ( x X ) σ < (3-7) Y X Y X (3) σ ( x X, Y ) < σ ( x X ) ( y X, Y ) σ ( y Y ) x σ < (3-8) Y X X Y Y X X Y X Y (4) ( x X, Y ) = σ ( x X, Y ) σ ( x X ) σ ( y X, Y ) σ ( y X, Y ) = σ ( y Y ) σ = x x = (3-9) Y X X Y X Y Granger(969) 36

44 y x = α0 + αy + Λ + αy n + βx + Λ + β = α0 + αx + + αx n + βy + Λ + β x n Λ y (3-0) n Granger x y x y x y (x y) F-saisic Wald saisic join hypohesis β Λ = β = = β = 0 x does no Granger-cause y y does no Granger-cause x Granger causaliy F-saisic p-vaule p-vaule>0.0 x does no Granger-cause y p-vaule<0.0 x Granger-cause y GARCH 37

45 GARCH ARCH (goodness-of-fi es) Kolomogorov-Smirnov D ( ) D=0 D>0 D 5 (skewness) (kurosis) ( ) ( ) r r = = 3 nσ n 3 (3-) 38

46 r r n σ 6 n Z 5% 6 n 6 n 5% ( ) 3 ( ) r r = = 4 nσ n 4 (3-) 3 4 n 3 Z 5% 3 4 n 4 n 5% 39

47 ( ) s ρ s ρ s ( r, r ) cov s = (3-3) σ ( ) s cov r, r s r r s (auocovariance) σ r ρ s 0 /n 0 Z 5% (.96 ) n n 5% ( ) Ljung-Box Q p Q( p) = n s χ n s ( n + ) ρ ~ ( P) s= (3-4) n s P 40

48 Ljung-Box ( ρ, ρ, ρ3, Κ, ρ p ) Q(P) 5% (heeroskedasiciy) (ime-varying) Fama(965) Ljung-Box Q(P) Q(P) ARCH GARCH Engle(98) (ARCH Model) q Bollerslev(986) ARCH (GARCH Model) q p ARMA(p,q) 4

49 ARCH ARCH(q) GARCH(p,q) ARCH ARCH(q) y = x β + ε, =,,T (3-5) Ω ( 0 h ) ε ~ N, (3-6) h ε ( Ω ) = E T + q = 0 α i ε i= α (3-7) x k T ß ε h Ω (3-7) q ( ) = 0 E ε (3-8) σ fori = j E( ε ) iε j = (3-9) 0 oherwise a 0 >0 a i >0 i =,,,q h (weakly 4

50 saionary) Engle(98) ARCH(q) α0 σ = q (3-30) α i= i q α < i= i a 0 >0 (3-7) Engle(98) ARCH (parsimonious parameerizaion) Bollerslev(986,988) (3-7) GARCH GARCH(p,q) y = x β + ε =,, T Ω ( 0 h ) ε ~ N, (3-3) h ε ( Ω ) = E T = α + + q p 0 α iε i γ jh j i= j= ARCH(q) α 0 > 0α i 0, i =,,..., q γ j 0, j =,,..., p ARCH GARCH (3-3) 43

51 o ( L) ε β ( L) h h = α + α + (3-3) ( ) ( ) p q α L = αl + α L α ql ; γ L = γ L + γ L γ pl L -ß(L) (3-3) h α0 = α α = = α * 0 ( ) 0 p i= + γ i= α + α + δ i ε i ( L) ε γ ( L) ( L) γ ( L) ε (3-33) α L γ L d ( ) ( ) GARCH ARCH GARCH(p,q) q Bollerslev(986) α γ < i= i p + j= j ARCH GARCH ( ) ARCH Engle(98) LM ARCH ) ). ε = Y β X. ε ) ε ) 44

52 ) ε ) q = α 0 + αiε i i= + v (3-34) 3. T- q R T T- q R ~? (q) LM H α α =... = α 0 0 : = q = ARCH ( )GARCH ARCH GARCH Bollerslev LM GARCH. GARCH(p,q) q p 0 + αiε i + γ j i= j= h = α h (3-35) j. R R (T-p) LM 3.LM GARCH EViews 45

53 - (CME) AREMOS (nearby conrac) (rollover) 46

54 4- Jarque-Bera 4- Jarque-Bera Jarque-Bera ( ) ( ) ( ) ( ) p 47

55

56

57 ADF PP AIC 4- ADF PP % ADF PP 50

58 4- ADF PP *** *** *** *** *** *** *** ***. *** %.ADF PP % ADF PP % I() 4-3 ADF PP

59 I() Engle and Granger(987) Johansen and Juselius(990) Johansen Johansen Johansen r=0 r=k k Johansen and Juselius(990) 4-4 % 0 5

60 4-4 Trace?-max 5% % r= E r r= E r % Trace?-max 5% % r= r r= r % 0 53

61 4-6 Trace?-max 5% % r= r r= r Granger and Engle(987) Engle and Granger(987) Granger Represenaion Theorem (Error Correcion Model ECM) 54

62 Granger VAR ECM Granger(988) VAR VAR AIC AIC 4-7 ECM AIC ECM AIC ECM AIC ECM AIC ECM AIC ECM AIC 4-7 ECM AIC * AIC * (AIC ) 55

63 4-8 ECM AIC * 6 AIC * (AIC ) 4-9 ECM AIC * AIC * (AIC ) ( ) ( ) S = a + bz n m + ci S + d j F + e (4-) i= j= (4-) Z - b b ( ) d 56

64 % ( ) % % ( ) % 57

65 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** Z(-) *** *** Consan *** % % ( ) % % 58

66 ( ) % 59

67 *** *** *** *** *** *** *** *** *** *** *** Z(-) *** Consan *** % % ( ) % % 60

68 ( ) % *** *** *** *** *** Z(-) *** *** C *** % Granger ECM Granger 6

69 Wald saisic F-Saisic Granger(969) X Y X Y X Y p-value( ) 0.0 p-value(0.706) F-es p-value TBF does no Granger Cause TBS.744 *** TBS does no Granger Cause TBF *** % 4-4 p-value( ) 0.0 6

70 p-value(0.043) F-es p-value EDF does no Granger Cause EDS 9.89 *** EDS does no Granger Cause EDF *** % 4-5 p-value( ) 0.0 p-value( )

71 4-5 F-es p-value TBFdoes no Granger Cause EDF *** EDF does no Granger Cause TBF *** *** % GARCH ( )GARCH GARCH GARCH GARCH Bollerslev(99) GARCH(,) GARCH(,) GARCH(,) Y = b0 + b X + ε ~ N ( 0, h ) ε (4-) h ε (4-3) = + + a0 ah a (4-) (4-) Y h Y ( ) 64

72 . ARCH 4-6 Jarque-Bera 4-6 Jarque-Bera Bollerslev(987) GARCH Jarque-Bera *** *** *** *** *** %.Ljung-Box 65

73 ρk Ljung-Box(976) Q n H 0 = 0 k=,,,n( ) H ρ 0( ) Q(k)> χ ( k) k 4-7 % % 4-7 Ljung-Box Q(6) Ljung-Box Q() Ljung-Box Q(4) (0.08) (0.04) (0.03). p (0.05) (0.06) (0.09). Ljung-Box Q Q( K ) = n( n + ) γ ~ χ ( k ) n = n + i k (0.03) (0.063) (0.070) 4.4 (0.08).895 (0.0) (0.085) 3. Q 3. Ljung-Box Q

74 Ljung-Box Q % Engle(98) LM ARCH ARCH LM ARCH ARCH GARCH 4-8 Ljung-Box Q (6) 93.9 (0.000) (0.000) (0.000) (0.000) Ljung-Box Q () 4.0 (0.000) 5.5 (0.000) (0.000) (0.000) Ljung-Box Q (4) 9.6 (0.000) 0.70 (0.000) 6.0 (0.000) 8.97 (0.000) ARCH LM (0.000) (0.000) (0.000) (0.000). p. Q ARCH ( )GARCH(,) GARCH(,) GARCH(.) GARCH(,) 4- - GARCH(,) 67

75 4-9 b a a a +a < GARCH GARCH(,) b *** *** b *** *** a *** *** a *** *** a *** ***.*** %.GARCH(,) Y = b 0 + b X + ε ε ~ N ( 0, h ) + h a a h a ε = b a a % a a a a 68

76 4-0 - GARCH(,) b *** b *** *** a *** *** a 0.45 *** *** a *** ***.*** %.GARCH(,) Y = b 0 + b X + ε ε ~ N ( 0, h ) + h a a h a ε = b a a a +a < GARCH 4- - GARCH(,) b *** b *** *** a *** *** a *** *** a *** ***.*** %.GARCH(,) Y = b 0 + b X + ε ε ~ N ( 0, h ) + h a a h a ε = + 0 Granger 69

77 (feedback) 70

78 ADF PP I() Johansen ECM 7

79 Granger Granger 7

80 GARCH Granger ECM GARCH a a % 50 73

81 ( ).. GARCH 74

82 GARCH 3. 75

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85 Phillips,P., and Perron,P.(988), Tesing for uni roo in ime series regression, Biomerika, Vol.75, Sargan, J. D.(964), Wages and Prices in he Unied Kingdom: A Sudy in Economeric Mehodology, in P. E. Har, G. Mills and J. K. Whiaker (eds.), Economeric Analysis for Naional Economic Planning, Buerworh, London; reprined in D.F. Hendry and K. F. Wallis (eds.), Economerics and Quaniaive Economics, Basil Blackwell, Oxford, 984. Schwar, G. W. (987), Effecs of Model Specificaion on Tess for Uni Roos in Macroeconomic Daa, Journal of Moneary Economics, Vol.0, pp Swanson, P. E. (987), Capial Marke Inegraion over he Pas Decade:The Case of he U.S.Dollar, Journal of Inernaional Money and Finance, Vol.6, pp.5-5. Swanson, P. E. (988a), The Inernaional Transmission of Ineres Raes:A Noe On Causal Relaioship Beween Shor-erm Exernal and Domesic U.S. Dollar Reurns, Journal of Banking and Finance, Vol., pp Swanson, P. E. (988b), Inerrelaionship Among Domesic and Eurocurrency Depois Yield: A Focus On The U.S. Dollar, The Financial Review,Vol.3, February, pp Schwar, W.(990), Sock marke volailiy, Finanacial Analys Journal, Vol.46, pp Working, H.(949), The Theory of he Price of Sorage, American Economic Review, Vol.39, pp

86 CME $,000, = 00- IMM =0.0% $5/ (0.000*000000*90/360) :0am - :00pm 9-day T-Bill ( ) 79

87 CME $,000,000 = 00- IMM =0.0% $5/ (0.000*000000*90/360) :0am - :00pm 80