Tài liệu Bài tập quản trị rủi ro kèm lời giải ( file bài giải)

Qu n tr R i ro ! ! "# $ $% &' &' &' $% $ ! " # ! ( ) * )+ , - . / 0 &' 1% 1% 1% &' 0 ($ 2 3 4 5 6* / - 71 8 ' 0$8& %% 8%% 908% $9 8&019 8$&77 8 $ : ;4 3 4 5 6* / - 71 8$9<$% $ $ !% & !!&! !'() * +, - . / . 0 $ !% &!&! ! ) * +, 12 3 4/ -2 . 5 5 64 / 7 &! !! , 08 / 9 5 9 5 69 5: 5 9 / ' !&! ! * +, . !&! !! , 08 ; <=> ? / !&! ! * +, . !% &!&! !3 / > @? / @ A B *;(*! C D !C % ;( ; ! * +, '() . % ! ' ; , *, = . ( E C *!&! !! ! +F1" ! () ( = 7+*; ( / 7 &! !! , 08 ' E + &> 9 0 ! * ! , 08 > / G = &> 2 − 4= . 9 9 O/ . O = @ P * ! + Q ; ! * ! , 08 E +& . ! > R S 9 @ N 5 9 @ T/R @ N T P * ! + Q !&! !! , 08 E +& . ! > R .@ ON . @OT ! * ! , 08 > / . G = &> 2 − 4= . 9 9 = @ P * ! + Q ; ! * ! , 08 E +& . ! > R . S 9 @ N . 5 9 @ T / R. @ N . @T P * ! + Q !&! !! , 08 E +& . ! R .@ N . . @ T ' 7(0 * & ; ! * U! , * RN 0T / R S N 5 T E) ; !# ! != Q • P / . * RN 0T / R N T E) * R @ N T. ! ! + ; !% &; ! * U! , * R N T *) Q % D + !%M 0 * & • P / . . * RN 0T / R . N . T E) * R. @ N . @T. ! ! + ; !% &; ! * U ! , * R. N . T = ) ) Q % D + !%M ! (0 * & • V ) * (< ! (0 * & E 0 * & %() %M ! ( () ! ,8 2 − 4 / / / B * () ! ,8 ! , C. ! 7(0 * & RN 0T / R S ; ! N 5 W6@ * U! , T / R N T E) * ; !# ! Th.s Tr n Quang Trung != Q 2 Sưu tầm bởi: www.daihoc.com.vn Qu n tr R i ro • • • P / . * RN 0T / R N T E) * R @ N T. ! ! + ; !% &; ! * U! , * RN T = ) ) Q % D + !%M ! (0 * & P / . . * RN 0T / R N . T E) * R. @ N . @T. ! ! + ; !% &; ! * U ! , * RN . T = ) ) Q % D + !%M ! (0 * & V ) * (< ! (0 * & E 0 * & %() %M ! ( () ! ,8 2 − 4 / / • / B * () ! ,8 ! , C. ! W6 C; '( 2F1"4 E +& . ! > . O9 / . OE) ' ; , *, = Q C ; '( 2F1"4 E +& . O9 . @ / . . @ OE) ' ; , *, = Q . ! > % ! ! , * 2; ! ! , 08 ! , 12 # ! ! ! ! , ! C C 4 4 / S 12 C 1 ;; C ! .! ; = ! , / 4 − / 0 Y K () < 12 Z $ X /6 6 Q = % . ;(*' 6= % ! , 6 () % C +! ' *D + !! ( ;(*' = % J;(*' = % # ! ! ! ! , 6 4 / S 12! , 6 +! ; / 2; ! ! , 08 ! , 6 ; !; ! * +, ! , 0 * '() % C + 6 1 6 6 66 7(% ! ! # %() ; ! K! 8 = 7(0 * & ; ! U! , RN 0T / R N 5 T / RN T E) Y) = ; D ; ! J &! ! # %() ; !; ! Th.s Tr n Quang Trung (' ! % =@! 4 4 @ @ @ Q * ; !# ! ! , != U! , Q * RN 0T = 3 Sưu tầm bởi: www.daihoc.com.vn Qu n tr R i ro 1 ($ ≤ 0 ) = 1 [ ≤ 0− =1 [≤ = 7(% ! = @ ≈ 26 ' ;(*' = % ! , 6 . + ;(*' 6= % ! , ! ) !8; : ;4 # E) ; ) ) / . @ . 6 . @ . 6 . . 6 . . 6 . @ . ? >@= > A2@B A2 C: D :2@C : ) ) ; ) ) F6 F . . . . . . . @. @. @. A F# ) ;) ) --- @ ------- 6 A F# : ;) ) --- . . --- 6. 6. --- . . --- . ) ;) ) : ;) ) * G * G H F ) GH 6 F 4 5 > GH 4 5 @ @ @ 6 6 @6 6 @ @ ,H ) ; ) ) ; - 4 I J 5H ) @ 6 ,- 5 3 ) ;) ) ; - 4 I J 5H ) . . . @ . @ Th.s Tr n Quang Trung 5 Sưu tầm bởi: www.daihoc.com.vn Qu n tr R i ro $ : *H ) ; ) ) J 5 H ) K 5 3 ) ; ) ) ------- 6 @ 1 C *!& !&! ! ! ( C * : ;4) ; ) ) . *!& !&! ! ! ( C @ @ =K J 5H ) 6 6 6 6 @ 1 C J 5 ; -4 I H ) * : ;4) ; ) ) . =K J 5H @ ) @ 6 @ 6 6 Th.s Tr n Quang Trung 6 Sưu tầm bởi: www.daihoc.com.vn Qu n tr R i ro & J 5H ) : *H ) ;) )L / - @ :: 1 C 1 ;; 9' *!K; !&! ! .! ; = 6 A @ @ 6 @ 6 6 % 7 &! ! 7# ! ,M +E > F2Z4 / 1 Z F2Z4 / .6 5 .6 5 . 7 K; .6 .6 . . . 5 . 5 . / 7# % = &> σ 2Z4 / 1 RZ S F2Z4T Z 1 .6 .6 . . . RZ S F2Z4T @ @ @ @ @ @ @ 1 RZ S F2Z4T 6 @ @ @ @ Y +σ 2Z4 / @ @ % % = &>σ ( L) = σ 2 ( L) = 4594600 = 2143,5 ≈ 2144 Th.s Tr n Quang Trung 7 Sưu tầm bởi: www.daihoc.com.vn Qu n tr R i ro 6 7# ; = > α 3 ( L) = Z 1 .6 .6 . . . 6 2Z4 = 6 Pi [ Li − M ( L)]3 [σ ( L)]3 RZ S F2Z4T6 @ @ 6 @@6 1 RZ S F2Z4T6 M @ 6 M @6 M @6 @ @ 6 @@ @ 6 @ 2 @6 46 =6 6 @ &07%7&0%999 @ @ Th.s Tr n Quang Trung 8 Sưu tầm bởi: www.daihoc.com.vn Qu n tr R i ro N 2 O @ 2 P@ :@ >2Q 2 2 R19S T U : I ) 5)+ 5) : R%9S T ) 5) * : ;4) H , H ) )+ F P>A $R> F4)VOU R&9S T @ R'9S T @ @ 6@ 6 @ 9 '0 9 %' 6 9 '1 U K @ JT $ ; ! ]^_7 Z < Z) ! ( ! ,() ! 7 2@ Q4 Z) ! ( ! K ) 7 & ! ; * Z) ; !! , CY"1 H ) )+ 4(W )+ F P>A 3 X3 ; 2 3 H ( ) F 6 @ @ @ @ @ @ 6 9 91 9 91% 911 Th.s Tr n Quang Trung 9 Sưu tầm bởi: www.daihoc.com.vn Qu n tr R i ro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h.s Tr n Quang Trung @ @ @ 10 Sưu tầm bởi: www.daihoc.com.vn Qu n tr R i ro 7 & !! , 0 * ; :GX3 Y L: 9S 9S H ) )+ 4(W )+ F P>A 9 91 9 3 X3 ; 9 91% 9 9171 2 3 H ( ) F 9 1 1 9 1&' &R> F4)VZ U ;4) H 19S 9 %% 9 90 9 <1 , '9S 9 &< 9 &1 9 70& :U T : )+ ( [4 $ ; ! ! ]^_7 Z < * ) L Z < * )' Z) ! ( ! ,() ! 7 2@ Q4 Z) ! ( ! K ) 7 & ! ; * UA R OT UA )+ 4(W 3 X3 ; :GX3 :U > ; # 6 @ 6 - 5 6 @ 6 6 @ @ @ 6 6 6 @ 6 6 6 6 @ @ @ @ % %$0 1<<0 1<<0 9%' 9 <11 &%00 < $0 6 % %90 Th.s Tr n Quang Trung 11 9 11 9 9 01% 9 100 ' 999 '' $ 11 Sưu tầm bởi: www.daihoc.com.vn Qu n tr R i ro A2@\ ]= :2 ]UC : O@ 2 K ? > @ 2 UD K RA P@ _ @ : ` " , *, = % = E % K !E) :^ T > Z = 2 i = 2@ 4 5 )+a)+ 4(W • M ) (W b F L1 + L 2 + ... + L n M (L1 ) + M (L 2 ) + ... + M (L n ) = / n n 3 X3 • D ,) ; ) ; ,) ; ) ) (W b F L1 + L 2 + ... + L n D(L1 ) + D(L 2 ) + ... + D(L n ) = n n2 / / Z +Z + • J 5H " #'( +Z )# 5 H ,Y 0 K!() Z9 1 Z Z9 7, 0 * =@ =1 [ CEM − !`G^` / =1 [ − @ 5 / = 1 ([ . ) &. ! 12[ 3 . 4 / . Q Y + !% & C ! + ; *= > . Q Th.s Tr n Quang Trung 12 Sưu tầm bởi: www.daihoc.com.vn Qu n tr R i ro $ 7 C !( ! # Z + +Z () ; *' + + I ≠I = 0 * ≠I = !& ! ! * ) %K 0 * = ; '() . ! %() D 2 Z + +Z + ≠I = 7 ! +! (*; ! , \= ; ! () !8 ! ,M! , 08 D rij rij & = a= !& * ! , 08 C ! &! ! ) 2 (; I C n+ 2 i & i≠ j E ; ! () rij ; ! () D . ' % !! * ; ! () ! , E C( C; D + + % K '() & ]2Z4 / σZ / σ .I / @ " , *, = Z + F = =& M(L i ) /µ / Z + Y) = +Z ! +Z + ≠I = I / 9 + 9@ = Th.s Tr n Quang Trung 13 Sưu tầm bởi: www.daihoc.com.vn Qu n tr R i ro = . 7() ! ( ! ,() J 5" ) # 1 Z .! !D *; 5 H ,Y Z9 Z9 ) =1 [ Y) ! ,M % b !( " 0+; − ≤ Z9 * ! E σ# J A c − () = () ! , C * ; ! ; *0 U 0 ! (; 6 @@ 6 6 @ 6 @ 6 @ 6 @ P ;(*' 0 !% b !( " 0+; E % &() = () ) ! , C * ; ! ; * ! !() %() ! ,M = ). != *7 C 0 ! # ; ! ; *= 0 C. J0 != C ! +0 * & K !8 ; ! + C E()!D @ Q 7, ! ,() ) , *, C % = E) .! &E8 C ! * < % K *%M = + ) D * * ; ! ; * ' J & E) !( " 0+; E. ! ! + ;( C = , != ) σ# 6 6 6 6 Th.s Tr n Quang Trung C ! &;(*' J ! , !C ; ! ! , C 0)*0 !% b 6 @ 6 14 Sưu tầm bởi: www.daihoc.com.vn Qu n tr R i ro σ# J A c JJ> ; 6 @@Q Q Q 6Q 6 6 @ Q Q 6 @ Q Q 6 @ 6 @ Q Q % • `) % K 0 * & * µc / 6 σc / ,c. I / c / . 7 ! # () ; ! ( C !( ; Z + * !& ! !08 D C ! , C + +Z = + I ≠I ≠I = rF,ij ! ) %K 0 * i & * I σ F = 158.2 • 7() ! (! ! # % = & ! (; & !& ! !08 D C ! , C ! ) %K 0 * σ A = 223.6 G = & * !& ! !08 D C ! , C ! ) % K 0 * & *d %() ! # '( E % = & !& ! !08 D C ! , C !) %K 0 * & * E ! (; > c ( c c + + d d) d = @ 0 G = & *!&! !08 D C! , C = +%() ! # (; !) %K 0 * &! , µZ / Th.s Tr n Quang Trung 15 Sưu tầm bởi: www.daihoc.com.vn Qu n tr R i ro σZ / 6 ,Z. I / Z / . 7 ! # Z + () ; * !& ! !08 D C ! , C = +! ( C !( ; +Z + ≠I = + I ≠I = rL,ij ! ) %K 0 * i &! , I σ L = 67.11 d E d ) !E) ! , C !) %K 0 * &0 U = E) !&! ! ! E ! , D / !! # () ; * !& ! !08 D C C !( E) *! !!&! ! * % = + F1 + ... + FnF + A1 + ... + An A + L1 + ... + LnL nF + n A + nL = n F2 σ F2 + n A2 σ A2 + n L2σ L2 + 2 i j rAi L j σ Aσ L (n F + n A + n L ) 2 6 G = &= 6 Th.s Tr n Quang Trung 16 Sưu tầm bởi: www.daihoc.com.vn Qu n tr R i ro ]= :2 ]UC : :2`: P C @ > 5 3 ## 4H ) 4 54Y ♦ " E 2d.^4 / ,d^9 σd9σ ^ / . 9 .@9 . / . ♦ " E 2d."4 / ,d"9σ d9σ " / .@9 .@9 . / . 6 ♦ " E 2^."4 / ,^"9σ ^9σ " /- . 9 . 9 . /- . ( P1 H )- 4 ,! *) Y / ed Pd 5 e^ P^ 5 e" P" / . 9 .6 5 . 9 . 5 2- .649 . / . 2 Q4 3 X3 1 = e / ; ,X H + 2 * [e d e ^ @ 5 9R . . . )- 4 ,! E2d. ^4 + e d e " - *) Y E2d. "4 + e ^ e " E2^. "4T 52- 64 5 5 . 2- .64 . 6 5 . 2- .64 2- . 4T / .6 ! :+ 4H F - , 54 5> 5 - G 7, ; '() \= % K! (0 *! KE E +! KE) =<; ! Q +0 ( * 4W d ( " . C= % K! ( = ); ! Q @ $ 4::>N R K TY β P / Vc 5 2 F - Vc 4 P > 7+*; !Z) %) >Z <; ! C , *, Vc > Z) ; ! %) *' F β > ; 0 C ! * ( *" ( P !M! ,() Th.s Tr n Quang Trung 17 Sưu tầm bởi: www.daihoc.com.vn Qu n tr R i ro B *;(* 7, 7+*; !Z) 0 7+*; !Z) !M! ,() F / 6Q β/ . β/ β/ G() !M! ,() ( 0 ! ; , *, 0 ! Vc / Q I / 6Q Q d/ ! * ( / Q %M = ); ! * ! ( % 7 Z +C K SML : ki = kRF + (kM - kRF).βi KA = 17 1 K0 % L , *, *"P KA = KM = 13 ^ % L, *, !M! ,() KL = 11 KRF = 9 kRF 0 0,5 1 2 Th.s Tr n Quang Trung ` ; βi 18 Sưu tầm bởi: www.daihoc.com.vn Qu n tr R i ro 4: a:+ 4P R>K T Y +E) =<; E(r) !rf CML " E +E) =<; !,A ]c- G() % K!( D * M rM rf σM V *, , σ(r) F=' % K! (!M! ,() ,A = =<; ! C , *, G() !M! ,() E !! + () % K! (%() % K! ( D * ! ) % K! (! , C !M! ,() ( E +E) =<; ! C , *, ,A @ & 7# = ); ! %) d ' C !( > / Vc 52 F - Vc4 β E) Vc / . F / . . d / . ^ / . " / / . . ] / % K! ( *% K J = " / βC = ! ( 52 52 52 52 52 ( . . . . . - *! ! ( %() E) E E +E > . . . . . 4 . 4 4 . 4 4 2- . / / / / 4/ . . . @ . . %() = ); ! %) ! , C & "= . ; , *, 0 ! * & " " ! & (; > . 52 . - . 4 β" / !8 K . 0.17 − 0.1 = 0.875 0.18 − 0.1 Th.s Tr n Quang Trung 19 Sưu tầm bởi: www.daihoc.com.vn Qu n tr R i ro :@= @\ : P@ : 7 > G() G() D *% K! (! ,() D *% K! (; * * @ : D :2@C : * +, >" 2 _4 / 6 _. * +, >" 2_f4 / 6 _. 7 !0M! ,M > O/ ! , " #E * C ! +>, / Q / F( % K! (! ( ! ,() !&! ! * +, 2 _9 4 = ! ,M! * F R" 2_4 ? 2 5,4 S_T / F R6 _ ? - _T Z +% ! _ * R" 2_4 ? 2 5,4 S_T E 0 U . ! %() 6 ?. 9 . 9 _ - / 9 _= *% ! _. +_9 /6. ! , 7(% ! ! # %() "2_4 / @. ! , B ! ,M% K! ( = ; !&! ! > _f/ 6 / ! , "2_f4 / 6 _ / 6 2 4 /6 Z) * # 0M * >@. S 6. / . @ + . @ ?@. / 6 Q. ! () ( E) K% K ! ( * S 2 . ?6. 4 / _VV *% K! (0 % KE ! % K! ( _VV / 2@. S 6. 4 ?6. / Q _VVf/ R2@. S6. 4 S . T ? . / 6 . Q . Q $ )% K ( E ! % K! ( ! &= ! ! C ! ,M )> • 1 KD C !% % ( D C!K! ! ,() !&! ! B *;(*D + C! ,() !&! != D + C= ( % ! ,M *' Z +!8%() D *% K! (0 % K= d^ B *;(*! + D * 9 9 9 % K! (= % K = A 2_4 . E) _ = ( % K ! (! ( 2_/ d"4 YM! ,#! !+ ( 9 E) ( % K! (! ( _ ! % _VV/ , P !&! !d] * +, > K= ( C C 0 !!8; !& ! !%() D *% K ! ( = ]c %) * J'M + & E K0 C ! , !% d] E C 0M0 ' . K % K! ( * ! ( d" ]". D *% K ! ( *! ("2 4 "2 4 E ! ! )*+ => " 2 4 S " 2 4 / A 2_94 - A 2_9 - d]4 G & K C = D + C !% % D + C!K ! ! ,() !& ! !!8' *% K ! (! C !% `" % &% ! ( % K ! (! ( _9 2]`/d"4 F( % K! ( +; < C = ( ! C' " 2 4 )* + (! ,() !& ! ! * + , 7+*; ! 0 C! = > Th.s Tr n Quang Trung 20 Sưu tầm bởi: www.daihoc.com.vn