black-litterman model in detail

Upload: ghaeek

Post on 07-Apr-2018

219 views

Category:

Documents


0 download

TRANSCRIPT

  • 8/6/2019 Black-Litterman Model in Detail

    1/51Electronic copy available at: http://ssrn.com/abstract=1314585Electronic copy available at: http://ssrn.com/abstract=1314585

    !"#$%&'()*+,--#./'0$123#&$40$5#-',&

    !"#$%"&'()"*+,-+.(/01(2334

    5(678.+$9:;(2334(-?;"+%1(6)@

    AB-?;"+%C*?-DE?$;;"+F-GH7+9

    !"#$%&'$(

    IG(;:$%(8-8"+((B"(%,+#".(;:"(?$;"+-;,+"(7G(;:"(J?-DE

  • 8/6/2019 Black-Litterman Model in Detail

    2/51Electronic copy available at: http://ssrn.com/abstract=1314585Electronic copy available at: http://ssrn.com/abstract=1314585

    F7+"(&$#"+%$M$"&(87+;M7?$7%(;:-G(8?-$G(F"-G$GE"?F-GG(T/444U(8+7#$&"(-(&"%D+$8;$7G(7M(

    ;:"$+(-%%";(-??7D-;$7G(8+7D"%%(TM7+($G;"+G-;$7G-?(M$P"&($GD7F"U(-G&(:7B(;:".(,%"(;:"(J?-DE$GE"?F-GG(T/44ZU(8+7#$&"(&";-$?%(7G(;:"(8+7D"%%(,%"&(;7(D7F8,;"(D7#-+$-GD"(F-;+$D"%(-;(R7?&F-G(S-D:%H

    L:"(%;-G&-+&(J?-DE

  • 8/6/2019 Black-Litterman Model in Detail

    3/51

    J?-DE(-G&(K$;;"+F-G(T/442U(8-8"+H(I;(-?%7($%(D7G%$%;"G;(B$;:(7,+($G;,$;$7G(-*7,;(;:"(7,;D7F"($G(;:"(

    -*%"GD"(7M(-(D7G&$;$7G-?(&$%;+$*,;$7G(TG7(#$"B%($G(J?-DE

  • 8/6/2019 Black-Litterman Model in Detail

    4/51

    ,G&"+%;-G&(B:$D:(+"M"+"GD"(F7&"?($%(*"$G9(,%"&($G(7+&"+(;7(,G&"+%;-G&(:7B(;:"(#-+$7,%(8-+-F";"+%(B$??(

    $F8-D;(;:"(+"%,?;%H

    7+89-$.*:2$0127!;52

  • 8/6/2019 Black-Litterman Model in Detail

    5/51

    +$D:(*7&.(7M(+"%"-+D:(B:$D:(D?-$F%(;:-;(F"-G(#-+$-GD"(+"%,?;%(-+"(?"%%(%"G%$;$#"(;7("++7+%($G("%;$F-;$G9(

    ;:"(#-+$-GD"(-G&(;:-;(;:"(878,?-;$7G(D7#-+$-GD"($%(F7+"(%;-*?"(7#"+(;$F"(;:-G(;:"(+";,+G%1(%7(+"?.$G9(7G(

    :$%;7+$D-?(D7#-+$-GD"(&-;-(%:7,?&(G7;($G;+7&,D"("PD"%%$#"(F7&"?("++7+H((J.(D7F8,;$G9($;(M+7F(-D;,-?(

    &-;-(B"(EG7B(;:-;(;:"(+"%,?;$G9(D7#-+$-GD"(F-;+$P(B$??(*"(87%$;$#"(&"M$G$;"H((I;($%(87%%$*?"(B:"G("%;$F-;$G9(-(D7#-+$-GD"(F-;+$P(;7(D+"-;"(7G"(B:$D:($%(G7;(87%$;$#"(&"M$G$;"1(-G&(;:,%(G7;"(M$G&(;:"("P-D;(%7?,;$7G(*.(;-E$G9(;:"(M$+%;(&"+$#-;$#"(7M(

    T0U(B$;:(+"%8"D;(;7(;:"(B"$9:;%(TBU(-G&(%";;$G9($;(;7(3H

    +(

    +)'./0%)'3

    S7?#$G9(;:$%(M7+((r(T;:"(#"D;7+(7M("PD"%%(+";,+G%U(.$"?&%'

    TtU r(k(seB

    IG(7+&"+(;7(,%"(M7+F,?-(TtU(B"(G""&(;7(:-#"(-(#-?,"(M7+(s(1(;:"(+$%E(-#"+%$7G(D7"MM$D$"G;(7M(;:"(F-+E";H(

    O7%;(7M(;:"(-,;:7+%(%8"D$M.(;:"(#-?,"(7M(s(;:-;(;:".(,%"&H(J"#-G(-G&(>$GE"?F-GG(T/44ZU(&"%D+$*"(;:"$+(

    8+7D"%%(7M(D-?$*+-;$G9(;:"(+";,+G%(;7(-G(-#"+-9"(%:-+8"(+-;$7(*-%"&(7G(;:"$+("P8"+$"GD"H(()7+(9?7*-?(M$P"&($GD7F"(T;:"$+(-+"-(7M("P8"+;$%"U(;:".(,%"(-(%:-+8"(+-;$7(7M(/H3H((J?-DE(-G&(K$;;"+F-G(T/442U(,%"(-(S:-+8"(

    +-;$7(D?7%"+(;7(3H_($G(;:"("P-F8?"($G(;:"$+(8-8"+H

    >"(D-G(M$G&(s(*.(F,?;$8?.$G9(*7;:(%$&"%(7M(TtU(*.(BL(-G&(+"8?-D$G9(#"D;7+(;"+F%(B$;:(%D-?-+(;"+F%H

    (TQT+U(p(+MU(k(sq2

    TZU s(k(TQT+U(p(+MU(o(q2

    QT+U L7;-?(+";,+G(7G(;:"(F-+E";(87+;M7?$7(TQT+U(k(BLr(u(+MU+M !$%E(M+""(+-;"

    q

  • 8/6/2019 Black-Litterman Model in Detail

    6/51

    T4U )'!0%"//

    .

    IM(B"(M""&(r1(s1(-G&(e(*-DE($G;7(;:"(M7+F,?-(T4U1(B"(D-G(%7?#"(M7+(;:"(B"$9:;%(TBUH((IM(B"($G%;"-&(,%"&(

    :$%;7+$D-?("PD"%%(+";,+G%(+-;:"+(;:-G("V,$?$*+$,F("PD"%%(+";,+G%1(;:"(+"%,?;%(B$??(*"(#"+.(%"G%$;$#"(;7(

    D:-G9"%($G(rH((>$;:(;:"(J?-DE91'.4?.*:[email protected]#

    L:$%(%"D;$7G(B$??(&"%D+$*"(;:"(8+7D"%%(7M(%8"D$M.$G9(;:"($G#"%;7+%(#$"B%(7G(;:"("%;$F-;"&(F"-G("PD"%%(

    +";,+G%H((>"(&"M$G"(;:"(D7F*$G-;$7G(7M(;:"($G#"%;7+%(#$"B%(-%(;:"(D7G&$;$7G-?(&$%;+$*,;$7GH(()$+%;1(*.(D7G%;+,D;$7G(B"(B$??(+"V,$+"("-D:(#$"B(;7(*"(,G$V,"(-G&(,GD7++"?-;"&(B$;:(;:"(7;:"+(#$"B%H((L:$%(B$??(

    9$#"(;:"(D7G&$;$7G-?(&$%;+$*,;$7G(;:"(8+78"+;.(;:-;(;:"(D7#-+$-GD"(F-;+$P(B$??(*"(&$-97G-?1(B$;:(-??(7MM"(&7(G7;(+"V,$+"(-(#$"B(7G(-??(-%%";%H((IG(-&&$;$7G($;($%(-D;,-??.(87%%$*?"(M7+(;:"(#$"B%(;7(D7GM?$D;1(;:"(F$P$G9(8+7D"%%(B$??(F"+9"(;:"(#$"B%(*-%"&(7G(;:"(D7GM$&"GD"($G(;:"(#$"B%(-G&(;:"(D7GM$&"GD"($G(;:"(

    8+$7+H

    >"(B$??(+"8+"%"G;(;:"($G#"%;7+%(E(#$"B%(7G(G(-%%";%(,%$G9(;:"(M7??7B$G9(F-;+$D"%

    1 Y1(-(EyG(F-;+$P(7M(;:"(-%%";(B"$9:;%(B$;:$G("-D:(#$"BH(()7+(-(+"?-;$#"(#$"B(;:"(%,F(7M(;:"(B"$9:;%(B$??(*"(31(M7+(-G(-*%7?,;"(#$"B(;:"(%,F(7M(;:"(B"$9:;%(B$??(*"(/H(`$MM"+"G;(-,;:7+%(

    D7F8,;"(;:"(#-+$7,%(B"$9:;%(B$;:$G(;:"(#$"B(&$MM"+"G;?.1(c"(-G&(K$;;"+F-G(T/444U(-G&(I&\7+"E(

    T233_U(,%"(-(F-+E";(D-8$;-?$\-;$7G(B"$9:"&(%D:"F"1(B:"+"-%(S-;D:"??(-G&(SD7BD+7M;(T2333U(,%"(

    -G("V,-?(B"$9:;"&(%D:"F"H

    1 z1(-(Ey/(F-;+$P(7M(;:"(+";,+G%(M7+("-D:(#$"BH1 {(-((EyE(F-;+$P(7M(;:"(D7#-+$-GD"(7M(;:"(#$"B%H({($%(9"G"+-??.(&$-97G-?(-%(;:"(#$"B%(-+"(

    +"V,$+"&(;7(*"($G&"8"G&"G;(-G&(,GD7++"?-;"&H(({"(&7(G7;(+"V,$+"(Y(;7(*"($G#"+;$*?"H((O",DD$(T2330U(&"%D+$*"%(-(F";:7&(7M(-,9F"G;$G9(;:"(F-;+$D"%(;7(F-E"(;:"(Y(F-;+$P($G#"+;$*?"(B:$?"(G7;(D:-G9$G9(;:"(G";(+"%,?;%H

    5(678.+$9:;(23341(=-.(>-?;"+%((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((0

  • 8/6/2019 Black-Litterman Model in Detail

    7/51

    {($%(%.FF";+$D(-G&(\"+7(7G(-??(G7G

  • 8/6/2019 Black-Litterman Model in Detail

    8/51

    L:$%(%8"D$M$D-;$7G(7M(;:"(#-+$-GD"1(7+(,GD"+;-$G;.1(7M(;:"(#$"B%("%%"G;$-??.("V,-??.(B"$9:;%(;:"($G#"%;7+N%(

    #$"B%(-G&(;:"(F-+E";("V,$?$*+$,F(B"$9:;%H(J.($GD?,&$G9(w($G(;:"("P8+"%%$7G1(;:"(M$G-?(%7?,;$7G(*"D7F"%(

    $G&"8"G&"G;(7M(w(-%(B"??H((L:$%(%""F%(;7(*"(;:"(F7%;(D7FF7G(F";:7&(,%"&($G(;:"(?$;"+-;,+"H

    O",DD$(T2330U(&7"%GN;(*7;:"+(B$;:(;:"(&$-97G-?$\-;$7G(-;(-??1(-G&(A,%;(%";%(

    4'/

    2,%,

    3

    c"(%";%(D((/1(-G&(7G"(7*#$7,%(D:7$D"(M7+(D($%(w"(B$??(%""(?-;"+(;:-;(;:$%(M7+F(7M(;:"(#-+$-GD"(7M(;:"(

    #$"B%(?"G&%($;%"?M(;7(%7F"(%$F8?$M$D-;$7G%(7M(;:"(J?-DE:$?"(;:"(+"9+"%%$7G(F$9:;(.$"?&(-(M,??(

    5(678.+$9:;(23341(=-.(>-?;"+%((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((Z

  • 8/6/2019 Black-Litterman Model in Detail

    9/51

    D7#-+$-GD"(F-;+$P1(;:"(F$P$G9(F7&"?(B$??(*"(F7+"(+7*,%;($M(7G?.(;:"(&$-97G-?("?"F"G;%(-+"(,%"&H

    J"-D:(-G&(]+?7#(T2330U(&"%D+$*"(;:"$+(B7+E(,%$G9(R@!6c(%;.?"(M-D;7+(F7&"?%(;7(9"G"+-;"(;:"$+(#$"B%(

    M7+(,%"(B$;:(;:"(J?-DE$;:("$;:"+(-88+7-D:1(B"(B$??(*"(,%$G9(;:"(+"M"+"GD"(F7&"?(;7("%;$F-;"(;:"(F"-G(+";,+G%1(G7;(;:"(&$%;+$*,;$7G(7M(+";,+G%H((L:$%($%($F87+;-G;($G(,G&"+%;-G&$G9(;:"(#-?,"%(,%"&(M7+(w(-G&({1(-G&(M7+(;:"(D7F8,;-;$7G%(7M(;:"(#-+$-GD"(7M(;:"(8+$7+(-G&(87%;"+$7+(&$%;+$*,;$7G%(7M(+";,+G%H

    @G7;:"+(B-.(;7(;:$GE(7M(;:"("%;$F-;$7G(F7&"?(-G&(;:"(+"M"+"GD"(F7&"?($%(;:-;(B:$?"(;:"("%;$F-;"&(+";,+G(

    $%(F7+"(-DD,+-;"(;:"(#-+$-GD"(7M(;:"(&$%;+$*,;$7G(&7"%(G7;(D:-G9"(*"D-,%"(B"(:-#"(F7+"(&-;-H((L:"(

    8+7;7;.8$D-?("P-F8?"(7M(;:$%(B7,?&(*"(;7(*?"G&(;:"(&$%;+$*,;$7G%1(YT@U(x([T/3b1(23bU(-G&(YTJ~@U(x([T/2b1(23bUH((IM(B"(-88?.(J-."%(M7+F,?-($G(-(%;+-$9:;M7+B-+&(M-%:$7G1(YT@~JU(x([T//b1(/3bUH(

    6?"-+?.(B$;:(M$G-GD$-?(&-;-(B"(&$&(G7;(+"-??.(D,;(;:"(#-+$-GD"(7M(;:"(+";,+G(&$%;+$*,;$7G($G((A,%;(*"D-,%"(

    B"(:-#"(-(%?$9:;?.(*";;"+("%;$F-;"(7M(;:"(F"-GH

    c7B"#"+1($M(;:"(F"-G($%(;:"(+-G&7F(#-+$-*?"1(-G&(G7;(;:"(&$%;+$*,;$7G1(;:"G(7,+(+"%,?;(7M(YT@~JU(x(

    [T//b1(/3bU(F-E"%(%"G%"H((J.(*?"G&$G9(;:"%"(;B7("%;$F-;"%(7M(;:"(F"-G1(B"(:-#"(-G("%;$F-;"(7M(;:"(F"-G(B$;:(F,D:(?"%%(,GD"+;-$G;.(T?"%%(#-+$-GD"U(;:-G("$;:"+(7M(;:"("%;$F-;"%H

    !"#,&67$1,8#3$97-,/'-,20$123#&

    L:"$?N%(F$P"&("%;$F-;$7G(F7&"?(B-%(D+"-;"&(M7+(;:"(8,+87%"(7M("%;$F-;$G9(8-+-F";"+%(M+7F(-(F$P;,+"(7M(

    D7F8?";"(8+$7+(&-;-(-G&(8-+;$-?(D7G&$;$7G-?(&-;-H((L:$%($%(-(977&(M$;(B$;:(7,+(8+7*?"F(-%($;(-??7B%(,%(;7(

    "P8+"%%(#$"B%(7G(7G?.(-(%,*%";(7M(;:"(-%%";(+";,+G%1(;:"+"($%(G7(+"V,$+"F"G;(;7("P8+"%%(#$"B%(7G(-??(7M(;:"FH((L:"(#$"B%(D-G(-?%7(*"("P8+"%%"&(7G(-(%$G9?"(-%%";1(7+(7G(-+*$;+-+.(D7F*$G-;$7G%(7M(;:"(-%%";%H(

    L:"(#$"B%(&7(G7;("#"G(G""&(*"(D7G%$%;"G;1(;:"("%;$F-;$7G(F7&"?(B$??(;-E"("-D:($G;7(-DD7,G;(*-%"&(7G(

    ;:"($G#"%;7+%(D7GM$&"GD"H

    L:"$?N%(O$P"&(Q%;$F-;$7G(F7&"?(%;-+;%(M+7F(-(?$G"-+(F7&"?(M7+(;:"(8-+-F";"+%(;7(*"("%;$F-;"&H((>"(D-G(,%"(M7+F,?-(T2U(M+7F(7,+(+"M"+"GD"(F7&"?(-%(-(%;-+;$G9(87$G;H

    ],+(%$F8?"(?$G"-+(F7&"?($%(%:7BG(*"?7B'

    T/_U &'8 *(9

    >:"+"& $%(;:"(G(P(/(#"D;7+(7M(6@YO("V,$?$*+$,F(+";,+G%(M7+(;:"(-%%";%H

    5(678.+$9:;(23341(=-.(>-?;"+%((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((4

  • 8/6/2019 Black-Litterman Model in Detail

    10/51

    8 $%(;:"(G(P(G(F-;+$P(IG(B:$D:(-+"(;:"(M-D;7+(?7-&$G9%(M7+(7,+(F7&"?H* $%(;:"(G(P(/(#"D;7+(7M(,GEG7BG(F"-G%(M7+(;:"(-%%";(+";,+G(8+7D"%%H9 $%(-(G(P(G(F-;+$P(7M(+"%$&,-?%(M+7F(;:"(+"9+"%%$7G(B:"+"( !!9 "'3 : 5!9"'!!9 ; 9 "';

    -G&(($%(G7G:$D:(D-G(*"(%$F8?$M$"&(;7'

    T/0U 5!&"'%(;

    L:$%(;$"%(*-DE(;7(M7+F,?-(TWU($G(;:"(+"M"+"GD"(F7&"?H((L:"(;7;-?(#-+$-GD"(7M(;:"("%;$F-;"&(+";,+G($%(;:"(%,F(7M(;:"(#-+$-GD"(7M(;:"(-D;,-?(+";,+G(8+7D"%%(8?,%(;:"(#-+$-GD"(7M(;:"("%;$F-;"(7M(;:"(F"-GH((>"(B$??(

    D7F"(*-DE(;7(;:$%(+"?-;$7G(-9-$G(?-;"+($G(;:"(8-8"+H

    >"(B$??(8+-9F-;$D-??.(D7F8,;"(e(M+7F(:$%;7+$D-?(&-;-(M7+(;:"(-%%";(+";,+G%H

    ["P;(B"(D7G%$&"+(%7F"(-&&$;$7G-?($GM7+F-;$7G(B:$D:(B"(B7,?&(?$E"(;7(D7F*$G"(B$;:(;:"(8+$7+H((L:$%($GM7+F-;$7G(D-G(*"(%,*A"D;$#"(#$"B%(7+(D-G(*"(&"+$#"&(M+7F(%;-;$%;$D-?(&-;-H((>"(B$??(-?%7(-??7B($;(;7(*"(

    $GD7F8?";"1(F"-G$G9(;:-;(B"(F$9:;(G7;(:-#"(-G("%;$F-;"(M7+("-D:(-%%";(+";,+GH

    T/tU :"+"< $%(;:"(E(P(/(#"D;7+(7M(+";,+G%(M7+(;:"(#$"B%H' $%(;:"(E(P(G(#"D;7+(F-88$G9(;:"(#$"B%(7G;7(;:"(-%%";%H* $%(;:"(G(P(/(#"D;7+(7M(,GEG7BG(F"-G%(M7+(;:"(-%%";(+";,+G(8+7D"%%H= $%(-(E(P(E(F-;+$P(7M(7M(+"%$&,-?%(M+7F(;:"(+"9+"%%$7G(B:"+"

    !!= "'3 : 5! ="'!!= ; = "'4 -G&({($%(G7G"(D-G(D7F*$G"(;:"(8+$7+(-G&(D7G&$;$7G-?($GM7+F-;$7G(*.(B+$;$G9'

    2&< 3'2 8'3 :"+"(;:"("P8"D;"&(#-?,"(7M(;:"(+"%$&,-?($%(31(-G&(;:"("P8"D;"&(#-?,"(7M(;:"(#-+$-GD"(7M(;:"(+"%$&,-?($%

    5!29=3"'!!29= 32 9 ; = ; 33'2; 33 43>"(D-G(;:"G(-88?.(;:"(9"G"+-?$\"&(?"-%;(%V,-+"%(8+7D"&,+"1(B:$D:(?"-&%(;7("%;$F-;$G9( -?;"+%((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((/3

  • 8/6/2019 Black-Litterman Model in Detail

    11/51

    )7+(;:"(J?-DE & 3"'%(;

    >:$D:($%(;:"(#-+$-GD"(7M(;:"(8+$7+(&$%;+$*,;$7G(7M(+";,+G%H

    @88"G&$P(@(D7G;-$G%(-(F7+"(&";-$?"&(&"+$#-;$7G(7M(M7+F,?-%(T/4U(-G&(T23UH

    5(678.+$9:;(23341(=-.(>-?;"+%((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((//

  • 8/6/2019 Black-Litterman Model in Detail

    12/51

    :$;?",!?",!6"

    YT@~JU( L:"(D7G&$;$7G-?(T7+(A7$G;U(8+7*-*$?$;.(7M(@1(9$#"G(J((@?%7(EG7BG(-%(;:"(87%;"+$7+(

    &$%;+$*,;$7GH((>"(B$??(D-??(;:$%(;:"(87%;"+$7+(&$%;+$*,;$7G(M+7F(:"+"(7GH

    YTJ~@U L:"(D7G&$;$7G-?(8+7*-*$?$;.(7M(J(9$#"G(@H((@?%7(EG7B(-%(;:"(%-F8?$G9(&$%;+$*,;$7GH((>"(B$??(D-??(;:$%(;:"(D7G&$;$7G-?(&$%;+$*,;$7G(M+7F(:"+"(7GH

    YT@U L:"(8+7*-*$?$;.(7M(@H((@?%7(EG7BG(-%(;:"(8+$7+(&$%;+$*,;$7GH((>"(B$??(D-??(;:$%(;:"(

    8+$7+(&$%;+$*,;$7G(M+7F(:"+"(7GH

    YTJU L:"(8+7*-*$?$;.(7M(JH(@?%7(EG7BG(-%(;:"(G7+F-?$\$G9(D7G%;-G;H

    >:"G(-D;,-??.(-88?.$G9(;:$%(M7+F,?-(-G&(%7?#$G9(M7+(;:"(87%;"+$7+(&$%;+$*,;$7G1(;:"(G7+F-?$\$G9(D7G%;-G;(B$??(&$%-88"-+($G;7(;:"(D7G%;-G;%(7M($G;"9+-;$7G(%7(M+7F(;:$%(87$G;(7G(B"(B$??($9G7+"($;HH

    @(9"G"+-?(8+7*?"F($G(,%$G9(J-."%(;:"7+.($%(;7($&"G;$M.(-G($G;,$;$#"(-G&(;+-D;-*?"(8+$7+(&$%;+$*,;$7GH(]G"(

    7M(;:"(D7+"(-%%,F8;$7G%(7M(;:"(J?-DE:"G(;:"(8+$7+(&$%;+$*,;$7G(-G&(;:"(

    87%;"+$7+(:-#"(;:"(%-F"(%;+,D;,+"1(;:"(8+$7+($%(EG7BG(-%(-((D7GA,9-;"(8+$7+H((R$#"G($G;"+"%;(;:"+"($%(G7;:$G9(;7(E""8(,%(M+7F(*,$?&$G9(#-+$-G;%(7M(;:"(J?-DE"(&"M$G"(;:"(%$9G$M$D-G;(&$%;+$*,;$7G%(*"?7B'

    L:"(8+$7+(&$%;+$*,;$7G

    T2WU YT@U(x([TP1SoGU

    B:"+"(S($%(;:"(%-F8?"(#-+$-GD"(7M(;:"(&$%;+$*,;$7G(-*7,;(;:"(F"-G1(B$;:(G(%-F8?"%(;:"G(SoG($%(;:"(

    #-+$-GD"(7M(;:"("%;$F-;"(7M(P(-*7,;(;:"(F"-GHL:"(D7G&$;$7G-?(&$%;+$*,;$7G

    T2lU YTJ~@U(x([Td1{U

    {($%(;:"(,GD"+;-$G;.($G(;:"("%;$F-;"(d(7M(;:"(F"-G1($;($%(G7;(;:"(#-+$-GD"(7M(;:"(&$%;+$*,;$7G(-*7,;(;:"(

    F"-GH

    L:"G(;:"(87%;"+$7+(&$%;+$*,;$7G($%(%8"D$M$"&(*.

    5(678.+$9:;(23341(=-.(>-?;"+%((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((/2

  • 8/6/2019 Black-Litterman Model in Detail

    13/51

    T2_U YT@~JU(x[T{7,0?$%'=#7$!"#2.#/$@2.$-"#$97-,/'-,20$123#&

    ]G"(7M(;:"(F-A7+(-%%,F8;$7G%(F-&"(*.(;:"(J?-DE

  • 8/6/2019 Black-Litterman Model in Detail

    14/51

    L:$%($%(%7F";$F"%(+"M"++"&(;7(-%(;:"(J?-DE"(%""(;:"($F8-D;(7M(;:$%(M7+F,?-($G(;:"(+"%,?;%(%:7BG($G(c"(-G&(K$;;"+F-G(T/444UH((IG(;:"$+(+"%,?;%1(;:"($G#"%;7+N%(B"$9:;%(%,F(;7(?"%%(;:-G(/($M(

    ;:".(:-#"(G7(#$"B%HW((I&\7+"E(T233_U(-G&(F7%;(7;:"+(-,;:7+%(&7(G7;(D7F8,;"(-(G"B(87%;"+$7+(#-+$-GD"1(

    *,;($G%;"-&(,%"(;:"(EG7BG($G8,;(#-+$-GD"(7M(;:"(+";,+G%(-*7,;(;:"(F"-GH((S"#"+-?(7M(;:"(-,;:7+%(%";(w(k(/(-?7G9(B$;:(,%$G9(;:"(#-+$-GD"(7M(+";,+G%H(>"(B$??(D7G%$&"+(;:"%"(&$MM"+"G;(+"M"+"GD"(F7&"?%($G(-(?-;"+(

    %"D;$7GH

    ]GD"(B"(&$9($G;7(;:"(;78$D(-(?$;;?"(F7+"(B"(+"-?$\"(;:-;($M(B"(:-#"(7G?.(8-+;$-?(#$"B%1(#$"B%(7G(%7F"(

    -%%";%1(;:"G(*.(,%$G9(-(87%;"+$7+("%;$F-;"(7M(;:"(#-+$-GD"(B"(B$??(;$?;(;:"(87%;"+$7+(B"$9:;%(;7B-+&%(

    -%%";%(B$;:(?7B"+(#-+$-GD"(T:$9:"+(8+"D$%$7G(7M(;:"("%;$F-;"&(F"-GU(-G&(-B-.(M+7F(-%%";%(B$;:(:$9:"+(#-+$-GD"(T?7B"+(8+"D$%$7G(7M(;:"("%;$F-;"&(F"-GUH(L:,%(;:"("P$%;"GD"(7M(;:"(#$"B%(-G&(;:"(,8&-;"&(

    D7#-+$-GD"(B$??(;$?;(;:"(78;$F$\"+(;7B-+&%(,%$G9(7+(G7;(,%$G9(;:7%"(-%%";%H((L:$%(;$?;(B$??(G7;(*"(#"+.(?-+9"($M(B"(-+"(B7+E$G9(B$;:(-(%F-??(#-?,"(7M(w1(*,;($;(B$??(*"(F"-%,+-*?"H

    S$GD"(B"(-+"(*,$?&$G9(;:"(D7#-+$-GD"(F-;+$P1(e1(M+7F(:$%;7+$D-?(&-;-(B"(D-G(D7F8,;"(w(M+7F(;:"(G,F*"+(

    7M(%-F8?"%H((>"(D-G(-?%7("%;$F-;"(w(*-%"&(7G(7,+(D7GM$&"GD"($G(;:"(8+$7+(&$%;+$*,;$7GH([7;"(;:-;(*7;:(7M(

    ;:"%"(;"D:G$V,"%(8+7#$&"(%7F"($G;,$;$7G(M7+(%"?"D;$G9(-(#-?,"(7M(w(B:$D:($%(D?7%"+(;7(3(;:-G(;7(/H((J?-DE(-G&(K$;;"+F-G(T/442U1(c"(-G&(K$;;"+F-G(T/444U(-G&(I&\7+"E(T233_U(-??($G&$D-;"(;:-;($G(;:"$+(D-?D,?-;$7G%(

    ;:".(,%"&(%F-??(#-?,"%(7M(w1(7G(;:"(7+&"+(7M(3H32_(p(3H3_3H((S-;D:"??(-G&(SD7BD+7M;(T2333U(%;-;"(;:-;(

    F-G.($G#"%;7+%(,%"(-(w(-+7,G&(/(B:$D:(&7"%(G7;(%""F(;7(:-#"(-G.($G;,$;$#"(D7GG"D;$7G(:"+"H((

    >"(D-G(D:"DE(7,+(+"%,?;%(*.(%""$G9($M(;:"(+"%,?;%(F-;D:(7,+($G;,$;$7G(-;(;:"(*7,G&-+.(D7G&$;$7G%HR$#"G(M7+F,?-(TW3U($;($%("-%.(;7(?";({((3(%:7B$G9(;:-;(;:"(+";,+G(,G&"+(/33b(D"+;-$G;.(7M(;:"(#$"B%($%

    TWlU

  • 8/6/2019 Black-Litterman Model in Detail

    15/51

    ),+;:"+F7+"1($M(Y($%($G#"+;$*?"(B:$D:(F"-G%(;:-;($;(B"(:-#"(-?%7(7MM"+"&(-(#$"B(7G("#"+.(-%%";1(;:"G(

  • 8/6/2019 Black-Litterman Model in Detail

    16/51

    !"#$:&-#.0'-,A#$B#@#.#0(#$123#&

    L:$%(%"D;$7G(B$??(&$%D,%%(;:"(F7%;(D7FF7G(-?;"+G-;$#"(+"M"+"GD"(F7&"?(,%"&(B$;:(;:"(J?-DE

  • 8/6/2019 Black-Litterman Model in Detail

    17/51

    SD7BD+7M;(T2333U(&"%D+$*"(-(F7&"?(B$;:(-(%;7D:-%;$D(w1(*,;(;:$%($%(+"-??.(%;7D:-%;$D(#-+$-GD"(7M(+";,+G%H

    R$#"G(;:"(J?-DE"(D-G(%,*%;$;,;"(;:$%($G;7(M7+F,?-(TW3U(-%

  • 8/6/2019 Black-Litterman Model in Detail

    18/51

    IG(*7;:(D-%"%1(7,+(D:7$D"(M7+({(:-%("#"G?.(B"$9:;"&(;:"(8+$7+(-G&(D7G&$;$7G-?(&$%;+$*,;$7G%($G(;:"(

    "%;$F-;$7G(7M(;:"(87%;"+$7+(&$%;+$*,;$7GH((L:$%(F-;D:"%(7,+($G;,$;$7G(B:"G(B"(D7G%$&"+(B"(:-#"(*?"G&"&(

    ;B7($G8,;%1(M7+(*7;:(7M(B:$D:(B"(:-#"(;:"(%-F"(?"#"?(7M(,GD"+;-$G;.H((L:"(87%;"+$7+(&$%;+$*,;$7G(B$??(*"(

    ;:"(-#"+-9"(7M(;:"(;B7(&$%;+$*,;$7G%H

    IM(B"($G%;"-&(%7?#"(M7+(;:"(F7+"(,%"M,?(9"G"+-?(D-%"(7M({(k((mYTweUYL((B:"+"(m(i(31(%,*%;$;,;$G9($G;7(

    TW3U(-G&(M7??7B$G9(;:"(%-F"(?79$D(-%(,%"&(;7(&"+$#"(Tl3U(B"(9";

    Tl/U

  • 8/6/2019 Black-Litterman Model in Detail

    19/51

    -%%";(D?-%%"%(%,D:(-%(8+$#-;"("V,$;.(7+(+"-?("%;-;"($G;7(;:"(F7&"?H((),+;:"+F7+"1(%"8-+-;$G9(8,*?$D(+"-?(

    "%;-;"(:7?&$G9%(M+7F("V,$;.(:7?&$G9%(T"H9H(!QILS($G(;:"(S^Y(_33($G&"PU(F-.(-?%7(*"(+"V,$+"&H((I&\7+"E(

    T2330U(8+7#$&"%(-G("P-F8?"(7M(;:"(-G-?.%$%(+"V,$+"&(;7($GD?,&"(D7FF7&$;$"%(-%(-G(-%%";(D?-%%H

    ]GD"(;:"(8+7P.(+";,+G(%"+$"%(:-#"(*""G($&"G;$M$"&1(-G&(+";,+G%($G("PD"%%(7M(;:"(+$%E(M+""(+-;"(:-#"(*""G(D-?D,?-;"&1(;:"G(-(D7#-+$-GD"(F-;+$P(D-G(*"(D-?D,?-;"&H((L.8$D-??.(;:"(D7#-+$-GD"(F-;+$P($%(D-?D,?-;"&(

    M+7F(;:"(:$9:"%;(M+"V,"GD.(&-;-(-#-$?-*?"1("H9H(&-$?.1(-G&(;:"G(%D-?"&(,8(;7(;:"(-88+78+$-;"(;$F"(M+-F"H(

    IG#"%;7+N%(7M;"G(,%"(-G("P87G"G;$-?(B"$9:;$G9(%D:"F"(;7(8+7#$&"($GD+"-%"&(B"$9:;%(;7(F7+"(+"D"G;(&-;-(-G&(?"%%(;7(7?&"+(&-;-H((];:"+(M$?;"+$G9(T!-G&7F(O-;+$P(L:"7+.U(7+(%:+$GE-9"(F";:7&%(D7,?&(-?%7(*"(,%"&($G(-G(-;;"F8;(;7($F8-+;(-&&$;$7G-?(%;-*$?$;.(;7(;:"(8+7D"%%H

    [7B(B"(D-G(+,G(-(+"#"+%"(78;$F$\-;$7G(7G(;:"(F-+E";(87+;M7?$7(;7(D7F8,;"(;:"("V,$?$*+$,F("PD"%%(

    +";,+G%(M7+("-D:(-%%";(D?-%%H((Y-+;(7M(;:$%(%;"8($GD?,&"%(D7F8,;$G9(-(s(#-?,"(M7+(;:"(F-+E";(87+;M7?$7H(L:$%(

    D-G(*"(D-?D,?-;"&(M+7F(;:"(+";,+G(-G&(%;-G&-+&(&"#$-;$7G(7M(;:"(F-+E";(87+;M7?$7H((J"#-G(-G&(>$GE"?F-GG(T/44ZU(&$%D,%%(;:"(,%"(7M(-G("P8"D;"&(S:-+8"(!-;$7(;-+9";(M7+(;:"(D-?$*+-;$7G(7M(sH(()7+(

    ;:"$+($G;"+G-;$7G-?(M$P"&($GD7F"($G#"%;F"G;%(;:".(,%"&(-G("P8"D;(S:-+8"(!-;$7(7M(/H3(M7+(;:"(F-+E";H(

    L:"($G#"%;7+(;:"G(G""&%(;7(D-?$*+-;"(w($G(%7F"(F-GG"+H((L:$%(#-?,"($%(,%,-??.(7G(;:"(7+&"+(7M(3H32_(x(3H3_3H

    @;(;:$%(87$G;(-?F7%;(-??(7M(;:"(F-D:$G"+.($%($G(8?-D"H((L:"($G#"%;7+(G""&%(;7(%8"D$M.(#$"B%(7G(;:"(F-+E";H(L:"%"(#$"B%(D-G($F8-D;(7G"(7+(F7+"(-%%";%1($G(-G.(D7F*$G-;$7GH((L:"(#$"B%(D-G(*"(D7G%$%;"G;1(7+(;:".(

    D-G(D7GM?$D;H((@G("P-F8?"(7M(D7GM?$D;$G9(#$"B%(B7,?&(*"(F"+9$G9(78$G$7G%(M+7F(F,?;$8?"(-G-?.%;%1(B:"+"(;:".(F-.(G7;(-??(-9+""H((L:"($G#"%;7+(G""&%(;7(%8"D$M.(;:"(-%%";%($G#7?#"&($G("-D:(#$"B1(;:"(

    -*%7?,;"(7+(+"?-;$#"(+";,+G(7M(;:"(#$"B1(-G&(;:"$+(,GD"+;-$G;.($G(;:"(+";,+G(M7+(;:"(#$"B(D7G%$%;"G;(B$;:(

    ;:"$+(+"M"+"GD"(F7&"?(-G&(F"-%,+"&(*.(7G"(7M(;:"(F";:7&%(&$%D,%%"&(8+"#$7,%?.H

    @88"G&$P(Q(%:7B%(;:"(8+7D"%%(7M(D+-GE$G9(;:+7,9:(M7+F,?-%(TW3U1(TW_U(-G&(TW2U(;7(D7F8,;"(;:"(G"B(87%;"+$7+("%;$F-;"(7M(;:"(+";,+G%(-G&(;:"(D7#-+$-GD"(7M(;:"(87%;"+$7+(+";,+G%H((L:"%"(#-?,"%(B$??(*"(;:"(

    $G8,;%(;7(%7F"(;.8"(7M(78;$F$\"+1(-(F"-G

  • 8/6/2019 Black-Litterman Model in Detail

    20/51

    Tl2U BG#(k(BoT/uwU

    R$#"G(;:$%(+"%,?;1($;($%(D?"-+(;:-;(;:"(7,;8,;(B"$9:;%(B$;:(G7(#$"B%(B$??(*"($F8-D;"&(*.(;:"(D:7$D"(7M(w(

    B:"G(;:"(J?-DE

  • 8/6/2019 Black-Litterman Model in Detail

    21/51

    ;7(F-;D:(I&\7+"EN%(+"%,?;%(I(M7,G&(;:-;(:"(,%"&(;:"(-?;"+G-;$#"(+"M"+"GD"(F7&"?H(B:$D:(?"-#"%(e1(;:"(

    EG7BG(#-+$-GD"(7M(;:"(+";,+G%(M+7F(;:"(8+$7+(&$%;+$*,;$7G1(-%(;:"(#-+$-GD"(7M(;:"(87%;"+$7+(+";,+F%H((L:$%(

    $%(-(%$9G$M$D-G;(&$MM"+"GD"(M+7F(;:"(-?97+$;:F(,%"&($G(c"(-G&(K$;;"+F-G(T/444U1(*,;($G(;:"("G&(9$#"G(;:-;(

    I&\7+"E(,%"&(-(%F-??(#-?,"(7M(w1(;:"(&$MM"+"GD"%(-F7,G;"&(;7(-88+7P$F-;"?.(_3(*-%$%(87$G;%(8"+(-%%";H(L-*?"%(2(-G&(W(*"?7B($??,%;+-;"(D7F8,;"&(+"%,?;%(B$;:(;:"(&-;-(M+7F(:$%(8-8"+(-G&(:7B(;:"(+"%,?;%(&$MM"+(

    *";B""G(;:"(;B7(#"+%$7G%(7M(;:"(F7&"?H

    L-*?"(2(D7G;-$G%(+"%,?;%(9"G"+-;"&(,%$G9(;:"(&-;-(M+7F(I&\7+"E(T233_U(-G&((;:"(J?-DE

  • 8/6/2019 Black-Litterman Model in Detail

    22/51

    L-*?"(W(p(@?;"+G-;$#"(!"M"+"GD"(O7&"?(#"+%$7G(7M(;:"(J?-DE

  • 8/6/2019 Black-Litterman Model in Detail

    23/51

    ,!?>6"##!2&2! B'! &4 ""//

    (! B2 "//33

    //

    2&28 ' ! B'!&4 ""//

    (82 ! B2 "//33$2&2!B' !&4 ""

    //

    (!B2"//33

    //

    "

    IG(;:"(F"-G(;"+F(;:"(FN%(D-GD"?(7,;(-G&(B"(%""(;:"(M7+F,?-(O-GE"+;(,%"&(;7(%,887+;(:"+(;:"%$%

    2!B'!

    &

    4""

    //

    (!B2 "//

    3

    //

    28 '!B' !

    &

    4""

    //

    (82 ! B2 "//

    3L:,%($M(B"(%";(e(k(S8(-G&({(k(SD((;:"G(B"(D-G(?";(w(k(FoG1(;:"(+-;$7(7M(,GD"+;-$G;.($G(;:"(#$"B%(;7(;:"(,GD"+;-$G;.($G(;:"(8+$7+H(()7+(;:"(-?;"+G-;$#"(+"M"+"GD"(F7&"?1(:"+(-88+7-D:($%(#-?$&H

    c7B"#"+($G(;:"(87%;"+$7+(#-+$-GD"(7M(;:"("%;$F-;"(-G("P;+-(F(;"+F(+"F-$G%1(;:$%(F-E"%(;:"(D7#-+$-GD"(

    ;"+F

    !/

    &"2! &4 B'"

    //

    (!B2"//3

    //

    L:$%(&7"%(G7;(?$G"(,8(B$;:(M7+F,?-(TW2U(-%(B"(B7,?&("P8"D;1(9$#"G(;:"(%,*%;$;,;$7G%($G(;:"(8-+-9+-8:(

    -*7#"1((c"+(-88+7-D:($%(G7;(D7G%$%;"G;(B$;:(;:"(J?-DE-?;"+%((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((2W

  • 8/6/2019 Black-Litterman Model in Detail

    24/51

    ),E+%1FG#2"(D-G(-D;,-??.(%7?#"(;:$%(-G-?.;$D-??.H((L:"(G"P;(%"D;$7G(B$??(8+7#$&"(-(&"+$#-;$7G(7M(;:"(M7+F,?-%(+"V,$+"&(M7+(;:$%(%7?,;$7GH

    )$+%;(B"(B$??(,%"(;:"(M7??7B$G9(M7+F(7M(;:"(,GD"+;-$G;.(7M(;:"(#$"B%

    Tl0U 4'+ ,%,*

    m1(;:"(D7"MM$D$"G;(7M(,GD"+;-$G;.1($%(-(%D-?-+(V,-G;$;.($G(;:"($G;"+#-?(31(H(>:"G(;:"($G#"%;7+($%(/33b(

    D7GM$&"G;($G(;:"$+(#$"B%1(;:"G(m(B$??(*"(31(-G&(B:"G(;:".(-+"(;7;-??.(,GD"+;-$G(;:"G(m(B$??(*"(H([7;"(

    ;:-;(M7+F,?-(Tl0U($%("P-D;1($;($%($&"G;$D-?(;7(M7+F,?-(TlWU(;:"({(,%"&(*.(c"(-G&(K$;;"+F-G(T/444U(*"D-,%"($;($%(-(/P/(F-;+$PH((L:$%(-??7B%(,%(;7(M$G&(-(D?7%"&(M7+F(%7?,;$7G(;7(;:"(8+7*?"F(7M({((M7+(

    I&\7+"EN%(D7GM$&"GD"H

    )$+%;(B"(%,*%;$;,;"(M7+F,?-(Tl/U(

    -?;"+%((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((2l

  • 8/6/2019 Black-Litterman Model in Detail

    25/51

    TlZU

  • 8/6/2019 Black-Litterman Model in Detail

    26/51

    L-*?"(l(p(6-?$*+-;"&(!"%,?;%(M7+(f$"B(/

    @%%"; | BFE; B B/33b IF8?$"&(67GM$&"GD"

    IG;?(`"#(QV,$;. H332/2002_ 2lH/Zb 2_Hl0b 24H2Zb 2_H33b

    L-*?"(_(p(6-?$*+-;"&(!"%,?;%(M7+(f$"B(2

    @%%"; | BFE; B B/33b IF8?$"&(67GM$&"GD"

    XS(J7G&% H333/l30_3 /4HWlb 24H30b WZHtZb _3H33b

    IG;?(J7G&% H333/l30_3 20H/Wb /0Hl/b 0H04b _3H33b

    L-*?"(0(p(6-?$*+-;"&(!"%,?;%(M7+(f$"B(W

    @%%"; | BFE; B B/33b IF8?$"&(67GM$&"GD"

    XS(KR H333l00/3Z /2H34b 4Hl4b ZH34b 0_H33b

    XS(Kf H333l00/3Z /2H34b /lH04b /0H34b 0_H33b

    XS(SR H333l00/3Z /HWlb /H3_b H43b 0_H33b

    XS(Sf H333l00/3Z /HWlb /H0Wb /HtZb 0_H33b

    L:"G(B"(,%"(;:"(M+"%:?.(D7F8,;"&(#-?,"%(M7+(;:"({(F-;+$P(B$;:(-??(#$"B%(%8"D$M$"&(;79";:"+(-G&(-++$#"(-;(;:"(M7??7B$G9(M$G-?(+"%,?;(%:7BG($G(L-*?"(t(*?"G&$G9(-??(W(#$"B%(;79";:"+H

    L-*?"(t(p()$G-?(!"%,?;%(M7+(I&\7+"EN%(67GM$&"GD"(QP;"G%$7G(QP-F8?"

    @%%"; f$"B(/ f$"B(2 f$"B(W q BFE; Y7%;"+$7+(>"$9:;

    D:-G9"

    XS(

    J7G&%

    3H3

  • 8/6/2019 Black-Litterman Model in Detail

    27/51

    @%%"; f$"B(/ f$"B(2 f$"B(W q BFE; Y7%;"+$7+(

    >"$9:;

    D:-G9"

    IG;?(`"# /H3 3H3 3H3 lHZ /0HZ (2lH2b (20H3b /HZb

    IG;?(QF9 3H3 3H3 3H3 0H0 2ZHW ((WH_b ((WH_b

  • 8/6/2019 Black-Litterman Model in Detail

    28/51

    +-G&7F(#"D;7+(B$;:(F"-G(3(-G&(D7#-+$-GD"({H

    L:"(-88+7-D:(B"(B$??(;-E"($%(#"+.(%$F$?-+(;7(;:"(-88+7-D:(;-E"G(B:"G(-G-?.\$G9(-(8+"&$D;$7G(M+7F(-(

    ?$G"-+(+"9+"%%$7GH

    >"(D-G(&"M$G"(-G("%;$F-;7+(M7+(n1(B"(B$??(D-??(;:$%("%;$F-;7+ "(D-G(F"-%,+"(;:"("%;$F-;$7G("++7+(*";B""G(;:"(8+$7+(-G&(;:"(#$"B%(-%'

    T_3U E'!&/8 "(B$??(M7+F(7,+(:.87;:"%$%(;"%;(,%$G9(;:"(M7+F,?-;$7G

    T_/U F'!!E "5!E"//

    !!E"

    L:"(V,-G;$;.1(1($%(EG7BG(-%(;:"(O-:-?-G7*$%(&$%;-GD"(TF,?;$"(B7+E($G(+";,+G(%8-D"(:"+"(T-%(7887%"&(;7(#$"B(%8-D"U(-%($;(%""F%(F7+"(G-;,+-?H(K-;"+(7G(B"(B$??(;+-G%M7+F(;:"(M7+F,?-($G;7(#$"B(%8-D"(;7(F-E"($;(D7F8,;-*?"H

    >"(;:"G(%,*%;$;,;"(;:"(G"B("%;$F-;7+($G;7(;:"(M7+F,?-(T_3U(-G&("?$F$G-;"(P(-%($;($%(;:"($&"G;$;.(F-;+$P($G(

    ;:"(J?-DE

  • 8/6/2019 Black-Litterman Model in Detail

    29/51

    D7G;-$G(-(#$"B(7G("#"+.(-%%";1(%"#"+-?(7M(;:"(;"+F%(-+"(G7;(-?B-.%(D7F8,;-*?"(-%(B+$;;"GH(c7B"#"+1(B"(

    D-G("-%$?.(D7G#"+;($;(;7(#$"B(%8-D"(*.(F,?;$8?.$G9(*.(Y(-G&(YLH

    T_WU :"+"(MTU($%(;:"(Y`)(7M(;:"(2TVU(&$%;+$*,;$7GH

    I

  • 8/6/2019 Black-Litterman Model in Detail

    30/51

    G,!< "

    G :"+"(MTOU($%(;:"(Y`)(7M(;:"(D:$(%V,-+"(&$%;+$*,;$7G(B$;:(G(&"9+""%(7M(M+""&7F(M7+(OTVUH

    L:".(B7+E(-G("P-F8?"($G(;:"$+(8-8"+(B:$D:(+"%,?;%($G(-G($G$;$-?(8+7*-*$?$;.(7M(4lb(;:-;(;:"(87%;"+$7+($%(D7G%$%;"G;(B$;:(;:"(8+$7+H((L:".(%8"D$M.(;:-;(;:"$+($G#"%;7+(&"%$+"%(;:$%(8+7*-*$?$;.(;7(*"(G7(?"%%(;:-G(

    4_b(T-(D7FF7G?.(,%"&(D7GM$&"GD"(?"#"?($G(:.87;:"%$%(;"%;$G9U1(-G&(;:,%(;:".(B7,?&(-&A,%;(;:"$+(#$"B%(;7(*+$G9(;:"(8+7*-*$?$;.($G(?$G"H((R$#"G(;:-;(;:".(-?%7(D7F8,;"(%"G%$;$#$;$"%1(;:"$+($G#"%;7+(D-G($&"G;$M.(

    B:$D:(#$"B%(-+"(8+7#$&$G9(;:"(?-+9"%;(F-+9$G-?($GD+"-%"($G(;:"$+(F"-%,+"(-G&(;:".($G#"%;7+(D-G(;:"G(

    -&A,%;(;:"%"(#$"B%H((L:"%"(%"G%$;$#$;$"%(-+"("%8"D$-??.(,%"M,?(%$GD"(%7F"(#$"B%(F-.(-D;,-??.(*"(8,??$G9(;:"(87%;"+$7+(;7B-+&%(;:"(8+$7+1(-G&(;:"($G#"%;7+(D7,?&(%;+"G9;:"G(;:"%"(#$"B%1(7+(B"-E"G(#$"B%(B:$D:(

    8,??(;:"(87%;"+$7+(-B-.(M+7F(;:"(8+$7+H((L:$%(?-%;(87$G;(F-.(%""F(G7G

  • 8/6/2019 Black-Litterman Model in Detail

    31/51

    =%//

    @//'!%(@

    //"//

    @//

    =%//

    @//'!%@(H"

    //

    =%//

    @//'%

    //!%

    //(@"

    //

    =%//

    @//'%

    //!%

    //(!7%"

    //(,4

    //,

    *"//

    =%//

    @//'%

    //!/(7

    7

    %//(,4

    //,

    *"//

    =%//

    @//'!,

    *7%,"

    //2!/(7"!,

    *%,"

    //(74

    //3//

    =%//

    @//'!,

    *7%,"

    //2!,

    *% ,"

    !/(7"/!,

    *7%,"

    !/(7"!,

    *%,"

    !/(7"247(

    ,*%,

    /(73//

    3

    =%//

    @//'

    7/(7

    2H/!,

    *%,"

    /(7!47(

    ,*%,/(7

    "//

    3

    L:"G(B"(D-G(&"M$G"

    T_4U ?'24

    7

    (,

    *%,

    /(7

    3

    @G&(M$G-??.(+"B+$;"(-%

    T03U=%//

    @//

    '7

    /(72H/!,

    *?

    //,"!

    %/(7

    "3

    ],+(97-?($%(;7(%$F8?$M.(;:"(M7+F,?-(;7(;:"(M7+F

    -?;"+%((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((W/

  • 8/6/2019 Black-Litterman Model in Detail

    32/51

    %.'?'$'03$K'-'$'03$!.'(),0?$9..2.$H2&'-,&,-=

    J+-9-(-G&([-;-?"(T233tU(8+787%"(;:"(,%"(7M(;+-DE$G9("++7+(*";B""G(;:"(87%;"+$7+(-G&(8+$7+(87+;M7?$7%(-%(-(F"-%,+"(7M(&$%;-GD"(M+7F(;:"(8+$7+H((L+-DE$G9("++7+($%(D7FF7G?.(,%"&(*.($G#"%;7+%(;7(F"-%,+"(+$%E(

    #"+%,%(-(*"GD:F-+E1(-G&(D-G(*"(,%"&(-%(-G($G#"%;F"G;(D7G%;+-$G;H((@%($;($%(%7(D7FF7G?.(,%"&1(F7%;(

    $G#"%;7+%(:-#"(-G($G;,$;$#"(,G&"+%;-G&$G9(-G&(9-(?"#"?(7M(D7FM7+;(B$;:(LQfH(L+-DE$G9("++7+(#7?-;$?$;.($%(&"M$G"&(-%

    T02U *!5'K)023=*

    % )023= )IC"C) 023=' "$9:;($G(;:"(+"M"+"GD"(87+;M7?$7

    % 67#-+$-GD"(F-;+$P(7M(+";,+G%

    L:".(-?%7(&"+$#"(;:"(M7+F,?-(M7+(;+-DE$G9("++7+(%"G%$;$#$;$"%(-%(M7??7B%'((R$#"G(;:-;(

    *!5' %!)023="

    -G&(B"(D-G(M,+;:"+(+"M$G"(

    ) 023='1! 3IC 2I0.4 "9EC

    G*!5

    G )023='

    G*!5

    G8

    G8

    G ) 023=G*!5G )023=

    '2/

    2K)023=*

    % )023=32 2 % ) 023=3

    G*!5

    G )023='

    % ) 023=

    K) 023=*

    % ) 023=

    S7?#$G9(M7+(;:"(%"D7G&(;"+F(7M(M7+F,?-(T0WU($%(%?$9:;?.(F7+"(D7F8?$D-;"&H

    5(678.+$9:;(23341(=-.(>-?;"+%((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((W2

  • 8/6/2019 Black-Litterman Model in Detail

    33/51

    G ) 023=G -?;"+%((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((Wl

  • 8/6/2019 Black-Litterman Model in Detail

    35/51

    @%%"; Y3 Y/ d d"V B"VoT/uwU (B( B(

  • 8/6/2019 Black-Litterman Model in Detail

    36/51

    ;7(:-#"(-(#"+.(?-+9"(LQfH

    ["P;(B"(D:-G9"(7,+(D7GM$&"GD"($G(;:"(#$"B%(*.(&$#$&$G9(;:"(#-+$-GD"(*.(l1(;:$%(B$??($GD+"-%"(;:"(D:-G9"(

    M+7F(;:"(8+$7+(;7(;:"(87%;"+$7+(-G&(-??7B(,%(;7(F-E"(%7F"(A,&9"F"G;%(*-%"&(7G(;:"($F8-D;(F"-%,+"%H

    L-*?"(/3(p(QP-F8?"(2(!";,+G%(-G&(>"$9:;%1("V,$?$*+$,F(M+7F(c"(-G&(K$;;"+F-G1(T/444UH

    @%%"; Y3 Y/ d B"VoT/uwU (B( B("(G7B(:-#"(-G(Z3b($GD+"-%"($G(;:"(-??7D-;$7G(;7(6-G-&-(-G&(-G(Z3b(&"D+"-%"($G(;:"(-??7D-;$7G(;7(;:"(XS@H(()+7F(

    L-*?"(T//U(B"(D-G(%""(;:-;(L:"$?N%(F"-%,+"(:-%($GD+"-%"&(-G&(B"(-+"(G7(?7G9"+(D7GM$&"G;(-;(;:"(_b(?"#"?(

    ;:-;(;:"(#$"B%(-+"(D7G%$%;"G;(B$;:(;:"(8+$7+("%;$F-;"%H((),%-$(-G&(O",DD$N%(F"-%,+"(G7B($%(D?7%"(;7(;:"(

    _b(D7GM$&"GD"(?"#"?(;:-;(;:"(87%;"+$7+($%(D7G%$%;"G;(B$;:(;:"(8+$7+H((I;($%(,GD?"-+($G(8+-D;$D"(B:-;(*7,G&(B"(B7,?&(B-G;(;7(,%"1(*,;(_b($%(-(#"+.(D7FF7G(D7GM$&"GD"(?"#"?(;7(,%"(M7+(%;-;$%;$D-?(;"%;%H

    ]GD"(-9-$G(B"(%""(;:"(c"(-G&(K$;;"+F-GN%(K-F*&-(%:7B%(;:"(%"D7G&(#$"B(:-#$G9(F7+"(7M(-G($F8-D;(

    7G(;:"(M$G-?(B"$9:;%H((IG(;:$%(%D"G-+$7($;($%(G7B(,8(;7(Z0bH

    L:"(LQf(:-%($GD+"-%"&1(-G&($%(G7B(/2H43b(B:$D:(%""F%(#"+.(:$9:(-G&(?$E"?.(7,;%$&"(;:"(;7?"+-GD"H

    L:"(aKI6(:-%($GD+"-%"&(ZP($G&$D-;$G9(;:-;(;:"(87%;"+$7+($%(%$9G$M$D-G;?.(&$MM"+"G;(M+7F(;:"(8+$7+H

    5(678.+$9:;(23341(=-.(>-?;"+%((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((W0

  • 8/6/2019 Black-Litterman Model in Detail

    37/51

    ["P;(B"(D:-G9"(7,+(D7GM$&"GD"($G(;:"(#$"B%(*.(F,?;$8?.$G9(;:"(#-+$-GD"(*.(l1(;:$%(B$??(&"D+"-%"(;:"(

    D:-G9"(M+7F(;:"(8+$7+(;7(;:"(87%;"+$7+(-G&(-??7B(,%(;7(F-E"(%7F"(A,&9"F"G;%(*-%"&(7G(;:"($F8-D;(

    F"-%,+"%H

    L-*?"(/2(p(QP-F8?"(W(!";,+G%(-G&(>"$9:;%1("V,$?$*+$,F(M+7F(c"(-G&(K$;;"+F-G1(T/444UH

    @%%"; Y3 Y/ d B"VoT/uwU (B( B(-?;"+%((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((Wt

  • 8/6/2019 Black-Litterman Model in Detail

    38/51

    $G&$D-;$G9(;:"(87%;"+$7+(B-%(9"G"+-??.(:$9:?.(D7G%$%;"G;(B$;:(;:"(8+$7+(*.(;:"$+(F"-%,+"H((),%-$(-G&(

    O",DD$(8+"%"G;(;:-;(-G($G#"%;7+(F-.(:-#"(-(+"V,$+"F"G;(;:-;(;:"(D7GM$&"GD"(?"#"?(*"(_bH((IG(?$9:;(7M(

    ;:"%"(+"%,?;%(;:-;(B7,?&(%""F(;7(*"(-(M-$+?.(?-+9"(#-?,"H((L:"(%"G%$;$#$;$"%(7M(;:"(67G%$%;"GD.(F"-%,+"(

    %D-?"(B$;:(;:"(F"-%,+"1(-G&(M7+(?7B(#-?,"%(7M(;:"(F"-%,+"(;:"(%"G%$;$#$;$"%(-+"(#"+.(?7BH

    c"(-G&(K$;;"+F-GN%(K-F*&-(+-G9"&(M+7F(-(?7B(7M(22b(M7+(;:"(%"D7G&(#$"B(;7(-(:$9:(7M(Z0bH((L:$%($%(

    D7G%$%;"G;(B$;:(;:"($F8-D;(7M(;:"(%"D7G&(#$"B(7G(;:"(B"$9:;%1(B:"+"($G(;:"(M$+%;(;B7(%D"G-+$7%(;:"(

    B"$9:;%(7M(;:"(XG$;"&(S;-;"%(-G&(6-G-&-(B"+"(%$9G$M$D-G;?.($F8-D;"&(*.(;:"(#$"BH

    @D+7%%(;:"(;:+""(%D"G-+$7%(;:"(LQf($GD+"-%"&(M+7F(WHlb($G(;:"(?7B(D7GM$&"GD"(D-%"(;7(/2H4b($G(;:"(:$9:(D7GM$&"GD"(D-%"H((L:"(?-;;"+(#-?,"(M7+(;:"(LQf($%(#"+.(?-+9"H((I;($%(G7;(D?"-+(B:-;(-(+"-?$%;$D(

    ;:+"%:7?&(M7+(;:"(LQf($%($G(;:$%(D-%"1(*,;(;:"%"(#-?,"%(-+"(?$E"?.(;7B-+&%(;:"(,88"+(?$F$;(;:-;(B7,?&(*"(

    ;7?"+-;"&H((L:"(%"G%$;$#$;$"%(7M(;:"(LQf(%D-?"(B$;:(;:"(LQf1(%7(M7+(87%;"+$7+%(B$;:(?7B(LQf(;:"(

    %"G%$;$#$;$"%(-+"(?7B"+(-%(B"??H

    L:"(aKI6(+-G9"&(7#"+(7G"(7+&"+(7M(F-9G$;,&"(M7+(;:"(/0P(D:-G9"($G(;:"(D7GM$&"GD"($G(;:"(#$"B%H

    IG(-G-?.\$G9(;:"%"(#-+$7,%(F"-%,+"%(7M(;:"(;$?;(D-,%"&(*.(;:"(#$"B%1(;:"(LQf(-G&(&$%D+";"(aKI6(7M(;:"(

    B"$9:;%(F"-%,+"(;:"($F8-D;(7M(;:"(#$"B%(-G&(;:"(78;$F$\-;$7G(8+7D"%%1(B:$D:(B"(D-G(D7G%$&"+(-%(;:"(

    M$G-?(7,;8,;%H((IM(;:"($G#"%;7+($%(D7GD"+G"&(-*7,;(?$F$;%(7G(LQf1(;:".(D7,?&(*"("-%$?.(-&&"&(-%(

    D7G%;+-$G;%(7G(;:"(78;$F$\-;$7G(8+7D"%%H

    c"(-G&(K$;;"+F-GN%(K-F*&-(F"-%,+"%(;:"(B"$9:;(7M(;:"(#$"B(7G(;:"(87%;"+$7+(B"$9:;%1(*,;(7G?.($G(;:"(

    D-%"(7M(-G(,GD7G%;+-$G"&(78;$F$\-;$7GH((L:$%(F-E"%($;(%,$;-*?"(M7+(F"-%,+$G9($F8-D;(-G&(*"$G9(-(8-+;(7M(

    ;:"(8+7D"%%1(*,;($;(D-GG7;(*"(,%"&(-%(-(D7G%;+-$G;($G(;:"(78;$F$\-;$7G(8+7D"%%H

    L:"$?N%(67F8-;$*$?$;.(F"-%,+"1(),%-$(-G&(O",DD$N%(67G%$%;"GD.(F"-%,+"1(;:"(aKI6(F"-%,+"(;:"(87%;"+$7+(&$%;+$*,;$7G1($GD?,&$G9(;:"(+";,+G%(-G&(;:"(D7#-+$-GD"(F-;+$PH(L:"(?-;;"+(F7+"(&$+"D;?.(

    F"-%,+"%(;:"($F8-D;(7M(;:"(#$"B%(7G(;:"(87%;"+$7+(*"D-,%"($;($GD?,&"%(;:"($F8-D;(7M(;:"(#$"B%(7G(;:"(

    D7#-+$-GD"(F-;+$PH

    /A+ND&'$+%2O6&'FNJ.$$1%8&*

    a+$%:G-G(-G&(O-$G%(T233_U(&"#"?78"&(-G("P;"G%$7G(;7(;:"(-?;"+G-;"(+"M"+"GD"(F7&"?(B:$D:(-??7B%(;:"(

    $GD7+87+-;$7G(7M(-&&$;$7G-?(,GD7++"?-;"&(F-+E";(M-D;7+%H((L:"(F-$G(87$G;(;:".(F-E"($%(;:-;(;:"(J?-DE$GE"?F-GG(T/44ZU(8+7#$&"(&";-$?%(

    7G(:7B(;:".(,%"(J?-DE

  • 8/6/2019 Black-Litterman Model in Detail

    42/51

    O-GE"+;(T2330U(8+7#$&"%(-(G$D"(%7?$&(B-?E(;:+7,9:(7M(;:"(F7&"?(-G&(8+7#$&"%(-(&";-$?"&(;+-G%M7+F-;$7G(

    *";B""G(;:"(;B7(%8"D$M$D-;$7G%(7M(;:"(J?-DE

  • 8/6/2019 Black-Litterman Model in Detail

    43/51

    3141%1*'1#

    O-G.(7M(;:"%"(+"M"+"GD"%(-+"(-#-$?-*?"(7G(;:"(IG;"+G";H((I(:-#"(8?-D"&(-(J?-DE:$;"(

    Y-8"+H

    a7D:(T233_U(67G%$%;"G;(@%%";(!";,+G(Q%;$F-;"%H(L:"(J?-DE

  • 8/6/2019 Black-Litterman Model in Detail

    44/51

    IG#"%;F"G;(O-G-9"F"G;'(@G(QV,$?$*+$,F(@88+7-D:(*.(J7*(K$;;"+F-G(-G&(;:"(z,-G;$;-;$#"(!"%"-+D:(

    R+7,81(R7?&F-G(S-D:%(@%%";(O-G-9"F"G;1(6:-8;"+(tH

    O-GE"+;(T2330U(L:"(J?-DE

  • 8/6/2019 Black-Litterman Model in Detail

    45/51

    !991*,.M2!

    L:$%(-88"G&$P($GD?,&"%(;:"(&"+$#-;$7G(7M(;:"(J?-DE:"+"(g($%(;:"(F"-G(7M(;:"(8+$7+(+";,+G(&$%;+$*,;$7G1(n($%(;:"("P8"D;"&(+";,+G(-G&(,($%(;:"(G7+F-??.(

    &$%;+$*,;"&(+"%$&,-?(B$;:(F"-G(3(-G&(#-+$-GD"(H

    ["P;(B"(D7G%$&"+(%7F"(-&&$;$7G-?($GM7+F-;$7G1(;:"(D7G&$;$7G-?(&$%;+$*,;$7GH

    @H2 :"+"(V($%(;:"(F"-G(7M(;:"(D7G&$;$7G-?(&$%;+$*,;$7G(-G&(#($%(;:"(G7+F-??.(&$%;+$*,;"&(+"%$&,-?(B$;:(F"-G(3(-G&(#-+$-GD"(H

    J7;:((-G&(e(-+"(-%%,F"&(;7(*"(G7G"(D-G(D7F*$G"(;:"(8+$7+(-G&(D7G&$;$7G-?($GM7+F-;$7G(*.(B+$;$G9'

    @HW 2&< 3'2 8'3*(29= 3>:"+"(;:"("P8"D;"&(#-?,"(7M(;:"(+"%$&,-?($%(31(-G&(;:"("P8"D;"&(#-?,"(7M(;:"(#-+$-GD"($%

    !

    !29=32

    9 ; = ; 33'2;

    33 43

    >"(D-G(;:"G(-88?.(;:"(9"G"+-?$\"&(?"-%;(%V,-+"%(8+7D"&,+"1(B:$D:(?"-&%(;7("%;$F-;$G9(n(-%

    @Hl "(D-G(&"+$#"(;:"("P8+"%%$7G(M7+(;:"(#-+$-GD"(,%$G9(%$F$?-+(?79$DH((R$#"G(;:-;(;:"(#-+$-GD"($%(;:"("P8"D;-;$7G(7M( !

  • 8/6/2019 Black-Litterman Model in Detail

    46/51

  • 8/6/2019 Black-Litterman Model in Detail

    47/51

    !991*,.M2O

    L:$%(-88"G&$P(D7G;-$G%(-(&"+$#-;$7G(7M(;:"(J?-DE8 "N"P8

    !%//

    !!!""/$

    "

    2

    "S,*%;$;,;$G9(JH/(-G&(JH2($G;7(M7+F,?-(T/U(M+7F(;:"(;"P;1(B"(:-#"(-G("P8+"%%$7G(B:$D:(;:"(Y`)(7M(;:"(87%;"+$7+(&$%;+$*,;$7G(B$??(%-;$%M.H

    JHW F!8>$"N"P8 !/!%// !!!""/$"2(! BB4"

    //!!!""/8 "

    2"" 1

    7+( F!8>$"N"P8 !/;"

    67G%$&"+$G9(7G?.(;:"(V,-G;$;.($G(;:"("P87G"G;(-G&(%$F8?$M.$G9

    ;'

    !%//

    !!!""/$

    "

    2(! BB4 "

    //

    !!! ""/8

    "

    2

    ";'!%//!!!""2/2!!""$($2"(! BB4 "//!!! ""2/2!! ""8 (82 "";'!!""

    2 !%//(!BB4"//"/2!!"" !$%//(8 !BB4"//"(%//$2(!BB4"//82

    IM(B"($G;+7&,D"(-(G"B(;"+F(.1(B:"+"

    5(678.+$9:;(23341(=-.(>-?;"+%((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((lt

  • 8/6/2019 Black-Litterman Model in Detail

    48/51

    JHl >'!$%//(8 !BB4"//"

    !%//(!BB4"//"-G&(;:"G(%,*%;$;,;"($G(;:"(%"D7G&(;"+F

    ;'!!""2 !%//(!BB4"//"/2!!"" > !% //(!BB4"//"(%//$2(!BB4"//82

    L:"G(-&&( 3'>2

    !%//

    (!BB4"//

    "/!$%//

    (8 ! BB 4"//

    "2

    !%//

    (!BB4"//

    "//

    ;'!!""2 !%//(!BB4"//"/2!!"" > !% //(!BB4"//"(%//$2(!BB4"//82

    (>2!%

    //(!BB4"

    //"/!$%

    //(8 ! BB4"

    //"

    2!%

    //(!BB4"

    //"

    //

    ;'!!""2 !%//(!BB4"//"/2!!"" > !% //(!BB4"//"(>2 !%//(!BB4"//"

    (%//

    $2(!BB4"

    //8

    2/!$%

    //(8 ! BB4"

    //"

    2!%

    //(!BB4"

    //"

    //

    ;'!%//(!BB4"//" 2!!""2/2!!"">(>2 3(!%//$2(!BB4"//82"/!$%

    //(8 !BB4"

    //"2!%

    //(!BB 4"

    //"//

    ;'!%//(!BB4"//" 2!!""2/2!!""> (>2 3/!$%//(8 ! BB 4"//"2!%//(!BB 4"//"//

    (!%//$2(!BB 4"//8 2"! %//(! BB4 "//"! %//(!BB 4"//"//

    ;'! %//(!BB4"//" 2!!""2/2!!"">(>2 3/!$

    2%

    /2(2 $8 %

    //! BB 4"

    //(8

    2! BB4 "

    /2"! %

    //(!BB4"

    //"

    //

    (!%/2

    $2(!BB4"

    //%

    //8

    2($

    2%

    //! BB 4"

    //(8

    2!BB 4"

    /2"! %

    //(!BB4"

    //"

    //

    ;'! %//(!BB4"//" 2!!""2/2!!"">(>2 3(!!BB4"

    //%

    //8

    2/2$8 %

    //!BB 4"

    //($

    2%

    //!BB4"

    //"! %

    //(! BB 4"

    //"

    //

    ;'!%//(!BB4"//" 2!!""2/2!!""> (>23(!%

    //(!BB4"

    //"

    //!8/$"!%

    //!BB4"

    //"

    L:"(%"D7G&(;"+F(:-%(G7(&"8"G&"GD.(7G(QT+U1(;:,%($;(D-G(*"($GD?,&"&($G(;:"(8+787+;$7G-?-?$;.(M-D;7+(-G&(

    B"(-+"(?"M;(B"

    JH_ F!8>$"N"P8 !/2 !%//(!BB4"// "//!!!M"/> "23"

    L:,%(;:"(87%;"+$7+(F"-G($%(.(-%(&"M$G"&($G(M7+F,?-(@H/21(-G&(;:"(#-+$-GD"($%

    JH0 !%//

    (!BB4"// "

    //

    5(678.+$9:;(23341(=-.(>-?;"+%((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((lZ

  • 8/6/2019 Black-Litterman Model in Detail

    49/51

    !991*,.M27

    L:$%(-88"G&$P(8+7#$&"%(-(&"+$#-;$7G(7M(;:"(-?;"+G-;"(M7+F-;(7M(;:"(87%;"+$7+(#-+$-GD"H((L:$%(M7+F-;(&7"%(G7;(+"V,$+"(;:"($G#"+%$7G(7M({1(-G&(;:,%($%(F7+"(%;-*?"(D7F8,;-;$7G-??.H

    TTweU

  • 8/6/2019 Black-Litterman Model in Detail

    50/51

    !991*,.M2P

    L:$%(-88"G&$P(8+"%"G;%(-(&"+$#-;$7G(7M(;:"(-?;"+G-;"(M7+F,?-;$7G(7M(;:"(J?-DE

  • 8/6/2019 Black-Litterman Model in Detail

    51/51

    !991*,.M2