1. No category

WHY DO FIRMS HEDGE? - Douglas T. Breeden

`Ov # 6W+5 O,#B,q 5v,A+W W6+AW #,w
#NBw5 +,,#,W
5 VW5`AOW
At ihtL?G 6iMh@h) bbH
W LhhitTL?_?}
@|LhG 5 Vt@?@|@?c Vt|?} ttLU@|i hLuittLh Lu 6?@?Uic
`@h|L? 5ULL*c N?iht|) Lu i??t)*@?@c *@_i*T@ bfec Ai*G 2DHbH
.S.c ,WwG t@?@|94@*_!ii_ Ai €ht| @|Lh t @ttLU@|i_ | |i 6^@
5ULL* Lu t?ittc #!i N?iht|) #h@4c 2..fH @?_ | 54| hii_i?
ttLU@|it @?_ |i tiUL?_ @|Lh t @ttLU@|i_ | |i 6^@ 5ULL* Lu t?itt
v@?} i?<t UL4T|@|L?@* @ttt|@?Ui t }hi@|*) @TThiU@|i_ `i Li @ tTiU@* _iM| |L
ih?@h_ #4@t uLh t UL44i?|t @?_ uLh ThL__?} t |L hiti |i T@Tih `i |@?!
a4 ?|L?c 5}@|L @||@U@h)@c LM #@44L?c i|ih #i@h3Lc !i 6t4@?c
#L} 6Lt|ihc +U! Bhii?c aLi* O@MhUc *| O@hhtc ki? U@h_*ic !i ihihc
5|i@h| )ihtc h| +@c #@_ 5U@hut|i?c it|ih 5T@||c +i?i 5|*3c ti4?@h
T@h|UT@?|t @| |i 6 4ii|?}t ? `@t?}|L?c @h?i}i i**L?c #!ic 6i_ih@*
+itihi Lu |*@?|@c O, @?_ Lh|it|ih? uLh |ih UL44i?|t Ai Wt*i @*}?i
6?_ @?_ |i t?itt ttLU@|it 6?_ Lu |i 6^@ 5ULL* Lu t?itt tTTLh|i_
|t hiti@hU

5A+A
`i Thiti?| @? @t)44i|hU ?uLh4@|L? 4L_i* Lu i_}?} |@| @t |i ?||L? |@|
i_}?} t ?_ih|@!i? M) }ih @M*|) 4@?@}iht L t |L R*LU!? |i }ih
ThL€|t |@| hit*| uhL4 |ih }ih @M*|) Atc i_}?} t @? @||i4T| |L 4ThLi
|i ?uLh4@|i?itt Lu |i *i@h??} ThLUitt M) |i }ih @M*|) 4@?@}ih `i @?@*)3i
|L 4L_i*t `i €ht| @?@*)3i @ 4L_i* ihi 4@?@}iht U@hi L?*) @ML| |ih hiT
|@|L?t W? |t U@tic i tL |@| @? ?||i i^*Mh4 |@| ?L*it i_}?} M)
}ih @M*|) 4@?@}iht @*@)t i t|t wLih @M*|) 4@?@}iht @*tL i_}i i? _gih
i?Uit ? @M*|it @hi *L M| _L ?L| i_}i i? _gihi?Uit ? @M*|it @hi } `i
UL?t_ih @ tiUL?_ 4L_i* ihi 4@?@}iht L*_ i^|) ? |i €h4 ? @__|L? |L U@h?}
uLh |ih 4@?@}ih@* hiT|@|L?t Ai Thiti?Ui Lu 6#W ?th@?Ui Lh Thii t|?} _iM|
4@!it i_}?} ULt|*) |L i^|)L*_iht @t | t @ @h@?Ui hi_U?} @U||) OLiihc
|t ULt| Lu i_}?} t *Lih uLh }ih @M*|) 4@?@}iht At *i@_t |L ML| !?_t Lu
4@?@}iht ?L| i_}?} i? |i _gihi?Ui ? @M*|) t *L | }ih _gihi?Uit ?
@M*|)c |i ?||i i^*Mh4 ? U |i }ih @M*|) 4@?@}ih i_}it i t|t W?
|t i^*Mh4c }hi@|ih tiT@h@|L? LUUht hi*@|i |L |i U@ti ihi 4@?@}iht ihi
L?*) UL?Uih?i_ @ML| |ih hiT|@|L?t
2
`Ov # 6W+5 O,#B,q 5v,A+W W6+AW #,w
W? hiUi?| )i@htc L*@|*|) ? ?|ihit| h@|it @?_ Uhhi?Uit @t *i_ ULhTLh@|i €
?@?U@* 4@?@}iht |L UL?t_ih @?_ ?_ih|@!i i_}?} L? @ tU@*i |@| t ?ThiUi_i?|i_
At @@hi?itt Lu i_}?} @t @ ht! 4@?@}i4i?| |LL* t _hi? M) @ ?4Mih Lu u@U|Lht
6ht|c |ihi t |i Tih@ti Mi*iu |@| _t@t|iht *!i |i t@?}t @?_ *L@? _t@t|ih Lu
bHft UL*_ @i Mii? @L_i_ u |i ?t|||L?t ihi ThLTih*) i_}i_ @}@?t| ?|ih
it| h@|i ht! E|t i t i Thitti_ ? |i `@** 5|hii| aLh?@* L? }t| . bb
54*@h*)c ?4ihLt @?iU_L|@* i @4T*it Lu €h4t @?} *@h}i *Lttit Lh }L?} M@?!hT|
_i |L |ih u@*hi |L i_}i i U@?}i h@|i 4Li4i?|t i t| ?i u@4Lt i @4T*i t
|i w@!ih h@)t i @4T*i ihi w@!ih<t ULt|t Lu MLhhL?} EL? @hT*@?it ihi ?
_L**@ht *i |t hii?it ihi tT*| ii?*) Mi|ii? _L**@ht @?_ TL?_t Etii 5@ThL<t
MLL!c W?|ih?@|L?@* 6?@?U@* @?@}i4i?|c Ah_ ,_|L?c T@}it 2.D.S uLh 4Lhi _i
|@*t L? |t i @4T*i 5iUL?_ @?_ i^@**) 4TLh|@?|c |ihi @t Mii? @? i?Lh4Lt
?Uhi@ti ? |i *^_|) Lu 4@h!i|t Ei|ih |h@_i_ Lh Lih |i UL?|ih |@| ThL_i
?t|h4i?|t uLh i_}?} ULhTLh@|i ht!
Bi? |t @||i?|L? |L i_}?} @| @ ULhTLh@|i *ii* @?_ |i ThL*uih@|L? Lu
UL4T*i i_}?} |iU?^it E*@h}i*) _hi? M) @U@_i4U hiti@hU L? LT|L? @?_ u
|hit ThU?} 4L_i*tc |i T@U|) Lu @U@_i4U hiti@hU L? |i u?_@4i?|@* ^it|L?
Lu ) @?_ i? €h4t tL*_ i_}i t thTht?} W? u@U|c |i |h@_|L?@* u** ?uLh4@
|L? TihuiU| U@T|@* 4@h!i|t 4L_i* Lu |i €h4 t@)t ih) *||*i @ML| ) €h4t i_}i
@?_ 4T*it |@| i|ih €h4t i_}i Lh ?L| t hhi*i@?| @t ?it|Lht U@? ?_ih|@!i
|i ?iUitt@h) i_}?} @U||it M) |i4ti*it At i t i Thitti_ ? @ hiUi?| @h
|U*i M) *T @?_ **ih EbbD ihi |i) t|@|i |@| R4Lt| @*i 4@ 43?} €h4t
_L ?L|c ? u@U|c i_}i
`*i |i u** ?uLh4@|L? TihuiU| U@T|@* 4@h!i|t T@h@_}4 @t *||*i |L t@)
@ML| ) €h4t i_}ic L|ih 4TLh|@?| T@h@_}4t *!i |i LT|L? ThU?} T@h@_}4

4T*) |@| €h4t ** ThLM@M*) ?_ih|@!i ht!) @U||it u |i) @hi h? M) i^|)L*_
iht @t |i LT|L? @*i Lu i^|) t ?Uhi@ti_ M) tU @h@?Ui ?Uhi@t?} @U||it
Oi?Uic |i 4@? _i@t Lu ULhTLh@|i €?@?Ui @i *||*i |L t@) L? ) €h4t i_}i @?_
tii4 |L ?_U@|i |@| Eu @?)|?} |ihi @hi t|hL?} ?Ui?|it @}@?t| i_}?}
h T@Tih Thiti?|t @? i T*@?@|L? @t |L ) €h4t i_}i M@ti_ L? @ |iLh) Lu
4@?@}ih@* hitTL?tit |L @t)44i|hU ?uLh4@|L? Ai !i) ?||L? t |@| 4@?@}iht
L @i tTihLh @M*|it | hitTiU| |L tL4i ht!t Lh ?Uih|@?|it ** |h) |L
i?thi |@| |ih tTihLh @M*|it @hi ^U!*) _tULihi_ M) |i 4@h!i| AL i?thi
|tc |i) ** |h) |L i_}i |Lti ht!t |@| @hi ?L| ?_ih |ih UL?|hL* @?_ ihi |i)
@i ?L i UiT|L?@* @M*|it At i_}?} hi_Uit |i ?Lti ? |i *i@h??} ThLUitt
M) R*LU!?}? |i tTihLh @M*|) W? UL?|h@t|c 4@?@}iht | ?uihLh @M*|it @i
?Ui?|it |L hi_Ui |i iUi?U) Lu |i *i@h??} ThLUitt Ai) L*_ Thiuih |@| @**
4@?@}iht ?_ih|@!i ht!) @h@?Ui ?Uhi@t?} @U||it OLiihc }i? |@| tTihLh
4@?@}iht ?_ih|@!i i_}?} @U||itc *Lih @M*|) 4@?@}iht 4@) Lh 4@) ?L| i_}i
t i ** tLc |ih _iUtL? |L i_}i Lh ?L| |L i_}i _iTi?_t L? L 4U *Lih
|ih @M*|) t hi*@|i |L 4@?@}iht Lu tTihLh @M*|)
Ai @MLi ?||L? @tt4it |@| 4@?@}iht @hi 4@?*) UL?Uih?i_ @ML| |ih
4@?@}ih@* hiT|@|L?t t|hL?} @h}4i?| U@? Mi 4@_i |@| 4@?@}ih@* UL4Ti?t@
|L? t hi*@|i_ |L i^|) TihuLh4@?Ui Oi_}?} @U||it @hi ?ihi?|*) ht! hi_U?}
@?_ hi_Ui |i @*i Lu |i i^|) i? |ihi t Thii t|?} _iM| Lh i? |ihi t
?th@?Ui *!i 6#W ?th@?Ui |L M@?!t Lh }Lih?4i?| *L@? }@h@?|iit Wu 4@?@}iht
L*_ tL4i uh@U|L? Lu i^|) @?_ @hi @*tL UL?Uih?i_ @ML| i^|) @*itc }ih @M*
|) 4@?@}iht ** ?L| i_}i ?*itt |i @M*|) _gihi?Ui t tMt|@?|@* `i? |i)
_L i_}ic |i i^|) LT|L? @*i uLhi}L?i @U|t *!i @ t}?@*?} ULt| ? @ |h@_|L?@*
t}?@*?} 4L_i* Ai }ih @M*|) 4@?@}ih !?Lt |@| t TihuLh4@?Ui t }L?} |L
Mi Mi||ih t @ UL?ti^i?Uic |i ThLM@M*|) Lu M@?!hT|U) t 4U *ittc 4@!?} |i
2
i^|) LT|L? *itt @*@M*i @| |i 4@h}? Ai *Lih @M*|) 4@?@}ih @t @ }hi@|ih
ThLM@M*|) Lu M@?!hT|U) @?_ i?Ui @t @ 4Lhi @*@M*i i^|) LT|L? @| |i 4@h}?
L?ti^i?|*)c |i i^|) LT|L? ?Uhi@tit |i ?Ui?|it Lu |i }ih @M*|) 4@?@}ih
|L i_}i
h 4L_i* |t ThL_it @ h@|L?@*i uLh ) €h4t i_}i @?_ i? €h4t
** ?_ih|@!i i_}?} @U||it W? T@h|U*@hc Lh 4L_i* ?_U@|it |@| u ULt|t Lu
i_}?} *!i |i hi_U|L? ? |i i^|) LT|L? @*i @hi Thiti?|c |i €h4 4@?@}iht
** ?_ih|@!i i_}?} @U||it L?*) i? |i) Mi*ii |@| |i) @i tTihLh
@M*|it @?_ i? |iti tTihLh @M*|it hit*| ? TihuLh4@?Ui tMt|@?|@**) }ih
|@? |@| Lu L|ih 4@?@}iht ? |i ?_t|h) Lu *ittih @M*|) tL @t |L UL4Ti?t@|i
uLh |iti ULt|t Lu i_}?} W? @__|L?c Lh 4L_i* ?_U@|it @ hi*@|L?tT Mi|ii?
4@?@}ih@* UL4Ti?t@|L? @?_ i_}?} TL*U) Ai }hi@|ih |i uh@U|L? Lu i^|) |@|
|i 4@?@}ih L?tc |i }ih t |i 4T*U| ULt| Lu i_}?} @?_ i?Ui i_}?} LUUht
L?*) i? |i 4@?@}ih @t @ tMt|@?|@* TihuLh4@?Ui _gihi?|@* Lih 4@?@}iht ?
L|ih hi*@|i_ €h4t
Aiti hit*|t @hi UL?tt|i?| | @ hiUi?| i4ThU@* t|_) M) Au@?L EbbD
L? |i }L*_ 4??} ?_t|h) Au@?L €?_t |@| )L?}ih 4@?@}iht @hi 4Lhi *!i*)
|L i_}i |@? L*_ih 4@?@}iht 5?Ui |ihi t *!i*) |L Mi }hi@|ih ?Uih|@?|) @ML|
|i @M*|) Lu )L?}ih 4@?@}ihtc |t t UL?tt|i?| | |i 4T*U@|L? Lu Lh 4L_i*
|@| }hi@|ih _tTihtL? Lu @M*|it *i@_t |L 4Lhi tiT@h@|L?c ic }ih @M*|) )L?}
4@?@}iht i_}i *i *Lih @M*|) )L?} 4@?@}iht _L ?L| i_}i `| @ ULt| Lu
i_}?}c |i 4L_i* _i*iht |i UL?U*tL? |@| @ } _gihi?Ui ? @M*|it *i@_t
|L @ RtiT@h@|?} i^*Mh4 *i @ *L _gihi?Ui ? @M*|it *i@_t |L @ RTLL*?}
i^*Mh4 Eihi 4@?@}iht Lu }ih @?_ *Lih @M*|it _L ?L| i_}i }@?c |t
t UL?tt|i?| | Au@?L<t hit*|t
tiUL?_ |it|@M*i 4T*U@|L? Lu Lh 4L_i* t @t uL**Lt `i? |i ULt|t Lu
i_}?} @hi *Lc *itt tiT@h@|L? LUUht W? UL?|h@t|c i? |i ULt|t Lu i_}?} @hi
}c 4Lhi tiT@h@|L? LUUht AihiuLhic |i @*i Lu €h4t |@| i_}i hi*@|i |L €h4t
|@| _L ?L| i_}i t 4U }ih i? |i ULt| Lu i_}?} t }ih At t @? 4
T*U@|L? Lu |i 4L_i* |@| t TL|i?|@**) |it|@M*i At 4T*U@|L? t UL?tt|i?| |
Au@?L<t hit*| |@| 4@?@}iht | t|LU! LT|L?t _L ?L| i_}i @t tU 4@?@}iht u@Ui
} ULt|t Lu i_}?} OLiihc @ |it| Lu Lh 4L_i* L*_ @*tL hi^hi |@| 4@?@}iht
| t|LU! LT|L?t L i_}i 4t| Mi Lu tMt|@?|@**) }ih @M*|) |@? 4@?@}iht
|L| t|LU! LT|L?t L i_}i E| |i t@* Ui|iht T@hMt @tt4T|L?
`*i i_}?} t ?L| LMtih@M*ic tMti^i?| |L |i ii?|c L?i tL4i|4it !?Lt
i|ih @ €h4 i_}it Lh ?L| At t MiU@ti i TLt| €h4t L*?|@h*) _tU*Lti
i_}?} @U||) ? |i ?L|it |L |i M@*@?Ui tii| Wu Lh t|Lh) Lu i_}?} t ULhhiU|c
|i ThL€|t Ei@h??}t Lu €h4t ? |i ^@h|ih Lh )i@h U |i) i_}i tL*_ Mi }ih
@?_ |i L*@|*|) Lu U@t Lt tL*_ Mi *Lih |@? t@* 5U @ |it| _giht uhL4
|it|t Lu t}?@*?} 4L_i*t ihi ThL€|t Ei@h??}t @hi }ih uLh €h4t |@| t}?@* @t ?L
L*@|*|) 4T*U@|L?t @hi Thiti?| iU@ti i_}?} hi_Uit L*@|*|)c |i L*@|*|)
hi_U|L? t @? @__|L?@* 4T*U@|L? 5L4i Thi*4?@h) i4ThU@* Lh! M) #iBiLh}ic
Lti**i @?_ ~iU!@tih EbbD t?} L4Tt|@| _@|@ t tTTLh|i Lu |t 4T*U@|L?
Lu |i i_}?} )TL|itt
h i T*@?@|L? _giht uhL4 |i L|ih ThiLt i T*@?@|L?t |@| @i Mii?
ThL_i_ W? @? i@h*) T@Tih L? |t |LTUc 54| @?_ 5|*3 EbHD ThLTLti ht! @ihtL?
@?_ |@ it @t h@|L?@*it uLh €h4 i_}?} @4TMi** @?_ kh@U@ EbH. ti |i _i@t ?
OL*4t|hL4 Eb.b |L ThLTLti i_}?} @t @ 4i|L_ uLh @4i*Lh@|?} @}i?U) ThLM*i4t
 Au@?L EbbD @*tL €?_t |@| |i }hi@|ih |i i^|) L*_?}t Lu |i 4@?@}ihc |i 4Lhi *!i*) L?i ** LMtihi
i_}?} W| t _U*| |L ti |t LMtih@|L? _hiU|*) @t @| 4@||iht ? Lh 4L_i* t |i ULt| Lu i_}?} @?_ ?L| |i
uh@U|L? Lu i^|) i*_ ThL ) uLh |i ULt| Lu i_}?} 4t| t4*|@?iLt*) @UUL?| uLh |i uh@U|L? Lu i^|) i*_
@?_ |i @*i Lu |i i^|) LT|L? Lh 6#W ?th@?Ui |@| i_}?} _it|hL)t
e
6hLL|c 5|i? @?_ 5U@hut|i? Ebb2 ti |@| u@U| |@| L|t_i U@T|@* t ULt|*) |L h@ti
@t @ h@|L?@*i uLh i_}?} W? @ T@Tih |@| t U*Ltih |L Lh _i@tc #i@h3L @?_ #i
Ebb Thiti?| @ 4L_i* | ht! @ihtL? @?_ t)44i|hU ?uLh4@|L? ihi i_}?}
t LT|4@* L?i Lu |iti T@Tiht Thiti?|t @| |L t tii4t |L Mi |i u?_@4i?|@*
h@|L?@*i uLh i_}?}G |i _i@ Lu R*LU!?}? TihuLh4@?Ui `i Mi*ii |@| |t t @?
4TLh|@?| hi@tL? ) i_}?} LUUht @?_ |t i4T@t3i | ? Lh 4L_i* L?i Lu
|i L|ih T@Tiht ? |i *|ih@|hi UL?t_ih @| |i ULt|t Lu i_}?} @hi @?_ L |iti
ULt|t uLh i_}?} @hi M@*@?Ui_ @}@?t| |i ?Ui?|it |L i_}i Ai U*Ltit| T@Tih ?
|i *|ih@|hi t |@| _i |L w?}^t| Ebbe L tLt ? @ 4L_i* | @t)44i|hU
?uLh4@|L? |@| |ihi t @? ?Ui?|i uLh €h4t | *L L|T| |L tTiU*@|i At t
tL4i@| t4*@h |L tL4i Lu Lh hit*|t L? |i 4L_i* |L| i_}?} ULt|t2
h i4T@tt L? i_}?} @t @ _iUtL? M) 4@?@}iht |L R*LU!? TihuLh4@?Ui
ihi |i) @i @? @_@?|@}i @?_ i*4?@|i ht!t |@| @hi ?L| ?_ih |ih UL?|hL*
t 4TLh|@?| Oi_}?} t ?L| i*4?@|L? Lu @** ht! M| |i 4@?@}i4i?| Lu ht!
*|ih?@|i i T*@?@|L?t *!i M@?!hT|U) ULt|t Lh |i }ih i |ih?@* ULt|t Lu u?_?}
L*_ 4T*) ULh?ih tL*|L?t ihi 4@?@}iht |h) |L i*4?@|i @** ht!t( |t _t|?U|L?
Mi|ii? ht!t ihi 4@?@}iht @i @? @_@?|@}i @?_ ht!t U @hi ?L| UL?|hL**@M*i
M) |i 4@?@}ih t *itt 4TLh|@?| `i _L ?L| Mi*ii |@| i_}?} ?L*it |i i*4
?@|L? Lu @** ht! M| h@|ih L?*) ht!t ihi |i 4@?@}ih Lh €h4 _Lit ?L| @i
@?) tTiU@* @_@?|@}i W? T@h|U*@hc Lh 4L_i* 4T*it |@| €h4t i_}i |ih ht!t
L?*) i? |i) @hi tUi?|*) _gihi?| uhL4 L|ih t4*@h €h4t ? |ih @M*|it |
hitTiU| |L |@| ht! ?*) ?_ih |iti UhU4t|@?Uit t | Lh|*i |L T@) |i 4
2
W? w?}^t|<t ti|Tc @Mti?| tTiU*@|L?c |ihi t TihuiU| _tUh4?@|L? Mi|ii? |i }LL_ @?_ M@_ |)Tit
Lu 4@?@}iht W? Lh ti|Tc |t t ?L| |hi @t L|T| t ?L| TihuiU|*) hii@*?} @ML| |i @M*|) Lu |i 4@?@}ih
W| t ?|ihit|?} |L ?L|i |@| *T @?_ **ih EbbD t|@|i |@| R @Mti?| tTihLh ?uLh4@|L?c @*i
4@ 43?} €h4t 4@) ?L| L?*) @L_ i_}?}c M| 4@) i** t? |i ?_ih*)?} @U||) |ti*u
D
T*U| ULt| Lu i_}?}c |i hi_Ui_ i^|) LT|L? @*i Lh |i hi_Ui_ 6#W ?th@?Ui
LT|L? @*i
6?@**)c i i4T@t3i |@| Lh 4L_i* t ?L| @ t}?@*?} 4L_i* @t i_}?} t @?
?LMtih@M*i @U||) At ?LMtih@M*|) Lu i_}?} 4@!it | U*Ltih |L |i 4L_i*t
Lu *i@h??} _i |L OL*4t|hL4 EbH2c @4TMi** @?_ @h?L Ebbec 6_i?Mih} @?_
AhL*i EbHSc @h@)@?@? EbHDc @*uhi) @?_ 5T@|| EbHDc 5U@hut|i? @?_ 5|i?
Ebbf @?_ 5|i? EbHb W? |iti 4L_i*t @}i?|t _L ?L| @i Th@|i ?uLh4@|L? M|
?_ih|@!i ?LMtih@M*i @U|L?t |@| @giU| |i @M*|) Lu |i 4@h!i| Lh L|ih @}i?|t |L
*i@h? @ML| |i @}i?|<t ?_ih*)?} |@*i?| h 4L_i* _giht uhL4 |iti 4L_i*t ? |@|
|i @}i?| ?_ih|@!?} |i ?LMtih@M*i @U|L? @t tL4i Th@|i ?uLh4@|L? @ML|
t @M*|)( |t T*@)t @? 4TLh|@?| hL*i ? _i|ih4??} t LT|4@* @U|L? Ai L|ih
T@Tiht |@| i @hi @@hi Lu | |t _i@ |@| @}i?|t @i _gih?} ?Ui?|it |L
4@?T*@|i |i 4i@thi4i?| ThLUitt @hi _i |L **i? @?_ B@*i Ebbfc hi?_ih}@t|
@?_ 5|L*i EbbS @?_ ~iMi* EbbDe 6?@**)c #iBiLh}ic Lti**i @?_ ~iU!@tih
EbbS Thiti?| @ t4*@h _i@D
W? **i? @?_ B@*ic |i ?Ui?|it Lu @}i?|t |L 4@?T*@|i |i *i@h??} ThLUitt
t ti_ ? |i UL?|i | Lu @ 4L_i* |@| |hit |L i T*@? ) UL?|h@U|t _L ?L| UL?|@?
@** UL?|?}i?Uit W? hi?_ih}@t| @?_ 5|L*i EbbSc 4@?@}iht i @}}ih@|i |ih L?
?uLh4@|L? |L @TTi@h @t u@t| *i@h?iht i? |i) @hi )L?} M| ii?|@**) MiUL4i
UL?tih@|i @?_ @hi ?**?} |L ti ?i ?uLh4@|L? W? ~iMi*<t EbbD Lh!
L? ULhTLh@|i UL?tih@|t4c 4@?@}iht L @hi Mi?_ |i?_ |L |@!i iUi?| _iUtL?t
e w?}^t| Ebbe @*tL @**Lt uLh 4@?T*@|L? Lu |i 4i@thi4i?| ThLUitt @||it @?_ h4@? EbH
t @*tL U*Ltih |L Lh 4L_i* | ULt|t Lu i_}?} Ai 4L_i* | ULt|t Lu i_}?} U@? Mi ii_ @ ?Lt) t}?@*?} @t
t |i U@ti Lu |i 4L_i* Lu @||it @?_ h4@? EbH
D
#iBiLh}ic Lti**i @?_ ~iU!@tih EbbS @tt4i |@| €h4t | }ih 4i@?t @i *Lih ULt|t Lu @h@?Ui
hi_U|L? W? UL?|h@t|c i 4@!i ?L tU @tt4T|L?t __|L?@**)c i 4L_i* @ ULt| uLh i_}?} |@| i Mi*ii |L
Mi Lu 4TLh|@?Ui @?_ L?i |@| )i*_t |i _gihi?|@* ULt|t Lu i_}?} uLh €h4t | _gihi?| 4i@? U@t Lt
S
*i |Lti @i@_ Lu |i }@4i |i?_ |L Mi UL?tih@|i ? |ih _iUtL? 4@!?}
`*i @** Lu |iti T@Tiht @*tL 4L_i* |i _i@ |@| |ihi @hi 4@?@}ih@* ?Ui?|it |L
_t|Lh| |i *i@h??} ThLUittc i Mi*ii |@| |i ?^i UL?|hM|L? Lu Lh T@Tih t
|L _i?|u) |i ULt|t @?_ Mi?i€|t Lu i_}?} W? T@h|U*@hc *i i_}?} 4ThLit
|i ?uLh4@|i?itt Lu |i *i@h??} ThLUitt E|i Mi?i€|c | @t |i @ttLU@|i_ ULt|
Lu }?} T tL4i Lu |i i^|) LT|L? @*i At Mi?i€|ULt| |h@_iLg t 4TLh|@?|
? _i*ih?} |i hit*|t |@| i LM|@? |@| i_}?} tL*_ Mi ?_ih|@!i? M) }ih
@M*|) 4@?@}iht L?*) i? |i Mi?i€|t E|i }hi@|ih ?uLh4@|i?itt Lu |i *i@h??}
ThLUitt i Uii_ |i ULt|t E|i i^|) LT|L? @*i hi_U|L?
Ai T@Tih t Lh}@?3i_ @t uL**Lt 5iU|L? W @?_ WW Thiti?| |i 4L_i* @?_
hit*|t i? 4@?@}iht U@hi L?*) @ML| |ih hiT|@|L?t 5iU|L?t WWW @?_ WV UL?
t_ih |i i |i?tL? ihi 4@?@}iht L*_ i^|) @?_ @hi UL?Uih?i_ @ML| |i igiU|
Lu i_}?} _iUtL?t L? i^|) @*i 5iU|L? V UL?U*_it ** ThLLut @hi ? |i
TTi?_ .
W AO, #,w `WAONA O,#BWB 5A5
`i UL?t_ih @ 4L_i* ihi 4@?@}iht h? @ €h4 uLh |L TihL_t W? |i €ht|
TihL_ |i 4@?@}ih U@? ?it| m ? @ ThLiU| Ai ThLiU| )i*_t @ h@?_L4 @4L?|
 n + e{o @| |i i?_ Lu |i tiUL?_ TihL_ Ai h@?_L4 T@)Lg + t |@| T@h| Lu
ThL€|t |@| t ?_ih |i UL?|hL* Lu |i 4@?@}ih @?_ U@? |@!i L?i Lu |L @*it + Lh
+, ihi + : +, Ai ThLM@M*|) Lu |i T@)Lg + )i*_?} |i } t|@|i E+ t R
U _iTi?_t L? |i @M*|) Lu |i 4@?@}ih
W? UL?|h@t|c |i h@?_L4 u@U|Lh {o t ?L| ?_ih |i UL?|hL* Lu |i 4@?@}ih
At h@?_L4 u@U|Lh {o U@? |@!i |i @*it B Lh B | i^@* ThLM@M*|) Ai
hi@*3@|L? Lu |i h@?_L4 u@U|Lh t LMtih@M*i |L |i 4@h!i| OLiihc |i €h4<t
i TLthi |L |t u@U|Lh e t ?L| !?L? |L |i 4@h!i| @?_ U@? |@!i L?i Lu |hii @*itc
c f Lh Ai i @?|i ThLM@M*|) Lu 3ihL i TLthi t r *i |i ThLM@M*|) Lu
i TLthit Lh t fDE r `i @*tL @tt4i |@| |i + +, ' B W? |t
_tUhi|i tT@Ui 4L_i*c |t @tt4T|L? t ?ii_i_ |L i?thi |@| t|LU@t|U ThLUitt _i
|L |i ThL_U| Lu |i i TLthi e UL?_|L?@* L? |i hi@*3@|L? Lu |i u@U|Lh {o t
?Lti uLh |i *i@h??} ?_ih|@!i? M) |i 4@h!i|
Aihi @hi @ ?4Mih Lu ?|ihThi|@|L?t |@| L?i U@? }i |L |i @MLi ti|T
?i t |@| Lu @ M@?! ihi |i T@)Lg + hiThiti?|t Uhi_| ht!t ihi _gihi?| M@?!t
_gih ? |ih @M*|) *i |i T@)Lg {o hiThiti?|t ?|ihit| h@|i ht!t uLh U
M@?!t ELh U*@tt Lu M@?!t _L ?L| @i @?) UL4Ti||i @_@?|@}i ? Thi_U|L? `*i
?|ihit| h@|i U@?}it @hi LMtih@M*ic |i i TLthi |L ?|ihit| h@|i ht!tc ec t ?L|
!?L? M) |i 4@h!i| u|i?c i ** ti |t ?|ihThi|@|L? |L **t|h@|i Lh _i@t
?L|ih ?|ihThi|@|L? t |@| Lu @ 4*|?@|L?@* €h4 ihi |i ThLUitt + hiThiti?|t
|@| T@h| Lu |i ThL€|t |@| t hi*@|i_ |L |i @M*|) Lu 4@?@}iht *i |i ThLUitt {o
hiThiti?|t i U@?}i h@|i ht!t @?_ e t |i ?!?L? i TLthi |L i U@?}i h@|i ht!t
H
Bi? |i @tt4T|L?t |@| i @i 4@_i L? |i _tUhi|i t|@|i tT@Uic |ihi
@hi uLh TLttM*i t|@|it Lu |i Lh*_ |@| U@? LUUh( i ** *@Mi* |i4 5 c 52 c 5 @?_
5e Ai ThLM@M*|) Lu i@U t|@|i LUUhh?}c UL?_|L??} L? |i ?|ihit| h@|i u@U|Lh
hi@*3@|L?c _iTi?_t L? i|ih |i 4@?@}ih ULLtit |L i_}i Lh ?L| i_}i |i U@t
L @?_ t tL? ? |i uL**L?} |@M*iG
b
Aw, W
5|@|i
O,#BWB
L?_|L?@* L? {o
5
52
5
5e
+ n B
+ c +, n B
+ Bc +,
+, B
hLM@M*|)
u UUhhi?Ui
RE5 mMc fDE rR
R r n fDE rE R fDE rR n E R r
fDE rE R O,#BWB
+
+,
hLM@M*|)
u UUhhi?Ui
RE5 mMc f
R
 R
f
ihi |i ?_i hiuiht |L |i 4@?@}ih<t tTiU€U @M*|) Ei ** _tUtt |t uh|ih
Mi*L @?_ |i ?_i it M @?_ M hiThiti?| |i @U|L?t ?L| i_}?} @?_ i_}?}
hitTiU|i*)
Ai ThLM@M*|) _t|hM|L? Lih |i L|UL4it 5 |L 5e t _gihi?| i? |i
4@?@}ih i_}it @?_ i? |i 4@?@}ih _Lit ?L| i_}i `i? |i 4@?@}ih _Lit ?L|
i_}i |i 4@h!i| U@??L| _t|?}t i|ih ThL€|t @hi } MiU@ti |i 4@?@}ih
@t }LL_ @M*|) Et!** Lh MiU@ti Lu *U! EUL?_|L?@* L? |i u@U|Lh {oc |i i TLthi
e @t ? |i h}| _hiU|L? 6Lh i @4T*ic | ?L i_}?} E? i|ih ?|ihit| h@|i
u@U|Lh hi@*3@|L? |i 4@h!i| _Lit ?L| !?L i|ih |i L|UL4i 52 '+ @t LUUhhi_
Lh i|ih |i L|UL4i 52 ' +, nB @t LUUhhi_ At ?@M*|) |L _iUL4TLti ThL€|t
TihuiU|*) t UhU@* uLh i_}?} |L Mi @*@M*i Wu |i 4@h!i| ihi @M*i |L !?L |i
i TLthit |L ?|ihit| h@|i ht!c |ihi L*_ ?L hL*i uLh 4@?@}ih@* i_}?}
W? |i i @4T*i i Thiti?|i_ Lu |i M@?! 4@?@}ihc |t ULhhitTL?_t |L @?
?@M*|) |L _t|?}t i|ih |i 4@?@}ih t t!**u* @| Uhi_| @?@*)tt Lh i|ih |i
4@?@}ih @_ @ TLt|i i TLthi |L ?|ihit| h@|i ht! @?_ |i ?|ihit| h@|i 4Li4i?|
@t u@Lh@M*i `i ?L|i |@| ? Lh ti| Tc |i t)44i|h) @tt4T|L? i?thit |@|
f |i i TLt| hi@*3@|L? Lu |i u@U|Lh {o t ??uLh4@|i @ML| |i i TLthi e @?_
|i TLt|ihLh ThLM@M*|it Lu |i L|UL4it 5 |L 5e UL?_|L?@* L? |i hi@*3@|L? {o
@hi t| |i ThLh ThLM@M*|it t @ UL?ti^i?Uic i tTThitt |i _iTi?_i?Ui Lu |i
*i@h??} ThLUitt L? |i hi@*3@|L? Lu |i u@U|Lh {o
6?@**)c i? |i 4@?@}ih _Lit i_}ic i @tt4i i UL4T*i|i*) i_}it |i
ht! @@) M) ti||?} t i TLthi |L 3ihLS W? |i i @4T*i i }@i Lu |i M@?!c |t
ULhhitTL?_t |L 4@!?} thi |@| |i i_}i_ M@?! t ?i|h@* |L ?|ihit| h@|i ht! W?
|i i @4T*i Lu |i 4*|?@|L?@* €h4c | ULhhitTL?_t |L *LU!?} ? hii?it Lh ULt|t
tL |@| |i) _L ?L| _iTi?_ L? |i U|@|L?t ? i U@?}i h@|it `i? |i 4@?@}ih
i_}itc |i L|UL4it 5 @?_ 5e _L ?L| LUUh Ai ThL€| ThLUitt t *itt ?Lt) @?_ 4Lhi
?uLh4@|i @ML| |i @M*|it Lu |i @}i?|t Eu ML| 4@?@}iht ihi ?L| |L i_}i
Ai i @U| ThLM@M*|) | U |i @hLt t|@|it LUUh E}i? |i 4@?@}ih
_iU_it |L i_}i Lh ?L| i_}i _iTi?_t L? |i @M*|) Lu |i 4@?@}ih AL U@T|hi
|t _gihi?|@* @M*|) Lu 4@?@}ihtc i @tt4i |@| |ihi @hi |L |)Tit Lu 4@?@}ihtc
|i } @M*|) 4@?@}ih E4@?@}ih  @?_ |i *L @M*|) 4@?@}ih E4@?@}ih 2 Ai
4@h!i|<t ThLh ThLM@M*|) |@| |i 4@?@}ih t Lu }ih @M*|) t fD `i @*tL @tt4i
|@| R2 ' R ( |t t)44i|h) @tt4T|L? i?thit |@| ?L?i Lu Lh hit*|t @hi _hi?
M) @t)44i|hU ThL€| t|hU|hit `i _i€?i _ ' R R2 At t @ 4i@thi Lu |i
_gihi?Ui ? @M*|it @?_ T*@)t @? 4TLh|@?| hL*i ? Lh hit*|t 6?@**)c r : *c @?
@tt4T|L? |@| t ?ii_i_ |L i?thi |@| i? ML| €h4t _L ?L| i_}i |i TLt|ihLh
ThLM@M*|it @hi 4L?L|L?i ? |i L|UL4i 5 At 6 ' r fDE r t @*@)t
TLt|i wL r @*it 4T*) }hi@|ih ?Lti _i |L U|@|L?t ? |i i L}i?Lt ?Lti
ThLUitt
S
W? |t _tUhi|i t|@|i 4L_i*c | t _U*| |L 4L_i* T@h|@* i_}?} 5?Ui i UL?t_ih 4 i_ t|h@|i}itc L?i
UL*_ i 4 ?} Mi|ii? i_}?} @?_ ?L| i_}?} @t T@h|@* i_}?}
 Bi? |t M@tU t|hU|hi i tTiUu) |i LMiU|i Lu |i 4@?@}ih `i uL*
*L OL*4t|hL4 EbH2 @?_ OL*4t|hL4 @?_ +U@h| Lt|@ EbHS @?_ @tt4i |@|
4@?@}iht hiUii |i i TiU|i_ @*i uLh |@| TihL_ T uhL?| @t |i @}i T@)4i?|
OLiihc UL?|h@U|t @hi hi?i}L|@|i_ @| |i i?_ Lu i@U TihL_ Wu |i @M*|) Lu |i
4@?@}ihc R c ihi !?L? 4@?@}ih L*_ hiUii @t @}it @*i R + n E R +, o
@t @}i T@)4i?|t 5i||?} q ' + +, @?_ V ' +, oc ?_ih u** ?uLh4@|L? |i
4@?@}ih hiUiit @ @}i qR n V
OLiih R t ?L| !?L?c @?_ i?Ui |i 4@?@}ih LM|@?t qEfDR n fDR2 n V
' qEfD n V Et?} |i u@U| |@| R2 '  R @t |i @}i uLh |i €ht| TihL_ Ai
hi?i}L|@|i_ @}i uLh |i tiUL?_ TihL_ t |i? }i? M)G .
q d Em5 R n E2m5 R2 o n V
Oihi Em5 t |i TLt|ihLh ThLM@M*|) Lu |i 4@?@}ih @?} }ih @M*|) }i?
|@| L|UL4i 5 t LMtihi_ E@ t4*@h _i€?|L? L*_t uLh E2m5 `i tTThitt |i
UL?t|@?|t q @?_ V |i) @hi tU@*?} @h@M*it @?_ T*@) ?L hL*i ? |i hit*|t Lu |t
tiU|L? 5?Ui |i Uhhi?| @}i t € i_c |i 4@?@}ih 4@ 43it |i i TiU|i_ @*i
Lu t u|hi i TiU|i_ @}i ? |i ?i | TihL_ At 4T*it |@| |i 4@?@}ih U@hit
L?*) @ML| t hiT|@|L? @?_ ?L| @ML| |i i^|) @*i Lu |i €h4 W? 5iU|L? 2
i hi*@ |t @tt4T|L? M) @**L?} 4@?@}iht |L L*_ i^|)
Oi_}?} t @? ?LMtih@M*i @U||) At |i 4@h!i| U@??L| UL?_|L? |t
TLt|ihLh Mi*iut @ML| |i @M*|) Lu |i 4@?@}ih L? i|ih @ €h4 i_}it Lh ?L|(
Mi*iut @hi u?U|L?t L?*) Lu LMtihi_ ThL€|t Bi? Lh tTiU€U@|L? Lu |i 4@?@}ih<t
LMiU|i i _i€?i |i @)it@? @t i^*Mh4 Lu |i T_@|?} }@4i @tGH
.
`i ?L|i |@| |i @}i _Lit ?L| _iTi?_ L? |i hi@*3@|L? Lu |i ?|ihit| h@|i u@U|Lhc {o
H
}@?c i ?L|i |@| |i T_@|i_ @}i _Lit ?L| _iTi?_ L? |i hi@*3@|L? Lu |i ?|ihit| h@|i u@U|Lhc {o
2 E@ @ 4@h!i| Mi*iu u?U|L? 6W G i5 c 52 c 5 c 5e j :$ dfcoc ihi 6W E5 t |i TLt|ihLh
ThLM@M*|)c }i? |i LMtih@|L? 5 c |@| |i 4@?@}ih t Lu }ih @M*|)
EM @ €h4 @U|L? u?U|L? @W Gi c2 j :$ dfcoc ihi @W E t |i ThLM@M*|) |
U |i 4@?@}ih i_}it Ei @hi @**L?} uLh 4 i_ t|h@|i}it ihi
`i hi^hi |@| |i T@h i6W Ec @W Ej t@|tu) |i UL?_|L?t |@|G
E }i? 6W Ec 4@?@}ih ULLtit
@W E 5 @h} 4@ L E6W Ec @Ec @ E ihi
3e
4
[
L E6W Ec @Ec ' @E C RE5 mMc 6W E5 ER R2 n R2 D
'
3e
4
[
W
n E @E C RE5 mMc 6 E5 ER R2 n R2 D
'
E }i? @W Ec ' c2c |i 4@h!i| Mi*iu u?U|L? ' c 2c |i 4@h!i| Mi*iu
u?U|L? 6W E t@|t€it
6W E5 '
RE5 m@W E
RE5 m@W E n RE5 m@W E2
uLh @** 5 LMtihi_ ? i^*Mh4 Oihi 6W E5 t |i i^*Mh4 TLt|ihLh ThLM@M*|)
|@| |i 4@?@}ih t Lu }ih @M*|) }i? |i ThL€| *ii* 5 ) _i€?|L?c
RE5 m@W E ' @W ERE5 mMc n E @W ERE5 mMc Ai _i€?|L? Lu 6W E5 hi^hit @)it UL?tt|i?U) Lih @** ThL€| *ii*t LM
tihi_ ? i^*Mh4 M| _Lit ?L| hit|hU| 4@h!i| Mi*iut i? @ ThL€| *ii* t ?L|
LMtihi_ At LUUht L?*) i? ML| €h4t i_}i W? |t U@ti ThL€| *ii*t 5 @?_ 5e
 @hi ?L| LMtihi_ @?_ |ihi t ?L hit|hU|L? L? 4@h!i| Mi*iut UL?_|L?@* L? LMtih?}
|iti t|@|it
6?@**)c i ?L|i |@| Lh _i€?|L? Lu |i t|h@|i}it ULti? M) |i 4@?@}ih
@**Lt uLh h@?_L43@|L? W? |i UL?|i | Lu Lh _tUhi|i tT@Ui 4L_i*c h@?_L43@|L?
U@? Mi ?|ihThi|i_ @t T@h|@* i_}?}
WW ,"NWwW+WN W AO, #,w `WAONA O,#BWB 5A5
!i) _i@ Mi?_ Lh @TThL@U |L i_}?} t |i ?L|L? |@| 4@?@}iht Lu
}ih @M*|it ** i_}i tL @t |L R*LU!? |ih ThL€|t @?_ 4ThLi |i ?uLh4@
|i?itt Lu ThL€|t @ML| |ih tTihLh @M*|it AihiuLhic i €ht| ?it|}@|i @?
?||i i^*Mh4 ihi |i }ih @M*|) 4@?@}ih @*@)t i_}it
AO,+, G ? i^*Mh4 ?L*?} |i } @M*|) 4@?@}ih i_}?} @*@)t
i t|t Ai *Lih @M*|) 4@?@}ih<t _iUtL? _iTi?_t L? |i _gihi?Ui ? @M*|it
Mi|ii? |i 4@?@}ihtc _c ? |i uL**L?} @)G 4@??ihG
E 6Lh f _ BM c @W E2 ' 
E 6Lh BM _ B7 c f @W E2 
E 6Lh B7 _ c @W E2 ' f
`i hiuih |L |t i^*Mh4 @t @ A)Ti i^*Mh4
hLLuG 5ii TTi?_ `i *@Mi* |t i^*Mh4 @ A)Ti i^*Mh4 A)Ti i^*Mh4 LUUht
uLh @** TLttM*i @*it Lu T@h@4i|ih r( |t ULhhitTL?_t |L @** TLttM*i @h@?Uit uLh
|i ?Lti ThLUitt o At |i A)Ti i^*Mh4 hi^hit ?L hit|hU|L?t L? |i
T@h@4i|ih tT@Ui
Ai ?||L? Mi?_ |i A)Ti i^*Mh4 t @t uL**Lt W| t ? |i ?|ihit|
Lu |i }ih @M*|) 4@?@}ih |L i_}i @t i_}?} *i@_t |L @ 4Lhi ?uLh4@|i *i@h??}
e ThLUitt OLiihc i? |i _gihi?Ui ? |i @M*|it Lu |i |L 4@?@}iht t *Lc |
T@)t uLh |i *Lih @M*|) 4@?@}ih |L uL**L t| @?_ @*tL i_}i *L _gihi?Ui ?
@M*|it 4T*it |@| |i *i@h??} ThLUitt t ?L| ?uLh4@|i ii? i? ML| 4@?@}iht
i_}i E@*|L} 4Lhi ?uLh4@|i |@? i? ML| 4@?@}iht _L ?L| i_}i( M) ?L|
i_}?} |i *L @M*|) 4@?@}ih h?t |i ht! Lu |i i |hi4i t|@|it 5 @?_ 5e LUUhh?}
@?_ hii@*?} t @M*|) ? |i L|ih @?_ i? |i _gihi?Ui t @M*|it t }c |i
*i@h??} ThLUitt t ih) ?uLh4@|i i? ML| €h4t i_}i( M) ?L| i_}?} |i *Lih
@M*|) 4@?@}ih @t tL4i U@?Ui Lu Mi?} 4t|@!i? @t |i }ih @M*|) 4@?@}ih
i? |i hi@*3@|L?t Lu |i ThLUitt h @hi u@Lh@M*i
`*i A)Ti i^*Mh4 t 4Lt| UL?tt|i?| | Lh ?||L? @?_ i t|t ?L
4@||ih @| |i T@h@4i|ih UL?€}h@|L? tc i ?ii_ |L ?it|}@|i L|ih i^*Mh@
`i €ht| tL |@| ?L i^*Mh4 i t|t ihi |i *Lih @M*|) 4@?@}ih i_}it
@?_ }ih @M*|) 4@?@}ih _Lit ?L| i_}i Lh h@?_L43it Mi|ii? i_}?} @?_ ?L|
i_}?}
AO,+, 2G Ai *Lih @M*|) 4@?@}ih i_}?} @?_ |i }ih @M*|) 4@?@}ih
?L| i_}?} Lh h@?_L43?} Mi|ii? i_}?} @?_ ?L| i_}?} U@? ?iih UL?t|||i
@? i^*Mh4
hLLuG 5ii TTi?_ Ai @MLi @?@*)tt UL?t_iht |i TLttM*|) Lu i^*Mh@ ihi i|ih |i
}ih @M*|) 4@?@}ih i_}it Lh |i *Lih @M*|) 4@?@}ih i_}it `i UL?t_ih
?L i^*Mh@ ihi |i }ih @M*|) 4@?@}ih h@?_L43it Mi|ii? i_}?} @?_ ?L|
i_}?} Aiti @hi U@h@U|ih3i_ Mi*L
AO,+, G Ai L|ih @)it@? @t i^*Mh@ Lu |i 4L_i* @hiGb
b
Aihi t @*tL @? i^*Mh4 |@| i _L ?L| _tUtt @t | L?*) i t|t uLh
@? i^*Mh4 ihi @E ' @E2' f
D r
' fD W? |t U@tic i U@? @i
A)Ti i^*Mh4G At i^*Mh4 4@) LUUh L?*) i? r fD E} i L}i?Lt
?Lti @h@?Ui Ai i^*Mh4 t|h@|i}it Lu |i 4@?@}iht Lu _gihi?| @M*|it tG
E @W E ' @W E2 ' *E2E r
A)Ti # i^*Mh4G
At i^*Mh4 LUUht i? r fD E} i L}i?Lt ?Lti
@h@?Ui Ai i^*Mh4 t|h@|i}it Lu |i 4@?@}iht Lu _gihi?| @M*|it tG
E @W E ' f(
E f @W E2 
hLLuG 5ii TTi?_ A)Ti i^*Mh4 ?L*it }ih @M*|) 4@?@}iht @?_ *Lih @M*|) 4@?
@}iht h@?_L43?} Mi|ii? i_}?} @?_ ?L| i_}?} i @U|*) |L |i t@4i _i}hii At
i^*Mh4 t !?uii_}i_ @t |i @*it @E ' @E2 @hi ULti? tL |@| 4@?@}iht Lu
@?) @M*|) R @hi ?_gihi?| Mi|ii? i_}?} @?_ ?L| i_}?} 5U i^*Mh@ 4@)
LUUh i? |i ?Lti ? |i ?|ihit| h@|i ThLUitt t } E*L r
A)Ti # i^*Mh4 *i@_t |L |i ??||i L|UL4i |@| }ih @M*|)
4@?@}iht _L ?L| i_}i *i *Lih @M*|) 4@?@}ih h@?_L43i Ai ?||L? t @t
uL**Lt `i? |i T@h@4i|ih r |@!it *L @*itc U|@|L?t ? |i o ThLUitt @__ @ *L|
Lu ?Lti |L |i ?uihi?Ui ThLUitt Wu |i }ih @M*|) 4@?@}ih _Lit ?L| i_}ic |i?
Mi*iut i? i |hi4i L|UL4it LUUh T*@Ui i}| L? |i ?uihi?Ui |@| |i 4@?@}ih
t }LL_ Wu |i *Lih @M*|) 4@?@}ih 44Ut @?_ @*tL _Lit ?L| i_}ic |i? i |hi4i
L|UL4it @hi ?uLh4@|iG 5 t 4Lhi UL?tt|i?| | @ }ih @M*|) 4@?@}ih *i
5e t 4Lhi UL?tt|i?| | @ *Lih @M*|) 4@?@}ih W?|ih4i_@|i L|UL4it @i *||*i
?uLh4@|L? @t |i ?Lti ? |i o ThLUitt t } At |i *Lih @M*|) 4@?@}ih @t
?Ui?|it ?L| |L i_}i |L @Uii |iti ?|ih4i_@|i L|UL4it ihi *i@h??} t *L
Oi?Ui i h@?_L43it Mi|ii? i_}?} @?_ ?L| i_}?}
S Ai Thiti?Ui Lu |iti ??||i i^*Mh@ uLh tL4i T@h@4i|ih @*it 4@)
tii4 L__ @| €ht| }*@?Ui W| t 4TLh|@?| |L hi4i4Mih |@| ? |t 4L_i* |ihi @hi ?L
ULt|t @ttLU@|i_ | i_}?} Lh ?L| i_}?} t @ UL?ti^i?Uic |i LT|4@* t|h@|i}it
_iTi?_ L? @| 4@h!i| Mi*iut i t| @ML| ?|ih4i_@|i t|@|it @?_ i |hi4i t|@|it W?
}i?ih@*c |i ?||L? |@| i_}?} t }LL_ uLh |i }ih @M*|) 4@?@}ih _iTi?_t L?
|i _i@ |@| | 4ThLit *i@h??} M) |i 4@h!i| t @ UL?ti^i?Uic |i 4@h!i| it
i |hi4i t|@|it @t ?_U@|?} @ *Lih @M*|) 4@?@}ih W? |i UL?|ih ?||i i^
*Mh4c i |hi4i t|@|it @hi 4Lhi ii_ 4Lhi ?uLh4@|i |@? ?|ih4i_@|i t|@|it
MiU@ti |i ?Lti ? |i ?|ihit| h@|i ThLUitt t } @?_ |i _gihi?Ui ? @M*|it t
*L Ai 4*|T*U|) Lu i^*Mh@ ? 4L_i*t | ?L t}?@*?} ULt|t t @ i** !?L?
u@U| Etii h@uLh_ @?_ 5LMi* EbH2 @?_ |i hi*@|i_ *|ih@|hi L? RUi@T |@*! `i
** @h}i ?i | |@| |ihi @hi ULt|t @ttLU@|i_ | i_}?} @?_ |@| |iti ULt|t @hi
*Lih uLh 4@?@}iht Lu }ih @M*|) t i ** tiic |t ULt| _gihi?|@* t tUi?|
|L i*4?@|i |iti UL?|ih?||i i^*Mh@
W? |t tiU|L?c i @i _i4L?t|h@|i_ |i i t|i?Ui Lu @? ?||i i^*Mh4
ihi |i } @M*|) 4@?@}ih i_}it *i |i *L @M*|) 4@?@}ih _Lit ?L| i_}i
At i^*Mh4 i t|t |L| @?) T@h@4i|ih hit|hU|L?t @?_ i4Mi_t |i _i@ |@|
|i | @t ? |i ?|ihit| Lu |i } @M*|) 4@?@}ih |L i_}i tL @t |L i?thi @ ThL€|
ThLUitt |@| t 4Lhi ?uLh4@|i Ai *Lih @M*|) 4@?@}ih ? |t i^*Mh4 4@)
Lh 4@) ?L| i_}i( |t _iUtL? _iTi?_i_ L? |i _gihi?Ui ? |ih @M*|it Wu |i
_gihi?Ui ? @M*|) @t *@h}i i?L}c |i *Lih @M*|) 4@?@}ih ** ?L| i_}i EtL |L
*Lih |i ?uLh4@|i?itt Lu |i ThL€| ThLUitt ? |i LTi |@| *U! ** |h? ? t
u@Lh
WWW AO, #,w `O, B,+5 Ow# ,"NWAv
W? _i4L?t|h@|?} |i hit*|t ? |i ThiLt tiU|L?c i @i }?Lhi_ |i TLtt
M*|) |@| i_}?} 4@) @i ULt|t @ttLU@|i_ | | Ai i t|i?Ui Lu L?i 4TLh|@?|
. ULt| t @ UL?ti^i?Ui Lu |i ?||L? Lu |i LT|L? ThU?} 4L_i* Wu |i €h4 t Mi?}
h? ? |i ?|ihit|t Lu i^|)L*_ihtc |i ?Ui?|it Lu |i i^|)L*_iht @hi |L ?
_ih|@!i @U||it |@| ?Uhi@ti @h@?Uic ?L| hi_Ui @h@?Ui Wu |i €h4 ?_ih|@!it
i_}?} @U||itc | t hi_U?} |i i TLthi Lu |i €h4 |L Uih|@? ht!t @?_ i?Ui
|i @h@?Ui Lu ThL€|t W? |i i @4T*i |@| i UL?t_ihi_ Lu |i M@?!c tU @h@?Ui
hi_U?} @U||it *Liht |i @*i Lu 6#W ?th@?Ui LT|L? L?ti^i?|*)c i_}?}
@t @? 4T*U| ULt| @ttLU@|i_ | | uhL4 |i TihtTiU|i Lu |i i^|)L*_iht `i
i T*Lhi |i 4T*U@|L?t Lu |i ULt|t @ttLU@|i_ | i_}?} ? |i ?i | tiU|L?
W| t hi@tL?@M*i |L @tt4i |@| 4@?@}iht ** Mi ti?t|i |L |i igiU|t Lu
|ih _iUtL? 4@!?} L? i^|)L*_iht @?_ |@| |i @}it |i) hiUii 4@) ?U*_i
@? i^|) UL4TL?i?| E|t L*_ ?_Ui tL4i @*}?4i?| Lu |ih LMiU|it | |@|
Lu |i i^|)L*_iht Oi?Uic i @tt4i |@| ? @__|L? |L U@h?} @ML| |i igiU|t
Lu |ih _iUtL?t L? 4@?@}ih@* hiT|@|L?c 4@?@}iht L*_ @ uh@U|L? k Lu |i i^|)
Lu |i €h4
W? @__|L? |L @**L?} |i 4@?@}ih |L L*_ @ uh@U|L? Lu |i €h4<t i^|) i
@**L uLh i |ih?@* U*@4@?|t *!i _iM|L*_iht Lh uLh ?th@?Ui tU @t 6#W ?th@?Ui
Ai igiU| Lu i|ih Lu |iti |L TLttM*|it t t4*@h @?_ i ULLti |L ti 6#W
?th@?Ui ? Lh @?@*)tt
W?t|||L?t *!i t@?}t @?_ *L@?t @?_ M@?!t @i @UUitt |L _iTLt| ?th@?Ui
Lti @*i t hi_Ui_ M) i_}?} At i_}?} @t @? @ttLU@|i_ ULt| OLiihc @
!i) ?||L? |@| t @!? |L |@| ? t}?@*?} 4L_i*t t |i uL**L?} At 4T*U| ULt|
Lu i_}?} t _gihi?| uLh 4@?@}iht Lu _gihi?| @M*|it 6h4t ihi 4@?@}iht @i
}ih @M*|) @i @ *Lih ThLM@M*|) Lu }L?} M@?!hT| Oi?Ui |i 4@h}?@* ULt| Lu
?_ih|@!?} i_}?} @U||itc U t |i hi_Ui_ @*i Lu |i 6#W ?th@?Ui ELh
|i hi_Ui_ i@*| |h@?tuih uhL4 _iM|L*_iht t *Lih uLh @ €h4 |@| @t @? }ih
@M*|)
H Aihi @hi |L UL?U*tL?t uhL4 |i @MLi ?||L? |@| @hi 4TLh|@?| 6ht|
i_}?} ** ?L| LUUh ?*itt |i _gihi?Ui ? @M*|it t *@h}i i?L} MiU@ti |ihi
t @? @ttLU@|i_ ULt| |L i_}?} OLiihc i? i_}?} LUUht |i 4@h}?@* ULt|
_gihi?|@* hit*|t ? |i }ih @M*|) 4@?@}ih i_}?} @?_ *Lih @M*|) 4@?@}ih
?L| i_}?} `i? i @?@*)3i |i i^*Mh@ Mi*L i ** tii |@| |iti |L ?||i
_i@t @hi tMt|@?|@|i_
AL LTih@|L?@*3i 6#W ?th@?Ui i @tt4i |@| 5e f *i 5 : 52 : 5
: f Ai M@?! }Lit M@?!hT| ? t|@|i 5e W? |t U@ti |i 6#W T@)t 5e |L |i
_iTLt|Lht
At |i i TiU|i_ @*i Lu €h4 i? | i_}it @?_ i? | _Lit ?L| i_}i
t }i? M)G
T EMc ' R 52 n E R 5
T EMc ' fDE rR 5 n dR 6 n fDE ro52
n dE R 6 n fDE ro5
T EMc T EMc ' fDE rE R 5e : f
`i? |i €h4 EM@?! 4@!it @ *Lttc |i 6#W t|iTt ? @?_ T@)t _iTLt|Lht Oi?Uic
|i i TiU|i_ @*i *i ?L| i_}?} t @*@)t }ih |@? |@| *i i_}?} Lhi
4TLh|@?|*)c |t _gihi?Ui ? i TiU|i_ @*it t }ih uLh |i *Lih @M*|) 4@?@}ih
@t |i 6#W LT|L? t 4Lhi @*@M*i |L |i *Lih @M*|) 4@?@}ih
Ai _i€?|L? Lu @ @)it@? @t i^*Mh4 t |i t@4i @t MiuLhi i UiT|
b |@| |i 4@?@}ih<t LMiU|ic }i? |i LT|4@* 4@h!i| Mi*iu u?U|L? 6W E t ?LG
L E6W Ec @Ec 3e
4
[
k
' @E C RE5 mMc 6W E5 ER R2 n R2 n T EMc D
q
'
3e
4
[
k
n E @E C RE5 mMc 6W E5 ER R2 n R2 n T EMc D q
'
Oihi q t ?L| + +, M| #E+ +, ihi # t |i uh@U|L? Lu L|T| |@| |i 4@?@}ih
hiUiit ? |i u|hi Ai @MLi uLh4*@|L? t t4*@h |L |@| ? hi?_ih}@t| @?_
5|L*i EbbS ? |@| |ih T@Tih @*tL tit @? LMiU|i u?U|L? ? U 4@?@}iht
U@hi uLh ML| ThL€|t @?_ i?_ Lu TihL_ hiT|@|L?t f Ai uh@U|L? k hiThiti?|t |i
i |i?| |L U |i 4@?@}ih U@hit uLh |i Uhhi?| @*i *i |i uh@U|L? q hiThiti?|t
|i i |i?| |L U |i 4@?@}ih U@hit uLh |i u|hi @*i
WV ,"NWwW+W W AO, #,w `WAO O,#BWB 5A5
`i €ht| ?it|}@|i |i i t|i?Ui Lu |i A)Ti i^*Mh4 E|i ?||i
i^*Mh4 ihi |i }ih @M*|) 4@?@}ih i_}it t i @i _tUtti_c |i
Thiti?Ui Lu ULt| Lu i_}?} tL*_ _i|ih i t|i?Ui Lu |i A)Ti i^*Mh4 i?
|i _gihi?Ui ? @M*|it t *L ? |i L|ih @?_ i? |i A)Ti i^*Mh4 _Lit
i t|c *Lih @M*|) 4@?@}iht tL*_ Mi *itt **?} |L i_}i hi*@|i |L |i U@ti ihi
4@?@}iht L?*) U@hi uLh |ih hiT|@|L?t MiU@ti Lu |i ULt| _gihi?|@* Mi|ii? |i
|L !?_t Lu 4@?@}iht At ?||L? |h?t L| |L Mi @*_@|i_
AO,+, eG A)Ti i^*Mh@ ?L*i @W E '  @?_ i t| uLh _ : BEr( BEr t
@*@)t i** _i€?i_ At A)Ti i^*Mh@ @*@)t i t| uLh } i?L} _gihi?Uit
? 4@?@}ih@* @M*|it Ai Mi@Lh Lu |i *Lih @M*|) 4@?@}ih t @t uL**LtG
f
Ai t}?@*?} 4L_i*t Lu +Ltt Eb..c @||@U@h)@ Eb.bc O@hht @?_ +@ EbHD @?_ hi??@? @?_
LTi*@?_ EbH. @i @ hi*@|i_ uLh4*@|L? Lu |i 4@?@}ih@* LMiU|i u?U|L?
2f BEr _ B,f @?_ _ : Bf c |i *Lih @M*|) 4@?@}ih _Lit ?L| i_}ic @W E2 '

B,f _ B, @?_ B _ Bf c |i *Lih @M*|) 4@?@}ih h@?_L43itc f @W E2

B, _ B c |i *Lih @M*|) 4@?@}ih i_}itc @W E2 ' 
t i_}?} ULt|t ?Uhi@tit uhL4 fc |i hi}L? EB, c B €ht| @?tit *i@?}
L?*) |i hi}L? EB,f c Bf ihi h@?_L43@|L? LUUht 6Lh *@h}i i?L} i_}?}
ULt|tc |i hi}L? EB,f c Bf @?tit @?_ |i *Lih @M*|) 4@?@}ih T*@)t @W E2 '
f
Ai hi}L? ihi @W E2 '  i? 4@?@}iht L*_ i^|) t @ t|hU| tMti| Lu |i
hi}L? ihi @W E2 '  i? 4@?@}iht L?*) U@hi Lu |ih hiT|@|L?t
hLLuG 5ii TTi?_ 6}hi  ThL_it |i i @U| hi}L?t U@h@U|ih3i_ ? AiLhi4 e @MLi uLh |i
@*it r ' fe E} i L}i?Lt ?Lti @h@?Ui @?_ r ' f.D E*L i L}i?Lt ?Lti
@h@?Ui
A)Ti i^*Mh@ _L ?L| i t| uLh *L _gihi?Uit ? @M*|) _i |L |i TLt|i
ULt|t Lu i_}?} tUi?|*) *@h}i _gihi?Ui ? @M*|) t hi^hi_ |L 4@!i i_}?} @
@M*i t|h@|i}) uLh |i }ih @M*|) 4@?@}ih #iTi?_?} L? |i ULt| Lu i_}?}c |i)
4@) Lh 4@) ?L| ?L*i @ hi}L? ihi |i *Lih @M*|) 4@?@}ih i_}it OLiihc
i? |ihi t @? hi}L? ihi |i *L @M*|) 4@?@}ih i_}itc |i i^*Mh4 |@!it
|i uL**L?} uLh4 uLh ?|ih4i_@|i _gihi?Uit ? @M*|) |i *Lih @M*|) 4@?@}ih
_Lit ?L| i_}i t |i _gihi?Ui ? @M*|) ?Uhi@titc i h@?_L43it @?_ ii?|@**)
i_}it 6Lh tUi?|*) } _gihi?Uit ? @M*|)c |i 4@?@}ih h@?_L43it @}@? @?_
ii?|@**) _Lit ?L| i_}i
2 FIGURE 1A
EQUILIBRIUM WHERE THE HIGHER ABILITY MANAGER HEDGES
(TYPE A EQUILIBRIUM) s=0.4
1
0.9
Difference in managerial abilities
0.8
Lower ability manager does not hedge
0.7
Lower ability
manager randomizes
between hedging
and not hedging
0.6
0.5
0.4
Lower ability manager
hedges
0.3
0.2
Type A Equilibrium Does Not Exist
0.1
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Cost of hedging
FIGURE 1B
EQUILIBRIUM WHERE THE HIGHER ABILITY MANAGER HEDGES
(TYPE A EQUILIBRIUM) s=0.75
1
0.9
Difference in managerial abilities
0.8
Lower ability manager does not hedge
0.7
Lower ability
manager randomizes
between hedging
and not hedging
0.6
0.5
0.4
Lower ability manager
hedges
0.3
0.2
Type A Equilibrium Does Not Exist
0.1
0
0
0.05
0.1
0.15
0.2
0.25
Cost of hedging
0.3
0.35
0.4
0.45
0.5
Ai ?||L? uLh tU Mi@Lh t @t uL**Lt `i? _gihi?Uit ? @M*|) @hi
t4@** @?_ |i }ih @M*|) 4@?@}ih €?_t | LT|4@* |L i_}ic |i *Lih @M*|)
4@?@}ih _Lit ?L| @t t ULt| t }ih t |i _gihi?Ui ? @M*|) ?Uhi@titc tL _L
|i ?Ui?|it |L 44U |i }ih @M*|) 4@?@}ih ThL_i_ |i *i@h??} ThLUitt t ?L|
|LL ?uLh4@|i At *i@_t |L @? ?|ih4i_@|i hi}L? ihi |i *Lih @M*|) 4@?@}ih
i_}it OLiihc @t |i _gihi?Ui ? @M*|) MiUL4it *@h}i |i *i@h??} ThLUitt i?
ML| 4@?@}iht i_}i t ih) ?uLh4@|i W? @__|L?c |i *Lih @M*|) 4@?@}ih u@Uit
@? ?Uhi@t?}*) }ih i_}?} ULt| @t |i ThLM@M*|) Lu }L?} M@?!hT| ?Uhi@tit
At *i@_t |L 4 |L Thiuih ?L| |L i_}i
`i ?i | |h? |L hi}L?t ihi |i _gihi?Uit ? @M*|) @hi ih) *L W? tU
hi}L?tc |i A)Ti i^*Mh4 _Lit ?L| i t| W?||i*)c ML| 4@?@}iht ** ?L|
i_}i `i |t ?it|}@|i |i A)Ti i^*Mh4 ihi |i }ih @M*|) 4@?@}ih
_Lit ?L| i_}i At i^*Mh4 t U@h@U|ih3i_ ? AiLhi4 D
AO,+, DG A)Ti i^*Mh4 t @? i^*Mh4 ihi @W E2 ' f @?_ f @W E  At |i *Lih @M*|) 4@?@}ih _Lit ?L| i_}i @?_ |i }ih @M*|)
4@?@}ih _Lit ?L| i_}i Lh h@?_L43it Mi|ii? i_}?} @?_ ?L| i_}?} E?L|i |@|
i _L ?L| ?U*_i |i U@ti ihi |i }ih @M*|) 4@?@}ih i_}it @t |t t @ A)Ti
i^*Mh@ A)Ti i^*Mh@ @i |L tMU@titG
,^*Mh4 | @W E ' f Aiti i t| uLh _ Er ihi Er : BEr Er
t _i|ih4?i_ M) |i Mi@Lh Lu |i }ih @M*|) 4@?@}ih i? r : fD @?_
M) |i Mi@Lh Lu |i *Lih @M*|) 4@?@}ih i? r fD
,^*Mh@ | f @W E  At i^*Mh4 i t|t uLh @ hi}L? ihi BEr
_ ZEr ihi ZEr Er
hLLuG 5ii TTi?_ 22 A)Ti i^*Mh@ UL?|@? |i 4TLh|@?| i^*Mh4 EA)Ti E ihi ML|
€h4t _L ?L| i_}i 5?Ui Er : BErc i @i UL?t|hU|i*) ThLi_ |@| @? i^
*Mh4 @*@)t i t|t W? u@U| @| BErc ML| |i RTLL*?} i^*Mh@ EML| €h4t ?L|
i_}?} @?_ |i RtiT@h@|?} i^*Mh@ E}ih @M*|) €h4 i_}itc *Lih @M*|)
€h4 _Lit ?L| @hi i^*Mh@ 6}hi 2 ThL_it |i i @U| hi}L?t ihi A)Ti @?_
A)Ti E i^*Mh@ i t| uLh |i @*it r ' fe E} i L}i?Lt ?Lti @h@?Ui @?_
r ' f.D E*L i L}i?Lt ?Lti @h@?Ui
AL UL4T*i|i |i U@h@U|ih3@|L? Lu |i 4L_i* i ?ii_ |L _LU4i?| @|
L|ih i^*Mh@c ? @__|L? |L |i @MLi i^*Mh@ i t| AiLhi4 S U@h@U|ih3it
|i L|ih i^*Mh@ ? |t 4L_i*
AO,+, SG W? @__|L? |L |i i^*Mh@ Lu AiLhi4t e @?_ Dc |i L?*) L|ih
@)it@? @t i^*Mh@ Lu |i 4L_i* @hiG
A)Ti # i^*Mh@ At i^*Mh@ ?L*it @W E ' f @?_ f @W E2  W|
U@??L| LUUh uLh r : fD W| 4@) LUUh uLh r fD _iTi?_?} L? |i T@h@4i|iht r
@?_ _
hLLuG 5ii TTi?_ Ai A)Ti # i^*Mh4 t |i UL?|ih?||i i^*Mh4 i @i _tUtti_
t _tUtti_ ? 5iU|L? Wc |t i^*Mh4 hi^hit } ?Lti ? |i ThLUitt o E*L
r t ThiLt*) 4i?|L?i_c i |?! |@| |i A)Ti # i^*Mh4 t *itt hi@tL?@M*i
i? |ihi t @ ULt| Lu i_}?} @t |i 4@h}?@* ULt| Lu i_}?} t *Lih uLh |i }ih
@M*|) 4@?@}ih `i Thiti?| @ ML?_ |@| i*4?@|it |t i^*Mh4 ,tti?|@**)c
|t UL?_|L? hi^hit |@| |i 4@?@}ih U@hit tUi?|*) uLh |i i^|) @*i Lu |i
€h4 hi*@|i |L t u|hi U@hiih hiT|@|L?

`| TLt|i ULt|t Lu i_}?} |i A)Ti i^*Mh4 |@| ?L*i h@?_L43@|L? M) 4@?@}iht Lu ML|
}ih @?_ *Lih @M*|it _Lit ?L| i t|
2 FIGURE 2A
EQUILIBRIUM WHERE BOTH MANAGERS DO NOT HEDGE (TYPE B(i))
AND
EQUILIBRIUM WHERE THE HIGHER ABILITY MANAGER HEDGES (TYPE A)
s=0.4
1
Type A Equilibrium Does Exist
Type B(i) Equilibrium Does Not Exist
0.9
Difference in managerial abilities
0.8
0.7
0.6
Type A and Type B(i) Equilibria Both Exist
0.5
0.4
0.3
0.2
Type A Equilibrium Does Not Exist
Type B(i) Equilibrium Does Exist
0.1
0
0
0.05
0.1
0.15
0.2
0.25
Cost of hedging
0.3
0.35
0.4
0.45
0.5
FIGURE 2B
EQUILIBRIUM WHERE BOTH MANAGERS DO NOT HEDGE (TYPE B(i))
AND
EQUILIBRIUM WHERE THE HIGHER ABILITY MANAGER HEDGES (TYPE A)
s=0.75
1
0.9
Type A Equilibrium Does Exist
Type B(i) Equilibrium Does Not Exist
Difference in managerial abilities
0.8
0.7
0.6
0.5
0.4
Type A and Type B(i) Equilibria Both Exist
0.3
0.2
Type A Equilibrium Does Not Exist
Type B(i) Equilibrium Does Exist
0.1
0
0
0.05
0.1
0.15
0.2
0.25
Cost of hedging
0.3
0.35
0.4
0.45
0.5
AO,+, .G Wu
k
_
%E_ ' 5e :
Lh
q
n_
Ek %E_# m+, Bm
: c
%E_#
m+ Bm
|i? A)Ti # i^*Mh@ _L ?L| i t|
hLLuG 5ii TTi?_ Ai ML?_ }i? ? AiLhi4 . _iTi?_t L? |i _gihi?Ui ? 4@?@}ih@* @M*
|it `i? |i _gihi?Ui ? 4@?@}ih@* @M*|it t *c |i @*i Lu |i ML?_ t *S
oe ƒ
`i? _ ' c |i ML?_ @t |t }it| @*i Lu *2 W? T@h|U*@hc tTTLti ƒƒ++o 3
k 3 oe ƒ
t *2 E} t|@|i ThL€|t @hi |Ui |i @MtL*|i @*i Lu *L t|@|i *Lttit @tt4?}
|i Lht| hi@*3@|L? Lu |i i L}i?Lt tLU! *tLc *i| # ' f E|i 4@?@}ih U@hit
uLh fI Lu u|hi L|T| Ai? |i ML?_ i? _ ' * )i*_t k : E*b# Lh k
: ff Ai ML?_ i? _ '  )i*_t k : D# Lh k : fD Oi?Ui ? |i Lht|
TLttM*i U@ti E_ ' c L?i ?ii_t |i i}| L? Uhhi?| i^|) |L Mi D |4it |i
i}| L? |i t@hi Lu u|hi L|T| Wu |i UL?_|L?t Lu AiLhi4 . @hi 4i|c |i ULt|
_gihi?|@* Mi|ii? 4@?@}iht Lu _gih?} @M*|it t tU |@| Mi@Lh ?L*?} |i
*Lih @M*|) 4@?@}ih i_}?} t 4T*@tM*i @?_ _Lit ?L| LUUh
`i ?L _tUtt |i i4ThU@* 4T*U@|L?t Lu Lh 4L_i* `*i i_}?} t ?L|
LMtih@M*ic tMti^i?| |L |i ii?|c L?i tL4i|4it !?Lt i|ih @ €h4t i_}it Lh
?L| At t MiU@ti i TLt| €h4t L*?|@h*) _tU*Lti i_}?} @U||) ? |i ?L|it
|L |i M@*@?Ui tii| Wu Lh t|Lh) Lu i_}?} t ULhhiU|c |i ThL€|t Ei@h??}t Lu €h4t
? |i ^@h|ih Lh )i@h U |i) i_}i tL*_ Mi }ih @?_ |i L*@|*|) Lu U@t
Lt tL*_ Mi *Lih |@? t@* 5U @ |it| _giht uhL4 |it|t Lu t}?@*?} 4L_i*t
ihi ThL€|t Ei@h??}t @hi }ih uLh €h4t |@| t}?@*( ?L L*@|*|) 4T*U@|L?t @hi
Thiti?| iU@ti i_}?} hi_Uit L*@|*|)c |i L*@|*|) hi_U|L? t @? @__|L?@*
4T*U@|L? 5L4i Thi*4?@h) i4ThU@* Lh! M) #iBiLh}ic Lti**i @?_ ~iU!@tih
2e EbbD t?} L4Tt|@| _@|@ t tTTLh|i Lu |t 4T*U@|L? Lu |i i_}?} )TL|
itt
tiUL?_ i4ThU@* 4T*U@|L? Lu Lh 4L_i* t @t uL**Lt `i? |i _gihi?Ui
? @M*|it t } @?_ |ihi @hi ULt|t |L i_}?}c i @hi 4Lhi *!i*) |L €?_ i_}?} W?
UL?|h@t|c i? |i _gihi?Ui ? @M*|it t *Lc |i i^*Mh4 |@| LUUht ?L*it ?L
i_}?} M) ML| !?_t Lu 4@?@}iht At 4T*U@|L? t MLh?i L| ? @ hiUi?| i4ThU@*
t|_) M) Au@?L EbbD L? |i }L*_ 4??} ?_t|h) 6ht| i €?_t |@| )L?}ih
4@?@}iht @hi 4Lhi *!i*) |L i_}i |@? L*_ih 4@?@}iht 5?Ui |ihi t *!i*) |L Mi
}hi@|ih E*ittih ?Uih|@?|) @ML| |i @M*|) Lu )L?}ih EL*_ih 4@?@}ihtc @ }ih
E*Lih _gihi?Ui ? @M*|it t UL?tt|i?| | )L?}ih EL*_ih 4@?@}iht Oi?Uic
Au@?L<t Lh! ThL_it 4U tTTLh| uLh Lh @TThL@U |L i_}?}2
|h_ i4ThU@* 4T*U@|L? Lu Lh 4L_i* t @t uL**Lt `i? |i ULt|t Lu
i_}?} @hi *Lc *itt tiT@h@|L? LUUht W? UL?|h@t|c i? |i ULt|t Lu i_}?} @hi
}c 4Lhi tiT@h@|L? LUUht AihiuLhic |i @*i Lu €h4t |@| i_}i hi*@|i |L
€h4t |@| _L ?L| i_}i t 4U }ih i? |i ULt| Lu i_}?} t }ih At t
@?L|ih 4T*U@|L? Lu |i 4L_i* |@| t TL|i?|@**) |it|@M*i Au@?L<t €?_?} |i
4@?@}iht | t|LU! LT|L?t _L ?L| i_}i t UL?tt|i?| | Lh _i@ |@| }ih
ULt|t Lu i_}?} *i@_ |L *itt Lih@** i_}?} OLiihc @ |it| Lu Lh @TThL@U L*_
hi^hi |@| u 4@?@}iht | t|LU! LT|L?t i_}ic |ih €h4 @*i t 4U }ih
|@? |@| Lu 4@?@}iht |L| t|LU! LT|L?t L i_}i
V wN5W5
2
`i @*tL ?L|i |@| Au@?L EbbD €?_t ?L tTTLh| uLh |i ULt|*) M@?!hT|U) @TThL@U |L i_}?} ? t
t|_) OLiihc BiU3)c ?|L? @?_ 5Uh@?_ Ebb. *LL! @| @ *@h}i UhLtttiU|L? Lu €h4t @?_ €?_ i_i?Ui 4Lhi
UL?tt|i?| | |i |h@?t@U|L?t ULt| Lu h@t?} U@T|@* @?_ Thiti?Ui Lu }hL| LTTLh|?|it )TL|itt T| uLh@h_
? 6hLL|c 5U@hut|i? @?_ 5|i? Ebb
 Au@?L EbbD @*tL €?_t |@| |i }hi@|ih |i i^|) L*_?}t Lu |i 4@?@}ihc |i 4Lhi *!i*) L?i ** LMtihi
i_}?} W| t _U*| |L ti |t LMtih@|L? _hiU|*) @t @| 4@||iht ? Lh 4L_i* t |i ULt| Lu i_}?} @?_ ?L| |i
uh@U|L? Lu i^|) i*_ ThL ) uLh |i ULt| Lu i_}?} 4t| t4*|@?iLt*) @UUL?| uLh |i uh@U|L? Lu i^|) i*_
@?_ |i @*i Lu |i i^|) LT|L? Lh 6#W ?th@?Ui |@| i_}?} _it|hL)t
2D `i @i Thiti?|i_ @ 4L_i* ihi? 4@?@}iht ti i_}?} @t @? ?_hiU| iU*i
|L UL44?U@|i |ih @M*|it `*i i_}?} |ti*u t ?L| LMtih@M*ic |i €h4<t
_iUtL? |L i_}i Lh ?L| |L i_}i @?_ |i 4@h!i|<t Mi*iut @ML| |t _iUtL? @giU|t
|i ?uihi?Uit |@| |i 4@h!i| 4@!it uhL4 ThL€|t W? @ 4L_i* ihi 4@?@}iht U@hi
L?*) uLh |ih hiT|@|L?tc i tL |i i t|i?Ui Lu @ U*@tt Lu i^*Mh@ ihi |i
}ih @M*|) 4@?@}ih i_}it *i |i *Lih @M*|) 4@?@}ih _Lit i_}i i? |i
@M*|) _gihi?Ui t *L M| _Lit ?L| i_}i i? |i @M*|) _gihi?Ui t } `i?
_gihi?Uit ? @M*|) @hi *L |i *i@h??} ThLUitt i? ML| 4@?@}iht i_}i t ?L|
ih) ?uLh4@|i E|L} 4Lhi ?uLh4@|i |@? i? ML| 4@?@}iht _L ?L| i_}i
*i ?L| i_}?} @**Lt |i *Lih @M*|) 4@?@}ih |L Mi _tULihi_ i? i |hi4i
t|@|it LUUh At |i *Lih @M*|) 4@?@}ih Thiuiht |L i_}i `i? |i _gihi?Ui t
@M*|it t }c |i *i@h??} ThLUitt i? ML| 4@?@}iht i_}i t ih) ?uLh4@|i
@?_ |i *Lih @M*|) 4@?@}ih Thiuiht ?L| |L i_}i @t |ihi t @ U@?Ui |@| *L
?|ihit| h@|it hi@*3@|L? *i@_t |L } ThL€|t
`i ?i | @**L 4@?@}iht |L L*_ i^|) ? |ih €h4t Wu 6#W ?th@?Ui i t|t
E@t ? |i U@ti Lu M@?!t Lh |i €h4 @t Thii t|?} _iM|c i_}?} t ULt|*) OLiihc
| t 4Lhi ULt|*) uLh |i *Lih @M*|) 4@?@}ih @t t ThLM@M*|) Lu }L?} M@?!hT| t
}ih W? tU @ U@tic ?L| i_}?} t |i i^*Mh4 i? |i @M*|) _gihi?Ui t
*L
6Lh @ tUi?|*) } _gihi?Ui ? @M*|itc |ihi t @? i^*Mh4 ihi |i
}ih @M*|) 4@?@}ih i_}it W? |t i^*Mh4c |i *Lih @M*|) 4@?@}ih Mi@it
@t uL**Lt uLh *Lih @M*|) _gihi?Uit i _Lit ?L| i_}i @t t ULt| Lu i_}?} t
}ih t |i @M*|) _gihi?Ui ?Uhi@titc |ihi 4@) Mi @ hi}L? ihi i i_}it
At LUUht i? hiT|@|L? igiU|t MiUL4i 4Lhi 4TLh|@?| @?_ |i _gihi?Ui ?
@M*|) t t|** ?L| |LL } 6?@**)c uLh *@h}i i?L} _gihi?Uit ? @M*|) i _Lit
?L| i_}i @t |i *i@h??} ThLUitt i? ML| 4@?@}iht i_}i t ih) ?uLh4@|i @?_
2S t ThLM@M*|) Lu }L?} M@?!hT| t ?Uhi@t?} +i*@|i |L |i 4L_i* i? 4@?@}ih
U@hi L?*) uLh |ih hiT|@|L?tc 4Lhi tiT@h@|L? LUUht ? |i U@ti ihi |i) L?
i^|)
h hit*|t ?_U@|i |@| i_}?} LUUht i? }ih @M*|) 4@?@}iht @hi
tMt|@?|@**) _gihi?| uhL4 *Lih @M*|) 4@?@}iht Lh |i ULt|t Lu i_}?} @hi *L
At tMt|@?|@|it |i U@t@* Mi*iu |@| i_}?} *LU!t T }ih ThL€| LTTLh|?|it
? |i t@4i @) |@| @? @hM|h@}ih *LU!t T @hM|h@}i LTTLh|?|it
2. +,6,+,,5
**i?c 6 @?_ # B@*ic bbfc Ri@thi4i?| #t|Lh|L? @?_ tt?} L?|?}i?Uit ?
L?|h@U|tc N?iht|) Lu i??t)*@?@c +L_?i) `|i i?|ih uLh 6?@?U@* +iti@hU
Lh!?} T@Tih
@||@U@h)@c 5c b.bc RW4TihuiU| W?uLh4@|L?c #_i?_ L*U) @?_ |ih_ ? |i
O@?_< 6@**@U)c i** aLh?@* Lu ,UL?L4Ut @?_ @?@}i4i?| 5Ui?Uic fc 2Db2.f
hii_i?c #c bHbc R@?! +t! @?@}i4i?|c ? O@?_MLL! Lu L_ih? 6?@?Uic i
vLh!G `@hhi?c BLh@4 @?_ w@4L?|
hi??@?c  @?_ A LTi*@?_c bH.c 5|LU! 5T*|tc 5|LU! hUi @?_ Ah@?t@U|L?t
Lt|tc aLh?@* Lu 6?@?U@* ,UL?L4Utc 22c Hf
hii_i?c #c bHec ROi_}?} @?_ 5}?@*?} M) 6?@?U@* W?|ih4i_@hitc ?TM*ti_
5|@?uLh_ N?iht|) 44iL}h@T
@4TMi**c A 5 @?_ ` kh@U@c bH.c RT|4@* @?@}ih@* L?|h@U|t @?_ |i
V@*i Lu LhTLh@|i W?th@?Uic aLh?@* Lu 6?@?Ui @?_ "@?||@|i ?@*)ttc 22Ec
D2H
@4TMi**c A @?_ @h?Lc bbec R)LTU W?it|4i?| #iUtL?t @?_ L4Ti||i
w@MLh @h!i|tc W?|ih?@|L?@* ,UL?L4U +iic DEec HDDH.D
h@uLh_c Vc @?_ a 5LMi*c bH2c R5|h@|i}U W?uLh4@|L? Ah@?t4ttL?c ,UL?L4i|
hU@c Dfc eeD
*Tc @?_  **ihc bbDc ROi_}?} W? Ai AiLh) Lu LhTLh@|i 6?@?UiG +iT*) AL h h|Utc aLh?@* Lu TT*i_ LhTLh@|i 6?@?Uic Hc 22.
#iBiLh}ic 6c Lti**i @?_ + ~iU!@tihc bbDc ROi_}?} @?_ 5LL|?}G LhTL
h@|i +t! LUit `i? W?uLh4?} |i @h!i|c N?TM*ti_ O, `Lh!?} @Tih
2H #i@h3Lc @?_ # #ic bbDc RLhTLh@|i W?Ui?|it uLh Oi_}?} @?_ Oi_}i U
UL?|?}c Ai +ii Lu 6?@?U@* 5|_itc Hc .e..
6hLL|c kc # 5U@hut|i? @?_ a 5|i?c bbc R+t! @?@}i4i?|G LLh_?@|?} Lh
TLh@|i W?it|4i?| @?_ 6?@?U@* L*Uitc aLh?@* Lu 6?@?Uic eHc S2bSDH
6_i?Mih}c #c @?_ a AhL*ic bHSc R Rt}?@*@44?} |iLh) Lu Thi_@|L?c+@?_
aLh?@* Lu ,UL?L4Utc .Ec SS.S
BiU3)c c ?|L? @?_ 5Uh@?_c bb.c R`) 6h4t Nti hhi?U) #ih@|itc
aLh?@* Lu 6?@?Uic D2c 2De
O@hhtc  @?_ OL*4t|hL4c bH2c R AiLh) Lu `@}i #)?@4Utc +ii Lu ,UL
?L4U 5|_itc ebc D
O@hhtc  @?_ +@c bHDc R 5i^i?|@* 5}?@*?} L_i* Lu LhTLh@|i 6?@?U@*
L*U)c aLh?@* Lu 6?@?Uic ec 2S2H2
OL*4t|hL4c c bH2c R@?@}ih@* W?Ui?|i hLM*i4tG #)?@4U ihtTiU|ic ?
,tt@)t ? ,UL?L4Ut @?_ @?@}i4i?| ? OL?Lh Lu w@ht `@*MiU!c Oi*t?!G 5i_t
5ULL* Lu ,UL?L4Ut
OL*4t|hL4c c b.bc Lh@* O@3@h_ @?_ Mtih@M*|)c i** aLh?@* Lu ,UL?L4Utc
fc .eb
OL*4t|hL4c @?_ a +U@h| Lt|@c bHSc R@?@}ih@* W?Ui?|it @?_ @T|@* @?
@}i4i?|c "@h|ih*) aLh?@* Lu ,UL?L4Utc fc HDSf
w?}^t|c w@htc bbec Rt)44i|hU W?uLh4@|L?G +@|L?@*i uLh LhTLh@|i 5TiU
*@|L?c aLh?@* Lu 6?@?U@* W?|ih4i_@|L?c c HH2f @||itc 5 @?_ w
h4@?c bHc R,^*Mh4 w4| hU?}G Ai ,giU|t Lu h@|i W?uLh4@|L? @?_
5|LU@t|U #i4@?_c ,UL?L4i|hU@c DEec bHbS
2b @h@)@?@?c  c bHDc RMtih@M*|) @?_ |i @)M@U! h|ihL?c aLh?@* Lu t
?ittc DHEc fb2e
i?_@h}h@t|c @?_ w 5|L*ic bbSc RW4Ti|Lt vL?}t|iht @?_ a@_i_ *_
A4ihtG U^h?} +iT|@|L? 6Lh wi@h??}c aLh?@* Lu L*|U@* ,UL?L4)c fec
fDe
+Lttc 5c b..c RAi #i|ih4?@|L? Lu 6?@?U@* 5|hU|hiG Ai W?Ui?|i 5}?@*?}
TThL@Uc i** aLh?@* Lu ,UL?L4Utc Hc 2ef
@*uhi)c A + @?_ 5T@||c 5c bHDc R+iTi@|i_ W?th@?Ui L?|h@U|t @?_ wi@h??}c
+@?_ aLh?@* Lu ,UL?L4Utc SEc DSS.
5U@hut|i?c # 5 @?_ a 5|i?c bbfc ROih_ i@Lh @?_ W?it|4i?|c 4ihU@?
,UL?L4U +iic Hfc eSDe.b
5@ThL c bHbc *|?@|L?@* 6?@?U@* @?@}i4i?|c Ah_ ,_|L?c **)? @?_
@UL?c Lt|L?c @tt@Uti||t
54|c `c @?_ +  5|*3c bHDc RAi #i|ih4?@?|t Lu 6h4t< Oi_}?} L*Uitc
aLh?@* Lu 6?@?U@* @?_ "@?||@|i ?@*)ttc 2fEec befD
5|i?c a c bHbc R,Ui?| @T|@* @h!i|tc W?iUi?| 6h4tG L_i* Lu )LTU
LhTLh@|i i@Lhc "@h|ih*) aLh?@* Lu ,UL?L4Utc feEec SDD.f
Au@?Lc c bbSc R`L @?@}ih +t!q ? ,4ThU@* , @4?@|L? Lu +t! @?@}i
4i?| h@U|Uit ? |i BL*_ ??} W?_t|h)c aLh?@* Lu 6?@?Uic Dc fb..
~iMi*c ac bbDc RLhTLh@|i L?tih@|t4 @?_ +i*@|i L4Ti?t@|L?c aLh?@* Lu
L*|U@* ,UL?L4)c fc 2D
f ,#Wj
hLLu Lu AiLhi4 G Bi? |@| @E '  @?_ |@| f @E2 c |i 4@h!i| Mi*iut
@hi
hL€|
@h!i| Mi*iut 6E
5
f
52
R %iR n @E2R2 n E @E2dR2 6 n fDE roj
5
R2 %iR2 n @E2R n E @E2dR 6 n fDE roj
5e
f
E
Ai TLt|ihLh Mi*iut @hi |Lti UL?tt|i?| | @)it h*i i UiT| i? @E ' 
W? |@| U@ti ML| €h4t i_}i @?_ |t 5 @?_ 5e @hi Lg |i i^*Mh4 T@| `i
@tt4i |i Lg i^*Mh4 TLt|ihLh uLh ThL€| *ii*t 5 @?_ 5e t f
6Lh |i }ih @M*|) 4@?@}ih |L €?_ | LT|4@* |L i_}i i 4t| @ic
LE6W Ec Mc  : L E6W Ec Mc 
+, R 6E52 n R2 6E5 : dR 6 n fDE ro6E52 n dR2 6 n fDE ro6E5 +, fDE rER 6E52 n fDE rER2 6E5 : f
E2
L|i |@| 6E52 : 6E5 At
fDE rER 6E52 n fDE rER2 6E5 : fDE rER 6E5 n fDE rER2 6E5 ' fDE r6E5 :f
At ?_ih |i @MLi 4@h!i| Mi*iut 4@?@}ih <t Mit| t|h@|i}) t |L i_}i
 E
i | UL?t_ih @}i?| 2 Wu @}i?| 2 h@?_L43it Mi|ii? i_}?} @?_ ?L| i_}?}
|i?
LE6Ec Mc 2 ' LE6Ec uc 2
+, R2 6E52 n R 6E5 ' dR2 6 n fDE ro6E52 n dR 6 n fDE ro6E5 R
 E @E2E rfDER2 
R2
n fDE rER 
'f
 E @E2E rfDER 
+, fDE rER2 
+, ER R2 d E @E2fDE rE2 R o
' E2 R R d E @E2fDE rER o
+, E @E2 '
ER E R n E2 R R
ER E2 R fDE r
Ee
Ai h}| @?_ t_i Lu |i @MLi i ThittL? t 4L?L|L?i ? R 5i||?} |i h}| @?_
t_i Lu |i *@t| i^@|L? ? Ee i^@* |L f )i*_t
ER E R n E2 R R ' f
+, SR2 SR n  ' f
ED
s
At )i*_t |i tL*|L? lM ' fD n fDE* 5i||?} |i h}| @?_ t_i Lu |i *@t|
i^@|L? ? Ee |L  )i*_t
R  R2 n R n 2R R2 ' ESR 2 bR2 n R fDE r
+, SR SR2  ' EbR bR2 2fDE r
+, R R2 '
ES
2r
br n t rn
At _i€?it l7 Er ' fD n fD
brn
U t _iUhi@t?} ? r +@?_L43i_ t|h@|i}it
@hi @M*i ? |i hi}L? R 5 ElM c l7 Er 5?Ui |i _gihi?Ui ? @M*|it _ t 4L?L|L?i
? c |ihi t i^@*i?|*) @ hi}L? EBM c B7 Er tU |@| uLh _ 5 EBM c B7 Er h@?_L4
3@|L? t LT|4@* uLh |i *Lih @M*|) 4@?@}ih `i? _ BM c |i Mit| t|h@|i}) uLh
2 |i *Lih @M*|) 4@?@}ih t |L i_}i @?_ i? _ : B7 Er |i Mit| hitTL?ti t |L ?L|
i_}i
hLLu Lu AiLhi4 2G
`i tL |@| ?L i^*Mh@ ihi |i *L @M*|) 4@?@}ih i_}it *i |i
} @M*|) 4@?@}ih h@?_L43it U@? i t| W? |t U@ti |i TLt|ihLh Mi*iut @hi
hL€|
@h!i| Mi*iut 6E
5

5
@ER4 nE3@EdR4 6nfDE3ro
@ER4 nE3@EdR4 6nfDE3ronR5
@ER5 nE3@EdR5 6nfDE3ro
@ER5 nE3@EdR5 6nfDE3ronR4
5e

52
E.
Ai *Lih @M*|) 4@?@}ih i_}it At
L E6Ec Mc 2 : L E6Ec Mc 2
+, fDE rER2 6E52 n fDE rER 6E5 : fDE rR2 6E5 n fDE rR 6E5e EH
+, ER2 6E52 n ER 6E5 : R2 6E5 n R 6E5e ' 
ihi 6E5 ' 6E5e '  t ti_ |
ER2 6E52 n ER 6E5 ' R2 6E52 n R 6E5 n E2R d6E5 6E52 o
R2 6E52 n R 6E5 t?} 6E52 : 6E5 Eb
R2 n R ' 
At L E6Ec Mc 2 : L E6Ec Mc  ?iih L*_t
hLLu Lu AiLhi4 G Ai ThLLu t UL?t|hU|i @?_ UL?tt|t Lu |hii T@h|tG
@ ThLLu |@| t|h@|i}it ihi @E2 ' f @?_ f @E  @hi ?L| i^*Mh@
M @ U@h@U|ih3@|L? Lu TLttM*i i^*Mh@ i? f @E  @?_ f @E2 
U @ U@h@U|ih3@|L? Lu TLttM*i i^*Mh@ i? @E ' f @?_ f @E2 
@h| @ `i €ht| UL?t_ih |i U@ti ihi |i *Lih @M*|) 4@?@}ih _Lit ?L| i_}i
*i |i }ih @M*|) 4@?@}ih h@?_L43it Mi|ii? i_}?} @?_ ?L| i_}?} Ai
4@h!i| Mi*iut ? tU @ U@ti @hi
hL€|
@h!i| Mi*iut 6E
5
dE @ER o % dE @ER n R2 o
52
@ER4 nE3@EdR4 6nfDE3ro
@ER4 nE3@EdR4 6nfDE3ronR5 6nfDE3r
5
@ER5 nE3@EdR5 6nfDE3ro
@ER5 nE3@EdR5 6nfDE3ronR4 6nfDE3r
5e
dE @ER2 o % dE @ER2 n R o
Ef
6Lh |t |L Mi @? i^*Mh4 i ?ii_ LE6Ec Mc  ' L E6Ec Mc  @?_
L E6Ec Mc 2 L E6Ec Mc 2 #i€?i |i u?U|L?t
8 E@E ' ER 
@EfDE rER  n R 6 n fDE r
@EfDE rER  n 6 n  r
n ER2 
R
@EfDE rER2  n R2 6 n fDE r
@EfDE rER2  n 6 n  r
E @ER
E @ER2
R2
 @ER
 @ER2
@EfDE rER  n R 6 n fDE r
82 E@E ' ER2 
@EfDE rER  n 6 n  r
n ER 
R2
E
@EfDE rER2  n R2 6 n fDE r
@EfDE rER2  n 6 n  r
E @ER
E @ER2
R
 @ER
 @ER2
`i ?ii_ |L €?_ T@h@4i|ih hit|hU|L?t |@| 4T*) 8 E@E ' f @?_ 82 E@E f
e LUUht 6ht| ?L|i |@|
8 Ef E ' E: f
+,
ER 
R 6 n fDE r
R2 6 n fDE r
n ER2 
R2 R22 E ' E: f
6nr
6nr
+, E2r 2dR2 n R22 o E ' E: E2r 
E2
`i? r : fDc 8 Ef : f @?_ i? r fDc 8 Ef f 5iUL?_ ?L|i |@| _8 E@E
% _@E : f At i? r : fDc 8 E@E : f uLh @** @E @?_ ?L i^*Mh4 i t|t
Ah_ ?L|i |@|
8 E ' ER 
fDE rER  n R 6 n fDE r
fDE rER  n 6 n  r
n ER2 
fDE rER2  n R2 6 n fDE r
fDE rER2  n 6 n  r
E
' R 6E52 n R2 6E5 n E2R d6E52 6E5 o : f
@t 6E52 : 6E5 At @ ?^i f @E  i t|t i? r fD
`i|ih i^*Mh4 i t|t _iTi?_t ? |t U@ti L? |i Mi@Lh Lu 82 E@E
6ht| ?L|i |@|
82 Ef E ' E: f
+, ER2 
R 6 n fDE r
R2 6 n fDE r
n ER 
2R R2 E ' E: f
6nr
6nr
+, eR R2 E2r  E ' E: 2r 
Ee
D At 82 Ef f i? r : fD @?_ 82 Ef : f i? r fD 5iUL?_ ?L|i |@|
_82 E@E
_@E
' ER ER2 fDE r
R2 6 n fDE r
d@EfDE rER  n 6 n  ro2
R 6 n fDE r
n ER2 ER fDE r
d@EfDE rER2  n 6 n  ro2
n
ED
R R22
R2 R2
n
E @ER 2 E @ER2 2
NT |L R 2* |t t thi*) TLt|i 5?Ui 82 Ef : fc 82 E@E : f uLh @** @E
@?_ ?L i^*Mh4 i t|t ? |i L|ih @?_ u R : 2*c i^*Mh4 4@) i t|
OLiihc @ }h_ ti@hU Lih |i hi}L? ihi * r fD @?_ 2* R  tLt
tL tL*|L? ihi 8 E@E ' f @?_ 82 E@E fe
@h| M `i UL?t_ih i? t|h@|i}it ?L*?} h@?_L43@|L? M) ML| 4@?@}iht @hi
UL?tt|i?| | i^*Mh4 `i? ML| 4@?@}iht h@?_L43ic 4@h!i| Mi*iut t@|tu)c
hL€|
@h!i| Mi*iut 6E
5
E @ER *iE @ER n E @E2R2 j
52
@EfDE3rER4 3nR4 6nfDE3r
fDE3rd@EER4 3n@E2ER5 3on6n3r
5
@EfDE3rER5 3nR5 6nfDE3r
fDE3rd@EER5 3n@E2ER4 3on6n3r
5e
E @ER2 *iE @ER2 n E @E2R j
ES
+@?_L43@|L?
hi^hit |@| LE6Ec Mc  ' L E6Ec Mc  @?_ L E6Ec Mc 2 ' L E6Ec Mc 2
? t4T*u)?} |iti i ThittL?t i LM|@? |@|G
8 Ebc w
'
R bfDE rER 
2 bR
 bR2
 bfDE r n fDE rwER2  b wR2 b wR
'f
e
At UL4T|ih ThL}h@4 t @@*@M*i uhL4 |i @|Lht L? hi^it|
S E.
@?_
82 Ebc w
'
R2 bfDE rER2 
 bR
2 bR2
 bfDE r n fDE rwER  b wR2 b wR
EH
'f
ihi f b ' @E  @?_ b w ' @E2 @E  b
Wu L?i ti|t w ' f @?_ b ' *E2E rc |i @MLi i^@|L?t @hi t@|t€i_ uLh
@?) R 5?Ui *E2E r  L?*) i? r fDc |t i^*Mh4 L?*) i t|t u |t
UL?_|L? t t@|t€i_
5hTht?}*)c |ihi t ?L L|ih i^*Mh4 |@| ?L*it h@?_L43@|L? At
t ThLi_ M) h???} @ UL4T|ih }h_ ti@hU Lih * r  @?_ fD R  @?_
ti@hU?} i|ih |ihi i t| @*it Lu b @?_ w t@|tu)?} i^@|L?t E. @?_ EH
@?_ t@|tu)?} |i hit|hU|L?t f b  @?_ b w  bD
@h| U `i ?L *LL! @| |i U@ti ihi |i }ih @M*|) 4@?@}ih _Lit ?L| i_}i
@?_ |i *Lih @M*|) 4@?@}ih h@?_L43it Mi|ii? i_}?} @?_ ?L| i_}?} Ai
4@h!i| Mi*iut @hi
hL€|
@h!i| Mi*iut 6E
5
R *iR n E @E2R2 j
52
R4 6nfDE3r
6n3rnfD@E2E3rER5 3
5
R5 6nfDE3r
6n3rnfD@E2E3rER4 3
5e
R2 *iR2 n E @E2R j
Eb
`i ?ii_ €?_ u T@h@4i|ih @*it i t| tU |@| LE6Ec Mc  D
At UL4T|ih ThL}h@4 t @@*@M*i uhL4 |i @|Lht L? hi^it|
. L E6Ec Mc  @?_ LE6Ec Mc 2 ' L E6Ec Mc 2 #i€?i |@| u?U|L?t
8 E@E2
' ER 
n ER2 
R 6 n fDE r
6 n  r n fD@E2E rER2 
R2 6 n fDE r
R
R2
R2
R
6 n  r n fD@E2E rER 
 @E2R2
 @E2R
82 E@E2
' ER2 
n ER 
R 6 n fDE r
6 n  r n fD@E2E rER2 
R2 6 n fDE r
R
R2
R2
R
6 n  r n fD@E2E rER 
 @E2R2
 @E2R
E2f
W| tUit |L €?_ UL?_|L?t ?_ih U 8 E@E f @?_ 82 E@E2 ' f
6ht| ?L|i |@|
8 Ef E ' E: f
+, ER 
R2
R 6 n fDE r
R2 6 n fDE r
n ER2 
6nr
6nr
R22
E2
E ' E: f
+, 2d2r oER2 n R22 E ' E: 2r 
5?Ui 2ER2 n R22 : c i? r : fDc i @i 8 Ef : f `i? r fD i @i 8 Ef
f
5iUL?_ ?L|i |@|
82 Ef E ' E:f
+, ER2 
R 6 n fDE r
R2 6 n fDE r
n ER 
2R R2 E ' E: f
6nr
6nr
+, d2r oeR R2 E ' E: 2r 
E22
5?Ui eR R2 c i? r : fD i @i 82 Ef f @?_ i? r fD i @i 82 Ef :
f
H Ah_ ?L|i |@| _8 E@E2 % _@E2 f
`i? r : fDc 82 E@E2 f uLh @** @*it Lu @E2 @?_ |t |i i^*Mh4
_Lit ?L| i t| W? u@U| |i i^*Mh4 ihi ML| 4@?@}iht _L ?L| i_}i u@*t |L
i t| @t 8 Ef : f Ai i^*Mh4 ihi 4@?@}ih  _Lit ?L| i_}i @?_ 4@?@}ih 2
i_}it _Lit ?L| i t| @t 82 E f
`i? r fDc |i i^*Mh4 ihi ML| 4@?@}iht _L ?L| i_}i u@*t |L i t|
@t 82 Ef : f ? |i L|ih @?_
82 E ' ER2 
R 6 n fDE r
6 n  r n fDE rER2 
n ER 
+,
R2 6 n fDE r
R
R2
R2
R
f
6 n  r n fDE rER 
 R2
 R
R 6 n fDE r
 f
6 n  r n fDE rER2 
E2
5?Ui |i *@t| t|@|i4i?| t |hi 82 E f At |i i^*Mh4 ihi 4@?@}ih 
_Lit ?L| i_}i @?_ 4@?@}ih 2 i_}it _Lit ?L| i t| OLiihc |ihi i t|t @? ?^i
@E2 tU |@| 82 E@E2 ' f Wu @| |t @E2c 8 E@E2 f i @i @? i^*Mh4
L
_8 E@E2
dR 6 n fDE roifDE rER2 j
' ER ER2 fDE r
_@E2
dE6 n  r n fDE r@E2ER2 o2
ER2 ER fDE r
dR2 6 n fDE roifDE rER j
dE6 n  r n fDE r@E2ER o2
R2 R2
R22 R
E @E2R2 2 E @E2R 2
E2e
`i? R 2*c _8 E@E2 * _@E2 f @?_ 8 Ef f 4T*) |@| 8 E@E2 f uLh @**
@E2 @?_ |t i^*Mh4 i t|t `i? R : 2*c @ tL*|L? @*@)t i t|t `i ihu)
b |t t?} @ UL4T|ih }h_ ti@hU Lih |i hi}L? * r fD @?_ |i R : 2*S
hLLu Lu AiLhi4 eG A)Ti i^*Mh@ hi^hi |@| L E6Ec Mc  : L E6Ec Mc 
@?_ LE6Ec Mc 2 E ' E: L E6Ec Mc 2 Ai ?i^@*|) uLh |i *Lih @M*|)
4@?@}ih tG
ER R2 dR2 6E52 n R 6E5 o n R2
E ' E: ER R2 diR2 6 n fDE rj6E52 n iR 6 n fDE rj6E5 o
k
R fDE r5e
q
+, ER R2 dER2 R d E @E2fDE rER o
n ER R2 d E @E2fDE rER2 oo
' E: ' E k
R fDE r5e q
d E @E2fDE rER od E @E2fDE rER2 o
+, ER R2 dSR R2  E @E2fDE rEbR R2 2o
E: ' E k
R 5e d E @E2fDE r n E @E22 f2DE r2 EbR R2 2o
q
E2D
`i €ht| *LL! @| |i U@ti ihi @E2 ' ( |i *Lih @M*|) 4@?@}ih i_}it
`i |t ?ii_ |@|
k
E2R ESR SR2  : 5e R
q
E2S
ihi R2 '  R t ti_ L|i |@| |i *iu| @?_ t_i t 3ihL @| R ' fD *i |i
h}| @?_ t_i t t|hU|*) TLt|i *tL |i *iu| @?_ t_i @t _ih@|i eEbR R2 2
@?_ |t t @ UL?U@i u?U|L? | @ 4@ 44 @| R ' 2* Ai h}| @?_ t_i
t @ *?i@h u?U|L? ? R Oi?Ui |ihi @hi i @U|*) |L ?|ihtiU|L?t Lh ?L?i Aihi
S
At UL4T|ih ThL}h@4 t @@*@M*i uhL4 |i @|Lht L? hi^it|
ef i t|t @ hi}L? R 5 El, c l ELh _ 5 EB, c B c TLttM*) i4T|) ? U |i *Lih @M*|)
4@?@}ih €?_t | LT|4@* |L i_}i
L UL?t_ih |i U@ti ihi |i *Lih @M*|) 4@?@}ih _Lit ?L| i_}i( @E2
' f Ai ?i^@*|) uLh |i *Lih @M*|) 4@?@}ih t4T*€it |L
E2 
dSR R2  fDE rEbR R2 2o
R
k
5e d fDE r n f2DE r2 EbR R2 2
q
E2.
Ai tiUL?_ _ih@|i Lu |i *iu| @?_ t_i Lu i^@|L? E2. t
2

b
E roE 2R dSR
R

fDE
rEbR
R
2o
n
dS

2

2
2
R2
R2
+
,


b
n dS E ro 2 E 2R 2E2 f
2
R
R
E2H
At |i *iu| @?_ t_i t UL?U@i ? R Ai h}| @?_ t_i @t _ih@|i kq 5e f2DE r2 bE 2R @?_ |t t @ _iUhi@t?} UL?U@i u?U|L? | R ' fD @?_
R 'c |i *iu| @?_ t_i ? ?i}@|i ELh 3ihL *i |i h}| @?_ t_i t @*@)t
TLt|i( |t u @? ?|ihtiU|L? LUUht @| *i@t| |L ?|ihtiU|L?t i t|
,^@|L? E2. t @ UMU i^@|L? @?_ @t @| 4Lt| |hii hi@* hLL|t( i ?ii_
|L i?thi |@| |t |h_ hLL| t ?L| Mi|ii? R ' fD @?_ R '  | @| R ' fc
|i *iu| @?_ t_i t r @?_ |i h}| @?_ t_i t f At @ hLL| i t|t Mi|ii? R
' f @?_ R ' fD @** |i |L ?|ihtiU|L? TL?|t Mi|ii? fD @?_  l,f @?_ lf c
l,f lf i | *i UL?t_ih?} h@?_L43i_ t|h@|i}itc i tL |@| l,f l, l
lf W? |i hi}L? L|t_i El,f c lf E|i ULhhitTL?_?} hi}L? uLh _ t EB,f c Bf c |i
*Lih @M*|) 4@?@}ih _Lit ?L| i_}i W? |i hi}L? |? El, c l E|i ULhhitTL?_?}
hi}L? uLh _ t EB, c B c |i *Lih @M*|) 4@?@}ih i_}it W? |i ?|ih4i_@|i hi}L?
i h@?_L43it
e +@?_L43@|L? t @? LT|4@* t|h@|i}) u LE6Ec Mc 2 ' L E6Ec Mc 2 Lh
E2 
dSR R2  E @E2fDE rEbR R2 2o
R
k
' 5e d E @E2fDE r n E @E22 f2DE r2 EbR R2 2o
q
E2b
Ai *iu| @?_ t_i t  E @E2E r : f @| R ' f *i |i h}| @?_ t_i t
f Aihi t @| *i@t| L?i hLL| Mi|ii? f @?_ fD | R ' fD |i *iu| @?_ t_i t f
*i |i h}| @?_ t_i t @ TLt|i ?4Mih 6?@**) uLh R ' c |i *iu| @?_ t_i
t d E @E2E ro f *i |i h}| @?_ t_i t t|** TLt|i At |ihi @|
|L ?|ihtiU|L?t Lh ?L ?|ihtiU|L?t @| @** Mi|ii? fD @?_ ( 4Lhi |@? |L U@??L|
LUUh @t |ihi @hi @| 4Lt| |hii hLL|t |L |i i^@|L? @?_ L?i hLL| *it Mi|ii? f
@E2
@?_ fD @** |iti ?|ihtiU|L? TL?|t l,
@E2
@?_ l
Ai *iu| @?_ t_i Lu E2b t UL?U@i ? R *i |i h}| @?_ t_i t _iUhi@t
?} @?_ UL?U@i ? R 5TTLti @E2 : @E2 Ai? uLh R 2*c wO5E@E2 c R :
wO5E@E2c R @?_ uLh R : 2*c wO5E@E2 c R wO5E@E2c R *tL -M7E@E2 c R : -M7E@E2c R @E2
5TTLti @E2 : @E2 `i €ht| tL |@| u @E2 2*c |i? l,
@E23
5?Ui l, 2*c |i @tt4T|L? |@| l,
@E23
l,
2* t t|€i_ M) |i ih) t@4i @h}
@E23
4i?| AL tL |t U*@4 ?L|i |@| @| R ' l,
c
uM7E@E2 c R ' -M7E@E2 c R +, ER R2 dSR R2  E @E2 fDE rEbR R2 2o
k
' R 5e d E @E2 ofDE r n E @E2 2 f2DE r2 EbR R2 2o
q
Ef
e2 @E23
Ai? @| R ' l,
c
uM7E@E2c R -M7E@E2c R +, ER R2 dSR R2  E @E2fDE rEbR R2 2o
k
R 5e d E @E2ofDE r n E @E22 f2DE r2 EbR R2 2o
q
+, E R R2 : ESR R2 fDE rEbR R2 2E2 @E2 @E2
f2DE r2 EbR R2 22 E @E2E @E2 E
ihi uM7E@E2 c R ' -M7E@E2 c R @t Mii? ti_ Ai *iu| @?_ t_i Lu |i *@t|
i^@|L? ? E t *Lit| i? R ' fD ihi |t @*i t f2D Ai h}| @?_
t_i Lu |i *@t| i^@|L? ? E t }it| @| fD ThL_i_ R 2* | R ' fDc
|i h}| @?_ t_i Lu *@t| i^@|L? ? E @t @*i f2DE r U t *itt |@|
@E23
f2D At @ hLL| Lu |i i^@|L? i t|t Mi|ii? fD @?_ l,
@E2
AL ThLi |@| l
@E23
: l
@E2
Oi?Ui l,
@E23
c UL?t_ih €ht| |i U@ti ihi l
@E23
l,
: 2* W? |t
@E2
U@ti uM7E@E2c R : uM7E@E2 c R ' -M7E@E2 c R : -M7E@E2c R At l
@E23
: l
@E23
? |i L|ih @?_ u l
@E23
T@h@}h@T Lh!t @?_ @| R ' l
2* @? @h}4i?| t4*@h |L |@| ? |i ThLh
c uM7E@E2c R : -M7E@E2c R Oi?Ui @ tiUL?_
@E23
hLL| i t| @| tL4i R @*i }hi@|ih |@? l
At ThLit |i ThLTLt|L?
6?@**) | t i@t) |L tL |@| @t kq 5e ?Uhi@tit |i hi}L? El, c l _t@TTi@ht
*i@?} |i hi}L? El,f c lf |? U h@?_L43@|L? LUUht ,i?|@**) |t hi}L?
@*tL _t@TTi@ht @?_ uLh @** R @*it |i *Lih @M*|) 4@?@}ih €?_t | LT|4@* ?L| |L
i_}i
e `i ?L |h? |L |i }ih @M*|) 4@?@}ih Oi i_}it @t *L?} @t *L?} @t
LE6Ec Mc  : L E6Ec Mc 
+, ER R2 dfDE rER 6E52 n fDE rER2 6E5 o
k
: R2 fDE r5e
q
%
R ER 
+, ER R2  E @E2fDE rER2 
&
R2 ER2 
k
n
: R 5e
 E @E2fDE rER 
q
E2
u|ih 4U t4T*€U@|L? |i @MLi ?i^@*|) hi_Uit |L
R R2
d2 SR R2 E @E2fDE rde DR R2 oo
R2
l
k k
: 5e  E @E2fDE r n f2DE @E22 E r2 EbR R2 2 q
E
Ai *iu| @?_ t_i Lu |i *@t| i^@|L? ? E t t|hU|*) ?Uhi@t?} ? R *i |i
h}| @?_ t_i Lu |i t@4i i^@|L? t t|hU|*) _iUhi@t?} ? R *tL |i *iu| @?_
t_i Lu |i *@t| i^@|L? ? E t 3ihL @| R ' fD *i |i h}| @?_ t_i Lu |i
t@4i i^@|L? t TLt|i | R ' c |i *iu| @?_ t_i Lu |i *@t| i^@|L? ? E
t 4 *i |i h}| @?_ t_i Lu |i t@4i i^@|L? t @ €?|i ?4Mih At lE@E2
i t|t tU |@| uLh R : lE@E2c i_}?} t LT|4@*
@E2
i |c i tL |@| lE@E2 l,
AL ThLi |t ?L|i |@| i ?ii_ |L UL4T@hi
i^@|L? E2b | i^@|L? E Ai h}| @?_ t_i Lu i^@|L? E @MLi
t *itt |@| ? i^@|L? E2b @t R2 R Ai *iu| @?_ t_i Lu i^@|L? E t
}hi@|ih |@? |i *iu| @?_ t_i Lu i^@|L? E2b ThL_i_ |@|
2 SR R2 E @E2fDE rde DR R2 o
: SR R2  E @E2fDE rEbR R2 2
+,  eR R2 E @E2E rE eR R2 : f
ee Ee
@E2
5?Ui |t ?i^@*|) L*_t lE@E2 l,
#i€?i lEr ' lE@E2 Ai? lEr l@f Ai i^*Mh4 UL?t|hU|i_ @MLi |i? L*_t uLh R : lEr Et4*@h*) i @i _ :
BEr W? |t hi}L?c }i? |i *Lih @M*|) 4@?@}ih<t LT|4@* @U|L?c |i }ih
@M*|) 4@?@}ih €?_t | LT|4@* |L i_}i
hLLu Lu AiLhi4 DG A)Ti i^*Mh@ ?L*i |i *Lih @M*|) 4@?@}ih ?L| i_}
?} dL E6Ec Mc 2 L E6Ec Mc 2o @?_ |i }ih @M*|) 4@?@}ih ?L| i_}?} Lh
h@?_L43?} d EL E6Ec Mc  LE6Ec Mc  Lh L E6Ec Mc  ' L E6Ec Mc 2o
Ai ?i^@*|) uLh |i *Lih @M*|) 4@?@}ih hi_Uit |L
k
ER R2 82 E@E R 5e q
ED
Ai ?i^@*|) uLh |i }ih @M*|) 4@?@}ih
k
ER R2 8 E@E ' R2 5e
q
ES
k
ER R2 8 Ef R2 5e
q
E.
u i h@?_L43it Lh
u i _Lit ?L| i_}i 8 E@E @?_ 82 E@E2 @hi @t _i€?i_ ? T@h| EM Lu |i ThLLu
Lu AiLhi4 6hL4 |@| ThLLu i !?L |@| i? r : fDc 8 Ef : f @?_ 82 Ef f 5?Ui f kq R2 5e kq R 5e c @? i^*Mh4 ihi ML| 4@?@}iht _L ?L| i_}i
i t|t i?
k
ER R2 8 Ef R 5e
q
+, ER R2 %
&
R 6 n fDE r
R2 6 n fDE r
2
2
ER 
n ER2 
R R2
6nr
6nr
k
R2 5e
q
k
+, ER R2 E2r d2ER2 n R22 o R2 5e E6 n  r
q
eD EH
Ai *iu| @?_ t_i Lu |i *@t| i^@|L? ? EH t ?Uhi@t?} ? R *i |i h}| @?_
t_i t _iUhi@t?} *tLc uM7EfD ' f -M7EfD *i uM7E : f ' -M7E
At @ ?^i tL*|L? /Er i t|t tU |@| uLh @** R /Er Et4*@h*) _ Erc
i^@|L? EH L*_t
AL ThLi |@| /Er : lEr ELh Er : BEr @h}i @t uL**Lt | lEr i? |i
4@h!i| Mi*iit |@| |i }ih @M*|) 4@?@}ih i_}it @?_ |i *Lih @M*|) 4@?@}ih
_Lit ?L| LE6Ec Mc  ' L E6Ec Mc  @?_ L E6Ec Mc 2 LE6Ec Mc 2 |
|t t t|
k
ER R2 8 E ' R2 5e
q
k
ER R2 82 E R 5e q
Eb
k
ER R2 8 Ef ER R2 8 E ' R2 5e
q
Eef
k
ER R2 82 Ef f R 5e q
Ee
5?Ui _8 E@E % _@E : fc
@?_
At ML| 4@?@}iht ?L| i_}?} t ?L| @? i^*Mh4 @?_ /Er : lEr ELh Er :
BEr
`i? r fDc 8 Ef f @?_ 82 Ef : f L @? i^*Mh4 | ML|
4@?@}iht ?L| i_}?} i t| @t *L?} @t
k
ER R2 82 Ef R 5e
q
k
+, ER R2 E2r EeR R2  R 5e E6 n  r
q
Ee2
Ai *iu| @?_ t_i t @ UL?i ?Uhi@t?} u?U|L? Ai h}| @?_ t_i t *?i@h u?U
|L? | t*LTi kq 5e E6 n  r 5?Ui uM7EfD ' f -M7EfDc L?i ?|ihtiU|L?
Lh ?L?i i t|t At /Er E@?_ i?Ui Er t i** _i€?i_
eS AL ThLi |@| /Er : lEr E@?_ Er : BEr @h}i @t uL**Lt | lErc
k
ER R2 8 E ' R2 5e
q
k
ER R2 82 E R 5e q
Ee
L 8 E : 82 E Wu i tL |@| 82 Ef 8 E i @hi _L?i @t |i?
k
k
ER R2 82 Ef ER R2 8 E ' R2 5e R 5e
q
q
k
ER R2 8 Ef f R2 5e q
Eee
`i? R 2*c _82 E@E%_@E : f Ai? 82 Ef 82 E 8 E uL**Lt
`i? R : 2*c |i ?i^@*|) 82 Ef 8 E t t4T*€i_ @t uL**LtG
%
&
E 2rE eR R2 6nr
k
l
E6 n  r2 n fDE rE6 n  r n f2DE r2 EbR R2 
ER 
dfDE rER  n R 6 n fDE rodfDE rER2  n 6 n  ro
n ER2 
dfDE rER2  n R2 6 n fDE rodfDE rER  n 6 n  ro
+,
E 2rE eR R2 6nr
k
l
E6 n  r2 n fDE rE6 n  r n f2DE r2 EbR R2 
dE6 n  rE r fDE roE2 bR R2 n E6 n  r26E R R2 n E6 n  rfDE r
EeD
? |i *iu| @?_ t_i |i |ih4 @ttLU@|i_ | bR R2 2 t ?i}@|i @t R : 2* ?
|i h}| @?_ t_ic 2 bR R2 @?_ E6 n fD rE r @hi TLt|i At | tUit
e. |@|
E 2rE eR R2 d6 n  r n fDE ro
E6 n  r26E R R2 n E6 n  rfDE r
+, E 2rE eR R2 E6 n  r26E R R2 n E6 n  rfDE r
EeS
ihi 6 n  r n fDE r '  t ti_ At ?i^@*|) t |hi @t

 2r E6 n  r26 n E6 n  rfDE r
e
r r r
n
o
+,  2r fDE n rd 2
e
2
Ee.
+, br
5?Ui r : * |t t |hi Oi?Ui /Er : lEr E@?_ Er : BEr
`i ?L |h? |L i^*Mh@ ihi |i } @M*|) 4@?@}ih h@?_L43it @?_ |i
*L @M*|) 4@?@}ih _Lit ?L| i_}i `i? * r fDc i !?L |@| 8 Ef f
@?_ |@| _8 E@E*_@E : f Oi?Ui |ihi t @ tL*|L? |L |i ThLM*i4 ER R2 8 E
' 6@% R2 At @ tL*|L? |L |i i^@|L? ER R2 8 E@E ' R2 i t|t ? |i
h@?}i Efc 6@% OLiih @| ' fc ER R2 82 Ef : f @?_ ?L tL*|L? i t|t |
' c ER R2 82 Ef ER R2 8 Ef ' R2 R @?_ @ tL*|L? i t|t wi| CE
' ER R2 82 E%E R ihi %E tL*it ER R2 8 E%E ' R2 Ai?
_C
_82 _%
' ER R2 R
_
_% _
_82
R2
' ER R2 R
4
_% ER R2 _8
_%
_85
_% R
' R2 _8

4
_%
EeH
f
t?} |i u@U| |@| _8 E%*_% : _82 E%*_%
Oi?Ui |ihi t @? ?^i hi}L?
E6? c 6@% ihi @ tL*|L? i t|t 6hL4 |tc }i? c i U@? tL |@| |ihi
eH t @? ?^i hi}L? BEr _ ZEr ihi ZEr Er E|i ML?_ BEr UL4it uhL4
?L|?} |@| |i i^@*|) ER R2 8 E ' R2 _i€?it BEr
`i? fD r c |i ThLLu t @ *||*i _gihi?| | ' fc i !?L |@|
82 Ef f Oi?Ui |i Mi@Lh Lu i^*Mh4 _iTi?_t L? |i }ih @M*|) @}i?|
5?Ui 8 Ef : fc |ihi t @? 6? tU |@| ER R2 8 Ef ' 6? R2 ) |i t@4i
@h}4i?| @t MiuLhic |ihi t @*tL @? 6@% tU |@| ER R2 8 E ' 6@% R2 `i U*@4 |@| i^*Mh4 i t|t ? |i hi}L? E6? c 6@% | 6? c i
!?L |@| ER R2 82 Ef f 6? R Oi?Uic i^*Mh4 i t|t Ai u@U| |@|
_8 E%*_% : _82 E%*_% |i? 4T*it |@| ER R2 82 E%E R ihi % ' @E
t |i h@?_L43i_ t|h@|i}) uLh |i }ih 4@?@}ih }i? 6hL4 |t i U@? _i_Ui
|@| }i? c |ihi t @? ?^i hi}L? BEr _ ZEr ihi ZEr ' Er }@?c
|i ML?_ BEr UL4it uhL4 ?L|?} |@| |i i^@*|) ER R2 8 E ' R2 _i€?it
BEr
hLLu Lu AiLhi4 SG Ai |iLhi4 UL?tt|t Lu |hii T@h|tG
@ @ ThLLu |@| t|h@|i}it ihi @E2 '  @?_ f @E  @hi ?L| i^*Mh@
M @ ThLLu |@| t|h@|i}it ihi f @E  @?_ f @E2  @hi ?L| i^*Mh@
Oi?Ui A)Ti i^*Mh@ _L ?L| i t|
U @ U@h@U|ih3@|L? Lu i^*Mh@ ihi @E ' f @?_ f @E2  Aiti @hi
A)Ti # i^*Mh@
@h| @ `i? i_}?} @t ULt|*itt i @i |@| LE6Ec Mc 2 L E6Ec Mc 2
`| i_}?} ULt|*)c |t ?i^@*|) 4t| t|** L*_ At ?L i^*Mh4 ihi @E2
' @?_ f @E  i t|t
@h| M ) 44U!?} |i ThLLu Lu T@h| EM Lu AiLhi4 c L?i U@? tL |@| ML|
eb 4@?@}ih h@?_L43?} hi_Uit |L €?_?} b @?_ w tU |@|
 kfDE r5e
8 Ebc w ' 8 Ebc w 'f
qER R2 2 kfDE r5e
82 Ebc w ' 82 Ebc w 'f
qER R2 Eeb
ihi 8 Ebc w @?_ 82 Ebc w @hi _i€?i_ ? ,^@|L?t E. @?_ EH ?i U@?
tL |@| |i hit|hU|L? @MLi 4T*it |@| 28 Ebc w ' 82 Ebc w Wu i 4TLti |t
hit|hU|L? @?_ @?) L?i Lu |i hit|hU|L?t ? ,^@|L?t Eeb @MLi @?_ ti@hU Lih
|i tT@Ui * r  @?_ *2 R c |ihi t ?L i^*Mh4 ihi ML| !?_t Lu
4@?@}iht h@?_L43i.
@h| U
W? |t U@tic |i }ih @M*|) 4@?@}ih _Lit ?L| i_}i @?_ i?Ui
L E6Ec Mc  L E6Ec Mc  Ai *Lih @M*|) 4@?@}ih i_}it Lh h@?_L43it
Mi|ii? i_}?} @?_ ?L| i_}?} @?_ |t L E6Ec Mc 2 L E6Ec Mc 2 ,^@
*i?|*)c |iti ?i^@*|it U@? Mi t|@|i_ @t
k
ER R2 8 E@E2 R2 5e
q
EDf
k
ER R2 82 E@E2 R 5e
q
ED
@?_
ihi 8 E@E2 @?_ 82 E@E2 @hi @t _i€?i_ ? T@h| EU Lu |i ThLLu Lu AiLhi4 E,^@|L? E2f
`i? r : fDc 8 Ef : f @?_ 82 Ef f *tL _82 E@E2%_@E2 f At
ER R2 82 E@E2 kq R 5e @?_ ?L i^*Mh4 ihi |i }ih @M*|) 4@?@}ih _Lit
?L| i_}i *i |i *Lih @M*|) 4@?@}ih i_}it Lh h@?_L43it Mi|ii? i_}?} @?_
?L| i_}?} t ?L| TLttM*i
.
}@?c |i UL4T|ih ThL}h@4 t @@*@M*i uhL4 |i @|Lht L? hi^it|
Df `i? r fDc 8 Ef f @?_ 82 Ef : f *tL 82 E f @?_ |t ER R2 82 E
f kq R 5e At ?L i^*Mh@ i t| ihi |i }ih @M*|) 4@?@}ih _Lit ?L|
i_}i @?_ *Lih @M*|) 4@?@}ih i_}it
,^*Mh@ ?L*?} h@?_L43@|L? _L i t| u ER R2 82 Ef : kq R 5e W?
u@U|c tU i^*Mh@ U*i@h*) i t| @| _ ' BEr @t |i *Lih @M*|) 4@?@}ih t ?_gihi?|
Mi|ii? i_}?} @?_ ?L| i_}?} @| |t TL?| Ai) i t| uLh |i hi}L? BEr _ H
hLLu Lu AiLhi4 .G AL UL4T|i |t ML?_c i ti ,^@|L? ED Wu @| @E2 ' fc
i U@? tL |@| ,^@|L? ED U@??L| L*_ i @hi _L?i @t _82 E@E2*_@E2 f
`i? @E2 ' fc ,^@|L? ED hi_Uit |LG
E2r EeR R2 
R R2
k
R 5e
6nr
q
ED2
Ai }it| @*i Lu |i *iu| @?_ t_i t hi@Ui_ i? r '* 5Mt|||?} |t ?c
i LM|@? |@|G
k

ER R2 E eR R2 R 5e
2
q
ED
U t _ithi_ ML?_ Ai hit| Lu |i |iLhi4 uL**Lt uhL4 tMt|||?} _ ' R R2
@?_ 5e ' +, oK @?_ t4T*u)?}
H
Ai i t|i?Ui T |L _ '  t ih€i_ M) @ UL4T|ih ThL}h@4 |@| t @@*@M*i uhL4 |i @|Lht
D

 Download  Report

Paperzz.com

Your Paperzz

© Copyright 2026 Paperzz