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ࢰ஼ѱ൑‫وޑ‬ӛ ӧፄᚇ‫܈‬όܴዴ‫ޑ‬௃‫ݩ‬ΠǴΓ ཮ ӵ Ֆ ຾ Չ ௢ ౛ ǻ ౜жЈ౛Ꮲ֋ນ‫ॺך‬ǴΓ ᜪ ‫ޑ‬ ᡄ ᒠ ௢ ౛ૈ Κ ѝ ࢂ ύ ΢ ำ ࡋǴԶ Ъ ѝ ଺ Α ፾ ࡋၮ Ҕ ՠ ‫ॺך‬ᒣ ᇡ ‫ ک‬ଛ ӝ ኳ Ԅ ‫ޑ‬ ૈ Κ ࠅ ຬ ம Ǵ೭ ᗺ ӧ ᄽ ϯ ΢ ߚ த Ԗ ճ Ƕ‫ॺך‬ಞ ᄍ ӧ ፄ ᚇ ‫ޑ‬ ୢ ᚒ ྽ ύ ‫ פ‬൨ ኳ Ԅ Ƕ -Brain Arthur ! ! " # $ % &' ( & )* + % &' , - # $- ! ( ( . # $ ( ! % &' / 0 )* + % ,' 1 ( . % ,' . 1 # $ 2 3 $ -1-
LTCM Ϻ ω ‫ޑ‬Ѩ ௳ 1992ԃ12ДǴ‫ ܌‬ᛥ ߐ л ‫ ׌‬Ϧ љ ȐSalomon Brothersȑ߻ ဠ ٣ ཮ ୋ Ь ৢ ऊ ᑣ ఘ ճ ࠶ ྶ ȐJohn Meriwetherȑྗഢ ಔ ᙃ ΋ ঁ ფ Є ი ໗ Ǵ຾ Ε ߎ ᑼ ѱ ൑ ት ఠ Ƕ30ԃ‫ ޑ‬ᙍ ཰ ғ ఱ ύ Ǵఘ ճ ࠶ ྶ ࢂ ঁ р Α Ӝ ‫ ޑ‬᛾ ‫ چ‬Ҭ ܰ ଯ Ћ ǴΨ ࢂ ঁ ߚ Υ ‫ ߎ ޑ‬ᑼ π ำ ৣ Ƕ ! ! . # $ ( ! . # $ 2 ! ( . 4 32 $ 3 . . ( . . 5 . !! * $ 67 8 . .* $ 66 -2-
LTCM Ϻ ω ‫ޑ‬Ѩ ௳ ఘ ճ ࠶ ȐJohn Meriwetherȑε ᖌ င ፎ Α ‫ ٿ‬Տ ᒍ ‫ ن‬ᅟ ዛ ள Ь Ǵ࿶ ᔮ ྶ Ꮲ ৎ ᗌ উ অ ථ ȐMyron Scholesȑ‫ک‬ᛥ դ ੝ ವ Ⴅ ȐRobert MertonȑǴ (Fischer Black ࡕٰ у Ε ) -3-
LTCM Ϻ ω ‫ޑ‬Ѩ ௳ ި ౻ ‫ ޑ‬ሽ ॶ ᔈ ၀ ӝ ౛ Ӧ ϸ ࢀ ΋ ৎ Ϧ љ ᕇ ճ ‫ޑ‬ ወ Κ ‫ک‬ଛ ว ި ճ ‫ ޑ‬Н ྗǶԶ ΋ ҽ ᒧ ᏷ ៾ ࠨ ऊ ‫ ޑ‬ሽ ॶ ό ໻ ໻ ‫ڗ‬ ، ‫ܭ‬ ኱ ‫ޑ‬ ި ౻ ‫ޑ‬ ሽ ਱ ǴԶ Ъ ᗋ ᆶ ࠨ ऊ ‫ډ‬ය ߻ ‫ ޑ‬೭ ΋ ԃύ ǴΓॺ ჹ ި ౻ ሽ ॶ ᅍ ຳ ‫ޑ‬ ղ ᘐ Ԗ ᜢ Ƕ ၮ Ҕ ኧ Ꮲ ‫ע‬྽ ύ ‫ ޑ‬ό ዴ ‫ࡋ ۓ‬ ᕭ λ Ǵᡣ Ҭ ܰ ঩ ჹ ‫ܭ‬ ި ౻ ሽ ਱ Ԗ ᆒ ྗ‫ޑ‬ ղ ᘐ ٩ Ᏽ Black-Scholes Model LCTMҬܰ฼ౣ ࡭ Ԗ ೏ ե ՗ ‫ޑ‬ Ԗ ሽ ᛾ ‫چ‬ ȐEX:໒ ว ύ ୯ ৎ ว Չ ‫ޑ‬ ໸ ‫چ‬ ȑ ፤ ‫ ޜ‬೏ ଯ ՗ ‫ޑ‬ Ԗ ሽ ᛾ ‫چ‬ ȐEX:ऍ ୯ ࡹ ۬ Ϧ ໸ ȑ -4-
LTCM Ϻ ω ‫ޑ‬Ѩ ௳ ଆ ߃ 1994‫5991ک‬೭ ‫ ٿ‬ԃེ ǴLTCM‫ ޑ‬ᵱ ‫ ׫‬ၗ ӣ ൔ ౗ ຬ ၸ Α 40ʘ Ƕௗ Π ٰ ‫ ޑ‬൳ ԃǴ௃ ‫ ݩ‬ຫ ٰ ຫ ӳ Ǵ‫ډ‬Α 1997ԃ‫11 ޑ‬ДǴLTCMૈ ୼ ӣ ൔ ๏ ‫׫‬ ၗ ‫ ޑ ޣ‬ຬ ᚐ ၗ ҁ ஒ ߈ 21ሹऍ ϡ Ƕ1998ԃ߃ ǴLTCM‫ ׫ע‬ၗ ಔ ӝ ቚ у ‫ډ‬Α 1300ሹऍ ϡ ǶǶ ࣮ ΢ ѐ ൩ ӳ Ⴝ LTCMว ౜ ࢌ ᅿ ё а வ ѱ ൑ డ ค ॥ ᓀ ᄧ р ᒲ ٰ ‫ޑ‬ ઝ ஏ 1994ԃΒДᕴၗౢ13ሹ ऍ ϡ 1994ԃࢂ 19.9% 1995ԃࢂ 42.8% 1996ԃࢂ 40.8% 1997ԃࢂ 17.1% LTCM‫ ޑ‬ၗౢᕴॶ ऊ 50ሹ ऍ ϡ ສ ී ߈ 1250ሹ ऍ ϡ ‫ ܫ‬ε ଄ ୍ ᄫ ఎ ຬ ၸ 20७ -5-
LTCM Ϻ ω ‫ޑ‬Ѩ ௳ 1998ԃ12ДǴѱ ൑ ว ғ Α “ཀ གྷ ό ‫ ୏ ޑ”ډ‬ᑲ Ǵ೽ ϩ চ Ӣ ࢂ җ ‫ ߮ ܭ‬ᛥ ථ ‫ ܦ‬Ж ໸ ୍ ǴᏤ ठ LTCM‫ޑ‬ ሽ ॶ ཞ Ѩ Α 90ʘ Ƕҗ ‫ ܭ‬Ԝ ໨ ୷ ߎ ᝢ ॷ ‫ޑ‬ ၗ ߎ ຬ ၸ Α 1250ሹऍ ϡ Ǵε ฽ ‫ ޑ‬ᖝ ཞ ‫ ݢ‬Ϸ Α ӄ ౚ ࿶ ᔮ Ƕ ࣁ Α ᗉ խ ߎ ᑼ ѱ ൑ ‫ ׳‬ε ጄ ൎ ‫ ޑ‬஝ ༥ Ǵફ ऊ ᖄ ٖ ᓯ ഢ ሌ Չ ಔ ӝ Α 36ሹ ऍ ߎ Ǵ‫ ڐ‬շ Ờ ֚ Ƕ LTCMҬܰ฼ౣ ວ ຾ ߮ ᛥ ථ ࡹ ۬ ໸ ‫چ‬ (Ⴃ ය ΢ ᅍ ) ፤ ‫ ޜ‬ऍ ୯ ࡹ ۬ ໸ ‫چ‬ (Ⴃ ය Π ຳ ) ่ ݀ ၶ ‫ډ‬ ߮ ᛥ ථ ᐽ К ቃ ຨ Ǵ໸ ‫ چ‬ሽ ਱ ε ຳ ၗ ߎ ෢ Ε ऍ ୯ ࡹ ۬ ໸ ‫ چ‬Ǵ໸ ‫ چ‬ሽ ਱ ε ᅍ ่ ֽ ӧ߮ ᛥ ථ ‫ ک‬ऍ ୯ ‫ ٿ‬ᓐ ᝄ ख़ ᖝ ཞ Π Ǵ LTCMઇ ౢ Ǽ 16ৎ Ϧ љ ಔ ԋ ‫ ޑ‬ሌ Չ ი ӕ ཀ ቚ ၗ 36.25 ሹ ऍ ϡ ๏ LTCMǴ٠ ௗ ᆅ LTCM FEDӧ9Дǵ10ДϷ 11 ДӚ फ़ ৲ 1ዸ (0.25%) -6-
LTCM Ϻ ω ‫ޑ‬Ѩ ௳ Ѩ ௳ ‫ޑ‬ ‫ޔ‬ ௗচ Ӣ ࢂ ߮ ᛥ ථ ϸ த ‫ޑ‬ ଄ ࡹ֚ ᜤǴؒ Ԗ ΋ ঁ Γૈ Ⴃ ਑ ‫ډ‬Ƕ LTCMϣ ೽ ‫ ޑ‬Γ ‫ ע‬೭ ൑ ߎ ᑼ ‫ ؠ‬ᜤ К բ ԭ ԃ΋ ၶ ‫ ܁ ޑ‬౦ ॥ ኪ Ǵᄛ ྄ Α д ॺ ֹ ऍ ค લ ‫ ޑ‬ᙔ კ ी Ⴤ ‫ ک‬ᆅ ౛ ೘ ᘻ Ƕ ਥ ҁ চ Ӣ ӧ Ӛ ᅿ ᜪ ࠠ ‫ ߎ ޑ‬ᑼ ѱ ൑ Ǵவ ફ ऊ ᛾ ‫ چ‬Ҭ ܰ ‫܌‬ ȐNYSEȑ‫ډ‬ ቺ ୯ ‫ޑ‬ DAXࡰ ኧ ǴӸ ӧ ๱ “ཀ ਑ ϐ Ѧ ”‫ ޑ‬ε ൯ ‫୏ ݢ‬ ਥ Ԕ ጕ ჹ ѱ ൑ ୏ ᑲ ‫ ޑ‬Ⴃ ी Ǵި ౻ ሽ ॶ ൂ В फ़ ൯ ၲ ‫01 ډ‬ʘ Ǵᔈ ၀ Ᏽ ដ ࠠ ѝ Ԗ ‫005 ؂‬ԃω ཮ ว ғ ΋ ԛ Ƕฅ Զ Ǵ౜ ჴ ‫ ޑ‬ኧ Ᏽ ࠅ ๏ р Α ΋ ঁ ‫ ׳‬ё ᎞ ‫ޑ‬ Ⴃ ෳ Ǻ‫ ؂‬ϖ ԃ൩ ཮ ว ғ ΋ ԛ ೭ ΋ ᓎ ౗ ჹ ‫ ܭ‬LTCMٰ ᇥ ϼ ‫ ז‬Α Ǵ٬ ள д ॺ ค ‫ ݤ‬ճ Ҕ Ҭ ܰ Ꮿ ౣ Ⴘ ۩ ၸ ᜢǴᝩ ុ ғ Ӹ Π ѐ Ƕ B-Sኳ ࠠ ‫ޑ‬ ख़ ा ଷ ೛ ި ౻ ሽ ਱ Չ ࣁ ܺ வ ჹ ኧ த ᄊ ϩ թ ኳ Ԅ ǹ ӧය ៾ Ԗ ਏ Ǵค ॥ ᓀ ය ϣ ճ ౗ ‫ک‬ ߎ ᑼ ၗ ౢ ԏ ੻ ᡂ ኧ ࢂ ࡡ ‫ ޑ ۓ‬ǹ ѱ ൑ ค ነ ᔔ Ǵջ όӸ ӧิ ԏ ‫ک‬ Ҭܰԋ ҁǴ‫܌‬ Ԗ ᛾ ‫ ֹ چ‬ӄ ё ϩ പ ǹ ߎ ᑼ ၗ ౢ ӧය ៾ Ԗ ਏ ය ϣ ค आ ճ Ϸ ‫ځ‬ Ѭ ‫ ܌‬ள (၀ ଷ ೛ ࡕ ೏ ‫ ܫ‬క )ǹ ި ሽ ࢂ ೱុ ‫ ޑ‬Ǵό཮ Ԗ ँ ว ‫܄‬ ި ሽ ၢ ‫ޜ‬ ௃ ‫ ݩ‬ว ғ -7-
LTCM Ϻ ω ‫ޑ‬Ѩ ௳ 1963ԃǴୗ ቺ Ѳ ࢶ ੝ȐBenoit Mandelbrotȑჹ ޲ у ঢ ୘ ཰ Ҭ ܰ ‫܌‬ ‫ޑ‬ ා ޸ ሽ ਱ ‫ޑ‬ ੌ ୏ ௃ ‫ ଺ ݩ‬Α ࣴ ‫ ز‬Ǵд ૶ ᒵ Α ኧ В ‫܈‬ ኧ ‫ڬ‬ ‫ޑ‬ ሽ ਱ ৡ ౦ Ǵ ࣮ ࣮ ሽ ਱ ᡂ ϯ ‫ ޑ‬ᓎ ౗ ࢂ ࡛ ኬ ‫ ޑ‬Ǵฅ ࡕਥ Ᏽ ኧ Ᏽ ฝ р კ ‫׎‬ Ƕд ว ౜ Α ΋ ঁ ࡐ Ⴝ ႍ ࠠ Ԕ ጕ ‫ ޑ‬ኳ Ԅ Ǵՠ Ԗ ΋ ঁ ࡐ ख़ ा ‫ޑ‬ ୔ ձ ࢂ ˇ ˇ Ԕ ጕ ‫ޑ‬ “‫ ׀‬Ѓ ”ӧ फ़ Կ 0‫ ޑ‬ၸ ำ ύ К ႍ ࠠ Ԕ ጕ ‫ ׳‬጗ ᄌ Ȑ‫ـ‬ კ ȑǶ ؒ Ԗ Һ Ֆ ଄ ࿶ ౛ ፕ ૈ ୼ ှ ញ Ꮘ ԛ ‫ ࡓ ۓ‬ᆶ ࠆ ‫ ׀‬౜ ຝ ೭ ᅿ ౜ ຝ ᆶ ่ ݀ ё ૈ ٰ Ծ ‫ ཮ ޗ ܭ‬চ η ໔ ‫ ז ޑ‬ೲ ϕ ୏ ᆶ ፾ ᔈ Ƕ -8-
Ϟ Ϻ ѐ ό ѐ Pubǻ ଚ փ ‫ޑ‬ Γό ࢂ ࡐ Ᏹ ᔒ ‫ޑ‬ ൳ ঁ ఁ ΢ Ǵ٥ ྶ ӧ ٗ‫ވ‬ ள ࡐ ໒ Ј ՠ ࢂ ‫ځ‬ д ਔ ং Ǵଚ փ ჴ ӧ ϼ ၸ Ᏹ ᔒ Ǵ০ ค ຀ ৢ ϐ Ѧ Ǵ඀ ዗ ‫ک‬Ꮣ ॣ з д Μ ϩ ᜤ‫ ڙ‬Ǵ‫ ځ‬д ΓΨ Ԗ ӕ ኬ ‫ ޑ‬ག ‫ ڙ‬Ƕ ό ۩ ‫ޑ‬ ࢂ Ǵ‫ޑ ڬ ؂‬ р ৢ Γኧ р Ε ࡐ ε Ǵؒ Ԗ ܴ ᡉ ‫ޑ‬ ኳ Ԅ ё ൻ Ǵ‫܌‬ а ، ‫ۓ‬ ѐ ‫ ۓ ، ܈‬ό ѐ ՟ Я ԋ Α ‫؂‬ ‫ ڬ‬Ѹ ໪ ଺ ‫ޑ‬ ΋ ၰ ᒧ ᏷ ᚒ Ƕд ࡐ གྷ ѐ Ǵ ՠ ࢂ ѝ Ԗ ӧ д ᇡ ࣁ ε ೽ ϩ ‫ځ‬ д Γ೿ ό ཮ ѐ ‫ޑ‬ ఁ ΢ ω ѐ Ƕ ‫ځ‬ д ഻ ៿ ٗৎ ଚ փ ‫ ޑ‬Γ೿ य़ ᖏ Α ‫ک‬д ΋ ኬ ‫ޑ‬ ᜤᚒ Ǵ‫؂‬ ঁ Γ೿ ၂ კ ଺ ε ӭ ኧ ‫ ځ‬д Γό ཮ ଺ ‫٣ ޑ‬ 89 $2 $ 8 -9-
Ϟ Ϻ ѐ ό ѐ Pubǻ ‫ע‬El Farolଚ փ ‫ޑ‬ ៝ ࠼ Ӏ ៝ ౗ ࣮ բ ΋ ᅿ Ծ ฅ ౜ ຝ Ǵ٠ ଷ ೛ գ Ѹ ໪ ‫ פ‬р ࢌ ঁ ౛ ፕ ٰ у а ှ ញ Ǵٗ᥵գ ཮ ࡛ ᥵଺ ‫ګ‬ ǻ २ Ӄ Ǵգ Ѹ ໪ Ԗ ঁ ኳ ࠠ Ǵё а ኳ ᔕ Γॺ ӵ Ֆ ଺ ، ‫ۓ‬ ‫ ځ‬ԛ Ѹ ໪ ‫ޕ‬ ၰ д ॺ ࢂ ٩ Ᏽ ϙ ሶ ၗ ૻ Ǵٰ ղ ᘐ ଚ փ ࢂ ց Ᏹ ᔒ Ԝ Ѧ Ǵᗋ Ѹ ໪ Ե ቾ ‫ډ‬Ǵό ࢂ ‫؂‬ ঁ Γ‫ ޑ‬གྷ ‫ݤ‬ ೿ ࣬ ӕ Ǵό ӕ ‫ ޑ‬Γ཮ ਥ Ᏽ ό ӕ ‫ ޑ‬চ ߾ ٰ ଺ ، ‫ ۓ‬Ƕ 8 -10-
Ϟ Ϻ ѐ ό ѐ Pubǻ ٥ ྶ ම ࿶ ᠐ ‫ډ‬΋ ጇ 60ԃж ᙑ ൔ ર ΢ ‫ޑ‬ Ў ക Ǵբ ‫ࢂ ޣ‬ Julian Feldman ຤ ᅟ ቺ ୗ ᇡ ࣁ ǴΓࡐ Ͽ ٩ ᎞ ᡄ ᒠ Ե ٰ ଺ ࡘ ، ‫ۓ‬ ǴԶ ೸ ၸ ᙁ ൂ ‫ ޑ‬ೕ ߾ Ϸ ჋ ၂ ᒱ ᇤ ᒱ ᇤ ύ Ꮲ ಞ ǹ੝ ձ ࢂ Γॺ ಞ ᄍ வ ᕉ ნ ύ ᒣ ձ ኳ Ԅ Ǵ٠ ճ Ҕ ೭ ٤ ኳ Ԅ Ⴃ ෳ ௗΠ ٰ ཮ ว ғ ϙ ᥵Ƕ ި ѱ ‫ޑ‬ ӭ ‫ޜ‬ ‫܈‬ ଚ փ ࢂ ց Ᏹ ᔒ Ǵ೿ Ӛ Ծ Ԗ ΋ ঺ ӝ Я ᡄ ᒠ ‫ޑ‬ ࣮ ‫ݤ‬ ‫܈‬ ኳ Ԅ Γό ࢂ ԝ တ โ ‫ ޑ‬໿ Ґ Ǵᒱ ᇤ ‫” ޑ‬౛ ፕ ”཮ ೏ ‫ ܫ‬క ΋ ૓ Γ‫ޑ‬ ᓐ တ ӧ ӕ ΋ ਔ ‫཮ څ‬ р ౜ ೚ ӭ ᅿ ଷ ೛ Ǵௗ๱ ӆ ਥ Ᏽ ྽ Π ന ӝ ౛ ‫ޑ‬ ଷ ೛ ٰ ଺ р ، ‫ ۓ‬Ƕ೭ ΋ ᗺ ᡉ ฅ ᆶ ‫ ޑ ॺ ך‬В த ࿶ ᐕ ࣬ ֍ ӝ Ƕ => ჋ ၂ ࣮ ࣮ Ǵӆ வ Չ ୏ ύ Ꮲ ಞ ᆶ ፾ ᔈ 8: ; . 8 : < < 8: 7 $& < -11- 77
Ϟ Ϻ ѐ ό ѐ Pubǻ ᙖ ख़ ႝ တ ኳᔕ ᆶ ж ౛ Γ ന ӳ చ ҹ ǺΓኧ ό ӭ (<60Γ)‫ޑ‬ ௃ ‫ݩ‬ Π ‫ډ‬ଚ փ സ ΋ ݆ Ǵӵ ݀ Γϼ ӭ ߾ ࡑ ӧ ৎ ္ ೛ ‫ۓ‬ Ӛ ᅿ ଷ ೛ చ ҹ Ǵ٩ Ᏽ ന ߈ ൳ ຼ ‫ޑ‬ Ⴃ ෳ ่ ݀ Ǵᒧ Ҕ ന ӳ ‫ޑ‬ ΋ ঁ ٰ ، ‫ۓ‬ ѐ ‫܈‬ ό ѐ ΢ ‫ڬ‬ ؒ Ԗ ၸ ࡋ Ᏹ ᔒ ǵҁ ຼ ΋ ‫ۓ‬ ཮ Ᏹ ᔒ ೱ ុ Ο ຼ ၸ ࡋ Ᏹ ᔒ Ǵҁ ຼ ω ཮ Ᏹ ᔒ -12-
Ϟ Ϻ ѐ ό ѐ Pubǻ ӧ ೭ ঁᖻ ֽ ္ ೿ གྷ ྽ Ͽ ኧ (ި ౻ ѱ ൑ ҭ ӕ )Ǻ ε ৎ ձ Γѐ ଚ փ ਔ Ǵ‫ ࡑ ך‬ӧ ৎ ္ (ϸ ϐ ҭ ӕ ) ଷ ೛ Ԗ ࢌ ᅿ ೕ ߾ ‫ ܈‬ኳ Ԅ ૈ ᡣ ࢌ ٤ Ͽ ኧ Γၲ ԋ а ΢ Ҟ ኱ Ǵ΋ ࢤ ਔ ໔ ࡕǴ‫ ځ‬д Γ཮ ‫ ݙ‬ཀ ‫ډ‬೭ ঁ ೕ ߾ Ǵ຾ Զ ፓ ፾ ‫ک‬௦ Ҕ Ԝ ΋ ೕ ߾ Ǵ‫ܭ‬ ࢂ চ ҁ ᕇ ճ ‫ޑ‬ Ͽ ኧ ᡂ ԋ ӭ ኧ Ǵ໣ ᡏ ‫ ޑ‬ፓ ፾ Չ ࣁ ᄛ ྄ Α চ ٰ Ԗ ਏ ‫ ޑ‬ኳ Ԅ Ƕ -13-
౜ ж གྷ ‫ݤ‬ VS໺ ಍ གྷ ‫ݤ‬ ໺ ಍ གྷ ‫ ݤ‬Ǻ Black-Scholes Model (LTCM) / CAPM ‫ ೌ מ‬ϩ ‫( ݋‬ጕ и )Ǻ࣮ ި ሽ ‫ و‬༈ კ ǵҾ კ ‫ פ‬р ኳ Ԅ ᔅ շ Ծ ρ Ⴃ ෳ ҂ ٰ ި ሽ ‫ و‬༈ =࣮ ၸ ѐ ଚ փ ‫ ޑ‬р ৢ Γኧ ٰ Ⴃ ෳ ҂ ٰ р ৢ Γኧ Ҕ ӕ ኬ ‫ޑ‬ ᡄ ᒠ ٰ ኳ ᔕ ި ౻ ѱ ൑ చ ҹ Ǻ ວ ‫ޑ‬ Γ>፤ ‫ޑ‬ Γ => ި ሽ ΢ ᅍ (ϸ ϐ ҭ ฅ ) ‫؂‬ ঁ ႝ တ ж ౛ Γ(‫ ׫‬ၗ ‫) ޣ‬ё а ௦ ‫ ڗ‬྽ ਔ Ծ ᇡ ࣁ ന ӳ ‫ޑ‬ ೕ ߾ ၸ ѐ ‫ި ޑ‬ ሽ ኳ Ԅ ཮ ቹ ៜ ‫ ׫‬ၗ Γ౜ ӧ ‫ ޑ‬Չ ࣁ ౜ ӧ ‫ ޑ‬ວ ፤ ، ฼ (ᆶ ‫ ٮ‬ሡ ό ѳᑽ)Ǵ཮ ٬ ި ሽ ౢ ғ ᡂ ୏ ౢ ғ Α ΋ ᅿ ό ᘐ ൻ ᕉ ‫ ޑ‬Ӣ ݀ ᜢ ߯ -14-
౜ ж གྷ ‫ݤ‬ VS໺ ಍ གྷ ‫ݤ‬ ި ౻ ѱ ൑ ኳ ᔕ ่ ݀ Ǻ ި ሽ ᕏ а ό ೕ ߾ ‫ޑ‬ Б Ԅ ΢ Π ᎜ ᎜ ᕏ ᡂ ౦ চ Ӣ ٰ Ծ ‫ ܭ‬ж ౛ Γ(‫ ׫‬ၗ Γ)໔ ‫ޑ‬ ϕ ୏ ᆶ ፓ ፾ ǹԶ ߚ Ѧ ೽ ፂ ᔐ(ӵ ߮ ᛥ ථ ໸ ୍ ֚ ᜤ฻ Ѧ ೽ ख़ ε ٣ ҹ ) ި ሽ ‫ ޑ‬ᡂ ౦ Ԗ “ࠆ ‫ ݀ ่ ޑ” ׀‬౜ ຝ ่ ݀ ఼ က ࠆ ‫׀‬ ౜ ຝ Ǵค ‫ݤ‬ ٬ Ҕ ౛ ‫܄‬ Չ ࣁ ຾ Չ ှ ញ ᔈ ၀ ”፾ ᔈ Ꮲ ಞ ”ٰ ‫ ڗ‬ж ό ӝ ౛ ‫ ֹ” ޑ‬ӄ ౛ ‫” ܄‬ ٬ Ҕ ࣮ ՟ ӝ ౛ ‫ޑ‬ ࠆ ‫ ׀‬౜ ຝ ࢂ Ծ ฅ ੌ ౜ Ǵό ࢂ Ѧ ೽ ፂ ᔐ‫ ܌‬೷ ԋ Ǵҭ ߚ Һ Ֆ ΓՉ ୏ ‫ૈ ܌‬ Ѱ ѓ ද ၹ Ӹ ӧ ‫ ܭ‬Ӛ ᅿ ѱ ൑ ‫ ޑ‬ሽ ਱ ε ൯ ‫୏ݢ‬ᡂ౦౜ຝǴଆ ྍ ‫ ܭ‬Γ ᜪ ‫္ ཮ ޗ‬ ‫୏ݢ‬ᡂ౦౜ຝǴ ‫ ޑ‬চ η Ǵӵ Ֆ Ծ ‫ ך‬ಔ ᙃ ԋ ࣬ ϕ ٩ Ӹ ‫ ޑ‬ಒ ጏ ኳ Ԅ Ƕ -15-
౜ ж གྷ ‫ݤ‬ VS໺ ಍ གྷ ‫ݤ‬ ഡ ճ ୗ Ǻ ੿ ҅ ख़ ा Զ Ξ Ԗ ཀ က ‫ޑ‬ ଷ Ǵ஥ Ԗ ೚ ӭ ᇥ ”ଷ ೛ చ ҹ ”… ଷ ᇥ ૈ ୼ а ࡐ Ͽ ‫ޑ‬ ܿ Ջ ”ှ ញ ”ࡐ ӭ ٣ ௃ Ѭ வ ࡑ ှ ញ ‫ޑ‬ ᕷ ᚇ ౜ ຝ ‫ ڬ‬ൎ Ǵ‫ ܜ‬ᚆ р ख़ ा ‫ޑ‬ ϡ ન Ǵ‫ך‬ ॺ ω ૈ ᙖ Ԝ ଺ р Ԗ ਏ ‫ޑ‬ Ⴃ ෳ Ӣ Ԝ ख़ ा ଷ ᇥ ౛ ፕ ེ ‫ޑ‬ ଷ ೛ ഋ ॊ ΋ ‫ۓ‬ ό ҅ ዴ ౛ ‫܄‬ Γଷ ᇥ ེ ‫ޑ‬ ᒱ ᇤ ଷ ೛ Γό ཮ Ꮲ ಞ Γό ཮ ‫ׯ‬ ᡂ Ј ཀ Γό ཮ ࢎ ೛ р ଷ ᇥ ٠ у а ෳ ၂ ό Ե ቾ ੿ ჴ Ш ࣚ ྽ ύ ‫ޑ‬ Γᜪ Չ ࣁ ੝ ፦ ଷ ೛ ”Γ‫ ޑ‬Չ ࣁ Ԗ ፾ ᔈ Κ ”ǴК ଷ ೛ ”Γࢂ ౛ ‫ޑ ܄‬ ”Ǵ‫ ׳‬ຠ ߈ ౜ ჴ Ǽ ѱ ൑ ౜ ຝ ᜤа ှ ှ ‫ک‬Ⴃ ෳ Ǵό ࢂ ঁ ᡏ ‫ޑ‬ ፄ ᚇ ‫܄‬ ǴԶ ࢂ ѱ ൑ ္ ೚ ӭ Γ ϐ ໔ ‫ޑ‬ ༾ ֮ ‫ރ‬ ᄊ ‫ک‬ಔ ᙃ ᜢ ᗖ ӧ ኳ Ԅ ǴԶ ߚ Γ Ǽ -16-
Ⴃ ‫ޕ‬ ҂ ٰ ૈցႣෳ҂ٰ‫៏ݾޑ‬ ൳ Я ό Ӹ ӧ ё а ԋ ф Ⴃ ෳ ߎ ᑼ ѱ ൑ ‫ ޑ‬Б ‫ ݤ‬ǻ ࣽ Ꮲ ό ୼ Ӄ ຾ ǵ‫ ݩ ރ‬ϼ ፄ ᚇ Ǵό ‫ ى‬а ଺ р Ⴃ ෳ ǻ Ͽ ኧ ‫ ޣ‬ᖻ ֽ ‫ ঁ ؂‬Γ ‫ ؂‬ԛ ᒧ 0‫1܈‬ Ҟ ኱ ࢂ ԋ ࣁ Ͽ ኧ (ᒧ ‫ ډ‬ӭ ኧ Γ ؒ ᒧ ‫ ޑ‬ኧ ӷ ) ӧ Ͽ ኧ ‫ޣ‬ ᖻ ֽ ္ ǴΓ ኧ ቚ у Ǵ٣ ௃ ཮ ᡂ ள ࡐ ό ΋ ኬ ୖ ᖻ Γ ኧ ӵ ݀ ό ӭ Ǵ‫ ވ‬ৎ ‫ ฼ ޑ‬ౣ ό ӭ Ǵό ‫ ى‬а ఼ ᇂ ‫܌‬ Ԗ ё ૈ ‫ޑ‬ ኳ Ԅ ఼ ё Ⴃ က ǺԖ ෳ ‫ޑ‬ ኳ Ԅ (ѱ ൑ Ӹ ӧ ё Ⴃ ෳ ‫܄‬ )Ǵࠅ ؒ Γ ‫ ޕ‬ၰ =>่ ݀ (ѱ ൑ ሽ ਱ ᡂ ୏ )཮ ٩ Ᏽ ё Ⴃ ෳ ‫ ޑ‬ኳ Ԅ ‫و‬ ୖ ᖻ Γ ኧ ӭ Ǵ‫ވ‬ ৎ ‫฼ ޑ‬ ౣ ཮ ఼ ᇂ ‫ ܌‬Ԗ ё ૈ ‫ޑ‬ ኳ Ԅ ǴҺ Ֆ ё а Ⴃ ෳ ่ ݀ ‫ ޑ‬ኳ Ԅ ೿ ཮ ೏ ว ౜ ǴԶ Ъ ҥ ‫ څ‬௦ Ҕ ఼ က Ǻӵ ݀ ੿ ‫ ޑ‬Ԗ Γ ૈ ୼ ό മ Զ ᕇ Ǵ൩ ཮ ֎ Ї ‫ ׳‬ӭ Γ ຾ ΕǴՠ ‫ ؂‬຾ ٰ ΋ ঁ Γ ൩ ཮ ஥ ຾ ཥ ‫ޑ‬ ฼ ౣ Ǵ‫ ע‬೭ ٤ Ͽ ໆ ‫ޑ‬ ё Ⴃ ෳ ‫܄‬ Ӟ ௞ Ƕ (ѱ ൑ όӸ ӧ ё Ⴃ ෳ ‫) ܄‬ Damien Challet -17-
Ⴃ ‫ޕ‬ ҂ ٰ ம ғ (Neil Johnson)Ǻ ӵ ݀ ѱ ൑ (ଽ Զ )Ӹ ӧ ё Ⴃ ෳ ‫ ܄‬ǴٗԖ ؒ Ԗ Б ‫ ݤ‬ё а ୀ ෳ ‫ډ‬ǻ ่ ݀ д ॺ ‫ ޑ‬ኳ ࠠ ё а ୀ ෳ р Ǻѱ ൑ ӧ ࢌ ٤ ਔ ‫ څ‬К ‫ ځ‬д ਔ ‫څ‬ ‫׳‬ Ԗ Ⴃ ෳ ‫܄‬ ё Ⴃ ෳ ୔ ໔ (฼ ౣ ኧ Ҟ ෧ Ͽ ) 2 0 % .* 5 $ 2 ! 8 Ԗ Γ ଏ р ѱ ൑ 0 . $ $ .' ೚ ӭ Γ ٬ Ҕ Α ӕ ኬ ‫฼ ޑ‬ ౣ ) 5 # $= В ༝ ի ऍ ϡ ༊ ౗ 4000ԛ ‫ޑ‬ ሽ ਱ ᡂ ୏ ᒣ ᛽ р ΐ Μ ӭ ঁ ё Ⴃ ය ୔ * $ ໔ǵΨ Ⴃ ෳ р ‫ځ‬ ᡂ ϯ Б ӛ Ǵѝ Ԗ ΋ ԛ Ⴃ ෳ ᒱ ᇤ ӵ ݀ ೭ ᅿ (Ⴃ ෳ )ԋ ф ᡂ ԋ த ᄊ Ǵࡕ݀ ё ૈ ཮ ࡐ ။ ౦ 2 .* 5 $ 8 ε Њ ௦ Ҕ Ԝ ΋ Б ‫ݤ‬ =>‫ ׯ‬ᡂ ѱ ൑ ҁ ፦ =>ᄛ ྄ ೭ ໨ ‫ ޑ ೌ מ‬Ⴃ ෳ 2 0 $ ૈ Κ ! ( . <7 7, * 8 * $ ! * 2 .* 5 $ # $ ( . % $ 0*' / -18-
፾ ᔈ ҁ ሦ ຬ ம ‫ޑ‬ᐒ ཮ Ь က ‫ޣ‬ ѱ ൑ Ⴄ ‫ڰ‬ Һ ‫܄‬ (ό ౛ ‫܄‬ )‫ ޑ‬ୢ ᚒ ᆶ ࠆ ‫ ׀‬౜ ຝ ‫ ޑ‬ှ เ ό ࢂ ঁ ᡏ ‫ޑ‬ ‫ޑ‬ ፄ ᚇ ‫܄‬ Ψ ό ࢂ Γ Ԗ ᆟஏ‫ޑ‬ ࡘགྷ‫܈‬੝ਸಞᄍ(ୃ ӳ ) Զ ࢂ ࣮ Γ ᜪ Չ ࣁ ‫ޑ‬ ᙁ ൂ ‫܄‬ ᆶ ϕ ୏ (ኳ ү ǵ၂ ᇤ ǵ፾ ᔈ ) Γᜪ ό ࢂ ᎞ ౛ ‫܄‬ ࡘ Ե ٰ Ꮲ ಞ ྎ ೯ ‫ک‬ᇟ ‫ق‬ ᇟ ‫ق‬ ࢂ ፾ ᔈ ၸ ำ ‫ޑ‬ ౢ ‫ނ‬ ǴΨ ࢂ ᄽ ϯ ‫ޑ‬ ၸ ำ ӵ ݀ ೭ ᅿ (Ⴃ ෳ )ԋ ф ᡂ ԋ த ᄊ Ǵࡕ݀ ё ૈ ཮ ࡐ ။ ౦ ѱ ൑ ္ Һ Ֆ ό ᘐ ᙯ ᡂ ‫ޑ‬ ࡘ གྷ ‫ߞک‬ ‫ۺ‬ (ཀ ᛽ ࠠ ᄊ )ᡏ ‫ س‬Ǵ೿ ࢂ ‫ ॺ ך‬፾ ᔈ Κ ബ ೷ р ٰ ‫ޑ‬ ౢ ‫ނ‬ -19-

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Hidden logic

  • 1.
    ࢰ஼ѱ൑‫وޑ‬ӛ ӧፄᚇ‫܈‬όܴዴ‫ޑ‬௃‫ݩ‬ΠǴΓ ཮ ӵ Ֆ ຾ Չ ௢ ౛ ǻ ౜жЈ౛Ꮲ֋ນ‫ॺך‬ǴΓ ᜪ ‫ޑ‬ ᡄ ᒠ ௢ ౛ૈ Κ ѝ ࢂ ύ ΢ ำ ࡋǴԶ Ъ ѝ ଺ Α ፾ ࡋၮ Ҕ ՠ ‫ॺך‬ᒣ ᇡ ‫ ک‬ଛ ӝ ኳ Ԅ ‫ޑ‬ ૈ Κ ࠅ ຬ ம Ǵ೭ ᗺ ӧ ᄽ ϯ ΢ ߚ த Ԗ ճ Ƕ‫ॺך‬ಞ ᄍ ӧ ፄ ᚇ ‫ޑ‬ ୢ ᚒ ྽ ύ ‫ פ‬൨ ኳ Ԅ Ƕ -Brain Arthur ! ! " # $ % &' ( & )* + % &' , - # $- ! ( ( . # $ ( ! % &' / 0 )* + % ,' 1 ( . % ,' . 1 # $ 2 3 $ -1-
  • 2.
    LTCM Ϻ ω‫ޑ‬Ѩ ௳ 1992ԃ12ДǴ‫ ܌‬ᛥ ߐ л ‫ ׌‬Ϧ љ ȐSalomon Brothersȑ߻ ဠ ٣ ཮ ୋ Ь ৢ ऊ ᑣ ఘ ճ ࠶ ྶ ȐJohn Meriwetherȑྗഢ ಔ ᙃ ΋ ঁ ფ Є ი ໗ Ǵ຾ Ε ߎ ᑼ ѱ ൑ ት ఠ Ƕ30ԃ‫ ޑ‬ᙍ ཰ ғ ఱ ύ Ǵఘ ճ ࠶ ྶ ࢂ ঁ р Α Ӝ ‫ ޑ‬᛾ ‫ چ‬Ҭ ܰ ଯ Ћ ǴΨ ࢂ ঁ ߚ Υ ‫ ߎ ޑ‬ᑼ π ำ ৣ Ƕ ! ! . # $ ( ! . # $ 2 ! ( . 4 32 $ 3 . . ( . . 5 . !! * $ 67 8 . .* $ 66 -2-
  • 3.
    LTCM Ϻ ω‫ޑ‬Ѩ ௳ ఘ ճ ࠶ ȐJohn Meriwetherȑε ᖌ င ፎ Α ‫ ٿ‬Տ ᒍ ‫ ن‬ᅟ ዛ ள Ь Ǵ࿶ ᔮ ྶ Ꮲ ৎ ᗌ উ অ ථ ȐMyron Scholesȑ‫ک‬ᛥ դ ੝ ವ Ⴅ ȐRobert MertonȑǴ (Fischer Black ࡕٰ у Ε ) -3-
  • 4.
    LTCM Ϻ ω‫ޑ‬Ѩ ௳ ި ౻ ‫ ޑ‬ሽ ॶ ᔈ ၀ ӝ ౛ Ӧ ϸ ࢀ ΋ ৎ Ϧ љ ᕇ ճ ‫ޑ‬ ወ Κ ‫ک‬ଛ ว ި ճ ‫ ޑ‬Н ྗǶԶ ΋ ҽ ᒧ ᏷ ៾ ࠨ ऊ ‫ ޑ‬ሽ ॶ ό ໻ ໻ ‫ڗ‬ ، ‫ܭ‬ ኱ ‫ޑ‬ ި ౻ ‫ޑ‬ ሽ ਱ ǴԶ Ъ ᗋ ᆶ ࠨ ऊ ‫ډ‬ය ߻ ‫ ޑ‬೭ ΋ ԃύ ǴΓॺ ჹ ި ౻ ሽ ॶ ᅍ ຳ ‫ޑ‬ ղ ᘐ Ԗ ᜢ Ƕ ၮ Ҕ ኧ Ꮲ ‫ע‬྽ ύ ‫ ޑ‬ό ዴ ‫ࡋ ۓ‬ ᕭ λ Ǵᡣ Ҭ ܰ ঩ ჹ ‫ܭ‬ ި ౻ ሽ ਱ Ԗ ᆒ ྗ‫ޑ‬ ղ ᘐ ٩ Ᏽ Black-Scholes Model LCTMҬܰ฼ౣ ࡭ Ԗ ೏ ե ՗ ‫ޑ‬ Ԗ ሽ ᛾ ‫چ‬ ȐEX:໒ ว ύ ୯ ৎ ว Չ ‫ޑ‬ ໸ ‫چ‬ ȑ ፤ ‫ ޜ‬೏ ଯ ՗ ‫ޑ‬ Ԗ ሽ ᛾ ‫چ‬ ȐEX:ऍ ୯ ࡹ ۬ Ϧ ໸ ȑ -4-
  • 5.
    LTCM Ϻ ω‫ޑ‬Ѩ ௳ ଆ ߃ 1994‫5991ک‬೭ ‫ ٿ‬ԃེ ǴLTCM‫ ޑ‬ᵱ ‫ ׫‬ၗ ӣ ൔ ౗ ຬ ၸ Α 40ʘ Ƕௗ Π ٰ ‫ ޑ‬൳ ԃǴ௃ ‫ ݩ‬ຫ ٰ ຫ ӳ Ǵ‫ډ‬Α 1997ԃ‫11 ޑ‬ДǴLTCMૈ ୼ ӣ ൔ ๏ ‫׫‬ ၗ ‫ ޑ ޣ‬ຬ ᚐ ၗ ҁ ஒ ߈ 21ሹऍ ϡ Ƕ1998ԃ߃ ǴLTCM‫ ׫ע‬ၗ ಔ ӝ ቚ у ‫ډ‬Α 1300ሹऍ ϡ ǶǶ ࣮ ΢ ѐ ൩ ӳ Ⴝ LTCMว ౜ ࢌ ᅿ ё а வ ѱ ൑ డ ค ॥ ᓀ ᄧ р ᒲ ٰ ‫ޑ‬ ઝ ஏ 1994ԃΒДᕴၗౢ13ሹ ऍ ϡ 1994ԃࢂ 19.9% 1995ԃࢂ 42.8% 1996ԃࢂ 40.8% 1997ԃࢂ 17.1% LTCM‫ ޑ‬ၗౢᕴॶ ऊ 50ሹ ऍ ϡ ສ ී ߈ 1250ሹ ऍ ϡ ‫ ܫ‬ε ଄ ୍ ᄫ ఎ ຬ ၸ 20७ -5-
  • 6.
    LTCM Ϻ ω‫ޑ‬Ѩ ௳ 1998ԃ12ДǴѱ ൑ ว ғ Α “ཀ གྷ ό ‫ ୏ ޑ”ډ‬ᑲ Ǵ೽ ϩ চ Ӣ ࢂ җ ‫ ߮ ܭ‬ᛥ ථ ‫ ܦ‬Ж ໸ ୍ ǴᏤ ठ LTCM‫ޑ‬ ሽ ॶ ཞ Ѩ Α 90ʘ Ƕҗ ‫ ܭ‬Ԝ ໨ ୷ ߎ ᝢ ॷ ‫ޑ‬ ၗ ߎ ຬ ၸ Α 1250ሹऍ ϡ Ǵε ฽ ‫ ޑ‬ᖝ ཞ ‫ ݢ‬Ϸ Α ӄ ౚ ࿶ ᔮ Ƕ ࣁ Α ᗉ խ ߎ ᑼ ѱ ൑ ‫ ׳‬ε ጄ ൎ ‫ ޑ‬஝ ༥ Ǵફ ऊ ᖄ ٖ ᓯ ഢ ሌ Չ ಔ ӝ Α 36ሹ ऍ ߎ Ǵ‫ ڐ‬շ Ờ ֚ Ƕ LTCMҬܰ฼ౣ ວ ຾ ߮ ᛥ ථ ࡹ ۬ ໸ ‫چ‬ (Ⴃ ය ΢ ᅍ ) ፤ ‫ ޜ‬ऍ ୯ ࡹ ۬ ໸ ‫چ‬ (Ⴃ ය Π ຳ ) ่ ݀ ၶ ‫ډ‬ ߮ ᛥ ථ ᐽ К ቃ ຨ Ǵ໸ ‫ چ‬ሽ ਱ ε ຳ ၗ ߎ ෢ Ε ऍ ୯ ࡹ ۬ ໸ ‫ چ‬Ǵ໸ ‫ چ‬ሽ ਱ ε ᅍ ่ ֽ ӧ߮ ᛥ ථ ‫ ک‬ऍ ୯ ‫ ٿ‬ᓐ ᝄ ख़ ᖝ ཞ Π Ǵ LTCMઇ ౢ Ǽ 16ৎ Ϧ љ ಔ ԋ ‫ ޑ‬ሌ Չ ი ӕ ཀ ቚ ၗ 36.25 ሹ ऍ ϡ ๏ LTCMǴ٠ ௗ ᆅ LTCM FEDӧ9Дǵ10ДϷ 11 ДӚ फ़ ৲ 1ዸ (0.25%) -6-
  • 7.
    LTCM Ϻ ω‫ޑ‬Ѩ ௳ Ѩ ௳ ‫ޑ‬ ‫ޔ‬ ௗচ Ӣ ࢂ ߮ ᛥ ථ ϸ த ‫ޑ‬ ଄ ࡹ֚ ᜤǴؒ Ԗ ΋ ঁ Γૈ Ⴃ ਑ ‫ډ‬Ƕ LTCMϣ ೽ ‫ ޑ‬Γ ‫ ע‬೭ ൑ ߎ ᑼ ‫ ؠ‬ᜤ К բ ԭ ԃ΋ ၶ ‫ ܁ ޑ‬౦ ॥ ኪ Ǵᄛ ྄ Α д ॺ ֹ ऍ ค લ ‫ ޑ‬ᙔ კ ी Ⴤ ‫ ک‬ᆅ ౛ ೘ ᘻ Ƕ ਥ ҁ চ Ӣ ӧ Ӛ ᅿ ᜪ ࠠ ‫ ߎ ޑ‬ᑼ ѱ ൑ Ǵவ ફ ऊ ᛾ ‫ چ‬Ҭ ܰ ‫܌‬ ȐNYSEȑ‫ډ‬ ቺ ୯ ‫ޑ‬ DAXࡰ ኧ ǴӸ ӧ ๱ “ཀ ਑ ϐ Ѧ ”‫ ޑ‬ε ൯ ‫୏ ݢ‬ ਥ Ԕ ጕ ჹ ѱ ൑ ୏ ᑲ ‫ ޑ‬Ⴃ ी Ǵި ౻ ሽ ॶ ൂ В फ़ ൯ ၲ ‫01 ډ‬ʘ Ǵᔈ ၀ Ᏽ ដ ࠠ ѝ Ԗ ‫005 ؂‬ԃω ཮ ว ғ ΋ ԛ Ƕฅ Զ Ǵ౜ ჴ ‫ ޑ‬ኧ Ᏽ ࠅ ๏ р Α ΋ ঁ ‫ ׳‬ё ᎞ ‫ޑ‬ Ⴃ ෳ Ǻ‫ ؂‬ϖ ԃ൩ ཮ ว ғ ΋ ԛ ೭ ΋ ᓎ ౗ ჹ ‫ ܭ‬LTCMٰ ᇥ ϼ ‫ ז‬Α Ǵ٬ ள д ॺ ค ‫ ݤ‬ճ Ҕ Ҭ ܰ Ꮿ ౣ Ⴘ ۩ ၸ ᜢǴᝩ ុ ғ Ӹ Π ѐ Ƕ B-Sኳ ࠠ ‫ޑ‬ ख़ ा ଷ ೛ ި ౻ ሽ ਱ Չ ࣁ ܺ வ ჹ ኧ த ᄊ ϩ թ ኳ Ԅ ǹ ӧය ៾ Ԗ ਏ Ǵค ॥ ᓀ ය ϣ ճ ౗ ‫ک‬ ߎ ᑼ ၗ ౢ ԏ ੻ ᡂ ኧ ࢂ ࡡ ‫ ޑ ۓ‬ǹ ѱ ൑ ค ነ ᔔ Ǵջ όӸ ӧิ ԏ ‫ک‬ Ҭܰԋ ҁǴ‫܌‬ Ԗ ᛾ ‫ ֹ چ‬ӄ ё ϩ പ ǹ ߎ ᑼ ၗ ౢ ӧය ៾ Ԗ ਏ ය ϣ ค आ ճ Ϸ ‫ځ‬ Ѭ ‫ ܌‬ள (၀ ଷ ೛ ࡕ ೏ ‫ ܫ‬క )ǹ ި ሽ ࢂ ೱុ ‫ ޑ‬Ǵό཮ Ԗ ँ ว ‫܄‬ ި ሽ ၢ ‫ޜ‬ ௃ ‫ ݩ‬ว ғ -7-
  • 8.
    LTCM Ϻ ω‫ޑ‬Ѩ ௳ 1963ԃǴୗ ቺ Ѳ ࢶ ੝ȐBenoit Mandelbrotȑჹ ޲ у ঢ ୘ ཰ Ҭ ܰ ‫܌‬ ‫ޑ‬ ා ޸ ሽ ਱ ‫ޑ‬ ੌ ୏ ௃ ‫ ଺ ݩ‬Α ࣴ ‫ ز‬Ǵд ૶ ᒵ Α ኧ В ‫܈‬ ኧ ‫ڬ‬ ‫ޑ‬ ሽ ਱ ৡ ౦ Ǵ ࣮ ࣮ ሽ ਱ ᡂ ϯ ‫ ޑ‬ᓎ ౗ ࢂ ࡛ ኬ ‫ ޑ‬Ǵฅ ࡕਥ Ᏽ ኧ Ᏽ ฝ р კ ‫׎‬ Ƕд ว ౜ Α ΋ ঁ ࡐ Ⴝ ႍ ࠠ Ԕ ጕ ‫ ޑ‬ኳ Ԅ Ǵՠ Ԗ ΋ ঁ ࡐ ख़ ा ‫ޑ‬ ୔ ձ ࢂ ˇ ˇ Ԕ ጕ ‫ޑ‬ “‫ ׀‬Ѓ ”ӧ फ़ Կ 0‫ ޑ‬ၸ ำ ύ К ႍ ࠠ Ԕ ጕ ‫ ׳‬጗ ᄌ Ȑ‫ـ‬ კ ȑǶ ؒ Ԗ Һ Ֆ ଄ ࿶ ౛ ፕ ૈ ୼ ှ ញ Ꮘ ԛ ‫ ࡓ ۓ‬ᆶ ࠆ ‫ ׀‬౜ ຝ ೭ ᅿ ౜ ຝ ᆶ ่ ݀ ё ૈ ٰ Ծ ‫ ཮ ޗ ܭ‬চ η ໔ ‫ ז ޑ‬ೲ ϕ ୏ ᆶ ፾ ᔈ Ƕ -8-
  • 9.
    Ϟ Ϻ ѐ ό ѐ Pubǻ ଚ փ ‫ޑ‬ Γό ࢂ ࡐ Ᏹ ᔒ ‫ޑ‬ ൳ ঁ ఁ ΢ Ǵ٥ ྶ ӧ ٗ‫ވ‬ ள ࡐ ໒ Ј ՠ ࢂ ‫ځ‬ д ਔ ং Ǵଚ փ ჴ ӧ ϼ ၸ Ᏹ ᔒ Ǵ০ ค ຀ ৢ ϐ Ѧ Ǵ඀ ዗ ‫ک‬Ꮣ ॣ з д Μ ϩ ᜤ‫ ڙ‬Ǵ‫ ځ‬д ΓΨ Ԗ ӕ ኬ ‫ ޑ‬ག ‫ ڙ‬Ƕ ό ۩ ‫ޑ‬ ࢂ Ǵ‫ޑ ڬ ؂‬ р ৢ Γኧ р Ε ࡐ ε Ǵؒ Ԗ ܴ ᡉ ‫ޑ‬ ኳ Ԅ ё ൻ Ǵ‫܌‬ а ، ‫ۓ‬ ѐ ‫ ۓ ، ܈‬ό ѐ ՟ Я ԋ Α ‫؂‬ ‫ ڬ‬Ѹ ໪ ଺ ‫ޑ‬ ΋ ၰ ᒧ ᏷ ᚒ Ƕд ࡐ གྷ ѐ Ǵ ՠ ࢂ ѝ Ԗ ӧ д ᇡ ࣁ ε ೽ ϩ ‫ځ‬ д Γ೿ ό ཮ ѐ ‫ޑ‬ ఁ ΢ ω ѐ Ƕ ‫ځ‬ д ഻ ៿ ٗৎ ଚ փ ‫ ޑ‬Γ೿ य़ ᖏ Α ‫ک‬д ΋ ኬ ‫ޑ‬ ᜤᚒ Ǵ‫؂‬ ঁ Γ೿ ၂ კ ଺ ε ӭ ኧ ‫ ځ‬д Γό ཮ ଺ ‫٣ ޑ‬ 89 $2 $ 8 -9-
  • 10.
    Ϟ Ϻ ѐ ό ѐ Pubǻ ‫ע‬El Farolଚ փ ‫ޑ‬ ៝ ࠼ Ӏ ៝ ౗ ࣮ բ ΋ ᅿ Ծ ฅ ౜ ຝ Ǵ٠ ଷ ೛ գ Ѹ ໪ ‫ פ‬р ࢌ ঁ ౛ ፕ ٰ у а ှ ញ Ǵٗ᥵գ ཮ ࡛ ᥵଺ ‫ګ‬ ǻ २ Ӄ Ǵգ Ѹ ໪ Ԗ ঁ ኳ ࠠ Ǵё а ኳ ᔕ Γॺ ӵ Ֆ ଺ ، ‫ۓ‬ ‫ ځ‬ԛ Ѹ ໪ ‫ޕ‬ ၰ д ॺ ࢂ ٩ Ᏽ ϙ ሶ ၗ ૻ Ǵٰ ղ ᘐ ଚ փ ࢂ ց Ᏹ ᔒ Ԝ Ѧ Ǵᗋ Ѹ ໪ Ե ቾ ‫ډ‬Ǵό ࢂ ‫؂‬ ঁ Γ‫ ޑ‬གྷ ‫ݤ‬ ೿ ࣬ ӕ Ǵό ӕ ‫ ޑ‬Γ཮ ਥ Ᏽ ό ӕ ‫ ޑ‬চ ߾ ٰ ଺ ، ‫ ۓ‬Ƕ 8 -10-
  • 11.
    Ϟ Ϻ ѐ ό ѐ Pubǻ ٥ ྶ ම ࿶ ᠐ ‫ډ‬΋ ጇ 60ԃж ᙑ ൔ ર ΢ ‫ޑ‬ Ў ക Ǵբ ‫ࢂ ޣ‬ Julian Feldman ຤ ᅟ ቺ ୗ ᇡ ࣁ ǴΓࡐ Ͽ ٩ ᎞ ᡄ ᒠ Ե ٰ ଺ ࡘ ، ‫ۓ‬ ǴԶ ೸ ၸ ᙁ ൂ ‫ ޑ‬ೕ ߾ Ϸ ჋ ၂ ᒱ ᇤ ᒱ ᇤ ύ Ꮲ ಞ ǹ੝ ձ ࢂ Γॺ ಞ ᄍ வ ᕉ ნ ύ ᒣ ձ ኳ Ԅ Ǵ٠ ճ Ҕ ೭ ٤ ኳ Ԅ Ⴃ ෳ ௗΠ ٰ ཮ ว ғ ϙ ᥵Ƕ ި ѱ ‫ޑ‬ ӭ ‫ޜ‬ ‫܈‬ ଚ փ ࢂ ց Ᏹ ᔒ Ǵ೿ Ӛ Ծ Ԗ ΋ ঺ ӝ Я ᡄ ᒠ ‫ޑ‬ ࣮ ‫ݤ‬ ‫܈‬ ኳ Ԅ Γό ࢂ ԝ တ โ ‫ ޑ‬໿ Ґ Ǵᒱ ᇤ ‫” ޑ‬౛ ፕ ”཮ ೏ ‫ ܫ‬క ΋ ૓ Γ‫ޑ‬ ᓐ တ ӧ ӕ ΋ ਔ ‫཮ څ‬ р ౜ ೚ ӭ ᅿ ଷ ೛ Ǵௗ๱ ӆ ਥ Ᏽ ྽ Π ന ӝ ౛ ‫ޑ‬ ଷ ೛ ٰ ଺ р ، ‫ ۓ‬Ƕ೭ ΋ ᗺ ᡉ ฅ ᆶ ‫ ޑ ॺ ך‬В த ࿶ ᐕ ࣬ ֍ ӝ Ƕ => ჋ ၂ ࣮ ࣮ Ǵӆ வ Չ ୏ ύ Ꮲ ಞ ᆶ ፾ ᔈ 8: ; . 8 : < < 8: 7 $& < -11- 77
  • 12.
    Ϟ Ϻ ѐ ό ѐ Pubǻ ᙖ ख़ ႝ တ ኳᔕ ᆶ ж ౛ Γ ന ӳ చ ҹ ǺΓኧ ό ӭ (<60Γ)‫ޑ‬ ௃ ‫ݩ‬ Π ‫ډ‬ଚ փ സ ΋ ݆ Ǵӵ ݀ Γϼ ӭ ߾ ࡑ ӧ ৎ ္ ೛ ‫ۓ‬ Ӛ ᅿ ଷ ೛ చ ҹ Ǵ٩ Ᏽ ന ߈ ൳ ຼ ‫ޑ‬ Ⴃ ෳ ่ ݀ Ǵᒧ Ҕ ന ӳ ‫ޑ‬ ΋ ঁ ٰ ، ‫ۓ‬ ѐ ‫܈‬ ό ѐ ΢ ‫ڬ‬ ؒ Ԗ ၸ ࡋ Ᏹ ᔒ ǵҁ ຼ ΋ ‫ۓ‬ ཮ Ᏹ ᔒ ೱ ុ Ο ຼ ၸ ࡋ Ᏹ ᔒ Ǵҁ ຼ ω ཮ Ᏹ ᔒ -12-
  • 13.
    Ϟ Ϻ ѐ ό ѐ Pubǻ ӧ ೭ ঁᖻ ֽ ္ ೿ གྷ ྽ Ͽ ኧ (ި ౻ ѱ ൑ ҭ ӕ )Ǻ ε ৎ ձ Γѐ ଚ փ ਔ Ǵ‫ ࡑ ך‬ӧ ৎ ္ (ϸ ϐ ҭ ӕ ) ଷ ೛ Ԗ ࢌ ᅿ ೕ ߾ ‫ ܈‬ኳ Ԅ ૈ ᡣ ࢌ ٤ Ͽ ኧ Γၲ ԋ а ΢ Ҟ ኱ Ǵ΋ ࢤ ਔ ໔ ࡕǴ‫ ځ‬д Γ཮ ‫ ݙ‬ཀ ‫ډ‬೭ ঁ ೕ ߾ Ǵ຾ Զ ፓ ፾ ‫ک‬௦ Ҕ Ԝ ΋ ೕ ߾ Ǵ‫ܭ‬ ࢂ চ ҁ ᕇ ճ ‫ޑ‬ Ͽ ኧ ᡂ ԋ ӭ ኧ Ǵ໣ ᡏ ‫ ޑ‬ፓ ፾ Չ ࣁ ᄛ ྄ Α চ ٰ Ԗ ਏ ‫ ޑ‬ኳ Ԅ Ƕ -13-
  • 14.
    ౜ ж གྷ ‫ݤ‬ VS໺ ಍ གྷ ‫ݤ‬ ໺ ಍ གྷ ‫ ݤ‬Ǻ Black-Scholes Model (LTCM) / CAPM ‫ ೌ מ‬ϩ ‫( ݋‬ጕ и )Ǻ࣮ ި ሽ ‫ و‬༈ კ ǵҾ კ ‫ פ‬р ኳ Ԅ ᔅ շ Ծ ρ Ⴃ ෳ ҂ ٰ ި ሽ ‫ و‬༈ =࣮ ၸ ѐ ଚ փ ‫ ޑ‬р ৢ Γኧ ٰ Ⴃ ෳ ҂ ٰ р ৢ Γኧ Ҕ ӕ ኬ ‫ޑ‬ ᡄ ᒠ ٰ ኳ ᔕ ި ౻ ѱ ൑ చ ҹ Ǻ ວ ‫ޑ‬ Γ>፤ ‫ޑ‬ Γ => ި ሽ ΢ ᅍ (ϸ ϐ ҭ ฅ ) ‫؂‬ ঁ ႝ တ ж ౛ Γ(‫ ׫‬ၗ ‫) ޣ‬ё а ௦ ‫ ڗ‬྽ ਔ Ծ ᇡ ࣁ ന ӳ ‫ޑ‬ ೕ ߾ ၸ ѐ ‫ި ޑ‬ ሽ ኳ Ԅ ཮ ቹ ៜ ‫ ׫‬ၗ Γ౜ ӧ ‫ ޑ‬Չ ࣁ ౜ ӧ ‫ ޑ‬ວ ፤ ، ฼ (ᆶ ‫ ٮ‬ሡ ό ѳᑽ)Ǵ཮ ٬ ި ሽ ౢ ғ ᡂ ୏ ౢ ғ Α ΋ ᅿ ό ᘐ ൻ ᕉ ‫ ޑ‬Ӣ ݀ ᜢ ߯ -14-
  • 15.
    ౜ ж གྷ ‫ݤ‬ VS໺ ಍ གྷ ‫ݤ‬ ި ౻ ѱ ൑ ኳ ᔕ ่ ݀ Ǻ ި ሽ ᕏ а ό ೕ ߾ ‫ޑ‬ Б Ԅ ΢ Π ᎜ ᎜ ᕏ ᡂ ౦ চ Ӣ ٰ Ծ ‫ ܭ‬ж ౛ Γ(‫ ׫‬ၗ Γ)໔ ‫ޑ‬ ϕ ୏ ᆶ ፓ ፾ ǹԶ ߚ Ѧ ೽ ፂ ᔐ(ӵ ߮ ᛥ ථ ໸ ୍ ֚ ᜤ฻ Ѧ ೽ ख़ ε ٣ ҹ ) ި ሽ ‫ ޑ‬ᡂ ౦ Ԗ “ࠆ ‫ ݀ ่ ޑ” ׀‬౜ ຝ ่ ݀ ఼ က ࠆ ‫׀‬ ౜ ຝ Ǵค ‫ݤ‬ ٬ Ҕ ౛ ‫܄‬ Չ ࣁ ຾ Չ ှ ញ ᔈ ၀ ”፾ ᔈ Ꮲ ಞ ”ٰ ‫ ڗ‬ж ό ӝ ౛ ‫ ֹ” ޑ‬ӄ ౛ ‫” ܄‬ ٬ Ҕ ࣮ ՟ ӝ ౛ ‫ޑ‬ ࠆ ‫ ׀‬౜ ຝ ࢂ Ծ ฅ ੌ ౜ Ǵό ࢂ Ѧ ೽ ፂ ᔐ‫ ܌‬೷ ԋ Ǵҭ ߚ Һ Ֆ ΓՉ ୏ ‫ૈ ܌‬ Ѱ ѓ ද ၹ Ӹ ӧ ‫ ܭ‬Ӛ ᅿ ѱ ൑ ‫ ޑ‬ሽ ਱ ε ൯ ‫୏ݢ‬ᡂ౦౜ຝǴଆ ྍ ‫ ܭ‬Γ ᜪ ‫္ ཮ ޗ‬ ‫୏ݢ‬ᡂ౦౜ຝǴ ‫ ޑ‬চ η Ǵӵ Ֆ Ծ ‫ ך‬ಔ ᙃ ԋ ࣬ ϕ ٩ Ӹ ‫ ޑ‬ಒ ጏ ኳ Ԅ Ƕ -15-
  • 16.
    ౜ ж གྷ ‫ݤ‬ VS໺ ಍ གྷ ‫ݤ‬ ഡ ճ ୗ Ǻ ੿ ҅ ख़ ा Զ Ξ Ԗ ཀ က ‫ޑ‬ ଷ Ǵ஥ Ԗ ೚ ӭ ᇥ ”ଷ ೛ చ ҹ ”… ଷ ᇥ ૈ ୼ а ࡐ Ͽ ‫ޑ‬ ܿ Ջ ”ှ ញ ”ࡐ ӭ ٣ ௃ Ѭ வ ࡑ ှ ញ ‫ޑ‬ ᕷ ᚇ ౜ ຝ ‫ ڬ‬ൎ Ǵ‫ ܜ‬ᚆ р ख़ ा ‫ޑ‬ ϡ ન Ǵ‫ך‬ ॺ ω ૈ ᙖ Ԝ ଺ р Ԗ ਏ ‫ޑ‬ Ⴃ ෳ Ӣ Ԝ ख़ ा ଷ ᇥ ౛ ፕ ེ ‫ޑ‬ ଷ ೛ ഋ ॊ ΋ ‫ۓ‬ ό ҅ ዴ ౛ ‫܄‬ Γଷ ᇥ ེ ‫ޑ‬ ᒱ ᇤ ଷ ೛ Γό ཮ Ꮲ ಞ Γό ཮ ‫ׯ‬ ᡂ Ј ཀ Γό ཮ ࢎ ೛ р ଷ ᇥ ٠ у а ෳ ၂ ό Ե ቾ ੿ ჴ Ш ࣚ ྽ ύ ‫ޑ‬ Γᜪ Չ ࣁ ੝ ፦ ଷ ೛ ”Γ‫ ޑ‬Չ ࣁ Ԗ ፾ ᔈ Κ ”ǴК ଷ ೛ ”Γࢂ ౛ ‫ޑ ܄‬ ”Ǵ‫ ׳‬ຠ ߈ ౜ ჴ Ǽ ѱ ൑ ౜ ຝ ᜤа ှ ှ ‫ک‬Ⴃ ෳ Ǵό ࢂ ঁ ᡏ ‫ޑ‬ ፄ ᚇ ‫܄‬ ǴԶ ࢂ ѱ ൑ ္ ೚ ӭ Γ ϐ ໔ ‫ޑ‬ ༾ ֮ ‫ރ‬ ᄊ ‫ک‬ಔ ᙃ ᜢ ᗖ ӧ ኳ Ԅ ǴԶ ߚ Γ Ǽ -16-
  • 17.
    Ⴃ ‫ޕ‬ ҂ ٰ ૈցႣෳ҂ٰ‫៏ݾޑ‬ ൳ Я ό Ӹ ӧ ё а ԋ ф Ⴃ ෳ ߎ ᑼ ѱ ൑ ‫ ޑ‬Б ‫ ݤ‬ǻ ࣽ Ꮲ ό ୼ Ӄ ຾ ǵ‫ ݩ ރ‬ϼ ፄ ᚇ Ǵό ‫ ى‬а ଺ р Ⴃ ෳ ǻ Ͽ ኧ ‫ ޣ‬ᖻ ֽ ‫ ঁ ؂‬Γ ‫ ؂‬ԛ ᒧ 0‫1܈‬ Ҟ ኱ ࢂ ԋ ࣁ Ͽ ኧ (ᒧ ‫ ډ‬ӭ ኧ Γ ؒ ᒧ ‫ ޑ‬ኧ ӷ ) ӧ Ͽ ኧ ‫ޣ‬ ᖻ ֽ ္ ǴΓ ኧ ቚ у Ǵ٣ ௃ ཮ ᡂ ள ࡐ ό ΋ ኬ ୖ ᖻ Γ ኧ ӵ ݀ ό ӭ Ǵ‫ ވ‬ৎ ‫ ฼ ޑ‬ౣ ό ӭ Ǵό ‫ ى‬а ఼ ᇂ ‫܌‬ Ԗ ё ૈ ‫ޑ‬ ኳ Ԅ ఼ ё Ⴃ က ǺԖ ෳ ‫ޑ‬ ኳ Ԅ (ѱ ൑ Ӹ ӧ ё Ⴃ ෳ ‫܄‬ )Ǵࠅ ؒ Γ ‫ ޕ‬ၰ =>่ ݀ (ѱ ൑ ሽ ਱ ᡂ ୏ )཮ ٩ Ᏽ ё Ⴃ ෳ ‫ ޑ‬ኳ Ԅ ‫و‬ ୖ ᖻ Γ ኧ ӭ Ǵ‫ވ‬ ৎ ‫฼ ޑ‬ ౣ ཮ ఼ ᇂ ‫ ܌‬Ԗ ё ૈ ‫ޑ‬ ኳ Ԅ ǴҺ Ֆ ё а Ⴃ ෳ ่ ݀ ‫ ޑ‬ኳ Ԅ ೿ ཮ ೏ ว ౜ ǴԶ Ъ ҥ ‫ څ‬௦ Ҕ ఼ က Ǻӵ ݀ ੿ ‫ ޑ‬Ԗ Γ ૈ ୼ ό മ Զ ᕇ Ǵ൩ ཮ ֎ Ї ‫ ׳‬ӭ Γ ຾ ΕǴՠ ‫ ؂‬຾ ٰ ΋ ঁ Γ ൩ ཮ ஥ ຾ ཥ ‫ޑ‬ ฼ ౣ Ǵ‫ ע‬೭ ٤ Ͽ ໆ ‫ޑ‬ ё Ⴃ ෳ ‫܄‬ Ӟ ௞ Ƕ (ѱ ൑ όӸ ӧ ё Ⴃ ෳ ‫) ܄‬ Damien Challet -17-
  • 18.
    Ⴃ ‫ޕ‬ ҂ ٰ ம ғ (Neil Johnson)Ǻ ӵ ݀ ѱ ൑ (ଽ Զ )Ӹ ӧ ё Ⴃ ෳ ‫ ܄‬ǴٗԖ ؒ Ԗ Б ‫ ݤ‬ё а ୀ ෳ ‫ډ‬ǻ ่ ݀ д ॺ ‫ ޑ‬ኳ ࠠ ё а ୀ ෳ р Ǻѱ ൑ ӧ ࢌ ٤ ਔ ‫ څ‬К ‫ ځ‬д ਔ ‫څ‬ ‫׳‬ Ԗ Ⴃ ෳ ‫܄‬ ё Ⴃ ෳ ୔ ໔ (฼ ౣ ኧ Ҟ ෧ Ͽ ) 2 0 % .* 5 $ 2 ! 8 Ԗ Γ ଏ р ѱ ൑ 0 . $ $ .' ೚ ӭ Γ ٬ Ҕ Α ӕ ኬ ‫฼ ޑ‬ ౣ ) 5 # $= В ༝ ի ऍ ϡ ༊ ౗ 4000ԛ ‫ޑ‬ ሽ ਱ ᡂ ୏ ᒣ ᛽ р ΐ Μ ӭ ঁ ё Ⴃ ය ୔ * $ ໔ǵΨ Ⴃ ෳ р ‫ځ‬ ᡂ ϯ Б ӛ Ǵѝ Ԗ ΋ ԛ Ⴃ ෳ ᒱ ᇤ ӵ ݀ ೭ ᅿ (Ⴃ ෳ )ԋ ф ᡂ ԋ த ᄊ Ǵࡕ݀ ё ૈ ཮ ࡐ ။ ౦ 2 .* 5 $ 8 ε Њ ௦ Ҕ Ԝ ΋ Б ‫ݤ‬ =>‫ ׯ‬ᡂ ѱ ൑ ҁ ፦ =>ᄛ ྄ ೭ ໨ ‫ ޑ ೌ מ‬Ⴃ ෳ 2 0 $ ૈ Κ ! ( . <7 7, * 8 * $ ! * 2 .* 5 $ # $ ( . % $ 0*' / -18-
  • 19.
    ፾ ᔈ ҁ ሦ ຬ ம ‫ޑ‬ᐒ ཮ Ь က ‫ޣ‬ ѱ ൑ Ⴄ ‫ڰ‬ Һ ‫܄‬ (ό ౛ ‫܄‬ )‫ ޑ‬ୢ ᚒ ᆶ ࠆ ‫ ׀‬౜ ຝ ‫ ޑ‬ှ เ ό ࢂ ঁ ᡏ ‫ޑ‬ ‫ޑ‬ ፄ ᚇ ‫܄‬ Ψ ό ࢂ Γ Ԗ ᆟஏ‫ޑ‬ ࡘགྷ‫܈‬੝ਸಞᄍ(ୃ ӳ ) Զ ࢂ ࣮ Γ ᜪ Չ ࣁ ‫ޑ‬ ᙁ ൂ ‫܄‬ ᆶ ϕ ୏ (ኳ ү ǵ၂ ᇤ ǵ፾ ᔈ ) Γᜪ ό ࢂ ᎞ ౛ ‫܄‬ ࡘ Ե ٰ Ꮲ ಞ ྎ ೯ ‫ک‬ᇟ ‫ق‬ ᇟ ‫ق‬ ࢂ ፾ ᔈ ၸ ำ ‫ޑ‬ ౢ ‫ނ‬ ǴΨ ࢂ ᄽ ϯ ‫ޑ‬ ၸ ำ ӵ ݀ ೭ ᅿ (Ⴃ ෳ )ԋ ф ᡂ ԋ த ᄊ Ǵࡕ݀ ё ૈ ཮ ࡐ ။ ౦ ѱ ൑ ္ Һ Ֆ ό ᘐ ᙯ ᡂ ‫ޑ‬ ࡘ གྷ ‫ߞک‬ ‫ۺ‬ (ཀ ᛽ ࠠ ᄊ )ᡏ ‫ س‬Ǵ೿ ࢂ ‫ ॺ ך‬፾ ᔈ Κ ബ ೷ р ٰ ‫ޑ‬ ౢ ‫ނ‬ -19-