Asset Pricing A Brief Review

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(1)

Munich Personal RePEc Archive

Asset Pricing - A Brief Review

Li, Minqiang

2010

(2)

Asset Pricing Models – A Brief Review

Minqiang Li

Georgia Institute of Technology

Abstract

(3)

ˍ

ˍ

ˍ

ˍˊ

ˊ

ˊ

ˊ

ᇐ㿔

ᇐ㿔

ᇐ㿔

ᇐ㿔

Ā䌘ѻ˄

asset

˅āᰃϔϾ↨䕗ㄐ㒳ⱘ䞥㵡ᄺ䆡∛DŽㅔऩഄᴹ䇈ˈ䌘ѻৃҹߚ

Ўᰒᗻҹঞ䱤ᗻϸ໻㉏DŽᰒᗻ䌘ѻࣙᣀϾҎⱘഄѻˈӕϮⱘॖ᠓ˈ䆒໛ҹঞᅗথ㸠

ⱘ৘⾡᳝ᔶⱘ䆕ࠌˈ೑ᆊⱘ໪∛ټ໛ㄝ݋ԧⱘ৘⾡䌘ѻᔶᓣDŽ䱤ᗻ䌘ѻ߭ࣙᣀϔϾ

݀ৌᢹ᳝ⱘৡໄˈϧ߽ᴗˈҹঞ┰೼ⱘᅲԧᳳᴗᓣⱘᡩ䌘ᴎӮˈㄝㄝDŽ᠔䇧Ā䌘ѻ

ᅮӋ˄

asset pricing

˅ā乒ৡᗱНህᰃᇍ৘⾡ᰒᗻ៪䱤ᔶⱘ䌘ѻ䖯㸠ӋؐϞⱘ㉫⬹

䆘Ԅ៪㊒⹂䅵ㅫDŽĀᡩ䌘㒘ড়˄

portfolio

˅āᰃᣛ೼䌘ѻᅮӋ⧚䆎ⱘ෎⸔Ϟḍ᥂ϡ

ৠⱘᡩ䌘Ⳃᷛ䗝ᢽ䌘ѻⱘ᳔Շᨁ䜡DŽ

ҢҎ㉏᭛ᯢߎ⦄⠽䋼ѸᤶᯊˈҎ㉏ህᏆ㒣ᓔྟ䖯㸠䌘ѻᅮӋњDŽ೼ଚક㒣⌢

催ᑺথ䖒ⱘ⦄ҷ⼒Ӯˈ䌘ѻᅮӋᏆ㒣থሩ៤њϔϾ↨䕗៤❳ⱘˈϹ䇼ⱘ䞥㵡ᄺߚঝ

ᄺ⾥DŽ঺໪ˈ䌘ѻᅮӋᴀ䑿জᏆ㒣ߚ࣪ߎњ৘Ͼ⏙᱄ⱘߚᬃˈ↨བ䇈䞥㵡㸡⫳⠽

˄

financial derivatives

˅ˈ೎ᅮᬊⲞ䆕ࠌ˄

fixed income securities

˅ㄝㄝDŽ⬅Ѣ䌘ѻ

ᅮӋ੠ᡩ䌘㒘ড়ⱘ催ᑺⳌ݇ᗻˈᮽᳳⱘ㒣݌⧚䆎བ䌘ᴀ䌘ѻᅮӋ῵ൟᑊ᳾ᇍѠ㗙䖯

㸠㒚㟈ⱘऎߚDŽԚ䖥ᑈᴹˈ䱣ⴔ䌘ѻᅮӋ⧚䆎໻Ḛᶊᓎゟⱘᅠ៤ˈᡩ䌘㒘ড়⧚䆎ᓔ

ྟߎ⦄њ⣀ゟথሩⱘ䍟৥DŽ

䌘ѻᅮӋҹঞᡩ䌘㒘ড়⧚䆎ⱘ䞡㽕ᗻᰃϡ㿔㗠ஏⱘDŽҢϾҎሖ䴶ᴹ䇈ˈᅗӀ

ᇍϾҎᡩ䌘⧚䋶ᦤկњ⧚䆎ϞⱘᣛᓩDŽᇍ݀ৌᴹ䇈ˈ݀ৌⱘ৘乍䞥㵡އㄪ㒣ᐌձ䌪

Ѣ䌘ѻⱘᅮӋDŽ↨བ݀ৌ೼䳔㽕䌘䞥ᯊˈᅗৃҹḍ᥂ᔧࠡ㙵⼼ⱘᅮӋᴹއᅮᑨᔧথ

㸠؎ࠌ䖬ᰃ㙵⼼DŽ݀ৌгৃҹ߽⫼ϡৠⱘ䞥㵡Ꮉ݋ᴹᑨᇍ৘⾡┰೼ⱘ亢䰽DŽҢ೑ᆊ

ሖ䴶ᴹ䇈ˈ೑ᆊ䳔㽕䱣ᯊⲥ᥻ᏖഎϞ䌘ѻᅮӋⱘ⾽ᑣᰃ৺ℷᐌDŽ೑ᆊⱘ৘⾡ᬓㄪབ

⿢ᬊˈѸᯧ乱ᑺˈ⼒Ӯ⽣ֱ߽䱰ㄝজড䖛ᴹᕅડ䌘ѻⱘᅮӋDŽ঺໪ˈ䆌໮೑ᆊᢹ᳝

Џᴗᡩ䌘෎䞥˄

sovereign investment funds

˅DŽབԩᇍ䖭ѯ෎䞥䖯㸠៬⬹ᗻᡩ䌘гᰃ

ϔϾ䞡㽕ⱘ䌘ѻᅮӋঞᡩ䌘㒘ড়䇒乬DŽ

៥೼ᴀ᭛Ёᇚ

ҟ㒡

৘⾡䌘ѻᅮӋঞᡩ䌘㒘ড়ⱘ⧚䆎ˈ䞡

㹿ᬒ

೼䖥

ᑈᴹ

ⱘ⧚䆎থሩDŽ೼

෎⸔Ϟˈ៥г

ҟ㒡

᳔䖥ҹᴹ䖭Ͼ

乚ඳ

ⱘথሩᑊᦤߎ᳾ᴹⱘ

ⷨお

DŽ

Ѣ䌘ѻᅮӋ⧚䆎ⱘ

ᑺঞ

ᑺˈᴀ᭛ᇚ

䆩೒

ܼ

䴶ഄᇍ䖭Ͼ

乚ඳ

Ё᳔Ў䞡㽕

Ḍᖗ ݙᆍ

䖯 㸠

䯤䗄

DŽ៥ᇚ ⬹

ϔ ѯᏆ㒣

៤ԧ

ⱘߚ ᬃˈ↨ བ㸠Ў 䞥㵡ᄺ

˄

behavioral finance

˅ˈ䞥㵡Ꮉ

ᄺ˄

financial engineering

˅ˈㄝㄝDŽ៥гϡ

⡍ᛣ䯤

䗄া⡍

ᅮѢᡩ䌘㒘ড়ⱘ⧚䆎DŽ䌘ѻᅮӋЁϔϾ

Ḍᖗ

ⱘ䇒乬ᰃ㙵ᴗ

Ӌ

П䇰

˄

equity

premium puzzle

˅DŽᴀ᭛гϡ݋ԧ

䆎DŽ঺໪ˈ݇Ѣ⧚䆎੠ᅲ䆕

П䯈

ⱘ⾡⾡݇

ˈ

г

䇋䇏

খ㗗݊

ᅗ᭛

DŽ

೼ᓔྟᴀ᭛

П

ࠡˈ៥

Ў

ҟ㒡

ϔ

ϟ

Ꮖ㒣ߎ

㽓ᮍ

䌘ѻᅮӋϧ

ড়䆘䆎

ᵕ݊

᳝⫼ⱘDŽ↨䕗᳝

থᗻⱘ

ড়䆘䆎᳝

Campbell

˄

2000

˅ˈ

Mehra

Prescott

˄

2003

˅ˈҹঞ

Cochrane

˄

2005

˅DŽ

Campbell

ᰃᇍ

2000

ᑈҹࠡⱘ䌘ѻᅮӋ

乚ඳ

㓐䗄

ˈЏ㽕ⴔ

Ѣᅲ䆕੠⧚䆎

П䯈

Ѧࡼ

DŽ

Mehra

Prescott

ⴔ䞡

䯤䗄

㙵ᴗ

Ӌ

П

DŽ

Cochrane

Ѣ䌘ѻᅮӋ੠

ᅣ㾖

㒣⌢

П䯈

㘨㋏

DŽ݇Ѣϧ

ˈᮽᳳ↨䕗᳝ৡ

(4)

↨䕗ⴔ䞡䌘ѻᅮӋⱘ

ᖂ㾖

⧚䆎῵ൟDŽ

㔎ធ

⿡⿡

њϔѯˈ

঺໪ϸ

к

Ё

ϡ

㽚Ⲫ䖲㓁

῵ൟDŽ↨䕗

к

Duffie

˄

2001

˅ˈ

Cochrane

˄

2001

˅ˈ

LeRoy

Werner

˄

2001

˅ˈ

Pennacchi

˄

2008

˅ˈҹঞ

Skiadas

˄

2009

˅DŽ

݊

Ё

Cochrane

˄

2001

˅ˈ

LeRoy

Werner

ҹঞ

Skiadas

ϡ

䖲㓁

῵ൟDŽ

Cochrane

ܼ

к䛑

ᓎゟ೼䱣ᴎ

಴ᄤ

˄

stochastic discount factor

˅ⱘ෎⸔Ϟˈϡৠⱘ῵ൟ⬅ϡ

ৠⱘ䱣ᴎ

಴ᄤᇐ

ߎDŽᅗЏ㽕

䆆䗄⾏ᬷ

῵ൟDŽ

ℸк᭄

ᄺ㽕

Ԣ

ˈԚ

ὖᗉ䆆

Ⳍᔧ

䗣ᕏ

DŽ

LeRoy

Werner

гϡ

䖲㓁

῵ൟˈⴔ䞡

䯤䗄

䌘ѻᅮӋⱘ

ᖂ㾖

⧚䆎෎⸔DŽᅗᇍ

ᄺ㽕

∖⿟

ᑺ੠

Cochrane

Ⳍᔧˈ

Џ㽕

⡍㡆

ᰃ䌘ѻⱘ᳾ᴹᬊⲞ

⥛㹿

ᅮН೼ϔϾ᳝

䰤㓈

Ꮰᇨԃ⡍ぎ䯈

˄

Hilbert space

˅

П

Ϟˈ

ℸ䙓ܡ

њ৘⾡

ᄺϞ

ᡔᴃ

ೄ䲒

DŽ

Skiadas

LeRoy

Werner

ϸᴀ

к

↨䕗㉏

Ԑ

ˈ᠔ϡৠⱘᰃ

Skiadas

᳈ࡴ

⧚䆎࣪ˈᇍ

㗙ⱘ

ᑺ㽕

䕗催ˈԚгϡ

䖲㓁

῵ൟDŽ

Duffie

ᰃ↨

䕗ᴗ

ⱘ䆎

ˈ

䖲㓁

῵ൟˈԚᇍ䌘ѻᅮӋⱘ

߱

ᄺ㗙ৃ

䖛Ѣ

⏅༹

੠ㅔ

DŽ

ˈ੠໻

ߚ

݊

к

ϡৠˈ

Pennacchi

㽚Ⲫ

䴶↨䕗

ˈ෎ᴀ

⎉Ⲫ

њ䌘ѻᅮӋⱘ᠔

᳔᳝䞡㽕ⱘ

ߚˈ

ᑺг

Ёˈᰃϔᴀ

߱

ᄺ㗙ϡৃ໮

ܹ䮼к㈡

ˈᇍ

ᄺ㗙

ᴹ䇈гᰃϔᴀ

ᵕ݊

ᅲ⫼ⱘ

ܹ䮼ᬭᴤ

DŽԚᴀ

к

ᑺ↨

݊

ᅗⱘ

к

ѯDŽ঺໪ˈᇍ

੠䞥㵡Ꮉ

⿟ᛳ݈䍷

㗙ৃҹ

খ㗗

Björk

˄

2009

˅៪

Shreve

˄

2004

˅DŽ

ᴀ᭛ⱘ݋ԧ

ᅝᥦ

ϟ

DŽ೼

Ѡ

㡖䞠

ˈ៥

ҟ㒡

ᮽᳳⱘ䌘ѻᅮӋ㒣݌⧚䆎DŽ

㄀ϝ

㡖䆆䗄

ϔѯ

䖥ᳳⱘ䞡㽕

ὖᗉ

ᡔᎻ

ˈ෎ᴀϞᰃ

ܿक

ᑈҷҹ

ⱘ៤

DŽ

㄀ಯ㡖䞠

ⴔ䞡

䆆䗄

䌘ѻᅮӋ᳔䖥

ᑈҹᴹⱘ䖯ሩDŽ

㄀Ѩ㡖

ᘏ㒧

DŽ

ˎ

ˎ

ˎ

ˎˊ

ˊ

ˊ

ˊ

㒣݌⧚䆎

㒣݌⧚䆎

㒣݌⧚䆎

㒣݌⧚䆎

䌘ѻᅮӋ⧚䆎ⱘ

Ḍᖗ

ഄᓎゟ೼

ϝ

Ͼ

Ѧ

ⳌㄝӋⱘ෎

Ϟˈ

ህᰃˈ

߽

˄

arbitrage

˅ˈ

Ӭ

࣪˄

optimization

˅੠

ᑇ㸵

˄

equilibrium

˅DŽ᠔䇧

߽ᰃᣛᏖഎϞ

ϡ

߽ᴎӮˈ

Ӭ

࣪߭ᣛऩϔⱘҷ

ᗻᡩ䌘㗙䖯㸠

Ӭ

࣪އㄪˈ㗠

ᑇ㸵

߭ᣛᏖഎⱘ

կ

∖ᑇ㸵

DŽབ

៥Ӏ

؛

݊

Ёⱘ

ӏ

ԩϔϾˈ៥Ӏህ

䆕ᯢ䱣ᴎ

಴ᄤ

೼DŽϡ

ৠⱘ῵ൟ߭

ߎϡৠⱘ

಴ᄤ

DŽ೼䖭Ͼ

НϞˈ

ሑㅵ

ϡৠⱘ῵ൟৃ

Ӯ

ߎ

ϡ

ϔ

ⱘӋ

៪ᣛ

⼎ᕜ

ϡϔ

ⱘއㄪˈϡৠⱘ䌘ѻᅮӋ῵ൟᰃ㒳ϔⱘDŽ᳝ѯ῵ൟ߭

お⡍

ᅮⱘᏖഎ៪䌘ѻˈ↨བ೎ᅮᬊⲞ㉏ˈ䞥㵡㸡⫳ѻકˈㄝㄝDŽ೼

߱

ᄺ䌘ѻᅮӋ⧚

䆎ᯊˈབ

䖭Ͼ໻ḚᶊˈህϡӮ೼

ӫ

໮ⱘ῵ൟࠡ

㾝ᕫⴐ㢅㔁х

DŽ

೼ 䌘 ѻ ᅮ Ӌ ⧚ 䆎 ⱘ থ ሩ Ё ˈ ↨ 䕗 ᳝ ᕅ ડ ⱘ ⧚ 䆎 ࣙ ᣀ 䌘 ᴀ 䌘 ѻ ᅮ Ӌ ῵ ൟ

˄

Capital Asset Pricing Model

ˈ

⬹Ў

CAPM

˅ˈ

߽ᅮӋ⧚䆎˄

Arbitrage Pricing

Theory,

⬹Ў

APT

˅ˈ

ᳳ䌘ᴀ䌘ѻᅮӋ῵ൟ˄

Intertemporal Capital Asset Pricing

Model,

⬹Ў

ICAPM

˅ˈ

⍜䌍

䌘ᴀ䌘ѻᅮӋ῵ൟ˄

Consumption Capital Asset

Pricing Model,

⬹Ў

CCAPM

˅ˈҹঞᳳᴗᅮӋ⧚䆎˄

Option Pricing Theory

˅DŽ

݊

Ёˈ

Markowitz, Miller

Sharpe

Ўᦤߎ੠থሩ

CAPM

㦋ᕫ

1990

ᑈᑺ

䇎䋱ᇨ

㒣⌢ᄺ

ˈ

Merton

Scholes

߭

Ўᦤߎ੠থሩᳳᴗᅮӋ⧚䆎㗠

㦋ᕫ

1997

ᑈᑺ

䋱ᇨ

㒣⌢ᄺ

DŽ

ሑㅵ

䖭ѯᮽᳳ῵ൟⱘᅲ䆕

⦄ᑊϡᰃ

⡍߿

ߎ

ˈᇍᅗӀⱘ

䗣ᕏ

(5)

䌘ᴀ䌘ѻᅮӋ῵ൟ

䌘ᴀ䌘ѻᅮӋ῵ൟ

䌘ᴀ䌘ѻᅮӋ῵ൟ

䌘ᴀ䌘ѻᅮӋ῵ൟ

CAPM

ᰃ ϔ Ͼ ऩ ᳳ ⱘ ⧚ 䆎 ˈ ᇍ ᅗ ⱘ থ ሩ

䞡 㽕

԰

⫼ ⱘ ᭛

Markowitz

˄

1952

˅ ˈ

Sharpe

˄

1964

˅ ˈ

Lintner

˄

1965

˅ ˈ

Mossin

˄

1966

˅ ˈ ҹ ঞ

Black

˄

1972

˅DŽ

Markowitz

ⱘᎹ

԰

ᰃᓔ

߯

ᗻⱘDŽ೼

ҪП

ࠡˈҎӀᏆ㒣

䅸䆚ࠄ

њ亢䰽੠

ᳳᬊⲞ

⥛П䯈

ⱘ݇

DŽ

Markowitz

䋵⤂

೼Ѣᅗᦤߎњ亢䰽ߚ

˄

diversification

˅

䖭Ͼ

ὖᗉ

DŽϔϾ

ॠᙊ

亢䰽ⱘᡩ䌘㗙

Ꮰᳯ

೼೎ᅮ

ᳳᬊⲞ

ⱘৠᯊ

ᡓᢙሑ䞣ᇣ

ⱘ亢䰽DŽ

Markowitz

ᮍᏂ

ᦣ䗄

ϔϾ䱣ᴎᬊⲞ

ⱘ亢䰽DŽᡩ䌘㗙

䇗㡖

৘Ͼ䌘ѻ೼㒘ড়

Ёⱘ↨

՟

ՓᮍᏂ

࣪DŽ

ሑㅵ

ৃҹ䇈

Markowitz

њ៪

ϔ

䇈ᕅડњ

Ͼ⧚

䆎䞥㵡

ˈ೼ᔧᯊ

Ҫ

ⱘᎹ

԰

ⱘ䞡㽕ᗻᑊ

㹿偀

Ϟ

䅸䆚ࠄ

DŽ

џ

ᅲϞˈ೼

Markowitz

म຿

䆎᭛

ྨਬ

ӮЁⱘ

Friedman

˄

㗙ҹ

гᰃ

䇎䋱ᇨ༪㦋ᕫ

㗙˅䋼

Markowitz

ⱘ Ꮉ

԰

ᰃ ৺ 䖒

њ 㒣 ⌢ ᄺ

म ຿

∈ ޚ

DŽ

ᴹ ˈ

Sharpe

˄

1964

˅ ˈ

Lintner

˄

1965

˅ˈ

Mossin

˄

1966

˅ˈҹঞ

Black

˄

1972

˅জᇍ

Markowitz

ؐ

-

ᮍᏂ

⧚䆎

԰

њ

ᓊԌ

DŽ

Sharpe

㛮⊼

ЁᏆ㒣

ϔ

ߎ⦄њ⦄ҷ

CAPM

ᮍ⿟

ᓣˈ

Ҫ

੠⦄ҷ

⫼ⱘ᳝᠔ϡৠDŽ

Black

䆕ᯢњབ

ϡ

亢䰽䌘ѻᯊˈ

ᐌⱘ

CAPM

Ӯ

㹿

ϔϾ

– CAPM

᠔ҷ

DŽ䖭ѯᮽᳳⱘ᭛

ЁᏆ㒣ᦤߎњᏖഎ亢䰽˄

Ѻे㋏

亢䰽˅੠݀ৌ

ᅮ亢䰽˄

Ѻे䴲㋏

㒳亢䰽˅䖭ϾᬊⲞ

ߚ

ᔶᓣDŽ঺໪ˈ᳝

ᬜ䖍⬠

˄

efficient frontier

˅ ˈ

Ⳍ ݇ 㒘 ড় ˄

zero-correlated portfolio

˅ ˈ ෎ 䞥 ߚ

ᅮ ⧚

˄

fund separation theorem

˅ㄝгᰃ

CAPM

Ё

ᵕ݊

䞡㽕ⱘ

ὖᗉ

DŽ

乎֓

ᦤϔ

ϟ

ˈ

ѯ

ॳ㨫

ᯊ䳔

⊼ᛣ

೼ᮽᳳ᭛

Ё᳝

ᬜ䖍⬠೒

Ё

῾㒉ത

ᷛߚ

߿

ಲ᡹⥛

੠ᷛ

ޚᮍᏂ

ˈ

੠⦄ҷⱘ

дᛃ

ⳌডDŽ

⧚䆎Ϟˈऩᳳⱘ

CAPM

᥼ᇐ

᳝໮⾡ᔶᓣDŽ↨བ៥Ӏৃҹ

؛

ᅮℷ

ߚ

ⱘ䱣

ᴎᬊⲞ

ᅮⱘ

ߑ᭄

DŽ៥

⫼ⱘᳳ

ؐ

-

ᮍᏂӬ

ᮍ⊩

ϟ

DŽ

؛

䆒ᡩ䌘ᴎӮ

n

Ͼ

ᗻϡⳌ݇ⱘ

亢䰽䌘ѻˈᑊ

Ri

㸼⼎

䌘ѻ

i

೼ᯊᳳ

᳿

ⱘ䱣ᴎᬊⲞ

DŽ

؛

ಲ᡹⥛

णᮍᏂⶽ䰉

DŽ

DŽ

DŽ

DŽ

ϔϾᳳ

ؐ

-

ᮍᏂ

ᡩ䌘㗙

乬ᰃ

ᗢḋ

䗝ᢽ৘Ͼ䌘ѻⱘᴗ䞡 ᴹ

Փᕫ

ᡩ䌘㒘ড়ⱘ

ᮍᏂ

DŽ䖭

᳝ϸϾ

䰤ࠊ

ᴵӊ

DŽϔϾᰃᴗ䞡

ᕫࡴ

੠Ў

1

DŽ঺ϔϾ

ᴵӊ

ᰃᡩ䌘㒘ড়ⱘ

ᳳᬊⲞ

೎ᅮ೼ϔϾᅲ

ؐ

DŽ៥Ӏҹ ᴹҷ

᠔᳝ߚ

䞣䛑

1

ⱘ৥

DŽ݋ԧⱘ

Ӭ

乬བ

ϟ˖

(2.1)

⒵䎇

ᴗ䞡

੠Ў

1

ˈҹঞ䖒

Ⳃᷛ

ᳳᬊⲞ

(2.2)

ग़䘡

ᯊ᠔᳝ⱘ

㾷䛑㹿

Ў᳝

㒘ড়˄

efficient portfolio

˅ˈ

ᅗӀⱘ

ܼ

ԧ

ህᰃ᳝

ᬜ䖍⬠

DŽ䖭Ͼ

ᕜᆍ

ᯧ⫼

ᳫ᮹Ь

˄

Lagrangian multiplier

˅ⱘ

ᮍ⊩∖

DŽ

ⱘᔶ

ᰃϸϾ᳝

㒘ড়ⱘ

ᑇഛ

DŽ

ϔϾ㒘ড়ⱘᴗ䞡੠

៤ℷ↨DŽ

(6)

minimum variance portfolio

˅DŽৃҹ䆕ᯢ᳝

ᬜ䖍⬠

೼ᷛ

ޚᮍᏂ

-

ᳳᬊⲞ

⥛ぎ䯈

Ёᰃ

ϔ

ঠ᳆

ⱘℷᬃDŽ

㒘ড়ⱘᴗ䞡ᔶᓣⱘ঺ϔϾ

䞡㽕ⱘ

⡍⚍

ᰃ੠೎ᅮⱘ

ᳳᬊⲞ

៤ℷ↨DŽ

ᵰӏᛣ

೼᳝

ᬜ䖍⬠

Ϟ䗝ᢽϸϾ

䴲ܼ

ᮍᏂ

㒘ড়ˈ䖭Ͼ៤ℷ↨ⱘ

⡍⚍Փᕫ

᠔᳝

ᬜ䖍⬠

Ϟⱘ㒘ড়

ৃҹ

䖛䖭ϸϾ䗝ᅮⱘ㒘ড়ᴹѻ⫳DŽ䖭ህᰃϔϾ

݅

ৠ෎䞥ᅮ⧚ˈ

ЎѠ෎䞥ߚ

ᅮ⧚˄

Two Funds Separation Theorem

˅DŽѠ෎䞥ߚ

ᅮ⧚ᣛߎˈ

ሑㅵ

߱㒭

ᅮⱘᡩ䌘ᴎӮЁ᳝

n

Ͼ

亢䰽䌘ѻˈᇍϔϾᳳ

ؐ

-

ᮍᏂ

ᡩ䌘㗙ᴹ䇈ˈ

ᵰা㒭Ҫ

ϸϾ᳝

㒘ড়

԰

Ў

亢䰽䌘ѻˈᡩ䌘ᴎӮ੠

ᴹⱘ

n

Ͼ

亢䰽䌘ѻᰃᅠ

ܼ

ㄝৠⱘDŽ

CAPM

ЁϔϾ

䞡㽕ⱘ

ὖᗉ

ᰃ DŽ

೼䆆

೼䆆

೼䆆

೼䆆

ⱘᯊ

׭

ˈ៥Ӏ

ᅮϸϾ᳝ᑣⱘ㒘

p

q

˄ϡϔᅮ

˅DŽ䖭Ͼ

ⱘᅮНᰃ㒘ড়

p

q

ⱘ䱣ᴎᬊⲞ

णᮍᏂ

ҹ㒘ড়

q

ⱘ䱣ᴎᬊⲞ

ᮍᏂ

DŽ❳

㗙ৃ

Ꮖ㒣থ⦄䖭ህᰃऩϔ

䞣㒓

㋏᭄

DŽᓩ

ܹ

䖭Ͼ

ὖᗉ

ҹ

ˈᇍ

ӏ

ԩϔϾ

䴲ܼ

ᇣᮍᏂ

㒘ড়

m

ˈ

៥Ӏৃҹ䆕ᯢ

ϔⱘϔϾ᳝

㒘ড়

z,

Փᕫ

DŽ

DŽ

DŽ

DŽ

гህᰃ䇈

њ

ܼ

ᮍᏂ

㒘ড়ˈ

݊

ᅗⱘ᳝

㒘ড়

ᰃϔᇍϔᇍⱘˈ

ϔᇍ

ⱘϸϾ㒘ড়ᰃϡⳌ݇ⱘDŽ

䖯ϔ

ˈ

ϔᇍ

ⱘϸϾ㒘ড়ߚ

߿

Ѣ

ܼ

ᇣᮍᏂ

㒘ড়ⱘϸ

ջ

DŽᅗӀⱘϸϾ

ᳳᬊⲞ

Ϣ

ܼ

ᇣᮍᏂ

㒘ড়ⱘ

ᳳᬊⲞ

Ь⿃

ᰃϔϾϡձ䌪Ѣ䖭

Ͼ

ᅮᇍⱘᐌ

ˈᑊ

Ϩ

ᅗӀⱘϸϾ䱣ᴎᬊⲞ

ᮍᏂ

ᑇഛ

ܼ

ᇣᮍ

㒘ড়ⱘ

ᳳᬊⲞ

ᮍᏂ

ⱘϸ

ס

DŽ䖭ϸϾᗻ䋼

Ԑ

Т

೼᭛

Ёߎ⦄䖛DŽ߽

⫼䖭ѯᗻ䋼ˈᇍ೎ᅮⱘϔϾϡⳌ݇㒘ড়ᇍ

m

z

ˈৃҹ䆕ᯢ

ӏ

ԩϔϾ᳝

㒘ড়

p

䱣ᴎᬊⲞ

⥛䛑

m

z

ⱘ䱣ᴎᬊⲞ

ᑇഛ

ˈ㗠ϸϾᴗ䞡

ᙄᙄ

ህᰃ

p

݇Ѣ

m

z

ؐDŽ䖭ህᰃ

Black

˄

1972

˅

ᦤߎⱘ

– CAPM

῵ൟDŽҹϞⱘ䆕ᯢ

ᮍ⊩

Ӭ

Ѣ

ॳ㨫

Ё↨䕗෎ᴀ੠

⧤⹢

ᮍ⊩

DŽ

⊼ᛣ䳊

– CAPM

῵ൟᅲ

ϞᰃϔϾ䱣ᴎᬊⲞ

ߚ

ᔶᓣDŽ೼䖭Ͼߚ

ᔶᓣЁⱘϸϾ෎ህᰃ

m

z

ⱘ䱣ᴎᬊⲞ

DŽ

ᐌᔶᓣⱘ

CAPM

ᰃ᳝

亢䰽䌘ѻⱘDŽ೼ᷛ

ޚᮍᏂ

-

ᳳᬊⲞ

⥛ぎ䯈

Ё

亢䰽䌘ѻ੠

ӏ

ԩ

݊

ᅗ䌘ѻⱘ᠔᳝㒘ড়ⱘ

䔼䗍

ᰃϔ

DŽ៥ӀᏆ

᠔᳝

亢䰽䌘

ѻ

ߎⱘ᳔Շᡩ䌘ᴎӮህᰃ᳝

ᬜ䖍⬠

DŽ

಴ℸ

ˈ೼

ࡴܹ

ϔϾ

亢䰽䌘ѻ

ˈ᳔Շᡩ䌘

ᴎӮህ៤њϔ

Ϣ

ᬜ䖍⬠

ߛ

ⱘℷ

DŽ䖭

ߛ

ህᰃ᠔䇧ⱘ䌘ᴀᏖഎ

˄

capital market line

˅DŽ䖭Ͼ

ߛ

Ϟⱘ㒘ড়ህᰃ᠔䇧ⱘᏖഎ㒘ড়

m

DŽ᠔᳝ⱘᡩ䌘

㗙ˈϡ

ㅵҪ

Ӏⱘ亢䰽

བԩˈ

ৠϔϾᏖഎ㒘ড়DŽ

Ҫ

Ӏⱘϡৠ

ᰃ䗝ᢽϡৠ

亢䰽㒘䌘ѻ

Ϣ

Ꮦഎ㒘ড়

П䯈

ⱘ↨

՟

DŽ䖭ᰃ೼᳝

亢䰽䌘ѻᯊⱘѠ෎䞥ᅮ⧚ˈ

Ў

䋻Ꮥ

Ꮦഎ෎䞥ߚ

ᅮ⧚˄

Money Market Fund Separation Theorem

˅DŽ

ϔϾ㒘ড়ⱘ䱣ᴎᬊⲞ

Ϣ

亢䰽䌘ѻⱘᬊⲞ

Ꮒ㹿

Ў

乱䱣ᴎᬊⲞ

˄

excess return

˅DŽϔϾ䌘ѻ៪㒘ড়ⱘ

乱ᬊⲞ

Ϣ

ᅗⱘᷛ

ޚᮍᏂ

ⱘଚህᰃ

ԡ

亢䰽

ˈг

⿄໣᱂

˄

Sharpe ratio

˅DŽ䌘ᴀᏖഎ

Ϟⱘ㒘ড়݋᳔᳝໻ⱘ

(7)

亢䰽䌘ѻᯊˈϔ

乱䱣ᴎᬊⲞ

䖯㸠ߚ

DŽ

ᕫࠄ

ᮍ⿟

ᓣህᰃ

ৡⱘ

CAPM

ᮍ⿟

ᓣˈབ

ϟ

⼎˖

! " # (2.3)

!

ߚᰃ

Ў

ᡓᢙ

Ꮦഎ亢䰽㗠ᓩ

ⱘᬊⲞ

ˈ

ᰃϔϾ䌘ѻⱘ

ᅮ亢䰽ˈᅗ

Ϣ

Ⳍ݇ˈᑊ

Ϩ

ؐᰃ

0

DŽ᠔ҹ

㹿

Ў

䴲㋏

㒳ᗻ亢䰽˄

non-systematic risk

˅DŽ

ᡓᢙ䴲㋏

㒳ᗻ亢䰽

ࡴᮍᏂ

ˈԚϡᇍ

ᳳᬊⲞ

ӏ

ԩⱘ

䋵⤂

DŽ

ᇍϞᓣ

ؐˈ៥Ӏথ⦄

乱ᬊⲞ

Ϣ

ᗻ݇

ˈ䖭ህᰃ᠔䇧ⱘ䆕ࠌᏖ

˄

security market line

˅DŽ

CAPM

ᮍ⿟

ᓣЁ᳝

㒘ড়

m

ᰃ⬅

亢䰽䌘ѻ᳝

ᬜ䖍⬠

݅

ৠއᅮⱘDŽ

ৃҹ䆕ᯢᅗⱘᴗ䞡৥

!

៤ℷ↨DŽབ

ϡ

णᮍᏂⶽ䰉

ˈ৘

Ͼ

ྟ䌘ѻ೼Ꮦഎ㒘ড়

ⱘ↨䞡੠ᅗӀⱘ

乱ᬊⲞ

៤ℷ↨

,

䖭Ͼ

㒧ᵰヺ

ড়៥

Ӏⱘ

DŽ

CAPM

ҟ㒡

ࠡˈ៥ᦤϔ

ϟ

೼ᑨ⫼Ё

᳝⫼ⱘ

޴

Ͼ

ᓊԌ

DŽ೼

CAPM

Ё

m

ᰃϔϾ᳝

㒘ড়DŽབ

៥Ӏ⫼ϔϾϡϔᅮᰃ᳝

㒘ড়ⱘ

⍜ᵕ

ᡩ䌘㒘ড়

p

ᴹҷ

Ӯ

ᗢḋ

ਸ਼˛

೼䖭⾡

ᚙމ

ϟ

ᵰা㗗

亢䰽䌘ѻ੠

p

П䯈

ⱘ㒘ড়ⱘ

ˈ៥Ӏ

া㛑ᕫ

ϔϾ䕗

໣᱂

DŽ

Treynor

Black

˄

1973

˅ᓩ

ܹ

њ

ᵕㅵ

⧚㒘ড়ⱘ

ὖᗉ

DŽ

䖭Ͼ

ᵕㅵ

⧚㒘ড়

a

ৃҹ

䖛᳔໻࣪

ֵᙃ

˄

information ratio

˅

$

ᕫࠄ

DŽ

Black

Treynor

䖯ϔ

䆕ᯢњϔϾ

㙵ᅮ⧚

" $ (2.4)

䖭Ͼ

ᮍ⿟

ᣛߎ

ᵕㅵ

⧚㒘ড়੠

⍜ᵕ

㒘ড়ϸ

ˈ៥Ӏгৃҹ

ಲࠄॳ

ᴹⱘ䌘ᴀᏖ

Ϟ

DŽ

ᤳ༅

໣᱂

߮

ᵕㅵ

⧚㒘ড়ⱘ

ֵᙃ

DŽ

MacKinlay

˄

1995

˅߭ᣛߎ

ֵᙃ

ϞгᰃϔϾ㒘ড়ⱘ

໣᱂

DŽᇍϞ

䗄ᮍ⿟

ᓣгৃҹ⧚

Ў

m

⹂ᅲᰃ᳝

ⱘˈԚ෎䞥

⧚㗙ᢹ᳝

ֵᙃ

ˈ᠔ҹ

Ҫ

ৃҹ

ᕫࠄ

↨Ꮦഎ

໣᱂

⥛᳈

催ⱘऩ

ԡ

亢䰽

DŽ

Treynor

Black

᭛Ё

ϔ⾡䕗

Нⱘ⧚

DŽ঺

໪ϔϾ

CAPM

ᓊԌ

Black-Litterman

῵ൟ˄

Black

Litterman

ˈ

1992

˅DŽ䖭

෎䞥

⧚㗙гᢹ᳝

ֵᙃ

ˈԚ

Ҫ

߽⫼

৊ᮃ

˄

Bayesian

˅⧚䆎ᴹ

᳈ᮄ乘

ᳳᬊⲞ

णᮍᏂⶽ䰉

ˈ

ݡ

䖯㸠ᳳ

ؐ

-

ᮍᏂӬ

࣪DŽ᳔

ˈ೼

CAPM

Ё亢䰽ᰃ⫼

ᴹ῵

ⱘˈ᳝Ⳍᔧϔ

ߚ

ⷨお

԰

݊

ᅗ৘⾡亢䰽ⱘ

ᑺᴹҷ

᳓ᮍᏂ

ˈ↨བ෎

㋏᭄

˄

Gini coefficient

˅ˈ

VaR

ˈㄝㄝDŽ䖭

ϡ

԰䆺

ҟ㒡

DŽ

༫߽ᅮӋ⧚䆎

༫߽ᅮӋ⧚䆎

༫߽ᅮӋ⧚䆎

༫߽ᅮӋ⧚䆎

ऩᳳⱘ

CAPM

Ё

᳝ϔϾ

ˈ

ህᰃᏖഎⱘ䱣ᴎᬊⲞ

DŽԚᮽ೼

1966

ᑈˈ

King

˄

1966

˅ህ೼ᅲ䆕Ёথ⦄

њᏖഎ

໪ˈᎹϮ

⬠಴

Ԑ

Т

гᕅડ䌘ѻⱘ

(8)

߽ᅮӋ⧚䆎˄

APT

˅੠

CAPM

ϡৠˈৃҹ᳝໮Ͼ

DŽᅗⱘ

؛

䆒г੠

CAPM

ϡৠˈϔ

ৃҹ

Ў

APT

؛

⿡ᖂ

ϔѯˈԚᰃҷӋᰃ

APT

䆎г

ϔ ѯ DŽ ೼

APT

ⱘ থ ሩ 䖛

Ё

䞡 㽕

԰

⫼ ⱘ ᭛

Ross

˄

1976

˅ ˈ

Huberman

˄

1982

˅ˈ

Chamberlain

Rothschild

˄

1983

˅ˈ

Chamberlain

˄

1983

˅ˈ

Ingersoll

˄

1984

˅ˈҹঞ

Connor

˄

1984

˅DŽ᳔ᮽⱘ

APT

ߎ⦄೼

Ross

ˈ

Ҫ

⧚䆎Ϲ

ഄᓎゟ

ᖂ㾖

㒣⌢ⱘ෎⸔ϞˈԚᰃ

ॳ㨫

ᯊᗱ

ϡ

ᯧ⧚⏙DŽ

Huberman

APT

ᇐ԰

њㅔ࣪DŽㅔ࣪ⱘ㽕

ᰃᓩ䖯њ

߽˄

asymptotic arbitrage

˅䖭Ͼ

ὖᗉ

DŽ

Chamberlain

Rothschild

ˈҹঞ

Chamberlain

㒚ഄ

њ

APT

ˈᳳ

ؐ

-

ᮍᏂ

ߚ

ߚ

П䯈

ⱘ݇

DŽ

Ingersoll

ҹঞ

Connor

জᇍ

APT

ⱘ৘Ͼ

԰

њ

㒚㟈

ⷨお

DŽ

݊

Ё

Ingersoll

Ң⧚䆎ϞϹ

ߚ

њ᠔䳔

ⱘϾ

ˈᰃ

থᗻⱘ᭛

DŽ

ϟ

䴶៥ㅔऩ

ҟ㒡

ϔ

ϟ

Huberman

˄

1982

˅ⱘЏ㽕

ⷨお㒧ᵰ

DŽ

Ҫ㗗

ϔ

І

ⱘᏖ

എˈ

ϔϾᏖഎ↨ᅗࠡϔϾ໮ߎϔϾϡৠⱘ䌘ѻDŽ೼

n

ϾᏖഎЁ᳝

n

Ͼ

亢䰽

䌘ѻˈԚᰃϡ

ϾᏖഎЁˈ᠔᳝䌘ѻⱘᬊⲞ

ҙҙ

k

Ͼ೎ᅮⱘ

ѻ⫳DŽ䖭

APT

᳔䞡㽕ⱘ῵ൟ

؛

䆒ˈ⫼

ᮍ⿟㸼⼎

ϟ˖

% & " ' " # (2.5)

%

n

Ͼ䌘ѻⱘᬊⲞ

ˈ

&

ᰃᅗӀⱘ

ᑇഛ

ᬊⲞ

ˈ

'

ᰃϔϾ

ⶽ䰉

ˈᅗⱘ

ϔϾ

߫

ҷ

ϔϾ

ˈ

㹿

Ў

㋴䋳㥋

ⶽ䰉

ˈ

#

ᰃϔϾ䱣ᴎ৥

DŽ

Huberman

؛

'

ℷѸ

ϔˈҹঞ

#

ⱘ݇

㘨ⶽ䰉

ᰃᇍ

ⱘˈᑊ᳝ϔ㟈ⱘϞ

DŽ

䖭ѯ

؛

ϡᰃ

䳔ⱘˈ㗠ᰃৃҹ

࣪DŽ

APT

ⱘⳂⱘᰃ

ߎϔϾ

ᑇഛ

ᬊⲞ

&

ⱘ῵ൟDŽЎ䖒

䖭ϾⳂⱘˈ

Huberman

ᓩ䖯њϔϾ

߽ⱘ

ὖᗉ

DŽϔϾᡩ䌘ㄪ⬹

೼䖭Ͼ῵ൟ

ᰃϔ

І

ⱘ৥

ˈ

Ͼ৥

ᰃϔϾ೼

n

ϾᏖഎ

ⱘᡩ䌘㒘ড়DŽབ

ϔϾᡩ䌘ㄪ⬹

c

೼᠔᳝Ꮦഎ

䞠䛑

ϡ䳔㽕

ӏ

ԩ

ޔ

ܹ

ˈԚᅗ೼

ϾᏖഎ

ᑇഛ

ᬊⲞ

䍟৥Ѣℷ

ˈৠᯊᅗ೼

ϾᏖഎ

ⱘ䱣ᴎᬊⲞ

ᮍᏂ

䍟৥Ѣ

ˈᅗህ

㹿

Ў

ϔϾ˄

䖯˅

߽㒘ড়DŽ

Huberman

Ё

᳝ᦤঞˈԚ

߽㒘ড়ⱘϸϾ݇Ѣ䱣ᴎᬊⲞ

ⱘᳳ

ؐ੠

ᮍᏂ

ᴵӊ

ৃҹㅔ࣪៤ϔϾ

ᴵӊ˖

ᵰᄬ

೼ϔϾ

ޔ

ܹ

Ў

ⱘᡩ䌘ㄪ

⬹ˈᑊ

Ϩ

ᅗ᳝ϔϾ

߫

Փᕫᑇഛ

ᬊⲞ

Ϣ

ޚᮍᏂ

ⱘଚ䍟৥Ѣ

ˈ

М

Ꮦഎ

Ϟህ

߽㒘ড়DŽ

߮

ᓔྟⱘᏖഎ

؛

䆒ˈ

APT

ⱘ⧚䆎ᓎゟ೼

ϔⱘϔϾ

؛

П

Ϟˈ

ህᰃᏖഎ

ϡ

߽DŽ

APT

䆎ᰃ

˖

Ꮦഎ

ϡ

߽ˈ

М

ᳳᬊⲞ

⥛ᖙ

Ԑ

⒵䎇

ϔϾ

ᗻ݇

ˈ

гህᰃ䇈ˈ

ᑇഛ

ᬊⲞ

ৃҹ䖥

Ԑ

⫼ᐌ

'

Ёⱘ৥

㸼⼎

DŽབ

ᵰՓ

⫼ҹϞⱘㅔ࣪

ᴵӊ

ˈ

APT

᥼ᇐ݊

ᅲⳌᔧⱘㅔ

ऩDŽϔ

Փ

⫼ড䆕

DŽ

؛

ᑇഛ

ᬊⲞ

ϡ䖥

Ԑ

⒵䎇

Ϟ

䗄㒓

ᗻ݇

DŽབ

៥Ӏ

&

ᡩᕅ

⬅ᐌ

'

Ёⱘ৥

៤ⱘ

ᄤぎ䯈

Ϟˈ

М

ৃҹ䆕ᯢ

ᔦ⅟

(9)

APT

CAPM

ᰃᓎゟ೼ϡৠ

؛

П

ϞⱘϸϾϡৠⱘ⧚䆎ˈϹ

Ϟ䇈ϡ

䖛Ѣ

ㅔऩഄ䖯㸠↨䕗DŽԚབ

៥Ӏ೼

APT

Ё

⬹Ā

䖯ā䖭Ͼ䞡㽕ⱘ

؛

䆒ˈ

М

CAPM

ৃҹㅔऩഄ

៤ᰃ

APT

ⱘϔϾ

⡍՟

DŽ

⍜䌍䌘ᴀ䌘ѻᅮӋ῵ൟ

⍜䌍䌘ᴀ䌘ѻᅮӋ῵ൟ

⍜䌍䌘ᴀ䌘ѻᅮӋ῵ൟ

⍜䌍䌘ᴀ䌘ѻᅮӋ῵ൟҹঞ

ҹঞ

ҹঞ䎼ᳳ䌘ᴀ䌘ѻᅮӋ῵ൟ

ҹঞ

䎼ᳳ䌘ᴀ䌘ѻᅮӋ῵ൟ

䎼ᳳ䌘ᴀ䌘ѻᅮӋ῵ൟ

䎼ᳳ䌘ᴀ䌘ѻᅮӋ῵ൟ

⍜䌍

䌘ᴀ䌘ѻᅮӋ῵ൟ˄

CCAPM

˅ҹঞ

ᳳ䌘ᴀ䌘ѻᅮӋ῵ൟ˄

ICAPM

˅ᰃ

CAPM

APT

П

໪ϸϾ↨䕗᳝ᕅડ

ⱘ῵ൟDŽᅗӀৃҹ

㹿

៤ᰃ

CAPM

⡍՟

᥼ᑓ

DŽ೼

CCAPM

Ёˈ

⍜䌍

੠ᡩ䌘㒘ড়

㹿

ϔ

䍋㗗

DŽ

DŽ

DŽ

DŽ

ICAPM

߭ᰃ

໮ᳳⱘ῵

ൟˈ䖭ѯ῵ൟৃҹᰃ

⾏ᬷ

໮ᳳⱘˈ

гৃҹᰃ

䖲㓁

໮ᳳⱘDŽ䖭ϸϾ῵ൟᑊ

ϡᰃϔϾ೎ᅮⱘ

ゟⱘ῵ൟˈ㗠ᰃϸϾ໻ḚᶊDŽ

CCAPM

ICAPM

ᑊϡᅠ

ܼѦ

DŽ

CCAPM

ৃҹᰃ

ᳳⱘˈ

ICAPM

гৃҹࣙ

৿

⍜䌍

䖭Ͼ

DŽ⬅Ѣ䖭ϸϾ῵

ൟ㒣ᐌᰃ

Դ

Ё᳝៥ˈ៥Ё᳝

Դ

ˈ᠔ҹ៥Ӏϔᑊ

ҟ㒡

DŽ

ᮽ೼

1928

ᑈˈ

Ramey

˄

1928

˅ህ

њϔϾ

⍜䌍

䌘ᴀ䌘ѻᅮӋ῵ൟDŽ

ㅵҪⷨお

њ໮ᳳ῵ൟˈ

Ԛ

Ҫা㗗

ऩϔ೎ᅮᬊⲞ

䌘ѻDŽ

޴

ᑈҹ

ˈ

Mossin

˄

1968

˅

, Samuelson

˄

1969

˅੠

Merton

˄

1969

˅

އ

䱣ᴎᗻⱘ໮

ᳳⱘ

⍜䌍

੠䌘ѻ㒘ড়

乬DŽ

⿡ৢ

ⱘ῵ൟ㒣ᐌᰃ

䖲㓁

໮ᳳⱘˈ

↨བ

Merton

˄

1971

˅ҹ ঞ

Merton

˄

1973

˅DŽ

䞡 㽕ⱘ᭛

䖬ࣙ ᣀ

Lucas

˄

1978

˅

, Breeden

˄

1979

˅

, Cox, Ingersoll

Ross

˄

1985

˅

,

ҹঞ

Cox

Huang

˄

1989

˅DŽϔϾ↨䕗

᱂䘡

㒧ᵰ

⍜䌍

䌘ᴀ䌘ѻᅮӋ῵ൟϔ

Ӯ

ߎ໮

䱣ᴎᬊⲞ

῵ൟDŽ

݊

Ё

Ꮦഎ㒘 ড়Ӯᰃ ϔϾ

ˈ঺ ໪

ϔϾ 䱣ᴎ

ϔ

Ӯ᳝ϔ Ͼᇍ

ކ

˄

hedge

˅

DŽ

಴ℸ

೼ᔶᓣϞ

ICAPM

APT

䕗㉏

Ԑ

DŽ

՟

໪ᰃᇍ

᭄ᬜ

ߑ᭄

˄

log

utility

˅ⱘ

⅞ᚙމ

ϟ

ˈᡩ䌘㗙㒣ᐌӮ᳝

⬹䱣ᴎ

ⷁ㾚

˄

myopic

˅㸠Ўˈ

಴ℸ

㋴ҡᮻ

៤ゟDŽ

CCAPM

Ёˈ䌘ѻⱘ

ᑇഛ

ᬊⲞ

⥛㹿ᭈ

Ͼ㒣⌢Ёⱘ

ᘏ⍜䌍

ⱘ៤

᠔އᅮˈ

гህᰃৃҹ

Ўˈ೼

CCAPM

Ёˈ

CAPM

ЁⱘᏖഎᬊⲞ

੠ᇚᴹ

⍜䌍

ߑ

ᰃᅠ

ܼ

Ⳍ݇ⱘDŽ೼䖭ϔ

Ϟˈৃҹ

Ў

CCAPM

CAPM

⡍՟

DŽԚ

CCAPM

ৃҹᰃ

ᳳⱘˈ䖭ϔ

ৃҹ

៤ᰃ

CAPM

᥼ᑓ

DŽ঺໪ˈ᳔ㅔऩⱘ

CCAPM

˄

Breeden

ˈ

1979

˅

ৃҹ

៤ᰃϔϾㅔ࣪њⱘ

ICAPM

῵ൟˈ

ϔϾ໮

ICAPM

῵ൟ⫼ϔϾ

⍜䌍಴

ᣀњDŽ䖭⾡ㅔ࣪ⱘḍᴀ

ॳ಴

ᰃᮽᳳⱘ῵ൟϔ

Փ

Ϟৃߚ

˄

time-separable

˅ⱘ

ߑ᭄

DŽ

ICAPM

῵ൟ

ᐌ᳝ϸ⾡

ᡔᎻ

ˈϔ⾡ᰃ

ࡼᗕ

㾘ߦ

˄

dynamic programming

˅ˈ

ϔ⾡ᰃ

˄

martingale approach

˅DŽ೼

ࡼᗕ

㾘ߦ

Ёˈ

῵ൟⱘ䖛

ᰃҢ᳔

ৢࠄ

᳔ࠡˈ

᠔䇧ⱘ

צ

ᔦ㒇

˄

backward induction

˅DŽ೼

⾏ᬷ

῵ൟЁˈ

ϔ

ℹ䛑

ЎњϔϾऩᳳ῵ൟDŽ೼

䖲㓁

Ёˈ㉏

Ԑ

᥼ᇐ

ৃҹ

ߎ᳝ৡⱘ

Bellman

أ

ߚ

DŽ

Bellman

ᮍ⿟

ϔ

䴲㒓

ᗻⱘᑊ

ˈԚৃҹ⫼

ؐ

㾷⊩

DŽ

ᳳ᭛

Џ㽕ᰃ

Pliska

˄

1986

˅

, Karatzas, Lehoczky

Shreve

˄

1987

˅

,

ҹঞ

Cox

Huang

˄

1989

˅DŽ䖭⾡

ᮍ⊩

ϔ

䳔㽕

؛

䆒Ꮦഎᰃᅠ

ⱘˈԚ

He

Pearson

˄

1991

˅

(10)

њⱘᡩ䌘㒘ড়ⱘӋؐˈ㗠

⍜䌍

ህⳌᔧѢ䖭Ͼᡩ䌘㒘ড়ⱘ

߽DŽ߽⫼䱣ᴎ

಴ᄤ

ὖᗉ

ˈ䋶ѻৃҹ

㸼⼎

៤᳾ᴹ

߽

ⱘ⦄ᯊӋؐDŽ

Փ

⫼䖭Ͼ

㑺ᴳ

˄

budget

constraint

˅

ᮍ⿟

ᓣˈ໮ᳳⱘᡩ䌘

⍜䌍䯂

㹿

࣪៤ϔϾ݇Ѣ᳔Շ

⍜䌍

䗨ᕘ

ߚ

乬˄

variational problem

˅DŽ䖭Ͼ

ߚ

乬ⱘ

㾷䗮

ᐌӮᓩ

ϔϾ

ᗻⱘ

أ

ߚ

ᮍ⿟

DŽ

⬅Ѣᰃ

ᗻⱘˈ䖭Ͼ

ᮍ⿟

Ӯ↨

Bellman

ᮍ⿟᳈ᆍ

DŽ᳔Շᡩ䌘㒘ড়ⱘ↨

՟

߭

ϔ

ߎ

⍜䌍

䏃ᕘ

੠䋶ѻ

ݡ

ऩ⣀

އDŽ

ˏ

ˏ

ˏ

ˏˊ

ˊ

ˊ

ˊ

䖥ᳳ

䖥ᳳ䞡㽕

䖥ᳳ

䖥ᳳ

䞡㽕

䞡㽕⧚䆎ঞ

䞡㽕

⧚䆎ঞ

⧚䆎ঞᡔᎻ

⧚䆎ঞ

ᡔᎻ

ᡔᎻ

ᡔᎻ

䱣ᴎᡬ⦄಴ᄤ

䱣ᴎᡬ⦄಴ᄤ

䱣ᴎᡬ⦄಴ᄤ˄

䱣ᴎᡬ⦄಴ᄤ

˄

˄

˄

Stochastic Discount Factor

˅

˅

˅

˅

䱣ᴎ

಴ᄤ

ᰃϔϾ

ⱘ䱣ᴎ

ᅗৃҹ

ߎᏖഎϞ᠔᳝䌘ѻⱘӋ

DŽ

ҹऩᳳ῵ൟЎ

՟

ˈབ

ϔϾ䌘ѻⱘ䱣ᴎᬊⲞᰃ

%

М

ᅗⱘӋ

ህ⬅݀ᓣ

%

ߎDŽᇍ

ӏ

ԩ䱣ᴎᬊⲞ

㗠㿔ˈ᳝߭

DŽ᠔᳝䌘ѻᅮӋ⧚䆎ৃҹ

䖛䱣ᴎ

಴ᄤ

ᦣ䗄

DŽ

џ

ᅲϞˈ

Cochrane

˄

2001

˅ҹঞ

Shefrin

˄

2008

˅

䖭ϸ

㨫䗮

䛑Փ

⫼䱣ᴎ

಴ᄤ

䖭⾡

㿔DŽ

䱣ᴎ

಴ᄤ

೼ᗻˈ

Ϣ

৺ˈ

ϔᗻˈߚ

ⱘℷ

ᗻˈऩ

ᗻˈ

ᮍᏂ

ˈ

Ϣ

Ꮦഎⱘ

ᵘᆚߛ

Ⳍ݇DŽ↨བ䇈ˈ೼᳝

䰤㓈

ऩᳳ䌘ѻᏖഎЁˈ

ऩϔӋ

Ḑ⊩

߭އᅮ䱣ᴎ

಴ᄤ

ᗻⱘ

˗

Ꮦഎᰃᅠ

ⱘˈᔧ

Ϩҙ

ᔧ䱣ᴎ

಴ᄤ

ϔⱘ

˗

ϔϾᅠ

ᏖഎЁ

߽ˈজᔧ

Ϩҙ

ᔧ䱣ᴎ

಴ᄤ

ⱘ৘Ͼߚ

䞣䛑

ЎϹ

˗

ᔧ䱣ᴎ

಴ᄤ

ϡ

ϔᯊˈ

೼㗠

Ϩҙ

ϔϔϾ

㹿

Ѹᯧⱘ䱣ᴎ

಴ᄤ

DŽ

䱣ᴎ

಴ᄤ

ⱘ䞡㽕ᗻᰃϡ㿔㗠ஏⱘDŽ

՟

བˈ೼

ߑ᭄

῵ൟЁˈᅗ

Ϣ

Ⳍ݇DŽ೼

CCAPM

Ёᅗ੠

⍜䌍

๲䭓

Ⳉ᥹

Ⳍ݇DŽ೼

НϞˈϡৠⱘ䌘ѻᅮ

Ӌ῵ൟৃҹ

㹿䅸

Ўᰃ೼

ⷨお

ϡৠⱘ䱣ᴎ

಴ᄤ

DŽ

Hansen-Richard

ᬊⲞ⥛ߚ㾷

ᬊⲞ⥛ߚ㾷

ᬊⲞ⥛ߚ㾷

ᬊⲞ⥛ߚ㾷

Chamberlain

Rothschild

˄

1983

˅䆕ᯢˈ

– CAPM

ৃҹ

㹿

Ꮰᇨԃ⡍ぎ

੠ˈԚ៥Ӏ䳔㽕ϔ⾡↨䕗

णᮍᏂݙ

˄

inner product

˅DŽ೼䖭⾡Ḛᶊ

ϟ

ˈ

ӏ

ԩ 䌘 ѻ ⱘ 䱣 ᴎ ᬊ Ⲟ

Ꮰ ᇨ ԃ ⡍ ぎ 䯈

Ё ⱘ ϔ Ͼ ৥

ˈ ৃ ҹ ⫼ ᡩ ᕅ

˄

projection

˅ᴹߚ

៤ᐌ

䞣䚼

ߚˈᏖഎ䱣ᴎᬊⲞ

⥛䚼

ߚˈҹঞϔϾ

˄

residual vector

˅DŽ䖭

ϝ

Ͼߚ

Ꮰᇨԃ⡍ぎ䯈

Ё

Ѧ

ൖⳈ

DŽ䖭⾡

CAPM

Ў

ᰃϔ⾡৥

ൖⳈ

ߚ

㾖⚍

೼䞥㵡ᄺЁᑊϡᰃ

Ӵ

㒳ⱘ

㾖⚍

ˈϔ

к䛑

CAPM

ᦣ䗄

៤ᰃϔϾ

ˈ

಴ℸϝ

Ͼߚ

䳊णᮍᏂ

DŽ䖭ϸ⾡ϡৠⱘ

⚍䛑

ᕜࡽ

Ѣ

CAPM

ⱘ⧚

ⱘDŽ

݊

Ё

ϔ⾡

㾖⚍

䌟ќ

њ

CAPM

޴

ԩ

Нˈ

಴ℸՓ

ᕫᕜ

ὖᗉ

DŽ↨བ䌘ѻ㒘ড়ⱘ᳝

ᬜ䖍⬠

೼Ϟ

䗄Ꮰᇨԃ⡍ぎ䯈

Ёᰃϔ

DŽ

䱣ᴎ

៤ⱘ

Ꮰᇨԃ⡍ぎ䯈

ݙ

Ϟᑊϡᰃ

णᮍᏂݙ

ˈ

㗠ᰃ

Ь

ݙ

˖

( )

DŽ

Փ

⫼䖭⾡

ݙ

㟈঺ϔ⾡ϡৠⱘ䱣ᴎᬊⲞ

ⱘߚ

㾷ᮍ

ᓣˈ

䖭ህᰃ

Hansen-Richard

ᬊⲞ

ߚ

DŽ

⊼ᛣ

Hansen

Richard

˄

1987

˅Ё

԰

㗙Ӏ䖬

(11)

Ͼ䌘ѻⱘ䱣ᴎᬊⲞ

⥛㹿

ߚ

ϝ

Ͼ

ߚDŽ

ϔϾ

ߚᰃϔϾᇍ᠔᳝䌘ѻ

Ⳍৠⱘ䱣

ᴎᬊⲞ

ˈᅗ੠䱣ᴎ

಴ᄤ

៤ℷ↨DŽ

ѠϾ

ߚⱘ෎৥

ϔ

㠀প

ᬊⲞ

⥛ぎ䯈

ϞⱘᡩᕅDŽ

㄀ϝ

Ͼ

ߚᰃϔϾ

DŽ䖭

ϝ

Ͼ

ߚ೼ҹ

Ь⿃

Ў

ݙ

ぎ䯈

Ё

Ѧ

ൖⳈ

DŽ

Hansen-Richard

ᬊⲞ

ߚ

އ

ѯ

乬Ё↨

CAPM

ߚ

㾷᳈ࡴ

ᮍ֓

ˈ

՟

Hansen

Richard

ҹঞ

Cochrane

Saa-Requejo

˄

2000

˅DŽ

ᐌ೼

Փ

Hansen-Richard

ᬊⲞ

ߚ

ᯊˈӮৠᯊ

Փ

Hansen-Richard

䱣ᴎ

಴ᄤ

ߚ

DŽ

Hansen-Richard

䱣ᴎ

಴ᄤ

ߚ

Hansen-Richard

ᬊⲞ

ߚ

㾷ᵕ݊

Ԑ

ˈ

ϡ䖛

೼ߚ

䱣ᴎ

಴ᄤ

Ёˈ

ѠϾ

ߚⱘ෎ϔ

㠀প

乱䱣ᴎ

಴ᄤぎ䯈

ϞⱘᡩᕅDŽ

Hansen-Jaganathan

䖍⬠

䖍⬠

䖍⬠

䖍⬠

ᇍϔϾᏖഎ

ˈ

ӏᛣ

ϸϾϡৠⱘ䱣ᴎ䌘ѻᬊⲞ

*+

*,

ҹঞ᠔᳝ৃ㸠

ⱘ䱣ᴎ

಴ᄤ

-

ˈৃҹ䆕ᯢ

./

0 1

1

(3.1)

䖭ህᰃ

ৡⱘ

Hansen-Jaganathan

˄

1991

˅

䖍⬠

DŽЎњ

ഄ⧚

Ϟᓣˈ៥

Ӏৃҹ

ϔϾᅠ

ⱘᏖഎˈ

಴ℸ

ᏖഎϞ

亢䰽䌘ѻˈᑊ

Ϩ

ҹঞ᠔᳝ৃ㸠ⱘ䱣

಴ᄤ

ϔⱘDŽ

಴ℸ

ህᰃᏖഎⱘ

Sharpe

಴ᄤ

ˈгህᰃऩ

ԡ

亢䰽

㛑ᕫ

ⱘ᳔໻

ಲ᡹

DŽ

Hansen-Jaganathan

䖍⬠

⫼䱣ᴎ

಴ᄤ㒭

ߎњ

Sharpe

಴ᄤ

DŽ೼

䘡ᚙމ

ϟ

ˈϡϔᅮ

亢䰽䌘ѻˈ䱣ᴎ

಴ᄤ

гϡ

ϔDŽ⫼

Hansen-Richard

ߚ

ҹঞ䱣ᴎ

಴ᄤ

ߚ

ৃҹ

ᕜᮍ֓

ᕫࠄ

ㄝᓣⱘϸ

ҔМ

׭প

ࠄᵕ

ؐˈ

Ң⬹DŽ঺໪ˈ

Hansen-Richard

ᬊⲞ

ߚ

г

៥Ӏৃҹ

ഄ೼

Ꮰᇨԃ⡍ぎ䯈

ЁԧӮ

Hansen-Jaganathan

䖍⬠

޴

ԩ

НDŽ

Hansen-Jaganathan

䖍⬠

ⱘϔϾ᳔

Ⳉ᥹

ⱘᑨ⫼ᰃ⫼ᴹ䆘Ԅϡৠⱘ䌘ѻᅮӋ῵ൟDŽ

Hansen, Heaton

Luttmer

˄

1995

˅

,

ҹঞ

Hansen

Jaganathn

˄

1997

˅DŽϡৠ

ⱘ䌘ѻᅮӋ῵ൟӮ

ߎϔ

߫

ৃ㸠ⱘ䱣ᴎ

಴ᄤ

DŽ

಴ℸ

៥Ӏৃҹ䅵ㅫ

Hansen-Jaganathan

䖍⬠

ˈᑊ

Ϩ

੠Ꮦഎⱘ

Sharpe

಴ᄤ

䖯㸠↨䕗DŽབ

Ўњ

ߎড়⧚ⱘ

Sharpe

಴ᄤ

ˈ῵ൟЁⱘ

খ᭄

ህϡ

ড়ᳳ

ⱘℷᐌؐˈ

М

῵ൟህϡᰃ

ⱘDŽ݇Ѣ䆘Ԅ䌘

ѻᅮӋ῵ൟⱘ䞡㽕᭛

䖬ࣙᣀ

Snow

˄

1990

˅

, Bansal

Viswanathan

˄

1993

˅

,

ҹ

Jaganathan

Wang

˄

1996

˅DŽ঺໪೼

ℸ乎֓

ᣛߎˈ䆘Ԅ䌘ѻᅮӋ῵ൟⱘ঺ϔϾ

䞡㽕

᠟↉

Ẕ偠

Euler

ᮍ⿟

DŽ

ϔϾ䌘ѻᇚᴹ

ᬊⲞᅠ

ܼ

ϡঞ঺ϔϾᡩ䌘㒘ড়ˈ

М

ᅗⱘӋ

ᑨᔧ

Ԣ

Ѣ

䖭Ͼ㒘ড়ⱘӋ

DŽ䖭ህᰃ

᮴༫

߽

䖍⬠

˄

no-arbitrage boundary

˅DŽ

Hansen-Jaganathan

䖍⬠

ৃҹ䇈ᰃ݇Ѣ

᮴༫

߽

䖍⬠

ⱘϔϾ

䆎DŽԚ೼

ᚙމ

ϟ

ˈ

᮴༫

߽

䖍⬠

㒣ᐌ

໾ᆑ

ˈ

ҹ

Ѣϡ

ᅲ⫼DŽ

Cochrane

Saa-Requejo

˄

2000

˅

ऩᳳˈ໮ᳳˈҹঞ

䖲㓁

Ѹᯧ˄

good deal

˅

䖍⬠

DŽ೼ৠϔᳳ

ߞ

⠽Ёˈ

Bernardo

Ledoit

˄

2000

˅

(12)

᮴༫

߽

䖍⬠

DŽ᳔䖥ˈ

ⷨお

㗙г

њ৘⾡

݊

ᅗⱘ

䴲᮴༫

߽

䖍⬠

DŽ৘⾡

䖍⬠

ϔ

ܹ

ϡৠⱘ

㑺ᴳ

ᴵӊ

ˈ

಴ℸᕜ䲒

᱂䘡

ഄ↨䕗৘⾡

䖍⬠

Ӭ㔎⚍

DŽ

亢䰽ЁᗻᅮӋ

亢䰽ЁᗻᅮӋ

亢䰽ЁᗻᅮӋ˄

亢䰽ЁᗻᅮӋ

˄

˄

˄

Risk-neutral Pricing

˅

˅ҹঞ݊ᅗ⌟ᑺবᤶᮍ⊩

˅

˅

ҹঞ݊ᅗ⌟ᑺবᤶᮍ⊩

ҹঞ݊ᅗ⌟ᑺবᤶᮍ⊩

ҹঞ݊ᅗ⌟ᑺবᤶᮍ⊩

亢䰽ЁᗻᅮӋ⧚䆎ᑊϡᰃ

ゟഄথሩ

ᴹⱘDŽ

џ

ᅲϞˈ

ेՓ

ᰃऩᳳⱘ

CAPM

гৃҹ⫼亢䰽ЁᗻᅮӋ⧚䆎ᴹ

ᦣ䗄

DŽ⧚䆎ⱘᓎゟЁˈЏ㽕᭛

Cox

Ross

˄

1976

˅

, Harrison

Kreps

˄

1979

˅

,

ҹঞ

Harrison

Pliska

˄

1981

˅DŽ঺໪ˈ

Cox

ˈ

Ross

Rubinstein

˄

1979

˅

њѠঝ

˄

binomial tree

˅ᳳᴗ῵ൟDŽ䖭Ͼㅔऩⱘ

῵ൟᇍ⧚

亢䰽ЁᗻᅮӋ⧚䆎

ᵕ݊

᳝⫼DŽ

ৡⱘ

Black-Scholes

˄

Black

Schole, 1973

˅ᳳᴗ῵ൟгৃҹ⫼亢䰽ЁᗻᅮӋ⧚䆎ᴹ

ᦣ䗄

DŽ

Փ

⫼䱣ᴎ

಴ᄤ

ⱘ῵ൟЁˈ䌘ѻⱘӋ

ᰃ⬅ᇚᴹⱘᬊⲞ੠䱣ᴎ

಴ᄤ

ݙ

ߎⱘDŽ䖭Ͼ

ݙ

ᰃ೼⠽⧚

ᑺˈгህᰃᅲ

Ёⱘ

Пϟ

ⱘᳳ

DŽߚ

ϸ

ˈ៥Ӏ

ܜ

೼⠽⧚

ϟ

䅵ㅫ᳾ᴹᬊⲞⱘᳳ

ؐˈ

ݡ

⫼亢䰽

䇗ᭈ

䖛ⱘ

ᴹ䅵ㅫ⦄೼ⱘӋ

DŽ῵ൟⱘ

ೄ䲒

ᐌᐌ೼䅵ㅫ亢䰽

䇗ᭈ

䖛ⱘ

ˈ

Ў䖭Ͼ

ᇍϡৠⱘ䌘ѻᰃϡৠⱘDŽ೼亢䰽ЁᗻᅮӋЁˈ៥Ӏ⫼

亢䰽

ӏ

ԩ䌘ѻⱘᳳ

ؐDŽ

Ў䖭Ͼ

ॳ಴

ˈ

ӏ

ԩ䌘ѻ

䛑㹿

Ўϡ

ᏺӏ

ԩ亢䰽ˈ

಴ℸ

䖭⾡

ᮍ⊩

㹿

Ў亢䰽ЁᗻᅮӋDŽҷӋᰃ៥Ӏϡ

⫼⠽⧚

ᑺᴹ䅵ㅫᳳ

ؐˈ㗠ᰃ

ᕫՓ

⫼亢䰽

Ёᗻ

ᑺDŽৃҹ

Ўˈᇍ

Ͼ䌘ѻ㗠㿔ˈ䖭Ͼ

ᑺᰃ⫼亢䰽

䇗ᭈ

䖛ⱘϔϾ

ᑺDŽԚ

ᏖഎϞ亢䰽Ёᗻ

ᑺᐌᐌᰃ

ϔⱘˈᑊ

Ϩ

ϡ䱣

Ͼ䌘ѻ㗠

DŽ䖭ህ

Փᕫ

亢䰽Ё

ᗻᅮӋ݋᳝

໻ⱘ

Ӭ

ᗻDŽᇍ

ӏ

ԩϔϾ䌘ѻˈ៥Ӏ

䳔䅵ㅫᅗ೼亢䰽Ёᗻ

ϟ

ؐˈ

ৢ؛

䖭Ͼ䌘ѻϡ

亢䰽ˈ㗠

Փ

亢䰽߽

䖯㸠

DŽҢ

ᑺϞ

䇈ˈ亢䰽ЁᗻᅮӋህᰃ

䫭䫭

ᇍˈ៥Ӏ

Փ

䫭䇃

ᑺˈ

ݡ

Փ

䫭䇃

DŽ䖭ϸϾ

䫭䇃

ⱘৠᯊ

Փ

ߎℷ⹂ⱘ䌘ѻӋ

DŽ⫼

ᴹ䇈ˈ᠔᳝䌘ѻⱘӋ

ˈབ

亢䰽؎ࠌᴹ

㸵䞣

ˈ೼亢䰽Ёᗻ

ᑺЁህᰃϔϾ

˄

martingale

˅

DŽ

⠽⧚

ᑺ੠亢䰽Ёᗻ

ᑺᰒ

ᰃ᳝

㘨㋏

ⱘDŽᅗӀⱘ

㘨㋏

ℷᰃᡩ䌘㗙ᇍ亢䰽ⱘ

ᑺDŽ䖭ϸϾ

ᑺⱘ

Radon-Nikodym

ଚᰃ⬅ᡩ䌘㗙ⱘ

ߑ᭄

އᅮⱘDŽབ

ᓎ῵㗙ϡ݇

ᖗ䖍

ߑ᭄

ˈ

Ҫ

ৃҹ

Ⳉ᥹ݭ

ϟ

亢䰽Ёᗻ

ᑺˈ

೼䖭Ͼ

ϟ

䅵ㅫ䌘ѻⱘӋ

DŽ䖭⾡

ᮍ⊩㹿ᑓ

Փ

⫼ˈ

݊

ᰃ೼䞥㵡㸡⫳⠽ᅮӋ

䴶DŽ঺໪ˈབ

ᵰⷨお

㗙᳝෎ᴀ䌘ѻҹঞᓎゟ೼ᅗ

П

Ϟⱘ㸡⫳⠽ⱘӋ

ˈ

߭Ϟ

Ҫ

ৃҹ

ᡩ䌘㗙ⱘ

ߑ᭄ಲ

ㅫߎᴹDŽ↨བˈ

Ҫ

ৃҹ

ⷨお

䏇䎗

ᰃϡᰃ೼ᅮӋЁ

䍋԰

⫼DŽ

Pan

˄

2002

˅DŽ

䳔㽕

ⱘᰃˈ

ᤶ˄

measure change

˅ᰃϔ⾡

᱂䘡

ᡔᎻ

DŽḍ᥂

ⱘ䳔㽕ˈ᳝ᯊ

׭

Փ

⫼亢䰽Ёᗻ

П

໪ⱘ

ᑺᇍ䅵ㅫӮ

᳈ࡴᮍ֓

DŽ

՟

བ೼

䱣ᴎ

߽

⥛㒧

῵ൟᯊˈ᠔䇧ⱘ

ᑺ˄

forward measure

˅㒣ᐌӮ↨䕗

ᮍ֓

DŽৃҹ䇈᠔

᳝ⱘ

ᤶ෎ᴀϞ

ᰃҢ

⾡䅵Ӌऩ

ԡব

ᤶ˄

change of numeraire

˅㗠ᴹDŽབ

Figure

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References

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