Testing for tail independence in extreme value models – application on polish stock exchange

! " # $ % & ' ( ) * & " " & * # + , - . & ( % * & * # /,+& #,(!,%,0&! #1223#1455# 65789# !"#$%&# '"()*+,3#-./,%&# 0#123/4#

!"#!$%& '() !*$+ $%,"-"%,"%." $% "/!)"0"

1*+2" 0(,"+# 3 *--+$.*!$(% (% -(+$#4 #!(.5

"/.4*%&"

#

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

#################################################

# TFAB;<<AF3# !C@>F# AB# =C;# &:<=>=K=;# AB# # *=@=><=>G<# @:D# -;?AEF@PCL3# $:>N;F<>=L# AB# (GA:A?L## >:##V@=AI>G;O#

# TC-# <=KD;:=# >:# =C;# &:<=>=K=;# AB# # *=@=><=>G<# @:D# -;?AEF@PCL3# $:>N;F<>=L# AB# (GA:A?L## >:#V@=AI>G;O#

_F@`L:@#"FaP>A=3#bK<=L:@#0@c;I<R@#

57d

IAFR>:E# I>=C# =@>M# D;P;:D;:G;3# <>:G;# @MM# ;<=>?@=AF<# AB# =C;# =@>M# D;P;:D;:G;# GA;BB>G>;:=# @F;# <=FA:EML# ?><M;@D>:E# IC;:# =C;# D@=@# DA;<# :A=# <=;?# BFA?# @# =@>M# D;P;:D;:=#<;==>:EO#

$< !*$+ ,"-"%,"%." .(%."-! #

"C;# ,#*5 72)2&72&82 8+2::*8*2&,# ><# FAKECML# <P;@R>:E# =C;# PFAH@H>M>=L# =C@=# @#F@:DA?# N@F>@HM;# ;QG;;D<# @# G;F=@>:# =CF;<CAMD# E>N;:# =C@=# @:A=C;F# F@:DA?# N@F>@HM;# C@<#@MF;@DL#;QG;;D;D#=C@=#=CF;<CAMDO#"C;#BAMMAI>:E#@PPFA@GC3#*>HKL@#Y5]^4Z#@:D#bA;# Y5]]8Z#@?A:E#A=C;F<3#F;PF;<;:=<#=C;#?A<=#GA??A:#D;B>:>=>A:#AB#=@>M#D;P;:D;:G;O#+;=# Z 3 Y> = #H;#@#F@:DA?#P@>F#I>=C#cA>:=#GK?KM@=>N;#D><=F>HK=>A:#BK:G=>A:#? @:D#?@FE>:@M<# @ ? #@:D#?_%O#"C;#JK@:=>=L# M>? Y 5Y Ze 5Y ZZ 5 B > ?> A = ?= A A . ! ! ! " # # $ % #><#=C;#.))2" ,#*59

72)2&72&82 8+2::*8*2&,# YKPP;F# "-!Z3# PFAN>D;D# =C;# M>?>=# ;Q><=<O# W;# <@L# =C@=# Z

3

Y> = # ><# KPP;F# =@>M# D;P;:D;:=# >B#%_. #4# @:D# KPP;F# =@>M# >:D;P;:D;:=# >B#%_. &4O# *>?>M@FML3#I;#D;B>:;#=C;#MAI;F#=@>MXD;P;:D;:G;#GA;BB>G>;:=#%_CO##

"C;#"-!#G@:#@M<A#H;#D;B>:;D#N>@#=C;#:A=>A:#AB#GAPKM@3#>:=FADKG;D#HL#*RM@F# Y5]2]ZO# # GAPKM@# D ><# @# GK?KM@=>N;# D><=F>HK=>A:# BK:G=>A:# ICA<;# ?@FE>:<# @F;# K:>BAF?ML#D><=F>HK=;D#A:#643#59O#"C;#cA>:=#D><=F>HK=>A:#BK:G=>A:#?#AB#@:L#F@:DA?# P@>F#Y>3=Z# G@:# H;# F;PF;<;:=;D#@<# ?Y@Z$DY?_>Y@Z3?₌Y%ZZ# YF;B;F# =A#bA;# Y5]]8Z# BAF#?AF;#>:BAF?@=>A:#A:#GAPKM@<ZO#"C;#GA;BB>G>;:=#AB#KPP;F#=@>M#D;P;:D;:G;#G@:# H;#IF>==;:#>:#=;F?<#AB#GAPKM@f# A A A D A A E _! ' ! $ ! " ₅ Z 3 Y 1 5 M>? 5 % O# :@MAEAK<ML3#I;#C@N;# A A A D + A C Z 3 Y M>? ' " $ % O# $$< C$1*)$*!" "/!)"0" ,$#!)$C2!$(%# # "C;#GM@<<>G@M#;Q=F;?;#H>N@F>@=;#=C;AFL#><#GA:G;F:;D#I>=C#=C;#M>?>=#H;C@N>AKF# AB#Y Y Z3 Y ZZ Y?@Q 3?@Q Z 3OOO 5 3OOO 5 & * * & * * & & > 0 = > = 0 $ $

$ # @<# &"(O# g;G@K<;# AB# =C;# D;B>:>=>A:3# =C;# ?@FE>:@M<# AB# Y0_&Y>Z30_&Y=ZZ# H;MA:E# =A# =C;# E;:;F@M>a;D# ;Q=F;?;# N@MK;# Y_('Z# D><=F>HK=>A:# B@?>MLO# "C;# E;:;F@M# BAF?# AB# @# E;:;F@M>a;D# ;Q=F;?;# N@MK;# _('# D><=F>HK=>A:# ><# _+3*3)Y Z ;QPY 65 9 5)Z

*

+

)

! ! ' ! $ @ @ !FG # I>=C#

+

,H3# 4 #

*

3#),H#Y!AM;<#1445ZO#"A#<>?PM>BL#=C;#PF;<;:=@=>A:3#!AM;<#Y1445Z#@<<K?;<# I>=CAK=# MA<<# AB# E;:;F@M>=L# =C@=# ?_> -?₌ -?3# IC;F;# ?Y.Z# ><# =C;# K:>=# /F;GC;=# D><=F>HK=>A:O#"C;#BAMMAI>:E#=C;AF;?#YD;#h@@:#@:D#);<:>GR3#5]88Z#GC@F@G=;F>a;<# =C;#M>?>=#cA>:=#D><=F>HK=>A:#AB#Y0_&Y>Z30_&Y=ZZf#

";<=>:E#BAF#"@>M#&:D;P;:D;:G;#>:#(Q=F;?;#'@MK;#0AD;M<i# 57]

&B# BY0_&Y>Z0&@30_&Y=Z0&%Z/_&/ "_"/₍ !Y@3%Z# IC;F;# _# ><# @# :A:X D;E;:;F@=;# D><=F>HK=>A:# BK:G=>A:3# =C;:# !Y ..3Z# =@R;<# =C;# BAF?#

ZZ 3 Y ;QPY Z 3 Y@ % G @ % ! $ ! I>=C# Y 3 Z 1 ?@QY 3Y5 Z Z Y Z 5 4 1 1 1 @ % 7I % @ G $

2

! # @:D#I# ><# @#D><=F>HK=>A:#A:#64359#I>=C#?;@:#

5

1

O# $$$< "#!$0*!$(% (' !4" !,. "C;F;#@F;#=IA#PA<<>H>M>=>;<#=A#K<;#(Q=F;?;#'@MK;#"C;AFL#BAF#=C;#;<=>?@=>A:# AB#=C;#"-!O#"C;#B>F<=#A:;#><#=A#D;N;MAP#;<=>?@=AF<#H@<;D#A:#=C;#@<<K?P=>A:<#AB# =C;#_;:;F@M>a;D#T@F;=A#-><=F>HK=>A:O#"C;F;BAF;3#A:;#@<<K?;<#GA:N;FE;:G;#YAN;F# <A?;# =CF;<CAMDZ# =A# @# H>N@F>@=;# _;:;F@M>a;D# T@F;=A# -><=F>HK=>A:O# "C><# ?AD;M# ><# G@MM;D# T;@R<# AN;F# =CF;<CAMDO# "C;# A=C;F# PA<<>H>M>=L# ><# =A# @<<K?;# =C@=# =C;# @<<K?P=>A:<#AB#=C;#_('#@F;#BKMB>MM;DO#"C><#GA:G;P=>A:#>:#@#B>:@:G>@M#@PPM>G@=>A:# F@F;ML# H;# =C;# G@<;O# gA=C# ?;=CAD<# GA?;# =A# =C;# <@?;# ;<=>?@=>A:# PFAHM;?f# =C;# D;P;:D;:G;# BK:G=>A:# ><# =A# H;# ;<=>?@=;DO# "C;# D>BB;F;:G;# ><# =C;# =F;@=?;:=# AB# =C;# D@=@f#>:#=C;#B>F<=#G@<;3#I;#GCAA<;#=C;#F;@M>a@=>A:<#=C@=#M>;#@HAN;#@#=CF;<CAMD3#>:#=C;# <;GA:D# G@<;# X# HMAGRX?@Q>?@O# /F@C?# 2, #5O# Y1442Z# E>N;# ;<=>?@=AF<# BAF# =C;# "-!# K:D;F# D>BB;F;:=# @<<K?P=>A:<f# K<>:E# @# <P;G>B>G# D><=F>HK=>A:# Y;OEO# =XD><=F>HK=>A:Z3# I>=C>:# @# GM@<<# AB# D><=F>HK=>A:<# Y;OEO# ;MM>P=>G@MML# GA:=AKF;D# D><=F>HK=>A:<Z3# K<>:E## @#<P;G>B>G#GAPKM@#Y;OEO#_K?H;MZ3#I>=C>:#@#GM@<<#AB#GAPKM@;#Y;OEO# FGC>?;D;@:Z#AF# @# :A:P@F@?;=F>G# ;<=>?@=>A:# YI>=CAK=# @:L# P@F@?;=F>G# @<<K?P=>A:ZO# "C;# @K=CAF<# GA?P@F;#=C;#P;FBAF?@:G;#AB#=C;#D>BB;F;:=#;<=>?@=AF<#BAF#D>BB;F;:=#G@<;<f#IC;=C;F# =C;#@<<K?P=>A:#><#=FK;#AF#IFA:E#@:D#IC;=C;F#=C;F;#><#=@>M#D;P;:D;:G;#AF#:A=O#&=# =KF:<#AK=#=C@=#<A?;#AB#=C;#;<=>?@=AF<#P;FBAF?#I;MM#>B#=C;F;#><#=@>M#D;P;:D;:G;#HK=# H@D#>B#=C;F;#><#:A=O#&:#PF@G=>G@M#@PPM>G@=>A:<3#A:;#I>MM#:;N;F# R:AI#IC>GC#GAPKM@# ?AD;M#><#=C;#GAFF;G=#A:;O#"C;#;<=>?@=>A:#G@:#A:ML#H;#K:D;F#?><<P;G>B>G@=>A:O#*A# D>BB>GKM=>;<# >:# <;M;G=>:E# @# GAPKM@# ?AD;M3# HF>:E<# K<# =A# =C;# >?PAF=@:=# ><<K;# AB# =;<=>:E#BAF#=@>M#D;P;:D;:G;O#

$1<#4(D !( !"#! ,"-"%,"%.$"# E * ,$''")"%! *--)(*.4 '() !"#!$%& '() !*$+ $%,"-"%,"%."

#

,:;# AB# =C;# ?A<=# >:=;F;<=>:E# @PPFA@GC# BAF# =;<=>:E# BAF# =@>M# >:D;P;:D;:G;# ><# E>N;:#>:#/@MR#@:D#0>GC;M#Y144^ZO#"C;L#PFAN;#=C;#BAMMAI>:E#=C;AF;?f#

_F@`L:@#"FaP>A=3#bK<=L:@#0@c;I<R@# 5\4 3 4 5 $ # ' # ' 25/2 , 72)2&72&82 ,#*5 &+ */ ,K2"2 , 8 = > 8, = > B j j Z e Y 1 O# #

$<>:E# =C><# =C;AF;?3# /@MR# @:D# 0>GC;M# PFAPA<;# BAKF# D>BB;F;:=# =;<=<# BAF# =@>M# >:D;P;:D;:G;3# IC>GC# G@:# H;# EFAKP;D# >:=A# 1# D>BB;F;:=# GM@<<;<f# @# %;L?@::X T;@F<A:# =;<=# Y%TZ# @:D# =CF;;# EAAD:;<<# AB# B>=# =;<=<f# /><C;FU<#

6

3# VAM?AEAFANX *?>F:AN# @:D

7

1O# &:# =C;# M@==;F# GM@<<3# =C;# VA?AMEAFANX*?>F:ANX=;<=# YV*Z# =KF:<# AK=#=A#H;#=C;#H;<=#>:#=C;#<>?KM@=>A:#<=KDL#HL#/@MR#@:D#0>GC;M#Y144^ZO#"C;F;BAF;3# >:#=C;#BAMMAI>:E3#A:ML#%T#@:D#V*#=;<=<#@F;#D;<GF>H;DO

%=>F:GH -=:97@G 8=78

<<K?;# I;# C@N;# @# F@:DA?# <@?PM;# Y>₅3OO3>_&Z Y=₅3OO3=_&Z# AB# >:D;P;:D;:=# GAP>;<#AB#Y>3=ZO#"C;#?@FE>:@M#D><=F>HK=>A:#><#@<<K?;D#=A#H;#F;N;F<;#;QPA:;:=>@M# Y>O;O?Y@34Z$?Y43@Z$;QPY@ZZO# %AI3# B>Q# @# =CF;<CAMD# 8&4# @:D# GA:<>D;F#

k j lD > = D 8 F$ _* $ _*' _{* *} # O# +;=# MY&Z$mF# @:D# D;B>:;# G_*$D_*n8# Z Y 3OOO3 5 4 & * $

8 O# "C;# %T# =;<=# GA:<>D;F<# =C;# D><=F>HK=>A:# BK:G=>A:# AB#G_*# @:D# =;<=<# IC;=C;F# >=# ><# ?AF;# M>R;ML# BFA??_Y4ZY,Z$ # AF#,1 ?_Y5ZY,Z$,O# "C;# =;<=# <=@=><=>G# BAF# =;<=>:E#? #Y=@>M#>:D;P;:D;:G;Z#@E@>:<=#_Y4Z ? #><#YBAF#B>Q;D#_Y5Z

&

Zf#

# O Z 1 MAEY Z Y Z MAEY Z 1 5 MAEY f Z Y 5 Z Y 5

9

:

$ $ ! ! $ $ & 4 * & 4 * * * NB G 4 & G ' # # Z 4 Y

? # ><# F;c;G=;D# IC;:#'_NB# E;=<# M@FE;# PF;G><;ML3# >B# =C;# @PPFAQ>?@=;# PXN@MK;# ZZ 5 Z MAEY 1 Y Z Y Y f Z Y 5 1 5

:

$ ! _' ; $ & 4 * * NB 4 & G

) # ><# =AA# GMA<;# =A# 43# =LP>G@MML# >B# )_NB 0O42j##

;#X#<=@:D@FD#:AF?@M#DBO## 5@IF@J@9@K #FL9G@K 8=78

#D>BB;F;:=#PA<<>H>M>=L#AB#K<>:E#/@MR#@:D#0>GC;M#Y144^Z#=C;AF;?#><#=A#G@FFL# AK=# @# EAAD:;<<XABX# B>=# =;<=3# >:# =C><# G@<;# K<>:E# =C;# VAM?AEAFAN# *?>F:AN# =;<=O# "C;F;BAF;3#D;B>:;3#GA:D>=>A:@M#A:#MY&Z$<f## # Z ;QP Z 5 Y 5 Y ZZ ;QPY Z 5 Y 5 Y Z n YD 8 D D 8 8 ? E_*$ _{8 *} $ ! ! _{* *} ! ! 3#8* ,l53OOO<kO##

";<=>:E#BAF#"@>M#&:D;P;:D;:G;#>:#(Q=F;?;#'@MK;#0AD;M<i# 5\5

-;:A=;# _< $

:

O _,D_*

< ,

?o Y Z 5 ₆₄₃₉ # =C;# ;GDB# AB#E 3#_* *$53OO3<O# "C;# VAM?AEAFAN# =;<=#<=@=><=>G#><#=C;:f# ? , , < ' _< , MP $ ! , Z Y o <KP 5 f 9 5 3 4 6 O##

"C;# @PPFAQ>?@=;# PXN@MK;# ><#

)

_MP $

5

!

M

Y

'

_MP

Z

3# IC;F;#M# ><# =C;# GDB# AB# =C;# VAM?AEAFAN#D><=F>HK=>A:O# GGAFD>:E#=A#@#FKM;#AB#=CK?H#E>N;:#HL#=C;#@K=CAF<f BAF#

74 # < 3#=@>M#>:D;P;:D;:G;#><#F;c;G=;D#>B#'_MP # 8₄₃₄₂ $537^O## 1< "#!$0*!$(% (' !4" !,. *%, !"#!$%& '() !*$+ $%,"-"%,"%." H "0-$)$.*+ *%*+M#$# #

(>EC=# D>BB;F;:=# D@=@# <;=<# @F;# @:@MLa;D3# :@?;MLf# 0&++(%&$03# _("&%3# TV%,)+(%3#T_%&_3# *(!,T,+3#!,0 )!h3#%("& 3#"T* 5O#,KF#<@?PM;# P;F>AD# GAN;F<# @# =A=@M# ^45# AH<;FN@=>A:<# BFA?# 4dn4dn144^# =A# 45n45n144]O# # "C;# <;F>;<#@F;#:A:#_@K<<>@:#Yb@FJK;Xg;F@#=;<=#I>=C#]2p#M;N;MZO#W;#K<;#D@=@#A:#<=AGR# F;=KF:#P@>F<#=A#;<=>?@=;#=C;#=@>M#D;P;:D;:G;<#GA;BB>G>;:=<#@:D#=A#=;<=#CLPA=;<><#A:# =@>M<#>:D;P;:D;:G;O#W;#PFAG;;D#>:#=C;#BAMMAI>:E#<=;P<f#

5O ?*,,*&; <#";*&#5 7*/,"*Q.,*+&/f K<>:E# =C;# T;@R# ,N;F# "CF;<CAMD# ?;=CAD3# I;# ;<=>?@=;# =C;# =@>M# D><=F>HK=>A:# AB# ;@GC# <;F>;<O# "C;# ?@FE>:@M# =@>M# ;<=>?@=>A:#

BAF?KM@<# # # Y oY Z 5 Y5 Y ZZ 5 *3

* *

*

* @ 4 & @

? $ ! . ') * . !+ ! ) # * $53OOO3&3# IC;F;# 4 ><# =C;# :K?H;F# AB# D@=@# ;QG;;D>:E# =C;# B>Q;D# =CF;<CAMD# .L ) L *L + S# P@F@?;=;F<# AB# <C@P;3#<G@M;#@:D#?;@:Z @F;#;<=>?@=;D#HL#GCAA<>:E#=C;#=CF;<CAMD<#BAF#;@GC#<;F>;<O

1O ?*,,*&; # 8+).5# ,+ #55 )#*"/ +: 1+*&, /,#&7#"7*(27 7#,# ./*&; <#@*<.< 5*425*K++7R I;# GA:<>D;F =CF;;# I>D;ML# K<;D# FGC>?;D;@:# GAPKM@<3# :@?;ML# =C;# _K?H;M3# /F@:R3# !M@L=A:# @:D# =XGAPKM@<1O# &=# ><# D>BB>GKM=# =A# GA?P@F;# =C;# B>=# AB# =C;# =IA# GAPKM@<# D>F;G=ML# H;G@K<;# =C;L# @F;# :A:X:;<=;D# ?AD;M<O# hAI;N;F3# I;# D>D# GA?PK=;# R@>R;U<# &:BAF?@=>A:# !F>=;F>@# BAF# ;@GC# ?AD;MO# /AF# =C;# BAKF# ?AD;M<#

#################################################

5

#,KF#AHc;G=>N;#I@<#=A#GF;@=;#PAF=BAM>A#I>=C#<;M;G=;D#<=AGR<#IC>GC#@GGKF@=;ML#F;B;M;G=#=C;#D@>ML# F;=KF:<#AB#=C;#<KHX>:D;Q;<f#W&_#S#g@:R<3#W&_#X#&"#3#W&_#X#";M;GA?3#W&_#X#/K;M#O#W;#C@D#PF;X <;M;G=;D#d#<=AGR<O# #

1_{#_K?H;M#GAPKM@#Y_K?H;M3#5]^4Zf# Y 3 Z ;QPY YYMAE Z YMAE Z Z}

!

D A A ! A " A #

###!M@L=A:#GAPKM@#Y!M@L=A:3#5]8dZf#D_DCY 3 ZA A YA! "A! !5Z!5 #

###/F@:R#GAPKM@#Y/F@:R3#5]8]Zf#D_?Y 3 ZA A 5 MAE6Y5 ;QP!A 5ZY;QP!A 5Z Y2! 5Z9

# " ! ! ! #

###=XGAPKM@f#D A A_,Y 3 3 3 Z! " ,_!Y,_!!5Y Z3A ,_!!5Y Zj ZA " # #

_F@`L:@#"FaP>A=3#bK<=L:@#0@c;I<R@#

5\1

GA:<>D;F;D#BAF#KPP;F#@:D#MAI;F#=@>M#=CF;<CAMD<3#=C;#/F@:R GAPKM@#?AD;M#C@<#=C;# H;<=#P;FBAF?@:G;#Y^dp#P@>F<ZO##

7O D+<).,*&; :+" #55 Y 1*3 Z S*31$53OOOdZ# )#*"/ +: "2,."&/ ,K2 .))2" #&7 5+32" ,#*5 72)2&72&82 8+2::*8*2&,/ ./*&; ,K2 8+).5#/ )#"#<2,2"/ 2/,*<#,2/ S'#Q52 TU6 # # "@HM;#5f#+;B=#YH;MAI#D>@EA:@MZ#@:D#KPP;F#=@>M#>:D;P;:D;:G;#GA;BB>G>;:=<##Y@HAN;#D>@EA:@MZ # "T* # %("& # TV%# ,)+(%# T_%&_ *(!# ,T,+# !,0 )!h 0&++(X# %&$0# _("&%# "T* # 5# 435\78# 43772\# 43758^ 4314^8# 43172# 431]^8# 4315\2# %("& # 435^1\# 5# 43527\# 43557\ 434]8d# 435d^\# 43\5\1# 4354\2# TV%,)+(%# 437^d]# 4358^]# 5# 437^\5 431]^\# 431d72# 43721d# 4318\5# T_%&_# 4372^8# 4354^# 43\42# 5# 431781# 431782# 43742^# 431845# *(!,T,+# 431\^# 4348d# 4374^8# 4317^] 5# 431\41# 4375d^# 4315d7# !,0 )!h# 431\]^# 435^7# 431]^# 431\71 431\27# 5# 437^]1# 4371d2# 0&++(%&$0# 4371d# 435\d^# 43\4^5# 437^\8 437782# 43\4^\# 5# 43\^d1# _("&%# 4314d# 4355\# 43751# 431]^] 431^^^# 437\^1# 43\^]\# 5# ### #

\O '2/,*&; :+" ,#*5 *&72)2&72&82R g;G@K<;#=C;#P;FG;P=>A:#=C@=#M;B=#=@>M<#@F;# C;@N>;F#=C@:#=C;#F>EC=#=@>M<#I;#GA:<>D;F#=;<=<#BAF#MAI;F#=@>MO# GGAFD>:E#=A#%T#=;<=# A:;# G@:# <;;# @?A:E# =C;# <@?;# <;G=AF# A:ML# "T* X%("& # @:D# *(!,T,+X !,0 )!h#@F;#<=FA:EML#M>:R;D#>:#@#I@L#=C@=#=@>M#D;P;:D;:G;#G@:#H;#AH<;FN;DO# g@D# :;I<# BAF# "T* # @:D# !A?@FGC# <CAKMD# ?;@:# H@D# :;I<# BAF# %;=>@# @:D# *(!,T,+3# F;<P;G=>N;MLO# "C;# :KMM# CLPA=C;<><# AB# =@>MX>:D;P;:D;:G;# G@:# H;# F;c;G=;D#BAF#7\p#AB#GA:<>D;F;D#P@>F#AB#<=AGR<#Y"@HM;#1ZO#&:=;F;<=>:EML3#>:#=>?;<3# IC;F;# =@>M# >:D;P;:D;:G;# G@:# H;# F;c;G=;D3# =C;# ;<=>?@=;<# BAF# =C;# "-!# @F;# :A=# :;G;<<@F>ML# C>EC;F# =C@:#>:#A:;<# IC;F;#=C><#><# :A=#=C;#G@<;O#"C><# ;?PC@<>a;<#=C;# >?PAF=@:G;#AB#=C;#=;<=#BAF#=@>M#>:D;P;:D;:G;O#!CAA<>:E#=C;#=CF;<CAMD#.#><#D>BB>GKM=# >:# PF@G=>G;# @:D# ?@R;<# <A?;# =;GC:>G@M# PFAHM;?<O# "C;# C>EC;F# =C;# =CF;<CAMD3# =C;# MAI;F# =C;# N@F>@:G;# HK=# =C;# C>EC;F# =C;# H>@<O# "C;F;BAF;3# =C;# =CF;<CAMD# C@<# =A# H;# GCA<;:#@PPFAQ>?@=;ML#<KGC#=C@=#BAF#=C;#_@K<<>@:#D><=F>HK=>A:#I;#G@:#@GG;P=#=C;# :KMM#CLPA=C;<><#AB#=@>M#>:D;P;:D;:G;3#IC;F;@<#BAF#@MM#A=C;F<3#I;#@F;#@HM;#=A#F;c;G=# >=O# GGAFD>:E#=A#/@MR#@:D#0>GC;M#Y144^Z#<>?KM@=>A:<#I>=C#. GMA<;#;:AKEC#=A#4#@MM# =;<=<#@F;#;JK@MML#EAAD#BAF#>:D;P;:D;:=#D@=@#YGA:=FAM#"LP;#&#;FFAFZO#gK=#%;L?@:S T;@F<A:#E;=<#PFAHM;?<#I>=C#@#<?@MM;F#8#Y>=#DA;<#:A=#GA:=FAM#"LP;#&#;FFAF#=C;:ZO#*A# >B# =C;# =CF;<CAMD# ><# :A=# GMA<;# =A# 43# A:;# <CAKMD# =@R;# VAM?AEAFANX*?>F:AN# BAF# =;<=>:E#BAF#=@>M#>:D;P;:D;:G;O#

# # # #

";<=>:E#BAF#"@>M#&:D;P;:D;:G;#>:#(Q=F;?;#'@MK;#0AD;M<i# 5\7

"@HM;#1O_AAD:;<<#AB#B>=#

P@>F#AB#<=AGR<# )NB# )MP# P@>F#AB#<=AGR<# )NB# )MP#

"T* ##%("& ## NONNN N<NNPQR TV%,)+(%# *(!,T,+# 4314\# 431d28# "T* #TV%,)+(%# NONNS N<NNTUN TV%,)+(%#!,0 )!h# NONTN NONVNP "T* #T_%&_# NONQU N<NQWSU TV%,)+(%#0&++(%&$0# 432d]# 43^871# "T* # *(!,T,+# 4321d# 43878^# TV%,)+(%#_("&%# 43214# 43^54^# "T* #!,0 )!h# 4321d# 43842d# T_%&_# *(!,T,+# 43]\\# 43]]8d# "T* #0&++(%&$0# NONNN N<NSRPR T_%&_#!,0 )!h# 43522# 435d^8# "T* #_("&%# NONQV N<NQSXR T_%&_#0&++(%&$0# 43544# 435572# %("& #TV%,)+(%# 434]7# 435d7\# T_%&_#_("&%# 4372^# 43\815# %("& #T_%&_# NONSS N<NNVTQ *(!,T,+#!,0 )!h# NONNN N<NNQWV %("& # *(!,T,+# NONNN N<NNTUV *(!,T,+#0&++(%&$0# 43\^1# 43\^^\# %("& #!,0 )!h# NONNN N<NNPNV *(!,T,+#_("&%# 4324]# 43^458# %("& #0&++(%&$0# 43\81# 43^55d# !,0 )!h#0&++(%&$0# 4358\# 43145d# %("& #_("&%# 435d4# 435d27# !,0 )!h#_("&%# N<NNN NONNP TV%,)+(%#T_%&_# 43d87# 43]\88# 0&++(%&$0#_("&%# 437d1# 43\42d#

######### #

2O O&8+")+"#,*&; ,#*5 72)2&72&82 *&,+ 0#"4+3*,( 02#&9G#"*#&82 0+725R /AF# =C><# dXD>?;:<>A:@M# D@=@3# =C;# <@?PM;# GAFF;M@=>A:# GA;BB>G>;:=<# @F;# E>N;:# >:# "@HM;# 7O# W;# AH<;FN;# =C;L# @F;# @MM# PA<>=>N;O# !A?P@F>:E# N@MK;<# BAF?# "@HM;# 7# =A# =CA<;#>:#"@HM;#5#I;#AH<;FN;#=C@=#=C;#=@>M#@DcK<=;D#;<=>?@=;<#@F;#<?@MM;F#=C@:#=C;# T;@F<A:#GAFF;M@=>A:#GA;BB>G>;:=#H@<;D#A:#=C;#;:=>F;#D@=@#<;=O#0A<=#>?PAF=@:=3#=C;# <=F;:E=C# AB# GAFF;M@=>A:<# ;<=>?@=;D# BAF# cA>:=# :;E@=>N;# N@MK;<# @F;# D>BB;F;:=# BFA?# =CA<;#;<=>?@=;D#BAF#cA>:=#PA<>=>N;#F;=KF:<3#@:#@<L??;=FL#:A=#D;=;G=;D#>:#"@HM;#7O# ";<=>:E#=@>M#D;P;:D;:G;#P;F?>=<#=A#GA:<=FKG=#M;<<#F><RL#>:N;<=?;:=#PAF=BAM>A#=C@:# GM@<<<>G@M#A:;#Y"@HM;#\ZO### # "@HM;#7f#*=@:D@FD#<@?PM;#GAFF;M@=>A:#GA;BB>G>;:=<# # # "T* # %("& # TV%# ,)+(% T_%&_ *(!,X T,+# !,0 )!h 0&++(X %&$0# _("&%# "T* # 534444# # # # %("& # 4358d5# 534444# # # TV%,)+(%# 43\42d# 435d17# 534444 # # T_%&_# 437245# 4357d4# 43\122 534444 # # *(!,T,+# 43127\# 434dd1# 437d\7 431\84 534444 # # !,0 )!h# 4318^1# 435d24# 4375\^ 431d7d 431d51 534444 # # 0&++(%&$0# 4371d8# 4358\4# 43\\18 43\518 43\7]d 43\5d7 534444# # _("&%# 431]1^# 435^^2# 437dd8 43754^ 431d\8 437^42 43\d1]# 534444#

#

#

_F@`L:@#"FaP>A=3#bK<=L:@#0@c;I<R@# 5\\ "@HM;#\f#TAF=BAM>A<#GA?PA<>=>A:<# # (qT(!"(-# )("$)%# )&*V# "T* %("& TV%# ,)+(%T_%&_ *(!,X T,+# !,0 )!h 0&++(X %&$0# _("&%# !M@<<>G@M# 4O4\44# 4O]^d1# 4312# 431d# 434^# 435\# 435^# 4354# 4344# 4341# $PP;FX DcK<=;D# 4O4\44# 4Od77d# 4354# 4352# 4342# 4355# 435]# 4311# 4355# 434d# +AI;FX DcK<=;D# 4O4\44# 4Od8\4# 434]# 4351# 4347# 435]# 435\# 43\1# 4341# 4344# # # .(%.+2#$(% #

";<=>:E# =@>M# >:D;P;:D;:G;# ><# <>?PM;# @:D# =F@:<P@F;:=# ;:AKEC# =A# H;# >?PM;?;:=;D# @:D# ;@<>ML# ?A:>=AF;DO# ,?>==>:E# =C;# =;<=# BAF# =@>M# >:D;P;:D;:G;# IAKMD# >:=FADKG;# @# M@FE;# H>@<# >:# =C;# ;<=>?@=>A:# @:D# ?@R;# >=# D>BB>GKM=# =A# D;G>D;# IC;=C;F#=C;F;#><#cK<=#GAFF;M@=>A:#AF#>:#B@G=#=@>M#D;P;:D;:G;O#,:;#>?PAF=@:=#B;@=KF;# AB# =C><# P@P;F# ><# =C;# >?PM;?;:=@=>A:# AB# =C;# =;<=<# BAF# =@>M# >:D;P;:D;:G;3# IC>GC# ><# F;GAE:>a;D#=A#H;#>:D><P;:<@HM;#HK=#F@F;ML#K=>M>a;D#>:#@#B>:@:G>@M#GA:=;Q=O#,:#=C;# H@<><#AB#=@>M#D;P;:D;:G;#=;<=#I;#@F;#@HM;#=A#>?PFAN;#@MMAG@=>A:#F;<KM=<#H@<;D#A:# D@>ML#F;=KF:<O

)"'")"%."# #

:r3# "O3# VC@FAKH>3# !O# Y1447Z3# -;P;:D;:G;# <=FKG=KF;# @:D# F><R# ?;@<KF;3# -+."&#5 +: V./*&2//L# 8^3# \55S\7dO#

!M@L=A:# -O_O# Y5]8dZ3# # 0AD;M# BAF# <<AG>@=>A:# >:# g>N@F>@=;# +>B;# "@HM;<# @:D# >=<# PPM>G@=>A:# >:# (P>D;?>AMAE>G@M#*=KD>;<#AB/@?>M>@M#";:D;:GL#>:#!CFA:>G#-><;@<;#&:G>D;:G;3##g>A?;=F>R@3#^23# 5\5S525O#

!AM;<#*O#Y1445Z3#W& O&,"+7.8,*+& ,+ P,#,*/,*8#5 0+725*&; +: F@,"2<2 G#5.2/3#*PF>:E;F3#g;FM>:O## (?HF;GC=<#TO3#VMsPP;MH;FE#!O3#0>RA<GC#"O#Y5]]8Z3#0+7255*&; F@,"2<#5 FA2&,/ :+" O&/."#&82 #&7

?*&#&82L *PF>:E;F3#g;FM>:O# (?HF;GC=<#TO3#0G%;>M# O3#*=F@K?@::#-O#Y1441Z3#!AFF;M@=>A:#@:D#D;P;:D;:GL#>:#F><R#?@:@E;?;:=f# PFAP;F=>;<#@:D#P>=B@MM<O#&:f#)><R#0@:@E;?;:=f#'@MK;#@=#)><R#@:D#g;LA:D3#0O OhO#-;?P<=;F3# (DO#!@?HF>DE;#$:>N;F<>=L#TF;<<3#58^S117O# /@MR#0O3#0>GC;M#)O#Y144^Z3#";<=>:E#BAF#=@>M#>:D;P;:D;:G;#>:#;Q=F;?;#N@MK;#?AD;M<O#W&&#5/ +: ,K2 O&/,*,.,2 +: P,#,*/,*8#5 0#,K2<#,*8/3#2d3#1^5S1]4O#

/F@C?# _O3# bK:R;F# 0O3# *GC?>D=# )O# Y1442Z3# (<=>?@=>:E# =C;# =@>MXD;P;:D;:G;# GA;BB>G>;:=f# TFAP;F=>;<# @:D#P>=B@MM<3#O&/."#&82R 0#,K2<#,*8/ #&7 F8+&+<*8/3#783#d4X544O#

/F@:R# 0ObO# Y5]8]Z3# ,:# =C;# *>?KM=@:;AK<# <<AG>@=>N>=L# AB# /YQ3LZ# @:D# QL/YQ3LZ3# ;JK@=>A:;<# 0@=C;?@=>G@;#5]3#5]\S##11^O#

_K?H;M# (ObO# Y5]^4Z3# g>N@F>@=;# (QPA:;:=>@M# -><=F>HK=>A:<3# bAKF:@M# AB# =C;# ?;F>G@:# *=@=><=>G@M# <<AG>@=>A:3#223#^]dS848#

h@@:#+O#D;3#);<:>GR#*O&O#Y5]88Z3#+>?>=#=C;AFL#BAF#?KM=>N@F>@=;#<@?PM;#;Q=F;?;<3#X6 J#K"/8K6 G2"36

!2Q*2,2L#\43#758X778O#

bA;#hO#Y5]]8Z3#0.5,*A#"*#,2 0+725/ #&7 Y2)2&72&82 D+&82),/L#!C@P?@:#@:D#h@MM3#+A:DA:O# 0@M;N;FE:;#tO3#*AF:;==;#-O#Y144\Z3#&:N;<=>E@=>:E#;Q=F;?;#D;P;:D;:G>;<O#(Q=F;?;#/>:@:G>@M#)><R<#

";<=>:E#BAF#"@>M#&:D;P;:D;:G;#>:#(Q=F;?;#'@MK;#0AD;M<i# 5\2 *>HKL@#0O#Y5]^4Z3#g>N@F>@=;#;Q=F;?;#<=@=><=>G<#&O#W&&#5/ +: O&/,*,.,2 +: ,K2 P,#,*/,*8#5 0#,K2<#,*8/L 553#5]2X154O# *RM@F# O#Y5]2]Z3#/A:G=>A:<#D;#FrP@F=>=>A:#u#:#D>?;:<>A:<#;=#M;KF<#?@FE;<O#B.Q5*8#,*+&/ 72 5ZO&/,*,., 72 P,#,*/,*[.2 72 5ZE&*A2"/*,\ 72 B#"*/3#d3#11]X175O# # # !"#$%&# '"()*+,L -./,%&# 0#123/4## #

!"#!(D*%$" %$"Y*+"Z%([.$ D (&(%*.4 )(Y5\*,]D D*)!([.$ "5#!)"0*+%M.4 3 Y*#!(#(D*%$" %* -(+#5$"^ &$"\,Y$" -*-$")]D

D*)!([.$(DM.4 #

,RF;vM@:>;# <=AP:>@# a@M;`:AvG># ?>wDaL# @R=LI@?># c;<=# :>;aHwD:;# I# I>;MK# AH<a@F@GC# FL:RK# B>:@:<AI;EAO# VA:G;PGc@# a@M;`:AvG># I# AEA:>;# FAaRx@DK# <=@:AI># AH;G:L# =F;:D# I# AG;:>;# <>xL# ;R<=F;?@M:LGC# a@M;`:AvG>O# TFa;PFAI@DaA:@# aA<=@x@# @:@M>a@# a@M;`:AvG># I# AEA:>;# FAaRx@DK# :@# PAD<=@I>;# <=yP# aIFA=K# ILHF@:LGC# <Pyx;R# PAM<R>;c# E>;xDL# AF@a# @:@M>a@# PAFyI:@IGa@# ILHF@:LGC# =;<=yI# :>;a@M;`:AvG>f# %;L?@:XT;@F<A:# ># VAM?AEAFANX*?>F:ANO# !;M;?# PF@GL# c;<=# KILPKRM;:>;# PA=Fa;HL# KIaEMwD:>@:>@# a@E@D:>;:>@# ARF;vM@:>@# a@M;`:AvG># I# AEA:@GC# FAaRx@DK# <=AP# aIFA=K# <Rx@D:>RyI#PAF=B;M@#I#a@FazDa@:>K#PAF=B;M;?#>:I;<=LGLc:L?O#