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<=< > ?@ABCDC ?E C FGHC EICJCF @I?CGIKLC = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = M<=<=< = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = M<=<=N = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = M<=<=O PK JGQQCK REBK JC QGH@IDCKL@ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = M<=<=S PK JGQQCK REBK QKAH@ TT = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = M<=<=U = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = M<=<=V WKACKIH@ J@LLK JGQQCK REBK = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = X<=<=M TL Q@IJGLG ?E EI QCKIG AEGHKIH@ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = X<=<=X = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = X<=<=Y = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Y<=<=<Z = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Y<=<=<< = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Y<=<=<N [ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Y<=<=<O = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Y<=<=<S [ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Y<=<=<U [ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <Z<=<=<V = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <Z<=<=<M [ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <Z<=<=<X = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <Z<=<=<Y [ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <Z<=<=NZ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <Z<=<=N < [[ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <Z<=<=NN [[[ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <Z<=<=NO \GFKIJ@ RA@]C = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <<

<=N >ÊKDCGIC LCI@KAC = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <<<=N =< = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <<<=N =N = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <N<=N =O = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <N

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<=N =S [ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <N<=O `GHC aGADKHC @ ?F GADKHC = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <N

<=O =< = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <N<=O =N = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <N<=O =O [ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <O<=O =S [ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <O<=O =U [ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <O

<=S b LBEIC @?@ABCDC BcCK]@ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <O<=S =< PK JGQQCK REBK BGI KHHACHG = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <O<=S =N TL dACHGAIG e QKAH@ T = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <S<=S =O TL dACHGAIG e QKAH@ TT = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <S<=S =S [[ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <S<=S =U fI @?@FQCG JC CI]KACKIH@ KJCKRKHCBG = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <S<=S =V PK REBK ]KACKR CL@ AC]C?CHKHK = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <U<=S =M b LHAC @?@FQC JC CI]KACKIHC KJCKRKHCBC = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <U

<=U b LHAC @?@ABCDC ?EC F GHC EICJCF @I?CGIKLC gNZZ <h = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <V<=U =< = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <V<=U =N = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <V<=U =O = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <M<=U =S = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <M<=U =U = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <M<=U =V = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <M<=U =M = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <X<=U =X = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <X<=U =Y = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <X

i j0:3k2042 57l:2 787mn2k2 83 2 6 012 342526 7482049:2 .oN =< `GHC EICJCF @I?CGIKLC = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <X

N =<=< = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <XN =<=N = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <YN =<=O PK JGQQCK REBK JC QGH@IDCKL@ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <YN =<=S PK JGQQCK REBK QKAH@ TT = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <YN =<=U = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = <YN =<=V WKACKIH@ J@LLK JGQQCK REBK = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NZN =<=M TL Q@IJGLG ?E EI QCKIG AEGHKIH@ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = N <N =<=X = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NNN =<=Y = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NNN =<=<Z = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NNN =<=<< = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NNN =<=<N = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NNN =<=<O = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NON =<=<S = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NON =<=<U = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NON =<=<V = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NON =<=<M = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NON =<=<X = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NON =<=<Y = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NON =<=NZ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NON =<=N < = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NO

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N =<=NN = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NON =<=NO = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NS

N =N >ÊKDCGIC LCI@KAC = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NSN =O `GHC aGADKHC @ ?F GADKHC = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NSN =S b LBEIC @?@ABCDC BcCK]@ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NS

N =S =< PK JGQQCK REBK BGI KHHACHG = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NSq r :n342 n06s212 5 t7896 7 i;

O =Z =< P uv uwx y zGFQCHG JC ` @BBKICBK u a@RRAKCG eYM = = = = = = = = = = = = = = = = = = = = = = = = = = = = NMO =Z =N P uv uwx y wACF G BGFQCHG JC @?GI@AG u K =K = YO{YS = = = = = = = = = = = = = = = = = = = = = = = = = = = NXO =Z =O z| uP uv zGFQCHG JC ` @BBKICBK |KDCGIKL@ u V}V} eYV u T~ KQQ@LLG u ?@?? = @?HC]K = = = = = = = = = = = = NXO =Z =S z| uP uv zGFQCHG JC ` @BBKICBK |KDCGIKL@ u ?@?? = @?HC]K gwEL]CA@IHCh = = = = = = = = = = = = = = = NYO =Z =U z| uP uv zGFQCHG ?@??CGI@ @?HC]K K =K = YO{YS = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NYO =Z =V z| uP uv uwx y zGFQCHG JC ` @BBKICBK |KDCGIKL@ J@L V =<Z =YS = = = = = = = = = = = = = = = = = = = = NYO =Z =M z| uP uv uwx zGFQCHG J@L NZ =V =YS g` KABcCGAGh = = = = = = = = = = = = = = = = = = = = = = = = = = = OZO =Z =X z| uP uv uwx y zGFQCHG J@L <<=M =YS g` KABc CGAG h = = = = = = = = = = = = = = = = = = = = = = = = = = = OZO =Z =Y z| uP uv uwx >?GI@AG JC ` @BBKICBK |KDCGIKL@ J@L <S{U{YZ = = = = = = = = = = = = = = = = = = = = = OZO =Z =<Z z| uPv uwx >?GI@AG JC ` @BBKICBK |KDCGIKL@ J@L <S{U{YZ = = = = = = = = = = = = = = = = = = = = = OZO =Z =<< P u|f zGFQCHG JC ` @BBKICBK J@L NO =N =<YYU = = = = = = = = = = = = = = = = = = = = = = = = = = = = = O <O =Z =<N P u|f u� y wACF G BGFQCHG JC @?GI@AG u K =K =YS{YU = = = = = = = = = = = = = = = = = = = = = = = = = = = = O <O =Z =<O z| uP u|f y zGFQCHG JC ` @BBKICBK |KDCGIKL@ J@L NV =N =YV = = = = = = = = = = = = = = = = = = = = = = O <O =Z =<S z| uP uv u|f zGFQCHG ?@??CGI@ @?HC]K K =K = YO{YS = = = = = = = = = = = = = = = = = = = = = = = = = = O <O =Z =<U P uv u� v@BGIJG KQQ@LLG ` @BBKI CBK |KDCGIKL@ K =K = YO{YS = = = = = = = = = = = = = = = = = = = = = = ONO =Z =<V P uv u� = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = ONO =Z =<M P u|f u� u�� ubb zGFQCHG JC ` @BBKICBK |KDCGIKL@ u Y}M} eYV u TT~ KQQ@LLG u ?@?? = @?HC]K = = = = = = ONO =Z =<X z| uP u|f u� u�� zGFQCHG JC ` @BBKICBK |KDCGIKL@ u NS}Y} eYV u T~ KQQ@LLG u ?@?? = KEHEIIKL@ = = = = OOO =Z =<Y z| uP u|f u� u�� ubb zGFQCHG JC ` @BBKICBK |KDCGIKL@ u X}<Z} eYV u TT~ KQQ@LLG u ?@?? = KEHEIIKL@ = OOO =Z =NZ �z y zGFQCHG JC ` @BBKICBK J@L NO =N =<YYU = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = OSO =Z =N < �z = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = OSO =Z =NN �z ubb uw v@BGIJG BGFQCHG JC @?GI@AG K =K =YS = = = = = = = = = = = = = = = = = = = = = = = = = = = = OUO =Z =NO � u�� ubb uv y TT @?GI@AG <Z}U} eYV = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = OUO =Z =NS z| u� u�� uw y > ?GI@AG JC ` @BBKICBK |KDCGIKL@ J@L V{V{YZ = = = = = = = = = = = = = = = = = = = = = OV

� j0:3k2042 5 2 9:n342 n06s212 5 2 7896 7 q�S =Z =< P uv uwx y zGFQCHG JC ` @BBKICBK u a@RRAKCG eYM = = = = = = = = = = = = = = = = = = = = = = = = = = = = OVS =Z =N P uv uwx y wACF G BGFQCHG JC @?GI@AG u K =K = YO{YS = = = = = = = = = = = = = = = = = = = = = = = = = = = OVS =Z =O z| uP uv zGFQCHG JC ` @BBKICBK |KDCGIKL@ u V}V} eYV u T~ KQQ@LLG u ?@?? = @?HC]K = = = = = = = = = = = = OMS =Z =S z| uP uv zGFQCHG JC ` @BBKICBK |KDCGIKL@ u ?@?? = @?HC]K gwEL]CA@IHCh = = = = = = = = = = = = = = = OXS =Z =U z| uP uv zGFQCHG ?@??CGI@ @?HC]K K =K = YO{YS = = = = = = = = = = = = = = = = = = = = = = = = = = = = = OYS =Z =V z| uP uv uwx y zGFQCHG JC ` @BBKICBK |KDCGIKL@ J@L V =<Z =YS = = = = = = = = = = = = = = = = = = = = OYS =Z =M z| uP uv uwx zGFQCHG J@L NZ =V =YS g` KABcCGAGh = = = = = = = = = = = = = = = = = = = = = = = = = = = SZS =Z =X z| uP uv uwx y zGFQCHG J@L <<=M =YS g` KABc CGAG h = = = = = = = = = = = = = = = = = = = = = = = = = = = SZS =Z =Y z| uP uv uwx >?GI@AG JC ` @BBKICBK |KDCGIKL@ J@L <S{U{YZ = = = = = = = = = = = = = = = = = = = = = SZS =Z =<Z z| uPv uwx >?GI@AG JC ` @BBKICBK |KDCGIKL@ J@L <S{U{YZ = = = = = = = = = = = = = = = = = = = = = SZS =Z =<< P u|f zGFQCHG JC ` @BBKICBK J@L NO =N =<YYU = = = = = = = = = = = = = = = = = = = = = = = = = = = = = SZS =Z =<N P u|f u� y wACF G BGFQCHG JC @?GI@AG u K =K =YS{YU = = = = = = = = = = = = = = = = = = = = = = = = = = = = SZS =Z =<O z| uP u|f y zGFQCHG JC ` @BBKICBK |KDCGIKL@ J@L NV =N =YV = = = = = = = = = = = = = = = = = = = = = = S <S =Z =<S z| uP uv u|f zGFQCHG ?@??CGI@ @?HC]K K =K = YO{YS = = = = = = = = = = = = = = = = = = = = = = = = = = SNS =Z =<U P uv u� v@BGIJG KQQ@LLG ` @BBKI CBK |KDCGIKL@ K =K = YO{YS = = = = = = = = = = = = = = = = = = = = = = SNS =Z =<V P uv u� = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = SN

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S =Z =<M P u|f u� u�� ubb zGFQCHG JC ` @BBKICBK |KDCGIKL@ u Y}M} eYV u TT~ KQQ@LLG u ?@?? = @?HC]K = = = = = = SSS =Z =<X z| uP u|f u� u�� zGFQCHG JC ` @BBKICBK |KDCGIKL@ u NS}Y} eYV u T~ KQQ@LLG u ?@?? = KEHEIIKL@ = = = = SUS =Z =<Y z| uP u|f u� u�� ubb zGFQCHG JC ` @BBKICBK |KDCGIKL@ u X}<Z} eYV u TT~ KQQ@LLG u ?@?? = KEHEIIKL@ = SVS =Z =NZ �z = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = SVS =Z =N < �z = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = SVS =Z =NN �z ubb uw v@BGIJG BGFQCHG JC @?GI@AG K =K =YS = = = = = = = = = = = = = = = = = = = = = = = = = = = = SVS =Z =NO � u�� ubb uv y TT @?GI@AG <Z}U} eYV = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = SMS =Z =NS z| u� u�� uw y > ?GI@AG JC ` @BBKICBK |KDCGIKL@ J@L V{V{YZ = = = = = = = = = = = = = = = = = = = = = SX

� r :n342 787mn2k2 8�0:12 24 57119l:20 �oU =< wAGRL@F K = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = SY

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U =N wAGRL@F K = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = UOU =N =< PK J@H@AF CIKDCGI@ J@�LC @ÊCLCRAC @ LK LGAG ?HKRCLCH� = = = = = = = = = = = = = = = = = = = = = = = = USU =N =N P@ QCBBGL@ G?BCLLKDCGI C CIHGAIG KLL e@Ê CLCRACG ?HKRCL@ = = = = = = = = = = = = = = = = = = = = = = = = USU =N =O |@KDCGI@ ]CIBGLKA@ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = UU

U =O wAGRL@F K = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = UVU =O =< T �AKJC JC LCR @AH� @ LK ?B@LHK J@LL@ BGGGAJCIKH@ = = = = = = = = = = = = = = = = = = = = = = = = = = = UVU =O =N TL BKLBGLG J@LL e@I@A�CK BCI@HCBK = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = UVU =O =O TL BKLBGLG J@LL e@I@A�CK QGH@IDCKL@ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = UMU =O =S PK PK�AKI�CKIK @ L@ @ÊKDCGIC JC >EL@AG{PK�AKI�@ = = = = = = = = = = = = = = = = = = = = = = = = UMU =O =U P e�KF CLHGICKIK @ L@ @ÊKDCGIC JC �KF CLHGI = = = = = = = = = = = = = = = = = = = = = = = = = = = = = UXU =O =V PK J@H@AF CIKDCGI@ J@�LC @ÊCLCRAC = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = UYU =O =M PK ?HKRCLCH� J@LL@ QG?CDCGIC JC @ÊCLCRACG = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = UYU =O =X P@ QCBBGL@ G?BCLLKDCGI C CIHGAIG KLL@ QG?CDCGIC JC @ÊCLCRACG ?HKR CLC = = = = = = = = = = = = = = = = = VZU =O =Y �LC CIH@�AKLC QACF C @ LK ACJEDCGI@ J@C �AKJC JC LCR @AH� = = = = = = = = = = = = = = = = = = = = = = = V <U =O =<Z TL BGIHAGLLG JCF @I?CGIKL@ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = V <

U =S wAGRL@F K = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = V <U =S =< vB@LHK J@LL@ BGGAJCIKH@ @J @ÊKDCGIC J@L F GHG = = = = = = = = = = = = = = = = = = = = = = = = = = = V <U =S =N wG?CDCGI C JC @ÊCLCRACG = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = VNU =S =O | CJEDCGI@ J@C �AKJC JC LCR @AH� @ KIKLC?C ÊKLCHKHC]K = = = = = = = = = = = = = = = = = = = = = = = = = VNU =S =S PK AKQQA@?@IHKDCGI@ J@LL eGARCHK = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = VOU =S =U \GFKIJ@ ]KAC@ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = VO

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M =<=< TL QAGRL@F K = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = VUM =<=N fI @?@FQCG = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = VVM =<=O fI @?@FQCG FGLHG QKAHCBGLKA@ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = VV

M =N �AK?aGAF KDCGI C ?CFQL@HHCBc@ CIJCQ@IJ@IHC JKL H@FQG = = = = = = = = = = = = = = = = = = = = = = = = = = = = VMM =O �EIDCGIC �@I@AKHACBC @ HAK?aGAF KDCGIC BKIGICBc@ JCQ@IJ@IHC JKL H@FQG = = = = = = = = = = = = = = = = = = VY

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M =S =< > ?@FQCG = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = MNM =U zG?HAEDCGI@ J@LL@ ]KACKRCLC KDCGI@{KI�GLG = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = MO

M =U =< WKACKRCLC KDCGI@{KI�GLG Q @A L eG?BCLLKHGA@ KAFGICBG = = = = = = = = = = = = = = = = = = = = = = = = = MOM =U =N fI @?@FQCG = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = MOM =U =O fI KLHAG @?@FQCG = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = MU

M =V �@GACK J@LL@ Q @AHEARKDCGIC = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = MMM =V =< > ?@FQC = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = MX

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W@JC ?@DCGI@N =<=YÏÐÏÐÏ2fI QEIHG FKH@ACKL@ JC F K??K à ?C FEG]@ ?E EIK A@HHK ?GHHG L eKDCGI@ JC EIK aGADK JC @I@A�CK QGH@IDCKL@ Ñ ÒÓÔ Õ áÓý�Ó =zGI?CJ@AK C JKHC CI CDCKLC JC @I@A�CK HGHKL@ þ Õ 34 u @ ?CK ßÓÝ Õ 3 = \@H@AF CIK C ]KLGAC JC Ó ÒâÔ Q@A C ÊKLC CL FGHG ÌQ @ACGJCBG @ JKC EI e@?QA@??CGI@ J@L Q @ACGJG = W@JC ?@DCGI@N =< =<ZÏÐÏÐÏÏfI QEIHG FKH@ACKL@ JC F K??K à ?C FEG]@ ?E EIK A@HHK ?GHHG L eKDCGI@ JC EIK aGADK JC @I@A�CK QGH@IDCKL@ Ñ ÒÓ Ô Õ5Ó � à � 6Ó u BGI 6 � � =w@A ÊKLC ]KLGAC JC 6 HEHH@ L@ GAR CH@ ?GIG LCF CHKH@ãw@A ÊKLC ]KLGAC JC 6 L eGAC� CI@ Ì ?HKR CL@ãW@JC ?@DCGI@N =<=<<ÏÐÏÐÏÛ 7fI QEIHG F KH@ACKL@ JC F K??K àu ?E EIK A@HHK u CI CDCKLF @IH@ CI Ó Õ â BGI ]@LG BCH� ßÓ Õ àu ?C FEG]@ ?GHHG L eKDCGI@ JCEIK aGADK JC @I@A�CK QGH@IDCKL@ Ñ ÒÓÔ Õ á5Ó � à=

wAG]K Bc@ CL F GHG Ì CLLCF CHKHG =wAG]K Bc@ @?C?H@ EI eKBB@L@AKDCGI@ K?CIHGHCBK gBCG Ì äåæ çèéê ÜÓ Ì �ICHG hwAG]K Bc@ K?CIHGHCBKF @IH@ I@L H@FQG CL F GHG H@IJ@ KJ EI FGHG EICaGAF@F@IH@ KBB@L@AKHG = TI KLHAC H@AF CIC

@?C?HGIG 8Ó u 8ÿ u @ 6 HKLC Bc@ äåæ çèê Ö ßÓ ÒëÔ á Ò8ÿ � ë6 Ô Ö Õ â @ äåæ çèê ÖÓ ÒëÔ á Ò8Ó � ë 8ÿ � ç 6 Ô Ö Õ â =W@JC ?@DCGI@N =<=<N

ÏÐÏÐÏìfI QEIHG F KH@ACKL@ JC F K??K à ?C FEG]@ ?ELLK ?@F CA@HHK Ó � â ?G��@HHG KJ EIK aGADK JC @I@A�CK QGH@IDCKL@ Ñ ÒÓÔ Õá 3� � 3� =w@A ÊKLC JKHC CI CDCKLC CL F GHG Ì Q@ACGJCBGãw@A ÊKLC JKHC CI CDCKLC CL F GHG IGI Ì Q@ACGJCBGãw@A ÊKLC JKHC CI CDCKLC CL F GHG Ì CLLCF CHKHGã�EKLC ?GLG L@ ?GLEDCGIC ?HKDCGIKAC@ã

vCK ÓÝ Õ 3 @ ßÓÝ Õ à= \@H@AF CIK äåæ çèéê ßÓ ÒëÔ =vCK ÓÝ Õ 3 @ ßÓÝ Õ áà= �EKL Ì CL F K??CF G J@LLK ]@LG BCH� Bc@ CL QEIHG AK��CE�@ã > ÊKL Ì CL F CICF KãW@JC ?@DCGI@N =<=<O

ÏÐÏÐÏ� 7vCK Ñ ÒÓÔ Õ à � �� Ó Q@A ÖÓ Ö . ' u @ Ñ ÒÓ Ô Õ â Q@A ÖÓ Ö Ù ' =

\ C?BEHC ÊKLCHKHC]KF @IH@ CL F GHG =\ C?BEHC ÊKLCHKHC]KF @IH@ CL F GHG Q@A CL QGH@IDCKL@ Ñ9 ÒÓ Ô Õ Ñ Ò �9 Ô BGI : � â � BG?K KBBKJ@ I@L LCF CH@ : $ âã;

\C?BEHC ÊKLCHKHC]KF @IH@ CL F GHG Q@A CL QGH@IDCKL@ Ñ9 ÒÓ Ô Õ 39 Ñ Ò �9 Ô BGI : � â � BG?K KBBKJ@ I@L LCF CH@ : $ âã�EKL Ì CL F GHG JC EIK QKAHCB@LLK Bc@ ACFRKLDK BGIHAG EI ûFEAG CI�ICHKF @IH@ AC�CJGüãW@JC ?@DCGI@N =<=<SÏÐÏÐÏ� 7vCK Ñ ÒÓÔ Õ á Òà � �� ÓÔ Q @A ÖÓ Ö . ' u @ Ñ ÒÓ Ô Õ â Q@A ÖÓ Ö Ù ' =\ C?BEHC ÊKLCHKHC]KF @IH@ CL F GHG =

\ C?BEHC ÊKLCHKHC]KF @IH@ CL F GHG Q@A CL QGH@IDCKL@ Ñ9 ÒÓ Ô Õ 39 Ñ Ò �9 Ô BGI : � â u Q @A JKHC CI CDCKLC JC @I@A�CK HGHKL@QG?CHC]K = zG?K KBBKJ@ I@L LCF CH@ : $ âãW@JC ?@DCGI@N =<=<U

ÏÐÏÐÏ vCK Ñ ÒÓÔ Õ ÖÓ Ö= \ C?BEHC ÊKLCHKHC]KF @IH@ CL F GHG = �EKIH eÌ LK aGADK CI Ó Õ âã vCK Ñ ÒÓ Ô Õ á ÖÓ Ö= �AG]K CL F GHG JCJKHG CICDCKL@ ÒÓÝ Þ ßÓÝ Ô Õ ÒáàÞ ÿ Ô KL ]KACKA@ JC ÿ � â = zGI?CJ@AK GAK Ñ ÒÓÔ Õ á56 � Ó � 6 u BGI 6 � â = \@H@AF CIK CLF GHG JC JKHG CICDCKL@ ÒÓÝ Þ ßÓÝ Ô Õ ÒáàÞ ÿ Ô KL ]KACKA@ JC ÿ � â u @ CL LCF CH@ JC HKL@ F GHG Q@A 6 $ â =W@JC ?@DCGI@N =<=<VÏÐÏÐÏ� 7vCK Ñ ÒÓ Ô Õ á ÖÓ Ö× BGI Ø � â = zGI?CJ@AK CL JKHG CICDCKL@ ÒÓÝ Þ ßÓÝ Ô Õ ÒàÞ âÔ = TI ÊKIHG H@FQG CL QEIHG F KH@ACKL@AK��CEI�@ �% ã w@A ÊKIHG H@FQG CL F GHG @?C?H@ãvCK Ñ ÒÓÔ Ù < Q@A G�IC Ó A@KL@ = wAG]K Bc@ ÖÓ ÒëÔ Ö . =3 � = ë u Q @A =3 Þ = BG?HKIHC GQQGAHEI@ Bc@ JCQ @IJGIG JKLJKHG CICDCKL@ = wAG]K Bc@ CL F GHG @?C?H@ Q @A HEHHC C H@FQC =

W@JC ?@DCGI@N =<=<MÏÐÏÐÏ(vCK Ñ ÒÓ Ô Õ Ó � Ø �å� Ó u BGI Ø � â = \ C?BEHC ÊKLCHKHC]KF @IH@ CL F GHG KL ]KACKA@ JC Ø = TI QKAHCBGLKA@ HAG]K �LC Ø Q@ABEC @?C?HGIG ?GLEDCGIC ?HKDCGIKAC@ @ JC?BEHCI@ LK ?HKRCLCH� = \@H@AF CIK Q@A ÊKLC Ø @?C?HGIG GAR CH@ Q @ACGJCBc@ =

W@JC ?@DCGI@N =<=<XÏÐÏÐÏ0 7vCK Ñ ÒÓÔ Õ �å� ÒÓ Ô � �å� ÒØÓ Ô u BGI â > Ø > àu @ ÒÓÝ Þ ßÓÝ Ô Õ Òâ Þ ÚÔ = \@H@AF CIK äåæ çèê Ó ÒëÔ KL ]KACKA@ JC Ø =gvE��@ACF @IHG y ]@JC L e@?@ABCDCG ?EL ACHGAIG <=S =Nh

W@JC ?@DCGI@N =<=<YÏÐÏÐÛ2vCK Ñ ÒÓÔ Õ Òà � �� ÒÓ ÔÔ �å� ?�9 @ u @ ÒÓÝ Þ ßÓÝ Ô Õ Òâ Þ ÚÔ = w@A ÊKLC ]KLGAC JC : CL F GHG Ì CLLCF CHKHGã W@JC ?@DCGI@N =<=NZÏÐÏÐÛ Ï 77vCK Ñ ÒÓ Ô Õ Ú �å� ?�9 @ u ÓÝ Õ â @ ßÓÝ � Ú = \@H@AF CIK CL H@FQG I@B@??KACG Q @A AK��CEI�@A@ Ó Õ àu I@L LCF CH@ : $ â = W@JC?@DCGI@N =< =N <ÏÐÏÐÛÛ 777vCK Ñ ÒÓ Ô Õ Òà � �� ÒÓ ÔÔ �å� ?�9 @ u @ ÒÓÝ Þ ßÓÝ Ô Õ Òá' Þ ÚÔ = TIJCBK BGI ë9 CL H@FQG I@B@??KACG Q @A AK��CEI�@A@ Ó Õ ' =w AG]K Bc@ äåæ 9èÝ ë9 Ì �ICHG = vCK ë9 ÒÓ Ô CL H@FQG I@B@??KACG Q @A AK��CEI�@A@ Ó � ' = w AG]K Bc@ çA B�C� � = Q@A G�IC : @JG�IC Ó � 'W@JC ?@DCGI@N =<=NN

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ÏÐÏÐÛì EðF îøï÷ ó�÷G òKh TI �@I@AKL@ EI eGAR CHK Q @ACGJCBK Ì J@?BACHHK JK EI e@LLC??@ I@LLG ?QKDCG J@LL@ aK?CãR h vCK Ñ ÒÓ Ô Õ Ó � 3 �å� Ó = �EKIH eÌ äåæ çèéê Ó ÒëÔã TL FGHG Ì EICaGAF @F@IH@ KBB@L@AKHGãBh zGF@ Ì LK QKAH@ A@KL@ J@�LC KEHG]KLGAC JC EI ?C?H@F K BGI?@A]KHC]G LCI@KACDDKHG CIHGAIG

KJ EIK QG?CDCGI@ JC @Ê CLCRACG ?HKRCL@ãJh \ C?BEHC LK ?HKRCLCH� J@LL eGAC�CI@ Q @A L@ ?@�E@IHC @ÊKDCGIC JCH@A@IDCKLC y

<= ÜÓ Õ Ó � ßÓN = ÜÓ Õ Ó á ßÓO = ÜÓ Õ áÓ � ßÓS = ÜÓ Õ áÓ á ßÓ�EKL@ JC @??@ J@?BAC]@ EI G?BCLLKHGA@ KAFGICBG BGI KHHACHG K H@FQG CI]@AHCHGã > ÊKL@CL LCI@KACDDKHG JC EI Q@IJGLG BKQG]GLHG BGI KHHACHGã

@h w@A ÊKLC J@C ?@�E@IHC F GHC EICJCF @I?CGIKLC L e@I@A�CK F @BBKICBK Ì BGI?@A]KHKã<= ÜÓ Õ IJKL �N = ÜÓ Õ �� ÓO = ÜÓ Õ �å� Ó � ëS = ÜÓ Õ �å� Ó � àU = ÜÓ Õ Ó � ëV = ÜÓ Õ ÓëM = ÜÓ Õ Ó � ßÓX = ÜÓ � ßÓ � �å� Ó Õ âY = ÜÓ Õ ßÓ<Z = ÜÓ Õ MN�� ÒÓ á OëÔTI JE@ J@�LC @?@FQC QA@B@J@IHC u KIBc@ ?@ L e@I@A�CK F @BBKICBK IGI ?C BGI?@A]K u B eÌ EICIH@�AKL@ QACFG J@L FGHG u JCQ @IJ@IH@ JKL H@FQG u Bc@ I@ Q @AF@HH@ L eKIKLC?C ÊKLCHKHC{]K = �EKLC ?GIGã �EKL Ì L eCIH@AQA@HKDCGI@ �?CBK JC HKLC CIH@�AKLC QACF Cã g]@JC L eCI CDCGJ@LL e@?@ABCDCG <=S =Uh =

W@JC ?@DCGI@N =< =NO» ¼P ½QÄÊÃÂÆÈÂ ËÂÈ¿ÊÀÂ�@C H@?HC JC KIKLC?C F KH@F KHCBK L eK?Q@HHG ÊKLCHKHC]G Ì HCQCBKF@IH@ ?GHHGAKQQA@?@IHKHG = W@JC CI]@B@ C H@?HC JC b AIGLJÍ<u NÎ @ CI �@I@AKL@ C LCRAC JC ` @BBKICBK =ÏÐÛ ÐÏPCI@KACDDK L e@ÊKDCGI@ J@L Q @IJGLG ÜR Õ á# Ý �å� RCIHGAIG K STSSU L@ QG?CDCGIC JC @Ê CLCRACG =

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áà � Y ÞKL ]KACKA@ JC � � � gKIBc@ I@�KHC]Gh =ÏÐÛ Ðìzc@ A@LKDCGI@ J@]GIG ]@AC�BKA@ LK FKHACB@ W @ CL ]@HHGA@ Z K�IBc§ CL ?C?H@F K

ßV Õ WV � �� ÒëÔZKFF@HHK EIK ?GLEDCGI@ Q @ACGJCBK JC Q @ACGJG ëã gvE��@ACF @IHG y B@ABK ?GLEDCGIC J@L HCQG �å� ÒëÔ[ � �� ÒëÔ\ h =Ï ÐÛ Ð� 7zGI?CJ@AK CL ?C?H@F K LCI@KA@

ßV Õ WV ÞBGI JKHG CICDCKL@ V ÒâÔ Õ VÝ = wAG]K Bc@ LK ?GLEDCGI@ Ì LCI@KA@ I@L JKHG CICDCKL@ = �E@?HG CFQLCBK Bc@ @?C?H@ EIK F KHACB@] ÒëÔ HKL@ Bc@ V ÒëÔ Õ ] ÒëÔVÝ = wAG]K Bc@ LK FKHACB@ ] ÒëÔ QE^ @??@A@ GHH@IEHK BGF @ ?GFFK J@LLK ?@AC@ JC F KHACBC y] ÒëÔ Õ éê_a Ý ë`W`b c &w@A Ê@?HG FGHC]G ] ÒëÔ ?C CIJCBK ?Q @??G BGI Id ç = gvE��@ACF @IHG y LG ?QKDCG J@LL@ F KHACBC BGI LK IGAF K eW e Õæ Mf gh ga 3 ÖW Òÿ Ô Ö Ì BGFQL@HG @ ]KL@ eWi e . eW e ei e= PK ?@AC@ Ì EIK ?@AC@ JC QGH@ID@ CI ë ÊCIJC cK EI AK��CG JCBGI]@A�@IDK u J@H@AF CIKLG @ J@AC]K H@AF CI@ K H@AF CI@h =» ¼j k ÆÇÂ lÆÀÃÊÇÂ ¿ ¾ÅÆÀÃÊÇÂw@A L@ G?BCLLKDCGIC aGADKH@ @ ?FGADKH@ F C ]@I�GIG CI F @IH@ JE@ H@?HC y CL PKIJKE ÍYÎ @ CL �KLLK]GHHC ÍVÎ =Ï Ðì ÐÏ| C?GL]C CL F GHG ÜÓ Õ á� ßÓ � Òà � �� Ò# ëÔÔ = > ?C?HGIG ?GLEDCGIC ?HKDCGIKAC@ã > ?C?HGIG FGHC Q@ACGJCBCã > ?C?H@äåæ çèéê Ó ÒëÔãÏÐì ÐÛ| C?GL]C

ÜÓ Õ áÓ á Ú� ßÓ � �å� ÒëÔ � �� ÒÚëÔ ÞBGI JKHG CICDCKL@ Òâ Þ âÔ u Q @A � Õ â @ � Õ �m =

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PK aEIDCGI@ n QE^ @??@A@ ?]CLEQQKHK CI ?@AC@ JC �GEAC@A yn ÒëÔ Õ _rst=r Iup rç ÞJG]@ =r Õ 3v w vÝ xëIyup rç n ÒëÔ xë & |CBGAJK Bc@ =yr Õ z=r u Q @A LK A@KLH� JC n u @ Ö=r Ö . {r Q@A 1 |Õ â gQ@A L eCQGH@?C q h =

�AG]K Q@A ?@AC@ EIK ?GLEDCGI@ QKAHCBGLKA@ JCÜÓ Õ áÓ á Ú� ßÓ � n ÒëÔ Þ

Q @A � Õ â @ � Õ �m u KL ]KACKA@ JC # = zc@ BGIJCDCGIC J@]C CFQGAA@ ?E =r @ # K�IBc§ CL F GHG ?CK LCF CHKHGãÏÐì Ð� 7zGI?CJ@AK L eG?BCLLKHGA@ KAFGICBG aGADKHG

ÜÓ Õ á# Ý Ó � �� Ò# ëÔ &w@A ÊKLC ]KLGAC JC # @?C?HGIG FGHC Q @ACGJCBCãwAG]K Bc@ HEHHC C F GHC ?GIG Q@ACGJCBC ?@ @ ?GLG ?@ p }p Ì AKDCGIKL@ @ JC]@A?G JK à=wAG]K Bc@ ?@ p }p Ì CAAKDCGIKL@ u CL F GHG I@LLG ?QKDCG J@LL@ aK?C AC@FQC@ J@I?KF @IH@ EIK A@�CGI@ = zc@ A@�CGI@ Ìã

gvE��@ACF @IHG y ]@JC L e@?@ABCDCG <=S =NhÏÐì Ð� 7zGI?CJ@AK CL F GHG ÜÓ Õ áÓ � , ~â . Ó . à�, ~ ßÓ Ù â� =P e@I@A�CK F @BBKI CBK ?C BGI?@A]KãzGI?CJ@AK CL JKHG CI CDCKL@ ÒÓÝ Þ ßÓÝ Ô Õ Òâ Þ âÔ = | C?GL]C @?Q LCBCHKF@IH@ CL FGHG �IG KL QACF G H@FQG JC ACHGAIG J@LQEIHG F KH@ACKL@ CI Ó Õ â BGI ]@LGBCH� QG?CHC]K =zGF@ K]]C@I@ CL F GHG �IG KL ?@BGIJG ACHGAIGã> JGQGãvCK ër CL H@FQG CI BEC CL QEIHG F KH@ACKL@ ACHGAIK CI Ó Õ â BGI ]@LG BCH� QG?CHC]K = �AG]K äåæ rèéê Òër á ëry3 Ô =gW@JC LK QKAH@ ?ELLG û ?BKQQKF @IHG KJ KIBGAKü ?EL �KLLK]GHHC ÍVÎ h» ¼� � ËÁÄÈÂ ¿¾¿ÀÁÂÃÂ Á� ÂÊ�¿ÏÐ� ÐÏ íî ïðññòî óôõî õðø îöö� òöðzGI?CJ@AK CL F GHG ÜÓ Õ Ó á Óý á � ßÓ gF GHG I@LLK JGQQCK REBK JC QGH@IDCKL@ BGI KHHACHG h = P@ QG?CDCGIC JC @ÊCLCRACG?GIG Ó 3 Õ àu Ó Õ áàu Óý Õ â =Kh wAG]K Bc@ Ó 3 � ?GIG QG?CDCGIC JC @ÊCLCRACG ?HKRCLC u @ Ó ý Ì CI?HKRCL@ =R h wAG]K Bc@ Q @A ÊKLEIÊ@ JKHG CI CDCKL@ LK HAKC@HHGACK BGI]@A�@ KJ EIK J@LL@ QG?CDCGIC JC

@ÊCLCRACG =Bh zcC@JCHC ?@ @?C?HGIG HAKC@HHGAC@ IGI ?HKDCGIKAC@ Bc@ H@IJGIG K Óý =Jh \@H@AF CIK ÊKLCHKHC]KF@IH@ LK A@�CGI@ J@LLG ?QKDCG J@LL@ aK?C Bc@ Ì KHHAKHHK JK Ó 3 @ Ê@LLKKHHAKHHK JK Ó gvE��@ACF @IHG y JC?@�IK I@LLG ?QKDCG J@LL@ aK?C L@ GARCH@ J@L ?C?H@F K ?@IDKKHHACHG @ C FGHC J@L ?C?H@F K BGI KHHACHG Bc@ H@IJGIG KLLK QG?CDCGI@ JC @ÊCLCRACG Ó =

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ÏÐ� ÐÛ �ú �� òöð�øð � ñî�ö÷ �zGI?CJ@AK EIK QELB@ ?E EIK BCABGIa@A@IDK u Bc@ KL H@FQG CICDCKL@ ?CK I@L QEIHG JC KI�GLG KL B@IHAG R Õ â = bJ G�IC?@BGIJG LK QELB@ a� EI ?KLHG JC EI KI�GLG Ø = vCK Rr u BGI â . Rr > Ú' u LK QG?CDCGI@ J@LLK QELB@ KL ?@BGIJG 1 =K h wAG]K Bc@ ?@ ×" Ì AKDCGIKL@ CL F GHG J@LLK QELB@ Ì Q @ACGJCBG u BCGÌ @?C?H@ 1 HKL@ Bc@ Rr Õ âRh wAG]K Bc@ ?@ ×" Ì CAAKDCGIKL@ LK QELB@ IGI HGAIK F KC CI R Õ â =Bh v@FQA@ I@L BK?G ×" �� u QAG]K Bc@ @?C?H@ EIK ?EBB@??CGI@ BA@?B@IH@ JC CIH@AC br HKL@ Bc@äåæ rèéê R`� Õ â =Jh v@FQA@ I@L BK?G ×" �� u QAG]K Bc@ Q@A G�IC R @?C?H@ EIK ?EBB@??CGI@ BA@?B@IH@ JC CIH@ACbr HKL@ Bc@ äåæ rèéê R`� Õ R gCI KLHA@ QKAGL@ CL FGHG Ì dJ@I?G d ?ELLK BCABGIa@A@IDK u G

KIBc@ L e# áLCF CH@ J@L F GHG Ì HEHHK LK BCABGIa@A@IDK =gW@JC bAIGLJ ÍNÎhÏÐ� Ðì �ú �� òöð�øð � ñî�ö÷ ��zGI?CJ@AK CL ?@�E@IH@ FGHG J@LL@ ]KACKR CLC Q @ACGJCBc@ R3 ÒëÔ @ R ÒëÔ g ?GIG KI�GLC HAK â @ Ú' u BCG Ì ÒR3 Þ R Ô J@?BAC]GIGEI HGAG RCJCF @I?CGIKL@ h y R3 ÒëÔ Õ # 3 ëR ÒëÔ Õ # ë &TL FGHG CI G�IEIK J@LL@ ]KACKRCLC Ru Ì Q@ACGJCBG JC Q @ACGJG o u Õ "p� = w AG]K Bc@ CL F GHG BGFQL@??C]G Ì Q@ACGJCBG ?@ @?GLG ?@ p }p Ì AKDCGIKL@ = wAG]K Bc@ I@L BK?G IGI Q@ACGJCBG CL F GHG Ì J@I?G ?E L HGAG = gW@JC bAIGLJ ÍNÎhÏÐ� Ð� 77�AKHHG JKLL ebAIGLJ JC >^ = \ CH = ÍNÎzGI?CJ@AK LK ?EBB@??CGI@ aGAFKHK JKLL@ QACF K BCaAK J@LL e@?QA@??CGI@ J@BCF KL@ JC Ú` y

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Bc@ CL QAGJGHHG J@LLK ]@LG BCH� Q@A LK QG?CDCGI@ J@LLK RKAAC@AK KL H@FQG ë3 Ì CJ@IHCBG KL QAGJGHHG KL H@FQG ëÝ = > ?H@IJCACBGA?C]KF @IH@ Q @A C ACHGAIC ?EBB@??C] C u @ J@H@AF CIK LK ?EBB@??CGI@ J@C H@FQC JC EAHG BGI LK QKA@H@ �??K === 887m�9k2047

�C?CBKF @IH@ � Öÿ ÒëÔ� ÒëÔ Ö cK L@ JCF@I?CGIC JC EIK @I@A�CK Q@A CL H@FQG gcK L@ JCF @I?CGIC J@LL eKDCGI@h = w@A �BG?HKIH@ u L eKDCGI@ Ì QAGQGADCGIKL@ KLL eKA@K AKBBc CE?K JKLL eGAR CHK I@LLG ?QKDCG J@LL@ aK?C gBc@ CI Ê@?HG BK?G Ì EIA@HHKI�GLG �h =� G]]CG Bc@ äåæ 9èÝ Öÿ ÒëÔ� ÒëÔ Ö Õ ÿÝ �Ý u CIaKHHC Q@A : Õ â LK RKAAC@AK Ì a@AF K = �E@?HG LCF CH@ IGI Ì EICaGAF @ CI ë =\KLL e@?@ABCDCG QEGC IGHKA@ Bc@ KJ EI H@FQG J@LL eGAJCI@ JC 39 LK ]KACKDCGI@ JC ÖÑ ÒëÔ� ÒëÔ Ö AC?Q @HHG K ÿÝ �Ý Ì JC GAJCI@ : =zCGÌ L eKDCGI@ Ì QAKHCBKF @IH@ CI]KACKIH@ u AC?Q @HHG K ]KACKDCGIC L@IH@ gKJCKRKHCBc@h J@C QKAKF @HAC � ?CBC Bc@ �G]@A{IKIG CL F GHG =

w@A F K��CGAC J@HHK�LC ]@JC L eb AIGLJ Í<Î @ CL PKIJKE ÍYÎ =Ï Ð� Ð íî óôõî Gî� òîó òú÷ � òG ò�òöîöîgbEHGA@ > = zK�LCGHChP e@?@ABCDCG QA@B@J@IH@ cK EIK CIH@AQA@HKDCGI@ H@AFGJCIKF CBK =� aKBCL@ CJ@IHC�BKA@ L e@I@A�CK CIH@AIK y ] Õ 3 ÿ = � KIBc@ aKBCL@ CJ@IHC�BKA@ CL d]GLEF @ ey ?KA� Ñ Õ � = PK QA@??CGI@Ì �?CBKF @IH@ LK aGADK @?@ABCHKHK ?E LL eEICH� JC ?EQ@A�BC@ Bc@ AKBBcCEJ@ CL F @DDG = \ eKLHAK QKAH@ CI Ê@?HG BK?G LK?EQ@A�BC@ Ì EI QEIHG gÓ Õ â GQQEA@ Ó Õ � h = v@ EI QEIHG F KH@ACKL@ ?ERC?B@ CI EI B@AHG H@FQG � ë EIK ]KACKDCGI@JC CFQEL?G � Ò� ÿ Ô u LK aGADK Bc@ Ì ?HKHK @?@ABCHKHK ?E JC @??G Ì � B� hC�ç = w@A EI EAHG I Ó Õ â LK ]KACKDCGI@ JC CFQEL?GÌ Ú� Öÿ Ö= �@L IG?HAG BK?G IGI B eÌ ]KACKDCGI@ JC CFQEL?G ?@ IGI ÊKIJG LK F K??K HGBBK Ó Õ â = w@A JKA@ ?@I?GKLLK QA@??CGI@ u ?C QE^ Q@I?KA@ JC BGI?CJ@AKA@ L eCF QEL?G ?BKFRCKHG BGI LK QKA@H@ Q @A EI H@FQG ?E� BC@IH@F @IH@ LEI�GK�IBc§ K]]@I�KIG FGLHC EAHC u F K ?E� BC@IH@F @IH@ Q CBBGLG K�IBc§ LK ]KACKDCGI@ JG]EHK KL FGHG J@LLK RKAAC@AK FGRCL@IGI ?CK ?C�I C�BKHC]K gK??EIDCGI@ QG??CRCL@ ?@ : Ì FGLHG QCBBGLGh = TI KLHA@ QKAGL@ y� Õ Ú� Öÿ Ö1�r ÞJG]@ 1 Ì CL IEF @AG JC ]GLH@ Bc@ LK F K??K EAHK LK QKA@H@ CI Ó Õ â u @ �r Ì CL H@FQG I@B@??KACG Q @A aKA@ 1 EAHC =>]CJ@IH@F @IH@ �r � 1 �gh g gÚ� Ì LK JC?HKIDK JK Q@ABGAA@A@ Q@A HGAIKA@ CI Ó Õ â @ ÿ Ì LK ]@LGBCH�h =TI J@�ICHC]K u L eCIH@AQA@HKDCGI@ H@AFGJCIKF CBK J@L F GHG JC EIK QKAHCB@LLK HAK JE@ QKA@HC Q @Aa@HHKF @IH@ AC�CJ@ KJC?HKIDK � J� y ] Õ 3 � ÿ Ñ Õ �� Õ �h� &

wAG]K Bc@ ?@ � ]KACK FGLHG L@IHKF @IH@ u o x� Õ x] � � xÑ Õ â ÞBCG Ì LK HAK?aGAFKDCGI@ Ì KJCKRKHCBK = 887m�9k2047

�KA@ LK H@AFGJCIKF CBK JC EIK ?GLK QKAHCB@LLK Ì KRRK?HKIDK QAC]G JC ?@I?G = vC QG??GIG BGI?CJ@AKA@ u QC� BGA{A@HHKF@IH@ u F GLHC??CF @ QKAHCB@LL@ HAK L@ QKA@HC u Bc@ IGI EAHKIG HAK JC LGAG = �E@?HK ?CHEKDCGI@ QE^ aKA Q@I?KA@ KJEI �K? Q@Aa@HHG u Q @A BEC LK H@AFGJCIKF CBK cK ?@I?G u @ LK QA@??CGI@ Ì BCI@F KHCBKF @IH@ J@�ICHK KHHAK]@A?G L eCF QEL?G?BKFRCKHG BGI L@ QKA@HC = �@I@H@ QA@?@IH@ u Q@A^ u Bc@ EI CI ?C@F @ JC QKAHCB@LL@ Bc@ IGI EAHKIG HAK LGAG �x� ?GIG EI�K? Q @Aa@HHG = TIaKHHC F KIBK CL F @BBKIC?F G JC H@AF KLCDDKDCGI@ HCQCBG u KJ @?@FQCG u J@LL e@ÊKDCGI@ JC �GLHDF KII =ÏÐ� Ð� � úö� ò ÷�÷Fñò ïò òøGî� òîøöò îïòîóîöòõò�@GA@F K J@LL eCI]KACKIDK KJCKRKHCBK =

vEQQGIC JC K]@A@ EI FGHG EICJCF@I?CGIKL@ CI BE C L e@I@A�CK HGHKL@ u G LHA@ Bc@ JCQ @IJ@A@ JKLLK QG?CDCGI@ @ JKLLK]@LG BCH� u JCQ@IJK JK EI QKAKF @HAG � u BCGÌ þ Õ þ ÒÓ Þ ßÓ Þ �Ô = zGF @ @?@FQCG QEGC Q @I?KA@ K þ Õ 3 � ßÓ � Ñ ÒÓ Ô u JG]@LK F K??K ?H@??K Ì CL QKAKF@HAG � u GQQEA@ þ Õ 3 � � ß� á �� u JG]@ � cK L@ JCF @I?CGIC JC EIK LEI�c@DDK =

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Ö� Òþ ÒëÔÔ á � Òþ ÒâÔÔ Ö . =: ÞQ @A â . ë . 39 =TI KLHA@ QKAGL@ u Q@A ]KACKA@ L eKDCGI@ JC : J@]G K?Q @HHKA@ EI H@FQG JC GAJCI@ 39 =TI Ê@?HG @IEIBCKHG F KIBKIG J@LL@ CQGH@?C CFQGAHKIHC = w@A L e@IEIBCKHG QA@BC?G @ Q @A LK JCFG?HAKDCGI@ ]@JC u HAK �LCKLHAC u L eb AIGLJ Í<Î

zGI?CJ@AK EI Q@IJGLG LK BEC F K??K JCF CIEC?B@ L@IHKF@IH@ BGI CL H@FQG = \ C ÊKIHG ]KACK L eKFQC@DDK J@LL@G?BCLLKDCGI C ?@ LK F K??K ?C JCF @DDKãfIK F K??K Ì KQQ@?K KJ EI �LG @J G?BCLLK = v@ JCF @DDG L@IHKF @IH@ LK LEI�c@DDK J@L � LG u BGF @ BKFRCK L eKFQC@DDKJ@LL@ G?BCLLKDCGICãzGI?CJ@AK CL F GHG EICJCF @I?CGIKL@ JC @I@A�CK HGHKL@

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?HKRCLC¤ ?@ ÒÓÝ Þ ßÓÝ Ô Õ ÒÚ Þ ÿ Ô u Q@A ÊKLC ]KLGAC JC ÿ CL F GHG H@IJ@ K �% ã > Q@A ÊKLC H@IJ@ Ká% ã TI HKL BK?G BKLBGLKA@ CI ÊKIHG H@FQG CL QEIHG F KH@ACKL@ AK��CEI�@ á% =

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JC @ÊCLCRACG ?HKR CLC¤ Q@A Ø Õ àÚ J@H@AF CIKA@ LK aA@Ê@IDK J@LL@ QCBBGL@ G?BCLLKDCGI C CIHGAIG KLL@ QG?CDCGI C

JC @ÊCLCRACG ?HKR CLC¤ Q@A Ø Õ à @ Q@A CL JKHG CICDCKL@ ÒáàÞ ÿ Ô u J@H@AF CIKA@ C ]KLGAC JC ÿ Q @A ÊKLC CL F GHGQK??K Q@A Ó Õ à= \KA@ L e@?QA@??CGI@ J@L H@FQG CFQC@�KHG u CI aEIDCGI@ JC ÿ =¤ BGI C JKHC J@L BK?G QA@B@J@IH@ u BGI Bc@ ]@LG BCH� CL QEIHG F KH@ACKL@ QK??K Q @A Ó Õ âã¤ g[h J@H@AF CIKA@ äåæ §èéê o Òþ Ô u JG]@ o Òþ Ô Ì CL Q@ACGJG J@L FGHG JC @I@A�CK þ =¤ g[h ?@FQA@ Q@A Ø Õ àu JC?BEH@A@ C ]KLGAC JC o Q@A C ÊKLC @?C?H@ EI FGHG Q@ACGJCBG JCQ @ACGJG o =

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à � Ó = L e@I@A�CK QGH@IDCKL@ JC EI FGHG EICJCF@I?CGIKL@ = \ C?@�IKA@ ÊKLCHKHC]KF@IH@ L@GAR CH@ I@LLG ?QKDCG J@LL@ aK?C u KL ]KACKA@ JC Ø � � = TI QKAHCBGLKA@ u¤ J@H@AF CIKA@ L@ QG?CDCGIC JC @Ê CLCRACG @ JC?BEH@AI@ LK ?HKRCLCH�¤ J@H@AF CIKA@ LK aA@Ê@IDK J@LL@ QCBBGL@ G?BCLLKDCGIC CIHGAIG KLL@ QG?CDCGIC JC @Ê CLCRACG?HKRCLC¤ ?@ ÒáàÞ âÔ Ì CL JKHG CICDCKL@ u Q @A ÊKLC ]KLGAC JC Ø CL FGHG Ì Q@ACGJCBGã¤ ?CK Òâ Þ ÿ Ô CL JKHG CICDCKL@ � Q @A ÊKLC ]KLGAC JC ÿ CL FGHG Ì CLLCF CHKHGã¤ g[h I@L BK?G J@C F GHC CLLCF CHKHC J@L QEIHG QA@B@J@IH@ u J@H@AF CIKA@ äåæ çèéê ßÓ ÒëÔ

Ó ÒëÔ uKL ]KACKA@ JC ÿ =ÏÐ� Ð0vCK Ñ ÒÓ Ô Õ Ó � Ø

à � Ó = L e@I@A�CK QGH@IDCKL@ JC EI FGHG EICJCF @I?CGIKL@ = \ C?@�IKA@ ÊKLCHKHC]KF@IH@ L@ GARCH@ I@LLG?QKDCG J@LL@ aK?C u KL ]KACKA@ JC Ø � � = TI QKAHCBGLKA@ u¤ J@H@AF CIKA@ L@ QG?CDCGIC JC @Ê CLCRACG @ JC?BEH@AI@ LK ?HKRCLCH�¤ J@H@AF CIKA@ LK aA@Ê@IDK J@LL@ QCBBGL@ G?BCLLKDCGIC CIHGAIG KLL@ QG?CDCGIC JC @Ê CLCRACG?HKRCLC¨ ©´º¶ª +´)+ *-« º+ -¸-¬,+ª + ¸¶+ ·´µ+ ¶)+*+· -)¸+´)¹º+P ¼» k ÆÇÂ ÄÈÂÉ ÂÅ ¿È¾ÂÆÈÊËÂ

Û ÐÏÐÏP e@I@A�CK QGH@IDCKL@ Ì EIK aEIDCGI@ ?CFF@HACBK AC?Q @HHG KLL eK??@ J@LL@ = \EIÊ@o Òþ Ô Õ � ® �¯ B§ C

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x5 à á ×TL Q@ACGJG IGI JCQ@IJ@ JKLL e@I@A�CK ?GLG ?@ Ø Õ Ú gQGH@IDCKL@ KAFGICBGh = v@ Ø � Ú äåæ §èÝ o Òþ Ô Õ �% =Û ÐÏÐÛ� EI e @ÊKDCGI@ JCH@A@IDCKL@ LCI@KA@ = �AG]KIJG �LC D@AC J@L QGLCIGF CG BKAKHH@AC?HCBG � Õ àu GHHC@IC Bc@ LK ?GLEDCGI@Ì Ó ÒëÔ Õ =3Iyç � =Iç u BGI ßÓ Õ á=3Iyç � =Iç = TFQGI@IJG CL JKHG CICDCKL@ yà Õ =3 � =áà Õ á=3 � = ÞJEIÊ@ =3 Õ àu = Õ â @ CL F GHG Ì Ó ÒëÔ Õ Iyç = TL H@FQG Q@A AK��CEI�@A@ â Ì CI�ICHG = P@ HAKC@HHGAC@ BGI Ó ÒëÔ $ â?GIG HEHH@ @ ?GL@ Ê@LL@ BGI = Õ â � @??@ ?GIG KIBc@ HEHH@ @ ?GL@ L@ HAKC@HHGAC@ BGI ßÓ ÒëÔ $ â = \EIÊ@ C JKHC CI CDCKLCACBcC@?HC ?GIG ÒÓÝ Þ ßÓÝ Ô Õ Ò= Þ á=Ô u BGI = � � =Û ÐÏÐì íî ïðññòî óôõî ïò ñðö÷øùòîú÷TL ]KLGA@ F CICF G J@LL e@I@A�CK Ì á 3� = bJ @??G BGAAC?QGIJGIG JE@ QG?CDCGIC JC @ÊCLCRACG Ó Õ ² à= vGIG ?HKRCLC Q @ABcÌ?GIG QEIHC JC F CICF G J@LL e@I@A�CK QGH@IDCKL@ = w@A á 3� > þ > â @?C?HGIG JE@ GARCH@ Q@ACGJCBc@ = w@A þ Õ â u cKC HA@GAR CH@ u LK ?GLEDCGI@ JC @ÊCLCRACG Ó Õ â u Bc@ Ì CI?HKRCL@ @@?@IJG EI FK???CF G LG BKL@ J@LL e@I@A�CK QGH@IDCKL@ u @ JE@GAR CH@ K F @HK K?CIHGHCBK = w@A þ � â cKC EI eGARCHK Q@ACGJCBK =

\KL ACHAKHHG JC aK?@ ?C J@JEB@ aKBCLF @IH@ Bc@ LK HAKC@HHGACK JC JKHG CICDCKL@ ÒÓÝ Þ ßÓÝ Ô Õ ÒáàÞ ÿ Ô QK??K Q @A Ó Õ à ?@ @?GLG ?@ L e@I@A�CK HGHKL@ Ì F K��CGA@ JC â u Bc@ Ì CL ]KLGA@ J@L F K??CFG LG BKL@ JC Ñ = \EIÊ@ 3 ÿ á 3� � â u BCG Ì Öÿ Ö � 3³ =TL ]KLGA@ JC Ñ CI Ó Õ áà @ Ó Õ à Ì CJ@IHCBG � JEIÊ@ Q@A LK BGI?@A]KDCGI@ J@LL e@I@A�CK u KIBc@ CL ]KLGA@ JC Ö ßÓ Ì CJ@IHCBG =�ECIJC u KL QACF G QK??K��CG Q@A Ó Õ àu LK ]@LG BCH� Ì ßÓ Õ Öÿ Ö=

�@L ACHAKHHG J@LL eGARCHK I@LLG ?QKDCG J@LL@ aK?C u LK BEA]K JC @I@A�CK þ Õ â Ì J@?BACHHK JK ßÓ Õ ²´Ú Ò � á �� Ô = PKHKI�@IH@ J@LL eKI�GLG ACBc C@?HG Ìäåæ Ó $ âé xxÓ µÚ ÒÓ Ú á Ó�� Ô Õ à &

P eKI�GLG Ì "� =Û ÐÏÐ� íî ïðññòî óôõî ñî�ö÷ ��TL �AK�BG J@LL e@I@A�CK QGH@IDCKL@ Ì ÊKLCHKHC]KF @IH@ JC]@A?G I@C BK?C Ø > â @ Ø Ù â =w@A Ø > â u CL F GHG Ì ÊKLCHKHC]KF @IH@ E�EKL@ KL BK?G Ø Õ áàu J@?BACHHG I@LL e@?@ABCDCG QA@B@J@IH@ =w@A Ø Ù â u L e@I@A�CK QGH@IDCKL@ Ì ?HA@HHKF @IH@ BGI]@??K � L eEICBK QG?CDCGI@ JC @ÊCLCRACG Ì Ó Õ â u @J Ì ?HKRCL@ = TIQKAHCBGLKA@ Q@A Ø � â @?C?H@ LK aA@Ê@IDK J@LL@ QCBBGL@ G?BCLLKDCGIC u Q@A Ø Õ â IGI @?C?H@ g]@JC @?@ABCDCG <=< =<h =�@LLK ��EAK u CI K?BC??K BÌ C ]KLGA@ JC Ø u L@ BEA]@ AG??@ @ RLE ?GIG L@ K?BC??@ J@LL@ QG?CDCGI C JC @ÊCLCRACG u CI AG??G?@ L e@ÊCLCRACG Ì CI ?HKRCL@ u CI R LE ?@ Ì ?HKRCL@ = PK QG?DCGI@ Ó Õ â Ì ?HKRCL@ Q@A Ø Ù â u CI ?HKRCL@ Q@A Ø > â = P@ KLHA@QG?CDCGIC JC @ÊCLCRACG @?C?HGIG ?GLG Q @A Ø > â @ ?GIG ?HKRCLC =Û ÐÏÐ�w@A Ø � â L e@I@A�CK QGH@IDCKL@ Ì FGIGHGIK ?HA@HHKF @IH@ BA@?B@IH@ = �GI @?C?HGIG QG?CDCGIC JC @ÊCLCRACG u L@ GARCH@?GIG HEHH@ CLLCF CHKH@ u w@A HEHHC C JKHC CI CDCKLC Ó ÒëÔ H@IJ@ K á% = TL H@FQG Bc@ CFQC@�K LK QKAHCB@LLK Q @A AK��CEI�@A@á% Ì ª4210 u CIaKHHC w �yê ¶�· °Ú Òþ á Óý á ØÓÔ > % =

w@A Ø Õ â BÌ LK QG?CDCGI@ JC @ÊCLCRACG Ó Õ â = �EHH@ L@ KLHA@ GARCH@ ?GIG CLLCF CHKH@ BGF @ I@L BK?G QA@B@J@IH@ = PKQG?CDCGI@ JC @ÊCLCRACG Ì CI?HKRCL@ u @??@IJG EI QEIHG JC ¸@??G =

w@A Ø > â BC ?GIG JE@ QG?CDCGIC JC @ÊCLCRACG y Ó¹ Õ ²°á ×ý = PK QG?CGDCGI@ Óy Ì CI?HKRCL@ gF K??CFG LG BKL@ JCÑ h u LK QG?CDCGI@ Óé Ì ?HKR CL@ gF CICIG LG BKL@ JC Ñ h = TL ]KLGA@ JC Ñ I@C QEIHC JC @ÊCLCRACG Ì º zþ Õ º ý Ø°á ×ý = w@A

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þ > á zþ BÌ ?GLG EI e GARCHK CLLCF CHKHK = w@A þ Õ á zþ EI eGARCHK CLLCF CHK @ Ó Õ Óé @ÊCLCRACG ?HKRCL@ = w@A á zþ > þ > zþEI eGAR CHK CLLCF CHKHK @ EIK Q@ACGJCBK = w@A þ Õ zþ LK QG?CDCGI@ JC @ÊCLCRACG CI?HKR CL@ Ó Õ Óy u EI eGARCHK LCF CHKHK KF @HK K?CIHGHCBK I@LLK A@�CGI@ Ó � Óy u EI eGARCHK CLLCF CHKHK K F @HK K?CIHGHCBK I@L QK??KHG I@LLK A@�CGI@ Ó > Óy u ßÓ > â uEI eGAR CHK CLLCF CHKHK K F @HK K?CIHGHCBK I@L aEHEAG I@LLK A@�CGI@ Ó > Óy u ßÓ � â =

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Û ÐÏÐ �î� òîøö÷ ï÷úúî ïðññòî óôõîP e@I@A�CK QGH@IDCKL@ ]K K �% ?@ ÖÓ Ö $ �% = \EIÊ@ HEHH@ L@ GARCH@ ?GIG LCF CHKH@ = bIKLCDDG C BK?C u KL ]KACKA@ JC Ø =

PK J@AC]KHK Ì Ó ÒÓ� á ÚØÓ � Ø = \EIÊ@ Ó Õ ÓÝ Õ â Ì ?GLEDCGI@ JC @Ê CLCRACG Q@A HEHHC C ]KLGAC JC Ø = P@KLHA@ @]@IHEKLC QG?CDCGI C JC @ÊCLCRACG ]@AC�BKIG Ó Õ Ø ² °Ø ÒØ á àÔ = zGIJCDCGI@ I@B@??KACK K� IBc§ @?C?HKIG Ì Bc@Ø ÒØ á àÔ Ù â BCGÌ Ø Ù à G Ø . â = w@A Ø � àu 5Ø á Ø > Ø u JEIÊ@ @?C?HGIG ÊKHHAG QG?CDCGIC JC @Ê CLCRACG y

Ó 3 Õ á°Ø � 5Ø á ØÓ Õ á°Ø á 5Ø á ØÓý Õ �°Ø á 5Ø á ØÓ� Õ �°Ø � 5Ø á Ø &pD

w@A Ø > â u Ø � 5Ø á Ø � â = \EIÊ@ @?C?HGIG ?GLG L@ QG?CDCGIC Ó 3 @ Ó � =TI ?CIH@?C yØ > â y JE@ QG?CDCGIC JC @ÊCLCRACG ?HKRCLC Ó 3 @ Ó� u @J EIK CI?HKRCL@ ÓÝ �â . Ø . ày EIK ?GLK QG?CDCGI@ JC @ÊCLCRACG ÓÝ ?HKRCL@ =Ø � ày HA@ QG?CDCGIC JC @ÊCLCRACG ?HKRCLC Ó 3 u Ó � @ ÓÝ u @ JE@ CI?HKRCLC Ó @ Óý =

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Û ÐÏÐ� �ú ñ ÷øïðúð �ô ôø ñòîøð �ôðöîøö÷fIK QACF CHC]K CI � J@LLK aGADK K??@�IKHK Ì y Ñ Ò� Ô Õ á�� ! �� =

Ñ » Ò� Ô Õ �å� � Ò�� á �� Ô Õ �� Ò� á �� Ô &>]CJ@IH@F @IH@ u L e@?C?H@IDK JC KLBEI@ QG?CDCGIC JC @ÊCLCRACG JCQ @IJ@ JKL aKHHG Bc@ � ?CK F CIGA@ G FK��CGA@ JC à= TLQKAKF @HAG � Ì KJCF @I?CGIKL@ = w@A � � I à BC ?GIG ?GLG LK QG?CDCGI@ JC @ÊCLCRACG ?HKRCL@ � Õ â @ Ê@LLK CI?HKRCL@ � Õ ' =w@A � > àu Bc@ BGAAC?QGI@ KL BK?G JC J@RGL@ �AK]CH� u G JC �AKIJ@ ]@LG BCH� KI�GLKA@ J@L QCKIG u BGFQKCGIG KLHA@ JE@QG?CDCGIC JC @ÊCLCRACG y �¹ Õ ² MN�� = > ??@ ?GIG ?HKR CLC u F @IHA@ � Õ â Ì CI?HKRCL@ u BGF @ ?C J@JEB@ JC?@�IKIJG CL�AK�BG JC Ñ =

TL JKHG CICDCKL@ Ò�Ý Þ ß�Ý Ô Õ Òá " Þ â Ô cK @I@A�CK HGHKL@ â = T LC]@LLC BACHCBC J@LL e@I@A�CK ?GIG yQ@A � Ù ày þ 3 Õ á�� ?� á 3 @ gLC]@LLG JC F CICF G u � Õ âh @ þ Õ �� ?� � 3 @ gLC]@LLG JC F K??CF G u � Õ ' h =Q@A � > ày þ 3 JC]@IHK EI LC]@LLG JC F K??CF G LGBKL@ u CL LC]@LLG JC F CI CF G Ì þý Õ á�� ¼ u Bc@ BGAAC?QGIJ@ KLL@JE@ ?GLEDCGIC ?HKDCGIKAC@ �¹ =\EI^½@ þ Õ â Ì EI LC]@LLG BACHCBG ?GLG ?@ BGCIBCJ@ BGI þ 3 u CL Bc@ KBBKJ@ ?@ � |Õ 3 � CI HKL BK?G u @??@IJG â > þ uL eGARCHK Ì Q@ACGJCBK = TL Q @ACGJG Ì y o Õ � ® ¾Ý x�´ � ÒáÑ Ò� ÔÔ Þ?@ � � 3 u o Õ Ú ® ¿ÀÁÁÂJ B¼Cy ¾ x�´ � ÒáÑ Ò� ÔÔ Þ?@ � > 3 =PK QG?CDCGI@ � Õ " Ì AK��CEIHK ?GLG ?@ � � 3 � CL H@FQGÌ yë Õ ® ¾y ¾ x�´ � ÒáÑ Ò� ÔÔ &p_

TL ]KLGA@ JC ß� Ì JKHG JKLLK BGI?@A]KDCGI@ J@LL e@I@A�CK = > ??@IJG Ñ Ò " Ô Õ Ñ Òá " Ô u ß� J@]@ BGCIBCJ@A@ BGI CL ]KLGA@CICDCKL@ u BCG Ì ß� Õ â =v@FQA@ Q @A LK BGI?@A]KDCGI@ J@LL e@I@A�CK u ß� Õ ²´ � ÒáÑ Ò� ÔÔ u JEIÊ@ ÊKIJG � Õ â u ß� Õ ²´á � þ 3 Õ²�5 Ú� á à=TL ]KLGA@ J@L F K??CF G ß� Ì AK��CEIHG ÊKIJG u LEI�G L eGARCHK u Ñ Ò� Ô Ì F CICF G = v@ � Ù à CL F CICFG Ì AK��CEIHG CI � Õ â �?@ � > àu CL F CI CF G Ì AK��CEIHG CI � Õ � y =TL JKHG CICDCKL@ Ò�Ý Þ ß�Ý Ô Õ Òá " Þ Ã� I� 6Ô cK @I@A�CK HGHKL@ 3 ��# � Q @A # �AKIJ@ u L eGAR CHK Ì Q @ACGJCBK Q@ABc§ LK]KACKRCL@ Ì EI KI�GLG = TL F GHG Ì LK AGHKDCGI@ BGFQL@HK = TL Q @ACGJG Ìo Õ ® "y" x�´ � Ò 3 �� # á Ñ Ò� ÔÔ ÞBc@ Q@A # �AKIJ@ u KL QACF G GAJCI@ CI 3p u ]KL@ "p =� @LL@ QG?CDCGIC JC @ÊCLCRACG � Õ â @ � Õ ' u L eKBB@L@AKDCGI@ Ì IELLK Ü� Õ â u JEIÊ@ Q@A # �AKIJ@ LK ]K BGF @ # CI � Õ â@ á# CI � Õ ' =w@A � Õ " u CL BG?@IG Ì IELLG u @ JKLL e@ÊKDCGI@ J@L FGHG ACBK]G �� Ü� Õ á�� u BCG Ì Ü� Õ á �� = � @ ?@�E@ Bc@ LKBGFQGI@IH@ ]@AHCBKL@ J@LLK A@KDCGI@ Ì IELLK =Û ÐÏÐ(vHKIJKAJ =Û ÐÏÐ0vHKIJKAJ =Û ÐÏÐÏ2vHKIJKAJ =Û ÐÏÐÏÏP@ GARCH@ ?GIG HEHH@ LCF CHKH@ Q @A 6 � â = P eGAC�CI@ Ì ?HKRCL@ ?@ @ ?GLG ?@ 6 � 3 =Û ÐÏÐÏÛTL F K??CF G J@LL e@I@A�CK QGH@IDCKL@ Ì áà= TL JKHG CICDCKL@ cK @I@A�CK á 3 = \EIÊ@ CL F GHG Ì CLLCF CHKHG u @ ßÓ � â Q@AHEHHC C H@FQC QG?CHC]C = TL H@FQG Q@A AK��CEI�@A@ �% Ì JKHG JKo Õ ® éê

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vG?HCHE@IJG @ AKBBG�LC@IJG y 8ÿ Õ à á ® êÝ x� à´Ú Ò5 à � � á 3 Ô à� � �5 à � � � à Þ

Bc@ Ì �ICHG = w@A LK J@H@AF CIKDCGI@ JC 8Ó u JG]A^ BKLBGLKA@ äåæ çèéê ÒÓ ÒëÔ á 8ÿ ë á 3 ë Ô = vC QE^ QAGB@J@A@ BGF@ ?GQAKKIBc@ ?@ Ì Q C� BGFQLCBKHG =Û ÐÏÐÏìTL F GHG Ì Q @ACGJCBG Q @A HEHHC C JKHC CI CDCKLC BGI @I@A�CK I@�KHC]K u IGI Ì Q@ACGJCBG u @J Ì CLLCF CHKHG u Q @A C JKHC CI CDCKLCBGI @I@A�CK F K��CGA@ G E�EKL@ K â = z eÌ EIK ?GLK ?GLEDCGI@ ?HKDCGIKACK u CI Ó Õ à=

w@A ÓÝ Õ 3 @ ßÓÝ Õ à L e@I@A�CK ]KL@ 3 = Bc@ Ì QG?CHC]K = \EIÊ@ Ó $ % = TL ]KLGA@ K?CIHGHCBG J@LLK ]@LG BCH� Ì´Ú Ò 3 Ô Õ à=w@A ÓÝ Õ 3 @ ßÓÝ Õ áàu CL QEIHG ?C FEG]@ ]@A?G ?CI C?HAK JCF CIE@IJG CL ]KLGA@ K??GLEHG J@LLK ?EK ]@LGBCH� =

vEBB@??C]KF @IH@ CI]@AH@ LK ]@LG BCH� = \EIÊ@ CL F CICFG J@LLK ]@LG BCH� Ì áàu Ê@LLK J@L JKHG CICDCKL@ = TL F K??CF G ÌAK��CEIHG CI Ó Õ à gBc@ Ì CL F CICF G J@LL e@I@A�CK QGH@IDCKL@ h u @ ]KL@ ´Ú Ò 3 � à á 3 Ô Õ 5 Ú =Û ÐÏÐÏ��GI JC?QGI CRCL@Û ÐÏÐÏ��GI JC?QGI CRCL@Û ÐÏÐÏ �GI JC?QGI CRCL@Û ÐÏÐÏ��GI JC?QGI CRCL@Û ÐÏÐÏ(�GI JC?QGI CRCL@Û ÐÏÐÏ0�GI JC?QGI CRCL@Û ÐÏÐÛ2�GI JC?QGI CRCL@Û ÐÏÐÛ Ï�GI JC?QGI CRCL@Û ÐÏÐÛÛ�GI JC?QGI CRCL@

p�

Û ÐÏÐÛìKh �G u ?GLG ?@ CL Q GH@IDCKL@ Ì KAFGICBG =

R h TL LCF CH@ Ì �% u @ CL F GHG �x� Ì EICaGAF @F@IH@ KBB@L@AKHG =Bh IELLKJh vGLG I@L BK?G S L eGAC� CI@ Ì ?HKR CL@ = TL Q @IJGLG BKQG]GLHG LCI@KACDDKHG BGI KHHACHG Ì CL BK?G N = TL BK?G O Ì EI

G?BCLLKHGA@ KAFGICBG BGI KHHACHG K H@FQG CI]@AHCHG =@h <u N = T BK?C U @ <Z QG??GIG BGI?CJ@AKA?C BGF@ FGHC EICJCF @I?CGIKL@ ]C?HC CI EI ?C?H@FK JC ACa@ACF @IHG FGRCL@ u

JC ]@LG BCH� BG?HKIH@ = P e@I@A�CK I@L ?C?H@F K ?GLCJKL@ ?C BGI?@A]K =P ¼P ½QÄÊÃÂÆÈÂ ËÂÈ¿ÊÀÂP ¼j k ÆÇÂ lÆÀÃÊÇÂ ¿ ¾ÅÆÀÃÊÇÂP ¼� � ËÁÄÈÂ ¿¾¿ÀÁÂÃÂ Á� ÂÊ�¿Û Ð� ÐÏ íî ïðññòî óôõî õðø îöö� òöðzGI?CJ@AG I@L ?@�ECHG ?GLG CL BK?G JC � QCBBGLG = w@A � �AKIJC L@ KH@AF KDCGIC A@?HKIG ]@A@ u F K C �AK�BC BKFRCKIGgBGF@ BKFRCKIGãh =

9� P e@I@A�CK Ì EI CIH@�AKL@ QACF G J@L F GHG Q@A CL ?C?H@F K ?@IDK KHHACHG = TI QA@?@IDK JC KHHACHG xxë þ Õ á� ßÓ =�ECIJC KIBc@ CI QA@?@IDK JC KHHACHG þ Ì EIK aEIDCGI@ JC P½KQEIG] Q@A C QEIHC JC F CICF G J@LL e@I@A�CK QGH@IDCKL@ Ó 3@ Ó = \EIÊ@ ?@ID eKLHAG Ê@?H@ JE@ QG?CDCGIC ?GIG ?HKRCLC = TL H@GA@F K JC P½KQEIG] u QEA J@BA@?B@IJG L e@I@A�CK u IGIQ@AF @HH@ JC BGIBLEJ@A@ CFF@JCKHKF @IH@ Bc@ Ó 3 @ Ó ?GIG K?CIHGHCBKF @IH@ ?HKR CLC = TIaKHHC xxë þ Ì â IGI ?GLG I@LLKQG?CDCGI@ JC @ÊCLCRACG FK KIBc@ CI HEHHC C QEIHC J@LLG ?QKDCG J@LL@ aK?C CI BE C ßÓ Õ â = wAG B@JG JEIÊ@ BGI L eKIKLC?CJ@L LCI@KACDDKHG É = | C?BAC]G L e@ÊKDCGI@ J@L F GHG BGF @ EI ?C?H@F K gIGI LCI@KA@ h J@L QACF G GAJCI@ =xxë XÓÿY Õ X ÿ

Ó á Óý á �ÿY &PG �KBGR CKIG J@L BKFQG Ì X â à

à á OÓ á�Y &�@C QEIHC Ó Õ ² à ]KL@ X â à

áÚ á�Y ÞBc@ cK @IHAKFRC �LC KEHG]KLGAC BGI QKAH@ A@KL@ I@�KHC]K = �@L QEIHG â LK F KHACB@ ÌXâ à

à á�Y ÞBc@ cK HAKBBCK I@�KHC]K @ J@H@AF CIKIH@ QG?CHC]G u ÊCIJC cK JE@ KEHG]KLGAC A@KLC JC ?@�IG GQQG?HG = TI BGIBLE?CGI@ L@QG?CDCGIC Ó 3 � ?GIG K?CIHGHCBKF @IH@ ?HKRCLC u LK QG?CDCGI@ Ó Õ â Ì CI?HKR CL@ =

® � P e@I@A�CK F @BBKICBK IGI Ì BGI?@A]KHK @ J@BA@?B@ I@L H@FQG = \EIÊ@ @?C?H@ zþ Õ äåæ çèéê þ ÒëÔ gþ ÒëÔ ÌLCF CHKHK JKL RK??G JK á 3� h = \EIÊ@ CL F GHG u I@L LCF CH@ ë Bc@ ]K K CI�ICHG u H@IJ@ KJ K]@A@ @I@A�CK BG?HKIH@ = P eCJ@KCIHECHC]K Ì Bc@ CL F GHG J@]@ H@IJ@A@ KJ EIK ?GLEDCGI@ JC @ÊCLCRACG u ?@ IG L e@I@A�CK BGIHCIE@A@RR@ K J@BA@?B@A@ CI]@B@Bc@ H@IJ@A@ KL ]KLGA@ zþ =Éz eÌ BGFEIÊ@ EI H@GA@F K Bc@ K??CBEAK L eK?CIHGHCBK ?HKRCLCH� KIBc@ I@L BK?G CI BECLK J@AC]KHK J@LLK aEIDCGI@ JC P½KQEIG] ?C KIIELLK CI KLHAC QEIHC Bc@ IGI ?CKIG CL QEIHGJC @ÊCLCRACG = � CL H@GA@F K JC �KARK?CI g]@JC CL \@LL ebIHGICG ÍSÎh � L eCQGH@?C K��CEIHC]KI@B@??KACK Ì Bc@ L eCI?C@F @ J@C QEIHC CI BEC xxë þ Õ â IGI BGIH@I�K CIH@A@ GARCH@ J@L ?C?H@F KK QKAH@ CL QEIHG ?HKDCGIKACG = �@L IG?HAG BK?G Ê@?HK CQGH@?C Ì ?GJJC?aKHHK =

p�

P eKIKLC?C AC�GAG?K JC Ê@?HG aKHHG Ì EI QG e K?HAKHHK y vG Bc@ L e@I@A�CK CI aEIDCGI@ J@L H@FQG cK LCF CH@ zþ u CIQKAHCBGLKA@ þ ÒëÔ Ì LCF CHKHK = �@ ?@�E@ Bc@ CL F GHG u I@LLG ?QKDCG J@LL@ aK?C u Ì LCF CHKHG =vCK Ò8Ó Þ 8ÿ Ô EI QEIHG JC KBBEFELKDCGI@ Q @A LK HAKC@HHGACK u BCG Ì @?C?HK EIK ?@Ê@IDK BA@?B@IH@ JC H@FQC ër u BGIër $ �% Q@A 1 $ �% u HKL@ Bc@ äåæ rèéê ÒÓ Òër Ô Þ ßÓ Òër Ô Õ Ò8Ó Þ 8ÿ Ô Ê = zGI?CJ@AG KJ@??G u Q@A � � â K??@�IKHG u LK?EBB@??CGI@ JC QEIHC J@LL eGARCHK ÒÓ Òër � � Ô Þ ßÓ Òër � � ÔÔ =P eG??@A]KDCGI@ CFQGAHKIH@ u K Ê@?HG QEIHG u Ì Bc@ LK F KQQK Bc@ J� LK ?GLEDCGI@ KL H@FQG � J@L ?C?H@F K JCH@A@IDCKL@KEHGIGFG Bc@ ?HCKFG BGI?CJ@AKIJG Ì BGIHCIEK I@L JKHG CICDCKL@ =

TI KLHA@ QKAGL@ yäåærèéê ÒÓ Òër � � Ô Þ ßÓ Òër � � ÔÔ Õ Ò8Ó Ò� Ô Þ ß8Ó Ò� ÔÔ Þ

Bc@ Ì LK ?GLEDCGI@ KL H@FQG � JC JKHG CICDCKL@ Ò8Ó Þ 8ÿ Ô = �@ ?@�E@ Bc@ þ Òër � � Ô H@IJ@ K þ Ò8Ó Ò� Ô Þ ß8Ó Ò� ÔÔ = ` K þ ÒëÔ $ zþJEIÊ@ u ?@ Ò8Ó Þ 8ÿ Ô IGI Ì EI QEIHG JC @ÊCLCRACGzþ Õ äåærèéê þ Òër � � Ô Õ þ Ò8Ó Ò� Ô Þ ß8Ó Ò� ÔÔ > þ Ò8Ó Þ ß8Ó Ô Õ zþ ÞBc@ Ì CFQG??CR CL@ = \EIÊ@ C QEIHC JC KBBEFELKDCGI@ J@LLK HAKC@HHGACK ?GIG ?GLG L@ QG?CDCGIC JC @ÊCLCRACG = \KL aKHHGBc@ L e@I@A�CK J@BA@?B@ ?@�E@ Bc@ Q @A G�IC HAKC@HHGACK CL QEIHG JC KBBEFELKDCGI@ Ì EICBG =

fIK JCFG?HAKDCGI@ Q C� BG?HAEHHC]K Ì QG??CR CL@ @J C?HAEHHC]K u KIBc@ ?@ QC� BGFQL@??K =TL QACF G aKHHG CFQGAHKIH@ Ì Bc@ ?@ KJ EI B@AHG C?HKIH@ JC H@FQG zë CL QEIHG Ì CI zÓ BGI ]@LG BCH� zÿ � â KLLGAK

LK aEIDCGI@ ë $ Ó ÒëÔ Ì CI]@AHCRCL@ CI EI CIHGAIG JC zë u @??@IJG xxë Ó Òzë Ô Õ zÿ |Õ â = zCGÌ QG??G Q@I?KA@ CL H@FQG BGF@aEIDCGI@ J@LLK QG?CDCGI@ u ÊCIJC QG??G Q @I?KA@ L e@I@A�CK BGF @ aEIDCGI@ J@LLK QG?CDCGI@ yxxÓ þ Õ xxë þ xëxÓ Õ á� ßÓ ÒëÔ Õ á�°Ú Òþ ÒÓ Ô á Ñ ÒÓ ÔÔ & gN =Nh�E@?HK Ì EIK @ÊKDCGI@ JCH@A@IDCKL@ Q @A þ ÒÓÔ u BGI JKHG CICDCKL@ þ ÒzÓ Ô Õ 3 zÿ � Ñ ÒzÓÔ I@L QEIHG zÓ = > ??@IJG zÿ |Õ â?GIG I@LL@ BGIJCDCGIC JC @?C?H@IDK @ EICBCH� LG BKL@ J@LL@ ?GLEDCGIC gÊ@?HG IGI Ì ]@AG ?@ zÿ Õ â ===h = �ECIJC þ ÒÓÔ Ì EIKaEIDCGI@ J@BA@?B@IH@ CI Ó u @ L e@ÊKDCGI@ ]KL@ �IG KL QACFG 8Ó HKL@ Bc@ þ Ò8Ó Ô Õ Ñ Ò8Ó Ô g]@JC LK ��EAK <h = PK JGF KIJK

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CF QGAHKIH@ Ì ?@ CL H@FQG Q@A KAAC]KA@ CI 8Ó Ì �ICHG G CI�ICHG = TI HEHHC � LC Ó HAK zÓ @ 8Ó BC KAAC]G CI H@FQG �ICHG u Q@ABcÌÊP eCI?C@F @ J@C QEIHC JC KBBEFELKDCGI@ Q@A ë $ �% QA@IJ@ CL IGF @ JC # áLCF CH@ J@LLKHAKC@HHGACK =

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LK ]@LG BCH� Ì °Ú Òþ ÒÓÔ á Ñ ÒÓÔÔ Bc@ Ì JC]@A?K JK â ?@ Ó > 8Ó = \ eKLHAK QKAH@ u IGHK þ ÒÓ Ô u CL H@FQG Q@A KAAC]KA@ CI 8Ó ÌG]]CKF @IH@ 8ë á zë Õ ® Û�Ü� xÓ°Ú Òþ ÒÓÔ á Ñ ÒÓÔÔ & gN =Oh\EIÊ@ Q@A BKQCA@ ?@ CL H@FQG Ì �ICHG J@]G JC?BEH@A@ LK ?GFFKRCLCH� J@LL eCIH@�AKL@ CIHGAIG K 8Ó = vBAC]G L e@ÊKDCGI@JCH@A@IDCKL@ Q @A � ÒÓ Ô Õ þ ÒÓÔ á Ñ ÒÓÔ y xxÓ � ÒÓ Ô Õ á�°Ú� ÒÓ Ô á Ñ » ÒÓ Ô & gN =Sh�EKIJG � Ì QCBBGLG u @ ?@ 8Ó IGI Ì EI QEIHG JC @ÊCLCRACG u Ó Ì ]CBCIG K 8Ó u JEIÊ@ u KL QACF G GAJCI@ ?C�IC�BKHC]G uL e@ÊKDCGI@ N =S Ì xxÓ � ÒÓ Ô Õ á�°Ú� ÒÓ Ô á = ÞBGI = Õ Ñ » Ò8Ó Ô u BCG Ì F @IG LK aGADK CI 8Ó = �E@?H eELHCF K @ÊKDCGI@ Ì @?QLCBCHKF @IH@ AC?GLERCL@ @ J� y°Ú� ÒÓ Ô� á =� ä�Ý Þà � 5 Ú�= ß Õ 8Ó á Ó &v]CLEQQKIJG K � QCBBGLC ?C GHHC@I@ Bc@ � � =Ãbàë & Ò8Ó á ÓÔ u JEIÊ@ L eCIH@�AKL@ Ì ?GFFKRCL@ @J CL H@FQG Ì �ICHG =zG?K KBBKJ@ JGQG CL H@FQG 8ëã vEL QEIHG LK aGADK IGI Ì IELLK u JEIÊ@ ?C FEG]@A� ]@A?G ?CIC?HAK @ JC IEG]GL e@ÊKDCGI@ N =N J@?BAC]@ þ CI aEIDCGI@ JC Ó = | CQ @H@IJG CL AK�CGIKF @IHG u Ì @]CJ@IH@ Bc@ CL QEIHG JC a@AF K ?GLG ÊKIJGþ E�EK�LCK Ñ ÒÓ Ô CI EI QEIHG CI BEC LK aGADK Ì â u BCG Ì ?GLG ?@ CL QEIHG H@IJ@ KJ EIK QG?CDCGI@ JC @ÊCLCRACG =

n� �@L QEIHG Kh cG QAG]KHG Bc@ LK ?GLEDCGI@ ?HKDCGIKACK Óý Ì CI ?HKRCL@ = �GIG?HKIH@ BC^ @?C?HGIG HAKC@HHGAC@ Bc@H@IJGIG K Óý = fI FGJG Q@A BGI]CIB@A?C Bc@ Ì BG?á Ì Ê@LLG JC BGI?CJ@AKA@ EI BK?G QC� ?@FQLCB@ u BCG Ì CL LCI@KACDDKHGCIHGAIG K Óý = P e@ÊKDCGI@ J@L F GHG JC]@IHK ÜÓ Õ Ó á � ßÓ ÞBc@ Ì EI e@ÊKDCGI@ LCI@KA@ @?QLCBCHKF @IH@ AC?GLERCL@ = �GI Ì JC� BCL@ ]@AC�BKA@ Bc@ @?C?H@ EI KEHG]@HHGA@ JC KEHG]KLGA@I@�KHC]G Q@A LK F KHACB@ Xâ à

à á�Y &T F GHC Bc@ cKIIG JKHG CICDCKL@ ?E Ê@?HG KEHG]@HHGA@ H@IJGIG @?QGI@IDCKLF @IH@ K Òâ Þ âÔ u BCG Ì ?GIG KHHAKHHC JKLL eGAC�CI@ =�EHHC �LC KLHAC ?C KLLGIHKIKIG @?QGI@IDCKLF @IH@ = �E@?HG KEHG]@HHGA@ QA@IJ@ CL IGF @ JC âãäåUSæ çSãèåéU Q@A CL QEIHG JC@ÊCLCRACG gCI?HKRCL@h Òâ Þ âÔ = zG?K KBBKJ@ Q@A CL ?C?H@F K IGI LCI@KA@ J@LLK JGQQCK REBKã � AK�CGI@]GL@ Q@I?KA@ Bc@ LK]KAC@H� ?HKRCL@ BGIHCIEK KJ @?C?H@A@ F K IGI ?KA� QC� EIK A@HHK = vGLG Q @A ÒÓ Þ ßÓ Ô Q CBBGLG ?C BGIaGIJ@A� BGI LK ]KAC@H�?HKRCL@ J@L LCI@KACDDKHG = �GHK Bc@ KIBc@ I@L BK?G ?@IDK KHHACHG LK ]KAC@H� ?HKRCL@ @?C?H@ = � @?KHHKF @IH@ LK ?@QKAKHACB@ uBCG Ì LK BEA]K BGI @I@A�CK â = �@LLK ��EAK N cG JC?@�IKHG KLBEI@ GARCH@ J@L ?C?H@F K ?@IDK KHHACHG gCI I@AGh u LK ]KAC@H�?HKRCL@ I@L BK?G ?@IDK KHHACHG gLK ?@QKAKHACB@ CI RLE h u @ LK ]KAC@H� ?HKRCL@ I@L BK?G BGI KHHACHG gCI AG??Gh =

PK JCF G?HAKDCGI@ AC�GAG?K J@LL e@?C?H@IDK J@LLK ]KAC@H� ?HKRCL@ I@C BK?C IGI LCI@KAC Ì BGFQLCBKHK g]@JC \@LL ebIHGI CGÍSÎh u BGFEIÊ@ ÊC F C LCF CHG K aKA IGHKA@ Bc@ ?C QE^ QAG]KA@ K HAG]KA@ LK ?GLEDCGI@ JC N =S g Bc@ @ÊC]KL@ KLL e@ÊKDCGI@N =Nh Q@A ?@AC@ = �@L BK?G � Õ Úy } g@?@ABCDCGh ?C cK y� ÒÓ Ô Õ à� Ó á àê Ó� � & & & &�KBBCG IGHKA@ Bc@ Q@A � Õ â CI Ó Õ â CL H@AF CI@ JC J@?HAK IGI ]@AC� BK L@ BGIJCDCGIC ?HKIJKAJ Q@A L e@?C?H@IDK @ EICBCH�J@LL@ ?GLEDCGI C ===

5 � b??EIHK Q @A REGIK LK ��EAK N Ì aKBCL@ BKQ CA@ ÊKLC ?GIG C JKHC CI CDCKLC Bc@ ]@I�GIG KHHAKHHC JKLLK QG?CDCGI@ Ó 3@ ÊKLC Ê@LLC KHHAKHHC JKLLK QG?CDCGI@ Ó = TIaKHHC LK ]KAC@H� ?HKR CL@ JC]CJ@ CL Q CKIG J@LL@ aK?C CI JE@ A@�CGI C JC?HCIH@ uEIK Bc@ BGIHC@I@ CL QEIHG Ó 3 u L eKLHAK Bc@ BGIHC@I@ CL QEIHG Ó =p±

-2.0 -1.6 -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2 1.6 2.0

-1.41

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1.41

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1.41

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PK ��EAK N ?C �CE?HC�BK aKBCLF @IH@ BGI?CJ@AKIJG Bc@ L e@I@A�CK ?ELLK ]KAC@H� ?HKRCL@ BA@?B@ Q@A ë $ á% = �ECIJCF KI F KIG gBGI CL H@FQG CI]@AHCHG h @??K CIH@A?@BK BEA]@ JC LC]@LLG JC @I@A�CK ?@FQA@ QC� KLHK = TIGLHA@ G�IEIG J@C JE@AKF C J@LLK ]KAC@H� ?HKRCL@ CIBGIHAK EIK BEA]K JC LC]@LLG EIK @J EIK ?GLK ]GLHK u HAK?]@A?KLF @IH@ ?@ ßÓ |Õ â u HKI�@IH@ ?@ßÓ Õ â =

fIK ELH@ACGA@ JGF KIJK Bc@ BC ?C QE^ QGAA@ u Ì JC ÊKIHG KEF @IHK L e@I@A�CK G�IC ]GLHK Bc@ CL QEIHG QK??K Q @A LKQG?CDCGI@ Ó Õ â u F KIJKIJG CL H@FQG K á% = �GAIKIJG KLLK ��EAK <u @ CIJCBKIJG BGI þ 3 CL ]KLGA@ J@LL e@I@A�CK I@LQEIHG 8Ó JG]@ CL F GHG CI]@AH@ LK ]@LG BCH� y

þ ÒâÔ á þ 3 Õ � ® Û�Ý °Ú Òþ ÒÓÔ á Ñ ÒÓÔÔ &xAK Q@A â > Ó > 8Ó u þ ÒÓÔ Ù þ Ò8Ó Ô ÊCIJC

þ ÒâÔ á þ 3 Ù � ® Û�Ý °Ú Òþ 3 á Ñ ÒÓÔÔ ÞBc@ u ?@ þ 3 Ì FGLHG �AKIJ@ u J� L eKIJKF @IHG

þ ÒâÔ á þ 3 Ù =Ãbàë &þ }3 8Ó &`K ?@ þ 3 Ì �AKIJ@ 8Ó � =Ãbàë þ }�3 = TI J@�ICHC]K þ ÒâÔ á þ 3 Ù =Ãbàë &þ ò�3 = TL Bc@ ?C�IC� BK Bc@ F KI FKIG Bc@ F CKLLGIHKIG JK Òâ Þ âÔ LK JC?HKIDK HAK C QK??K��C J@LLK ]KAC@H� ?HKRCL@ Q @A L eK??@ ßÓ BA@?B@ =�@LLK ��EAK N =S =< cG JC?@�IKHG LK BEA]K ÒÓ Þ þ ÒÓÔÔ Q @A CL AKFG J@LLK ]KAC@H� ?HKRCL@ Bc@ KAAC]K I@LL eGAC�CI@ BGI]@LG BCH� I@�KHC]K = b ÊKL@ QG?CDCGI@ JC @ÊCLCRACG H@IJ@ CL FGHG Bc@ QKAH@ BGI ]@LG BCH� QG?CHC]K u @I@A�CK þ @ QG?CDCGI@CICDCKL@ IELLKãó ô º,¶)+ ,´·õ +µ+ * ö-¸¹·-ì Ð2 ÐÏ í ÷ø ÷ùú û üðFñòöð ïò ý ÷õõîøòõî ÷ þ÷óó�îòð �0�fI eK?HK GFG�@I@K JC @?HA@F C W @ i u F K??K < u @ LEI�c@DDK ) u § ]CIBGLKHK K FEG]@A?C ?E JC EI QCKIG ]@AHCBKL@ ' =TL ?EG @?HA@FG W Ì ]CIBGLKHG K FEG]@A?C ?E JC EIK A@HHK GACDDGIHKL@ � ÿ ' = TIGLHA@ u ' AEGHK BGI ]@LG BCH� KI�GLKA@BG?HKIH@ # CIHGAIG KLL eK??@ ]@AHCBKL@ à u GAHG�GIKL@ K � I@L QEIHG �??G � =

TL QEIHG W J@LL eK?HK Ì ACBcCKF KHG JKL QEIHG � JK EIK FGLLK CJ@KL@ JC BG?HKIH@ @LK?HCBK 1 =p�

-3.0 -2.4 -1.8 -1.2 -0.6 0.0 0.6 1.2 1.8 2.4 3.0

-0.62

0.09

0.79

1.50

2.21

2.91

3.62

-3.0 -2.4 -1.8 -1.2 -0.6 0.0 0.6 1.2 1.8 2.4 3.0

-0.62

0.09

0.79

1.50

2.21

2.91

3.62

-3.0 -2.4 -1.8 -1.2 -0.6 0.0 0.6 1.2 1.8 2.4 3.0

-0.62

0.09

0.79

1.50

2.21

2.91

3.62

vC CIHAGJEBKIG L@ BGGAJCIKH@ LK�AKI�CKI@ � Õ JC?HKIDK JC W JK � u @ � Õ KI�GLG HAK LK JCA@DCGI@ J@LL eK?HK @ LKJCA@DCGI@ J@LL eK??@ à =<h vC ?BAC]K LK PK�AKI�CKIK u @ u BGI?CJ@AKIJG HAK?BEAKR CLC � LC @H@HHC �AK]CHKDCGIKLC u @ ?C J@H@AF CICIG u BGI?@�E@IH@{F @IH@ u @]@IHEKLC ÊKIHCH� BGI?@A]KH@ =� U�� äU � Ué é �ã�� ä�ççå� ã� å��U å Tå ãé � T� S� ��

Nh ?C J@H@AF CICIG L@ ?GLEDCGIC JC @Ê CLCRACG u KL ]KACKA@ J@L QKAKF @HAG Õ r� p �Oh ?C JC?BEHK LK ?HKRCLCH� J@LL@ ?GLEDCGIC JC @ÊCLCRACG KL ]KACKA@ JC �S h I@L BK?G � à ?C BKLBGLCIG L@ aA@Ê@ID@ @ C FGJC IGAF KLC J@LL@ QCBBGL@ G?BCLLKDCGIC CIHGAIG KLL@ QG?CDCGIC JC

@ÊCLCRACG ?HKRCL@ =vGLEDCGI@ I@LLK ?@DCGI@ S =Z =<

ì Ð2 ÐÛ í ÷ø ÷ùú û ù� òF ð õðFñòöð ïò ÷�ðø÷�ð ÷ î Ðî Ð 0ì�0� Ð�@L QCKIG ]@AHCBKL@ u ?C � ??C EI ?C?H@F K JC ACa@ACF @IHG CI@ADCKL@ Òâ Þ Ó Þ Ô u BGI K??@ ½ GAC@IHKHG LEI�G LK A@HHK ]@AHCBKL@K?B@IJ@IH@ = bHHGAIG KL QEIHG �??G � § LCR @AK JC AEGHKA@ EI eK?HK CLLCF CHKHK g?@IDK Q@?Gh = vCK à LK BGGAJCIKHK ?E LL eK?HK u?B@LHK QG?CHC]K KLLK J@?HAK JC � u @ ?CK � L eKI�GLG gBGIHKHG CI ]@AG KIHCGAKACGh Bc@ L eK?HK aGAFK BGI L eK??@ Ó = vE LL eK?HK uCI à Õ 6 Þ 6 � â u § �??KHG EI QEIHG � 3 JC F K??K � 3 = TIGLHA@ u ?ELL eK?HK u Ì LCR @AG JC ?BGAA@A@ EI ?@BGIJG QEIHG F KH@ACKL@� u JC F K??K � = � Ì ACBcCKF KHG JK � 3 u BGI EIK aGADK @LK?HCBK � Õ á1 Ò� á �3 Ô Þ 1 � â &� äå� ã �� ã�ã = vC ?BAC]K LK LK�AKI�CKIK J@L ?C?H@F K =� U��ã �� ã�ã= \@HHG Ø Õ 61 B� }é� C�� u JC?BEH@A@ u KL ]KACKA@ JC Ê@?HG QKAKF @HAG u L@ ?GLEDCGI C ?HKDCGIKAC@ J@L?C?H@F K PK�AKI�CKIG u J@H@AF CIKIJGI@ u Q @A Ø |Õ àu L@ A@LKHC]@ QAGQAC@H� JC ?HKRCLCH� =�Uä�ã �� ã�ã � vC J@H@AF CI CIG L@ aA@Ê@ID@ J@LL@ �QCBBGL@ G?BCLLKDCGIC � KHHGAIG KLL@ QG?CDCGIC JC @Ê CLCRACG ?HKRCLC =�TãäSã �� ã�ã � vC BGI?CJ@AC GAK CL ?@�E@IH@ QAGRL@F K y L eK?HK �CAK BGI aA@Ê@IDK KI�GLKA@ BG?HKIH@ # KHHGAIG KJx = vC JC?BEHK CL BGAAC?QGIJ@IH@ QAGRL@F K KJ EI �AKJG JC LCR @AH� =

vGLEDCGI@ I@LLK ?@DCGI@ S =Z =Nì Ð2 Ðì ü� ÷í ÷ø üðFñòöð ïò ý ÷õõîøòõî � îùòðøîú÷ ÷ � � �0 ÷ �� îññ÷úúð ÷ �÷�� Ð ÷�öòGî ÐfIK BCABGIa@A@IDK � JC AK��CG � @ FK??K <3 AEGHK BGI ]@LG BCH� KI�GLKA@ BG?HKIH@ # CI EI QCKIG ]@AHCBKL@ u CIHGAIGKL ?EG B@IHAG � = vEL ?EG RGAJG CIH@AIG AGHGLK ?@IDK ?HAC?BCKA@ EI JC?BG � JC AK��CG � > � @ FK??K < = TL B@IHAG �JC HKL@ JC?BG § ACBcCKF KHG JK EIK FGLLK @LK?HCBK JC BG?HKIH@ 1 � â u JK EI QEIHG FKH@ACKL@ � JC F K??K � u LCR @AG JC?BGAA@A@ ?ELL eK??@ ]@AHCBKL@ QK??KIH@ Q@A � =

TIJCBK BGI � Õ # ë @ R �LC KI�GLC JC AGHKDCGI@ QAGQACK JC � @ � AC?Q@HHC]KF @IH@ u BGI � L eKI�GLG Bc@ �� aGAF KBGI LK JCA@DCGI@ QG?HCHC]K J@LL eK??@ GACDDGIHKL@ u @ BGI LK ÊGHK J@L QEIHG � AC?Q @HHG K � y

p/

<h ?BAC] C LK BGIJCDCGI@ JC QEAG AGHGLKF@IHG CI H@AF CIC JC ß� Þ ßR Þ ß� u @ JCF G?HAK Bc@ Ì EI ]CIBGLG GLGIGFG �Nh ?BAC] C LK PK�AKI�CKIK J@L ?C?H@F K I@LL@ ]KACKRCLC LK�AKI�CKI@ � Þ �Oh J@H@AF CIK L@ ?GLEDCGIC ?HKDCGIKA@ J@L A@LKHC]G ?C?H@F K JC PK�AKI�@ u KL ]KACKA@ J@L QKAKF @HAG KJCF @I?CGIKL@� Õ B� é�C�B y� Cr �S h JC?BEHC LK ?HKR CLCH� J@LL@ QG?CDCGIC JC @ÊCLCRACG KL ]KACKA@ JC � �Uh J@H@AF CIK L@ BGIJCDCGIC CI CDCKLC ?EL F GHG J@L RKACB@IHAG � J@L JC?BG � K BEC BGAAC?QGIJGIG ?GLG FGHC KAFGICBC

J@L QEIHG � =vGLEDCGI@ I@LLK ?@DCGI@ S =Z =O

ì Ð2 Ð� ü� ÷í ÷ø üðFñòöð ïò ý ÷õõîøòõî � îùòðøîú÷ ÷ �÷�� Ð ÷�öòGî �ùôúG ò�÷øöò vC BGI?CJ@AC EI ?C?H@F K JC ACa@ACF @IHG QCKIG CI@ADCKL@ JC GAC�CI@ � @ K??C ÒÓ Þ Ô u L eK??@ @??@IJG ?B@LHG KLLCI@KHG BGILK ]@AHCBKL@ K?B@IJ@IH@ = fI JC?BG GFG�@I@G u JC AK��CG � u B@IHAG � u @ F K??K HGHKL@ < u AGHGLK ?@IDK ?HAC?BCKA@ gBCG §QEAG AGHGLKF @IHGh LEI�G L eK??@ = PEI�G EI JCKF @HAG J@L JC?BG { JC @?HA@F C W Þi { Ì LCR @AG JC ?BGAA@A@ ?@IDK KHHACHGEI QEIHG F KH@ACKL@ JC F K??K � = �KL@ QEIHG Ì CIGLHA@ ACBcCKF KHG JKL B@IHAG J@L JC?BG HAKF CH@ EIK FGLLK CJ@KL@ JCBG?HKIH@ @LK?HCBK 1 g1 � âh = �@LL eC?HKIH@ CICDCKL@ CL B@IHAG J@L JC?BG ?C HAG]K ?E LL eK??@ Ó u CL J CKF@HAG W Þi Ì BGLLCI@KA@KLL eK??@ Ó @ Ód > Ó! > Ó" &vC BGI?CJ@AC EI ?C?H@F K ?GLCJKL@ Ò# Þ $ Ô JC K??C CIB@IHAKHC CI � u L eK??@ # GAC@IHKHG BGF@ Wi = vC K??EF KIG BGF@QKAKF @HAC PK�AKI�CKIC L eKI�GLG R gBGIHKHG CI ?@I?G KIHCGAKACGh Bc@ L eK??@ ?GLCJKL@ # aGAF K BGI L eK??@ J@LL@ Ó @ L eK?BC??K# J@L QEIHG � =à% 506 9459 « vC ?BAC]K LK PK�AKI�CKIK J@L ?C?H@F K =Ú% 506 9459 « vC J@H@AF CI CIG L@ @]@IHEKLC BGI��EAKDCGIC JC @ÊCLCRACG =O% 506 9459 « vC JC?BEHK LK ?HKRCLCH� J@LL@ ?GLEDCGI C JC @ÊCLCRACG J@H@AF CIKH@ KL QEIHG Ú =� % 506 9459 « vC BGI?CJ@AC GAK EI JC]@A?G QAGRL@F K u @ BCG § ?C BGI?CJ@AC CL QEIHG � ª88910 I@L B@IHAG = \@?BAC]@A@ CLF GHG J@L ?C?H@F K =

vGLEDCGI@ I@LLK ?@DCGI@ S =Z =Sì Ð2 Ð� ü� ÷í ÷ø üðFñòöð �÷��òðø÷ ÷�öòGî î Ðî Ð 0ì�0�TI EI QCKIG GACDDGIHKL@ ?GIG QG?H@ JE@ K?H@ W3i 3 @ Wi JC AC?Q @HHC]@ F K??@ <3 @J < gJC?HACREDCGI@ JC F K??KGFG�@I@Kh @ LEI�c@DD@ & 3 @J & = P@ K?H@ ?GIG LCR @A@ JC AEGHKA@ KHHGAIG KC AC?Q @HHC] C RKACB@IHAC � 3 @ � u � ??C I@LQ CKIG u BGI Ö� 3� Ö Õ ) � â =vCK � EI QEIHG KQQKAH@I@IH@ KLL eK?HK W3i 3 u �CKB@IH@ HAK � 3 @ W3 u � EI QEIHG KQQKAH@I@IH@ KLL eK?HK Wi u� CKB@IH@ HAK � @ W u Ö� 3� Ö Õ Ö� � Ö Õ � � â = �AK C QEIHC � @ � K�C?B@ EIK FGLLK CJ@KL@ u JC BG?HKIH@ @LK?HCBK 1 � â =vC ACBcC@J@ y

<h ?BAC]@A@ LK PK�AKI�CKIK J@L ?C?H@F K �Nh J@H@AF CIKA@ �LC @ÊCLCRAC �Oh JC?BEH@A@ LK ?HKRCLCH� J@�LC @ÊCLCRAC KL ]KACKA@ J@L QKAKF @HAG Ø Õ '� CI �é á ~à� �S h BGI?CJ@AKHG CL ?C?H@F K BGAAC?QGIJ@IH@ K ) Õ â u ?C JC?BEHK CL BGAAC?QGIJ@IH@ ?C?H@F K LK�AKI�CKIG u F G?HAKIJG

Bc@ Ì ACBGIJEBCRCL@ KJ EI ?C?H@F K KJ EI �AKJG JC LCR @AH� =vGLEDCGI@ I@LLK ?@DCGI@ S =Z =U

ì Ð2 Ð ü� ÷í ÷ø ÷ùú û üðFñòöð ïò ý ÷õõîøòõî � îùòðøîú÷ ï÷ú ÐÏ2 Ð0�TI EI QCKIG ]@AHCBKL@ ?C KJGHHK EI ?C?H@F K JC ACa@ACF @IHG CI@ADCKL@ Ò� Þ Ó Þ Ô u BGI � �??G u K??@ GAC@IHKHG LEI�G LK]@AHCBKL@ K?B@IJ@IH@ = vELL eK??@ Ì LCR @AG JC ?BGAA@A@ ?@IDK KHHACHG CL QEIHG � JC F K??K F = fI eK?HK JC @?HA@F C W Þi uF K??K ` u LEI�c@DDK Ú& Ì LCR @AK JC AEGHKA@ u ?@IDK KHHACHG u KHHGAIG KL ?EG QEIHG F @JCG u � ??KHG CI � = TL QEIHG @?HA@FGW gAC?Q = i h Ì ACBcCKF KHG JKL QEIHG � u HAKF CH@ EIK FGLLK @LK?HCBK CJ@KL@ u JC BG?HKIH@ 13 gAC?Q = 1 h = vC K??EF K6 Õ 13 á 1 � â =gTh = vC ?BAC]K LK PK�AKI�CKIK J@L ?C?H@F K @ ?C J@H@AF CICIG L@ BGI��EAKDCGIC JC @ÊCLCRACG KL ]KACKA@ J@L QKAKF @HAGØ (Õ ��%) � Òâ Þ% Ô =

p;

gTTh = vC JC?BEHK LK ?HKRCLCH� J@�LC @ÊCLCRAC KL ]KACKA@ J@L QKAKF @HAG Ø CI �é á ~à� =gT TTh = vC ?HEJC CL ?C?H@FK PK�AKI�CKIG GHH@IEHG Q @A LCI@KACDDKDCGI@ KHHGAIG KLLK QG?CDCGI@ JC @Ê CLCRACG Bc@ Ì ?HKRCL@Q @A G�I C Ø u I@LL eCIH@A]KLLG QA@J@HHG =

gTW h = vC K??EF K 0m9 6 Õ â & vC J@H@AF CICIG C F GHC J@L BGAAC?QGIJ@IH@ ?C?H@F K LK�AKI�CKIG =vGLEDCGI@ I@LLK ?@DCGI@ S =Z =V

ì Ð2 Ð� ü� ÷í ÷ø ÷ùú üðFñòöð ï÷ú Û2 Ð Ð0� �ý î�õ* òð�ð fIK ?RKAAK AC� CJK GFG�@IK Q@?KIH@ �+ JC LEI�c@DDK & @ FK??K < Ì QG?HK CI EI QCKIG ]@AHCBKL@ @J Ì LCR @AK JC AEGHKA@?@IDK KHHACHG KHHGAIG KL ?EG @?HA@FG � = w@A L eKLHAG @?HA@FG + QK??K EIK �ECJK JC F K??K HAK?BEAKRCL@ GAHG�GIKL@ KLLK?RKAAK = PEI�G HKL@ �ECJK ?C FEG]@ ?@IDK KHHACHG EI QEIHG F KH@ACKL@ Q @?KIH@ � JC FK??K � = > ??G Ì ?G��@HHG GLHA@ KLQ @?G KJ EIK aGADK @LK?HCBK � Õ á1 �� u 1 � â =vB@�LCKFG BGF @ ]KACKRCLC LK�AKI�CKI@ L eKI�GLG � Bc@ LK ?RKAAK aGAF K BGI LK ]@AHCBKL@ JC?B@IJ@IH@ @ L eK?BC??K Ó J@LQEIHG � LEI�G LK �E CJK =

<h vBAC]@A@ L@ @ÊKDCGIC J@L F GHG J@L ?C?H@F K =Nh �AG]KA@ L@ QG?CDCGIC JC @Ê CLCRACG @ JC?BEH@AI@ CL IEF@AG @ LK ?HKRCLCH� =Oh vHEJCKA@ L@ QCBBGL@ G?BCLLKDCGI C KHHGAIG KJ EIK QG?CDCGI@ JC @ÊCLCRACG ?HKRCL@ =vGLEDCGI@ I@LLK ?@DCGI@ S =Z =M

ì Ð2 Ð( ü� ÷í ÷ø ÷ùú û üðFñòöð ï÷ú ÏÏÐ� Ð0� �ý î�õ* òð�ð TI EI QCKIG GACDDGIHKL@ ?C FEG]GIG JE@ ?RKAA@HH@ GFG�@I@@ JC LEI�c@DDK & @ F K??K < JC @?HA@F C AC?Q @HHC]KF @IH@W Þ i u @ i Þ , u CI B@AIC@AKH@ HAK LGAG CI i FK LCR @A@ JC AEGHKA@ ?@IDK KHHACHG = � LC @?HA@F C W @ , ?GIG GRRLC�KHC K?BGAA@A@ ?@IDK KHHACHG LEI�G EI K??@ �??G Ó = vE W K�C?B@ EIK aGADK � 3 Õ á1+ 3W u ?E , EIK aGADK � Õ á1+ ,g1 � âh u G]@ + 3 @ + ?GIG QEIHC J@LL eK??@ Ó JC K?BC??@ AC?Q @HHC]KF@IH@ á ) @ ) = vB@�LCKFG BGF @ ]KACKRCLC LK�AKI�CKI@L eK?BC??K JC i Ó" u @ L eKI�GLG � Bc@ Wi aGAF K BGI L eK??@ Ó =

<h �AG]KA@ L@ @ÊKDCGIC J@L F GHG =Nh �AG]KA@ L@ QG?CDCGIC JC @Ê CLCR CACG @ JC?BEH@AI@ LK ?HKR CLCH� =Oh vBAC]@A@ L@ Q CBBGL@ G?BCLLKDCGIC KHHGAIG KJ EIK QG?CDCGI@ JC @ÊCLCRACG ?HKRCL@ =Sh �AG]KA@ ?@ @?C?HGIG BGIJCDCGIC CI CDCKLC Q @A BEC CL F GHG ?CK KAFGICBG BGI aA@Ê@IDK # IGI ?GLG Q @A QCBBGL@

G?BCLLKDCGI C F K KIBc@ Q@A G?BCLLKDCGIC �ICH@ =vGLEDCGI@ I@LLK ?@DCGI@ S =Z =X

ì Ð2 Ð0 ü� ÷í ÷ø ÷ùú - �ðø÷�ð ïò ý ÷õõîøòõî � îùòðøîú÷ ï÷ú Ï��02fI JC?BG GFG�@I@G Q@?KIH@ JC F K??K < @ AK��CG � Ì ]CIBGLKHG CI EI QCKIG ]@AHCBKL@ K AGHGLKA@ ?@IDK ?HAC?BCKA@ ?EEIK �ECJK GACDDGIHKL@ � = fI QEIHG F KH@ACKL@ JC F K??K � Ì ]CIBGLKHG ?@IDK KHHACHG KL ?EG RGAJG = vEL B@IHAG � J@LJC?BG K�C?B@ LK aGADK á1�� g1 Ù âh =<h \@H@AF CIKA@ �LC @ÊCLCRAC @ LK LGAG ?HKRCLCH� u gQ@A 1 � âh =Nh vBAC]@A@ LK LK�AKI�CKIK @ L@ @ÊKDCGIC JC PK�AKI�@ ?HEJCKIJG u Q @A 1 � â u L@ QCBBGL@ G?BCLLKDCGI C KHHGAIG KLLKQG?CDCGI@ JC @ÊCLCRACG ?HKRCL@ = vC BKLBGLCIG L@ aA@Ê@ID@ QAGQAC@ @ C F GJC IGAF KLC =O h w@A 1 Õ â ?C J@H@AF CICIG N CIH@�AKLC QACF C J@L F GHG =S h gaKBGLHKHC]G h w@A 1 Õ â J@H@AF CIKA@ C F GHC HKLC Bc@ LK ÊGHK J@L QEIHG FKH@ACKL@ ACF KI�K BG?HKIH@ I@L H@FQG =vGLEDCGI@ I@LLK ?@DCGI@ S =Z =Yì Ð2 ÐÏ2 ü� ÷íø ÷ùú - �ðø÷�ð ïò ý ÷õõîøòõî � îùòðøîú÷ ï÷ú Ï��02fI JC?BG GFG�@I@G Q@?KIH@ JC F K??K < @ AK��CG � Ì ]CIBGLKHG CI EI QCKIG ]@AHCBKL@ K AGHGLKA@ ?@IDK ?HAC?BCKA@ ?EEIK �ECJK GACDDGIHKL@ � = fI QEIHG F KH@ACKL@ JC F K??K � Ì ]CIBGLKHG ?@IDK KHHACHG KL ?EG RGAJG = vEL B@IHAG � J@LJC?BG K�C?B@ LK aGADK á1�� g1 Ù âh =<h \@H@AF CIKA@ �LC @ÊCLCRAC @ LK LGAG ?HKRCLCH� u gQ@A 1 � âh =

�D

Nh vBAC]@A@ LK LK�AKI�CKIK @ L@ @ÊKDCGIC JC PK�AKI�@ ?HEJCKIJG u Q @A 1 � â u L@ QCBBGL@ G?BCLLKDCGI C KHHGAIG KLLKQG?CDCGI@ JC @ÊCLCRACG ?HKRCL@ = vC BKLBGLCIG L@ aA@Ê@ID@ QAGQAC@ @ C F GJC IGAF KLC =O h w@A 1 Õ â ?C J@H@AF CICIG N CIH@�AKLC QACF C J@L F GHG =S h gaKBGLHKHC]G h w@A 1 Õ â J@H@AF CIKA@ C F GHC HKLC Bc@ LK ÊGHK J@L QEIHG FKH@ACKL@ ACF KI�K BG?HKIH@ I@L H@FQG =

vGLEDCGI@ I@LLK ?@DCGI@ S =Z =<Zì Ð2 ÐÏÏ í ÷�� üðFñòöð ïò ý ÷õõîøòõî ï÷ú Ûì ÐÛ ÐÏ00�fI QEIHG F KH@ACKL@ Q@?KIH@ Ì ]CIBGLKHG ?@IDK KHHACHG KLLK ?EQ @A�BC@ JC AGHKDCGI@ J eK??@ ]@AHCBKL@ � u J@?BACHHK CIBGGAJCIKH@ BCLCIJACBc@ JKLL e@ÊKDCGI@ � Õ Òà � 6 �� Ô u BGI â > � > Ú' u 6 BG?HKIH@ QG?CHC]K F CIGA@ JC à=Kh \ CFG?HAK Bc@ CL BGAAC?QGIJ@IH@ ?C?H@F K LK�AKI�CKIG Ì CIH@�AKRCL@ =

R h \ CFG?HAK Bc@ @?C?HGIG BGIJCDCGIC CI CDCKLC HKLC Bc@ CL QEIHG ?C FEG]K F KIH@I@IJG LK ÊGHK BG?HKIH@ = \@?BAC] CHKLC F GHC =

vGLEDCGI@ I@LLK ?@DCGI@ S =Z =<<ì Ð2 ÐÏÛ í ÷�� ÷. û ù� òF ð õðFñòöð ïò ÷�ðø÷�ð ÷ î Ðî Ð0��0� ÐvC BGI?CJ@AC LK aEIDCGI@ PK�AKI�CKIK y

& Õ àÚ Ò ß/ 3 � ß/ Ô � /3 � / á Ò/3 � / Ôý & gO =<h

<h vaAEHHKIJG LK ?CFF@HACK J@LLK PK�AKI�CKIK JCF G?HAKA@ Bc@ @?C?H@ EI CIH@�AKL@ QACF G J@L BGAAC?QGIJ@IH@ ?C?H@F K JCPK�AKI�@ u JC?HCIHG JKLL eCIH@�AKL@ QACF G J@LL e@I@A�CK = \@HHG � HKL@ CIH@�AKL@ QACF G u ?C BGI?CJ@AC CL ?C?H@F K JC PK�AKI�@AC?HA@HHG ?E C LC]@LLC � Õ = Þ = � � 0 ~â� = vC JCF G?HAC Bc@ HKL@ A@?HACDCGI@ Ì KIBGAK EI ?C?H@F K PK�AKI�CKIG u KJ EI �AKJGJC LCR @AH� u @ ?C ?BAC]K LK BGAAC?QGIJ@IH@ PK�AKI�CKIK & B1C = vC ?HEJCIG ÊCIJC L@ GARCH@ KL ]KACKA@ JC = =Nh vC BGI?CJ@ACIG Q @A CL ?C?H@F K JC PK�AKI�CKIK & L@ BGIJCDCGIC CI CDCKLC y

Ø/ 3 ÒâÔ � ¥ / ÒâÔ Õ âØ ß/ 3 ÒâÔ � ¥ ß/ ÒâÔ Õ â gO =NhØ Þ ¥ � � Þ ¥ |Õ â &

vC ?HEJCIG C BGAAC?QGIJ@IHC F GHC u CIJC]CJEKIJG CI QKAHCBGLKA@ u ?@ @?C?HGIG u F GHC K F @HK K?CIHGHCBK =vGLEDCGI@ I@LLK ?@DCGI@ S =Z =<N

ì Ð2 ÐÏì ü� ÷í ÷�� û üðFñòöð ïò ý ÷õõîøòõî �îùòðøîú÷ ï÷ú Û ÐÛ Ð0 fI JC?BG AC� CJG JC F K??K ` @ AK��CG � Ì LCR @AG JC ?BGAA@A@ ?@IDK KHHACHG ?E JC EI QCKIG GACDDGIHKL@ � ??G = vEL RGAJGJ@L JC?BG QE2 ?BGAA@A@ u KIBGAK ?@IDK KHHACHG u EI QEIHG F KH@ACKL@ JC F K??K � =

vC ACBcC@J@ JC J@H@AF CIKA@ CL F GHG J@L ?C?H@FK =vGLEDCGI@ I@LLK ?@DCGI@ S =Z =<O

ì Ð2 ÐÏ� ü� ÷í ÷ø ÷�� üðFñòöð �÷��òðø÷ ÷�öòGî î Ðî Ð 0ì�0�TI EI QCKIG GACDDGIHKL@ ?GIG QG?H@ JE@ K?H@ W3i 3 @ Wi JC AC?Q @HHC]@ F K??@ <3 @J < gJC?HACREDCGI@ JC F K??KGFG�@I@Kh @ LEI�c@DD@ & 3 @J & = P@ K?H@ ?GIG LCR @A@ JC AEGHKA@ KHHGAIG KC AC?Q @HHC] C RKACB@IHAC � 3 @ � u � ??C I@LQ CKIG u BGI Ö� 3� Ö Õ ) � â =vCK � EI QEIHG KQQKAH@I@IH@ KLL eK?HK W3i 3 u �CKB@IH@ HAK � 3 @ W3 u � EI QEIHG KQQKAH@I@IH@ KLL eK?HK Wi u� CKB@IH@ HAK � @ W u Ö� 3� Ö Õ Ö� � Ö Õ � � â = �AK C QEIHC � @ � K�C?B@ EIK FGLLK CJ@KL@ u JC BG?HKIH@ @LK?HCBK 1 � â =vC ACBcC@J@ y

<h ?BAC]@A@ LK PK�AKI�CKIK J@L ?C?H@F K �Nh J@H@AF CIKA@ �LC @ÊCLCRAC �Oh JC?BEH@A@ LK ?HKRCLCH� J@�LC @ÊCLCRAC KL ]KACKA@ J@L QKAKF @HAG Ø Õ '� CI �é á ~à� �

� _

Sh BGI?CJ@AKHG CL ?C?H@F K BGAAC?QGIJ@IH@ K ) Õ â u ?C JC?BEHK CL BGAAC?QGIJ@IH@ ?C?H@F K LK�AKI�CKIG u F G?HAKIJGBc@ Ì ACBGIJEBCRCL@ KJ EI ?C?H@F K KJ EI �AKJG JC LCR @AH� =vGLEDCGI@ I@LLK ?@DCGI@ S =Z =<S

ì Ð2 ÐÏ� í ÷ø ÷3 ø÷õðøïð îññ÷úúð ý ÷õõîøòõî � îùòðøîú÷ î Ðî Ð 0ì�0� ÐvC BGI?CJ@AC CI EI QCKIG GACDDGIHKL@ EI QEIHG F KH@ACKL@ � u JC F K??K � = TL QEIHG Ì ACBcCKF KHG u HAKF CH@ EIK FGLLKCJ@KL@ JC BG?HKIH@ @LK?HCBK 13 u g13 � âÔ u JKL QEIHG �??G � = TIGLHA@ u K JC?HKIDK ) JK � § QG?HG CL B@IHAG JC EI B@ABcCG uJC AK��CG � = TL B@ABcCG Ì �??G = vEL B@ABcCG Ì LCR @AG JC ?BGAA@A@ ?@IDK KHHACHG EI QEIHG F KH@ACKL@ � JC F K??K < = TQEIHC � @ � CIH@AK�C?BGIG HAKF CH@ EIK FGLLK CJ@KL@ JC BG?HKIH@ @LK?HCBK 1 u g1 � âÔ &� ~ & vC ?BAC]K LK PK�AKI�CKIK J@L ?C?H@F K @ ?C J@H@AF CICIG L@ ?GLEDCGIC ?HKDCGIKAC@ J@L BGAAC?QGIJ@IH@ ?C?H@F K JCPK�AKI�@ =� � ~ & vC JC?BEHK LK ?HKR CLCH� J@LL@ ?GLEDCGIC JC @ÊCLCRACG HAG]KH@ KL QEIHG � ~ u J@H@AF CIKIJG L@ aA@Ê@ID@ J@LL@ QCBBGL@G?BCLLKDCGI C KHHGAIG KLLK QG?CDCGI@ JC @ÊCLCRACG ?HKRCL@ =� � � ~ & vC BGI?CJ@AC CL BK?G y ) Õ â & vC JCF G?HAC Bc@ CL ?C?H@F K PK�AKI�CKIG cK EI CIH@�AKL@ QACF G CIJCQ @IJ@IH@JKLL e@I@A�CK = vC ?BAC]K LK aEIDCGI@ JC �KF CLHGI J@L ?C?H@F K BGAAC?QGIJ@IH@ KL ]KLGA@ IELLG JC J@HHG CIH@�AKL@ QACF G uE ?KIJG BGF@ BGGAJCIKHK ?QKDCKL@ CIJCQ @IJ@IH@ LK JCH@A@IDK J@LL@ KIGF KLC@ KI�GLKAC JC � @ JC � =� Ñ ~ & vC BGI?CJ@AC CL BK?G LCF CH@ CI BEC � Ö�� Ö Ì HAK?BEAKRCL@ AC?Q @HHG K < � � ?C ]KLEHC ÊCIJC CI Ê@?HK KQQAG??CF KDCG{I@ LK aEIDCGI@ JC �KF CLHGI K QKAHCA@ JK Ê@LLK J@H@AF CIKHK I@L QEIHG QA@B@J@IH@ u @ ?C JCF G?HAC Bc@ CL BGAAC?QGIJ@IH@?C?H@F K �KF CLHGICKIG Ì CIH@�AKRCL@ =

vGLEDCGI@ I@LLK ?@DCGI@ S =Z =<Uì Ð2 ÐÏ í ÷ø ÷.vC BGI?CJ@AC EI QEIHG F KH@ACKL@ JC F K??K � ?G��@HHG KJ EI BKFQG JC aGAD@ JC @I@A�CK QGH@IDCKL@ Ñ ÒÓ Þ Þ � Ô ?GJJC{?aKB@IH@ CL ?@�E@IH@ A@ÊC?CHG y CL Q GH@IDCKL@ Ì CI]KACKIH@ AC?Q@HHG KL �AEQQG JC JCH@GFGA�?F C y

4 ÒÓ Þ Þ � Ô Õ ÅÆ�� á �å� � â�å� � �� ââ â àÇÈ ÅÆÓ�ÇÈ � ÅÆ â

âØ� ÇÈ & gO =Oh

� äå� ã �� ã�ã= vC HAG]C L eCIH@�AKL@ QACF G BGAAC?QGIJ@IH@ KLLK ?CFF@HACK J@LL e@I@A�CK QGH@IDCKL@ @ ?C J@H@AF CI C EI?C?H@F K JC BGGAJCIKH@ KJKHHKHG Ò� Þ � Þ � Ô &� U��ã �� ã�ã= f ?KIJG LK ?CFF@HACK J@L ?C?H@FK ?C ACJEBK JC EIG CL IEF @AG J@C �AKJC JC LCR @AH� u BGI?CJ@AKIJGÊCIJC EIK GQQGAHEIK PK�AKI�CKIK ACJGHHK = \@H@AF CIKA@ �LC @ÊCLCRAC JC HKL@ PK�AKI�CKIK ACJGHHK @ JKAI@ EIKCIH@AQA@HKDCGI@ CI H@AF CIC J@LL@ BGGAJCIKH@ Ò� Þ � Þ � Ô &�Uä�ã �� ã�ã= vC ?HEJC LK ?HKRCLCH� J@�LC @Ê CLCRAC I@L BK?G QKAHCBGLKA@ y

Ñ Ò� Þ � Þ � Ô Õ à� Ò�� ÒØ� á � Ô á �å� ÒØ� á � ÔÔ & gO =ShvGLEDCGI@ I@LLK ?@DCGI@ S =Z =<V

ì Ð2 ÐÏ� í ÷�� ÷3 ÷35 ÷�� üðFñòöð ïò ý ÷õõîøòõî � îùòðøîú÷ ÷ 0�� 0 ÷ �� îññ÷úúð ÷ �÷�� Ð÷�öòGî

fI QEIHG F KH@ACKL@ JC F K??K EICHKACK Ì ]CIBGLKHG K FEG]@A?C ?E LLK ?EQ@A� BC@ JC AGHKDCGI@ JC @ÊKDCGI@ � Õ á 36 á 36 uJG]@ � Õ Ó � =vEL QEIHG K�C?B@ EIK aGADK BG?HKIH@ u JC CIH@?CH� EICHKACK u JCA@HHK ]@A?G LK JCA@DCGI@ I@�KHC]K J@LL eK??@ � =<h vBAC] C LK PK�AKI�CKIK @ L e� KF CLHGICKIK J@L ?C?H@FK =Nh \@H@AF CIK �LC CIH@�AKLC QACF C J@L F GHG =Oh \@H@AF CIK L@ BGIJCDCGIC ?EC JKHC CI CDCKLC Q @A BEC CL F GHG @?C?H@ Q @A HEHHC C H@FQC u Q @A BEC ?C cKIIG GARCH@

LCF CHKH@ u Q@A BE C ?C cKIIG GARCH@ CLLCF CHKH@ =

�p

Sh zGI?CJ@AK EI eGARCHK CLLCF CHKHK = � �ICHG L eKI�GLG äåæ çèéê � ÒëÔ á äåæ çè yê � ÒëÔã g� ÒëÔ Ì L eKI�GLG Bc@ LKBGI�CEI�@IH@ HAK CL QEIHG FKH@ACKL@ @ L eK??@ J@LL@ � aGAF K BGI EI K??@ GACDDGIHKL@ � ??Gh =Uh | C?GL]C CL F GHG Q@A ÊKJAKHEA@ F @JCKIH@ LK ?GLEDCGI@ J@LL e@ÊKDCGI@ JC �KF CLHGI {�KBGRC =

Vh \@H@AF CIK LK A@�CGI@ J@LLG ?QKDCG J@LL@ aK?C CI BE C CL F GHG ?C QE2 J@?BAC]@A@ CI ]KACKRCLC KDCGI@{KI�GLG @J@H@AF CIK L@ ]KACKRCLC J eKDCGI@ =

vGLEDCGI@ I@LLK ?@DCGI@ S =Z =<Xì Ð2 ÐÏ( ü� ÷í ÷�� ÷3 ÷35 üðFñòöð ïò ý ÷õõîøòõî �îùòðøîú÷ ÷ Û��0� �0 ÷ �� îññ÷úúð ÷ �÷�� Ð

îôöôøøîú÷vC BGI?CJ@AC u CI EI QCKIG �??G GACDDGIHKL@ u EIK �ECJK 7 u LC?BCK u K aGAF K JC KABG JC QKAKRGLK u LCR @AK JC AEGHKA@ ?@IDKKHHACHG KHHGAIG KL ?EG ]@AHCB@ � u � ??KHG ?EL QCKIG = vCK � CL ?EG FGF@IHG JC CI@ADCK AC?Q @HHG KJ � = TI EI ?C?H@F K JCBGGAJCIKH@ BKAH@?CKI@ Ò� Þ # Þ $ Ô u ?GLCJKL@ BGI LK �ECJK u @??K Ì AKQQA@?@IHKHK JKLL e@ÊKDCGI@ $ Õ 6# u 6 � â u Ö# Ö . � u� � â =

fI QEIHG FKH@ACKL@ � JC FK??K � u Ì LCR @AG JC ?BGAA@A@ ?@IDK KHHACHG ?E LLK �ECJK 7 = TL QEIHG � § ACBcCKF KHG JK� Q@A CL HAKF CH@ JC EIK FGLLK @LK?HCBK JC BG?HKIH@ 1 � â =vC J@IGHC BGI � L eKI�GLG Bc@ LK JCA@DCGI@ HKI�@IH@ CI � KLLK �ECJK aGAF K BGI EIK JCA@DCGI@ �??K J@L Q CKIG g]@JC��EAKh = .� vC ?BAC]K LK PK�AKI�CKIK J@L ?C?H@F K u ACBGIG?B@IJGI@ L@ @]@IHEKLC ?CFF@HAC@ @J C BGI?@�E@IHC CIH@�AKLC

-2.830 -2.264 -1.698 -1.132 -0.566 0.000 0.566 1.132 1.698 2.264 2.830

-2.0

-1.6

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

1.6

2.0

x

-2.830 -2.264 -1.698 -1.132 -0.566 0.000 0.566 1.132 1.698 2.264 2.830

-2.0

-1.6

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

1.6

2.0

y

-2.830 -2.264 -1.698 -1.132 -0.566 0.000 0.566 1.132 1.698 2.264 2.830

-2.0

-1.6

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-0.8

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0.0

0.4

0.8

1.2

1.6

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xi

-2.830 -2.264 -1.698 -1.132 -0.566 0.000 0.566 1.132 1.698 2.264 2.830

-2.0

-1.6

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

1.6

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eta

-2.830 -2.264 -1.698 -1.132 -0.566 0.000 0.566 1.132 1.698 2.264 2.830

-2.0

-1.6

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

1.6

2.0

P

-2.830 -2.264 -1.698 -1.132 -0.566 0.000 0.566 1.132 1.698 2.264 2.830

-2.0

-1.6

-1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

1.6

2.0

QACF C =i� \GQG K]@A ACBGIG?BCEHG L e@?C?H@IDK JC EI CIH@�AKL@ QACF G 8 gELH@ACGA@ AC?Q @HHG KLL e@I@A�CKh u ?C KIKLCDDCIG C F GHC J@L?C?H@F K EICJCF @I?CGIKL@ Bc@ ?C GHHC@I@ �??KIJG CL ]KLGA@ JC 8 =q � vC J@H@AF CICIG J@LL@ BGIJCDCGIC ?EC JKHC CI CDCKLC Q @A BEC CL FGHG J@L ?C?H@F K BGFQG?HG JKLLK �ECJK @ JKL QEIHGF KH@ACKL@ ?CK Q @ACGJCBG =� � vC ?BAC]K L e �KF CLHGI CKIK @ ?C JC?BEHK L e@ÊKDCGI@ JC �KF CLHGI{�KBGRC u BGI CL F @HGJG JC ?@QKAKDCGI@ J@LL@ ]KACKRCLC =

vGLEDCGI@ I@LLK ?@DCGI@ S =Z =<Xì Ð2 ÐÏ0 ü� ÷í ÷�� ÷3 ÷35 ÷�� üðFñòöð ïò ý ÷õõîøòõî � îùòðøîú÷ ÷ (�Ï2� �0 ÷ �� îññ÷úúð ÷�÷�� Ð îôöôøøîú÷zGI?CJ@AK EIK H@AIK JC ACa@ACF @IHG CI@ADCKL@ Ò� Þ 9 Þ: Þ VÔ = fI JC?BG AC� CJG JC F K??K < @ AK��CG � u @ e ] CIBGLKHG KJK]@A@ CL B@IHAG CI � = P eK??@ ; u QK??KIH@ Q@A � @J GAHG�GIKL@ KL JC?BG u Ì ]CIBGLKHG K FEG]@A?C ?EL Q CKIG 9 Þ : u @JCIGLHA@ CL JC?BG Ì LCR @AG JC AEGHKA@ CIHGAIG K HKL@ K??@ ; =

��

vEL RGAJG J@L JC?BG Ì � ??KHG EI QEIHG F KH@ACKL@ � JC FK??K � u Bc@ Ì ACBcCKF KHG JKLL eK??@ V JK EIK FGLLK JCBG?HKIH@ @LK?HCBK 1 =zGI?CJ@AK CL ?C?H@FK CI K??@IDK J@LLK aGADK JC �AK]CH� =

-2.1 2.1

-1.50

0.00

1.50

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-1.50

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1.50

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-1.50

0.00

1.50

y

z

x

-2.1 2.1

-1.50

0.00

1.50

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-1.50

0.00

1.50

phi

-2.1 2.1

-1.50

0.00

1.50

-2.1 2.1

-1.50

0.00

1.50

teta

P

<h TIJC]CJEK C �AKJC JC LCR @AH� J@L ?C?H@F K @ ?BAC] C LK PK�AKI�CKIK @ L e� KF CLHGICKIK =Nh \@H@AF CIK ?CFF@HAC@ @J CIH@�AKLC QACF C u @ ACJEBC LG ?HEJCG J@L F GHG J@L ?C?H@F K KJ EI QAGRL@F K KJ EI �AKJG

JC LCR @AH� =Oh vHEJCK ÊKLCHKHC]KF @IH@ CL F GHG EICJCF @I?CGIKL@ Bc@ cKC GHH@IEHG u @J CI QKAHCBGLKA@ KIKLCDDK LK ?HKRCLCH� J@LL@

?GLEDCGIC ?HKDCGIKAC@ u KL ]KACKA@ J@C QKAKF @HAC =S h | C?GL]C CL QAGRL@F K BGI CL F @HGJG JC �KF CLHGI{�KBGRC @ J@H@AF CIK LK A@�CGI@ J@LLG ?QKDCG J@LL@ aK?C I@LLK ÊKL@

CL F GHG QE2 @??@A@ J@?BACHHG CI ]KACKRCLC KDCGI@{KI�GLG =vGLEDCGI@ I@LLK ?@DCGI@ S =Z =<Y

ì Ð2 ÐÛ2 <ü û üðFñòöð ïò ý ÷õõîøòõî ï÷ú Ûì ÐÛ ÐÏ00�vC BGI?CJ@AC LK HAK?aGAFKDCGI@ �= ( �é $ � � Õ áKABHKI *·> +� Õ ¥ / � ? gO =Uh

Kh \@H@AF CIKA@ C ]KLGAC JC ¥ Q@A BEC �= § BKIGICBK �R h ?BAC]@A@ Q @A HKLC ]KLGAC L e@?QA@??CGI@ @?QLCBCHK JC � y3= =vGLEDCGI@ I@LLK ?@DCGI@ S =Z =NZ

ì Ð2 ÐÛ Ï <üvC BGI?CJ@AC LK HAK?aGAFKDCGI@ �= ( �é $ � � Õ áKABHKI *·> +� Õ ¥ / � ? gO =Vh

Kh \@H@AF CIKA@ C ]KLGAC JC ¥ Q@A BEC �= § BKIGICBK �R h ?BAC]@A@ Q @A HKLC ]KLGAC L e@?QA@??CGI@ @?QLCBCHK JC � y3= =vGLEDCGI@ I@LLK ?@DCGI@ S =Z =N <

��

ì Ð2 ÐÛÛ <ü ÷�� ÷ù ø÷õðøïð õðFñòöð ïò ÷�ðø÷�ð î Ðî Ð0� ÐvC BGI?CJ@AC LK aEIDCGI@ + Õ à

Ú ~ Ò? 3 á n Ò/ 3 ÔÔ � ? � � � Ò/ 3 Þ / Ô & gO =MhvC JCF G?HAC Bc@ LK HAK?aGAF KDCGI@ y ? 3 á n Ò/3 Ô Õ � 3/3 Õ � 3? Õ �/ Õ � gO =Xh

§ BKIGICBK =gNh = vC BGI?CJ@AC Ê CIJC LK ?@�E@IH@ �KF CLHGICKIK y8+ Õ à

Ú ~� 3 � � � � � Ò� 3 Þ� Ô & gO =YhJG]@ � Ò� 3 Þ� Ô Õ à

Ú Ò� 3 � # � Ô � :� 3� & gO =<ZhvC JCF G?HAC Bc@ Ì QG??CRCL@ CIHAGJEAA@ ]KACKR CLC KDCGI@{KI�GLG u CI FGJG Bc@ CI Ê@?H@ IEG]@ ]KACKRCLC L e�KF CLHG{

I CKIK K??EF K LK aGAF K y 8+ Ò�3 Þ � Þ R3 Þ R Ô Õ �3 � # � � :6�3 Ò� Ô } àIbR3àIbR Þ gO =<<hQ @A EI GQQGAHEIG ]KLGA@ J@LLK BG?HKIH@ 6 =gOh = vC J@H@AF CICIG L@ BGIJCDCGIC ?E # u HKLBc§ BGI EI BKFRCKF @IHG JC ]KACKRCLC ?CFQL@HHCBG Ò� Þ R Ô $ Ò8 Þ� Ô u LK�KF CLHGICKIK QA@IJK LK aGAF K y + Ò8 Þ� Ô Õ 83 � # 8 � � Ò: Ô & gO =<Nh

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ì Ð2 ÐÛ� ü� ÷3 ÷35 ÷ù û - �ðø÷�ð ïò ý ÷õõîøòõî � îùòðøîú÷ ï÷ú � �02fI eK?HK GFG�@I@K JC F K??K < LEI�K & cK EI @?HA@FG �??G CI Z = P eKLHAG @?HA@FG Ì ]CIBGLKHG ?@IDK KHHACHG ?E EIKBCABGIa@A@IDK JC AK��CG & �Ú Bc@ �CKB@ ?E EI QCKIG GACDDGIHKL@ @ CL BEC B@IHAG Ì ?ELLK ]@AHCBKL@ ?GHHG Z = fI QEIHGF KH@ACKL@ Q @?KIH@ w JC F K??K � Ì ]CIBGLKHG ?@IDK KHHACH C KLLK A@HHK BGIH@I@IH@ L eK?HK @J Ì KIBc@ ?G��@HHG KLLK aGADK@LK?HCBK á1â� u 1 � â =<h vBAC]@A@ L ecKF CLHGICKIK J@L ?C?H@FK @ CIJC]CJEKA@ JE@ CIH@�AKLC QACF C J@L F GHG =Nh vBAC]@A@ L@ @ÊKDCGIC JC �KF CLHGI{�KBGRC @ QGAHKAI@ KLL@ ÊKJAKHEA@ LK ?GLEDCGI@ =Oh TIH@�AKA@ L@ @ÊKDCGIC JC �KF CLHGI{�KBGRC KLL eGAJCI@ D@AG CI ��< @ JKA@ EI eCIH@AQA@HKDCGI@ �?CBK J@L AC?ELHKHG =S h gaKBGLHKHC]G h WKLEHKA@ LK BGAA@DCGI@ KL QACF G GAJCI@ CI � �< u A@LKHC]KF @IH@ KL QEIHG Oh =

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Esercizi di Meccanica Razionale АА -2000, corsi Marchioro, Negrini