Asset Pricing - A Brief Review

Transcription

1 MPRA Munich Personal RePEc Archive Asset Pricing - A Brief Review Minqiang Li 2010 Online at MPRA Paper No , posted 30. April :08 UTC

2 Asset Pricing Models A Brief Review Minqiang Li Georgia Institute of Technology Abstract I first introduce the early-stage and modern classical asset pricing and portfolio theories. These include: the capital asset pricing model (CAPM), the arbitrage pricing theory (APT), the consumption capital asset pricing model (CCAPM), the intertemporal capital asset pricing model (ICAPM), and some other important modern concepts and techniques. Finally, I discuss the most recent development during the last decade and the outlook in the field of asset pricing.

3 asset asset pricing portfolio financial derivatives fixed income securities sovereign investment funds behavioral finance financial engineering puzzle equity premium Campbell2000Mehra 2003 Prescott Cochrane2005Campbell Mehra2000 Prescott Cochrane Ingersoll1987 Huang Litzenberger

4 Duffie2001Cochrane2001LeRoy Werner2001Pennacchi2008 Skiadas LeRoy Werner Skiadas Cochrane stochastic discount factor LeRoy Werner Cochrane Hilbert Skiadas LeRoy Werner space Skiadas Duffie Pennacchi Björk2009 Shreve2004 arbitrage optimization equilibrium Capital Asset Pricing Model CAPM APT Arbitrage Pricing Theory, Intertemporal Capital Asset Pricing Model, ICAPM CCAPM Consumption Capital Asset Pricing Model, Option Pricing Theory Markowitz, Merton Miller Scholes Sharpe CAPM

5 1952Sharpe1964Lintner1965Mossin1966 Black CAPM Markowitz 1972Markowitz Markowitz diversification Markowitz Markowitz Markowitz Friedman Markowitz Sharpe1964Lintner 1965Mossin1966 Sharpe Black1972 CAPM Markowitz - Black CAPM CAPM efficient frontier zero-correlated portfolio fund separation theorem CAPM CAPM - n i i R (2.1) (2.2) efficient portfolio Lagrangian multiplier global 4

6 minimum variance portfolio - n - Two Funds Separation Theorem n pcapm q p q q m z, m z m z p p m z Black1972 CAPM CAPM m z CAPM - line m capital market Money Market Fund Separation Theorem excess return Sharpe ratio 5

7 CAPM!"# (2.3) 0! nonsystematic risk security market line CAPM m!, CAPM CAPM p p m a Treynor Black 1973 information ratio$ Black Treynor " $ (2.4) MacKinlay 1995 m Treynor Black CAPM Black-LittermanBlack Bayesian Litterman CAPM Gini coefficientvar King1966 CAPM

8 CAPM APT APT CAPM APT APT Ross1976Huberman 1982Chamberlain Rothschild1983Chamberlain1983Ingersoll 1984 Connor1984 APT Ross Huberman APT asymptotic Chamberlain Rothschild Chamberlain arbitrage APT- Ingersoll Connor APT Ingersoll Huberman1982 n n k APT % n % & & " '"# ' (2.5) # Huberman ' # APT & Huberman n c Huberman APT APT ' APT & ' 7

9 APT CAPM APT CAPM APT CAPM APT CCAPM ICAPM CCAPM ICAPM CAPM CCAPM ICAPM CCAPM ICAPM 1928Ramey1928 Mossin1968, Samuelson1969 Merton1969 Merton 1971 Merton1973 Lucas1978, Breeden 1979, Cox, Ingersoll Ross1985, Cox Huang1989 hedge ICAPM APT log utility myopic CCAPM CCAPMCAPM CCAPM CAPM CCAPM CAPM CCAPM Breeden ICAPM 1979 ICAPM time-separable ICAPM dynamic programming martingale approach backward induction Bellman Bellman Pliska1986, Karatzas, Lehoczky Shreve1987, Huang1989 He Pearson1991 Cox 8

10 budget constraint variational problem Bellman Stochastic Discount Factor % % Cochrane2001 Shefrin 2008 CCAPM Hansen-Richard Chamberlain Rothschild1983 CAPM inner product projection residual vector CAPM CAPM CAPM CAPM () Hansen-Richard Hansen Richard1987 conditional information Hansen-Richard 9

11 Hansen-Richard CAPM Hansen Richard Cochrane Saa-Requejo2000 Hansen-Richard Hansen-Richard Hansen-Richard Hansen-Richard Hansen-Jaganathan -, * +*./ (3.1) Hansen-Jaganathan1991 Sharpe Hansen-Jaganathan Sharpe Hansen-Richard Hansen-Richard Hansen-Jaganathan Hansen-Jaganathan Hansen, Heaton Luttmer1995, Hansen Jaganathn1997 Hansen- Jaganathan Sharpe Sharpe Snow1990, Bansal Viswanathan 1993, Jaganathan Euler Wang1996 no-arbitrage boundaryhansen-jaganathan Cochrane Saa-Requejo good deal Bernardo Ledoit2000 gain-loss ratio 10

12 Risk-neutral Pricing CAPM Cox Ross Ross Rubinstein1979 tree 1973 binomial Black-ScholesBlack Schole, martingale Radon-Nikodym Pan 2002 measure change forward measure change of numeraire Geman, Karoui 1976, Harrison Kreps1979, Harrison Pliska1981 Cox 11

13 Rochet1995 Black-Schole 1977 Vasicek, exchange option Li, 2008 General Equilibrium partial exogenous equilibrium production Cox, Ingersoll Ross1985a, 1985b ICAPM Cox, Ingersoll Ross Cox, Ingersoll Ross shadow price Cox, Ingersoll Ross Black-Scholes Cox, Ingersoll Ito Ross drift function Vasicek diffusion function Feller "16 27 (3.2) 12

14 341 7 motion CIR Brownian CIR CIR Vasicek Vasicek CIR CARA Merton time-separable CARA Mehra Prescott1985, Weil, 1989 Mehra Prescott Mehra Prescott CARA CARA 1990 habit internal Constantinides Ferson Constantinides1991 habit 2000 external Campbell Cochrane1999, Joneses catching up with the 13

15 CARA recursive Kreps Porteus1978Weil Epstein Zin Duffie Epstein1992 Epstein Zin > : ;<8 5= 8 5=? 8 5 9: 5 ;<8 5= > (3.3) 9 ;<8 5= > 8? (3.4) aggregator 9: 5 <: A " A (3.5) A? CARA CARA Pennacchi2008 Skiadas2009 Duffie Campbell Campbell Campbell Campbell Duffie

16 Hansen-Jaganthn OtrokRavikumar Whiteman2002 Grishchenko2010 MenzlySantos 2004 Veronesi general equilibrium Lynch Randall2009 BansalKiku Yaron2009 Temporal Pricing of Risk Hansen- Jaganathan Sharpe Alvarez Jermann2005 Hansen- Jaganathan 15

17 Alvarez Jermann2005 Alvarez Jermann2005 Hansen, Heaton Li2008 Koijen, Nijman Werker2009 life cycle Hansen Scheinkman2009 investor Pastor Stambaugh2009 Markov Long-Run Risk Bansal Yaron2004 Bansal Yaron Epstein Zin1991 Kiku Yaron2007 Euler Bansal Fama French1996 Beeler Campbell2009 Bansal Yaron2004 Bansal Yaron2004 Beeler Campbell2009 Disaster Risk Rietz1988 Barro2006 Gabaix2010 Gabaix 16

18 Gabaix linear generating process, Gabaix2010 Farhi Gabaix2009 Gourio2010Wachter2009 Imperfect Market non-diversifiable labor income information asymmetry heterogeneous limited participation limited commitment limited arbitrage limited attention risk risk liquidity model Mankiw1986 Constantinides Duffie1996 Storeletten, Telmer Yaron 2004 Krueger Lustig2009 Krueger Lustig2009 Guvenen2009 Guvenen Guvenen Guvenen 2 Lustig van Nieuwerburgh 2005 ChienCole Lustig

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