CHPT13- Factor pricing model--CAPM.pdf

Chapter 13 Factor pricing model
Fan Longzhen
Introduction
• The consumption-based model as plete
answer to most asset pricing question in principle,
does not work well in practice;
• This observation motivates effects to tie the
discount factor m to other data;
• Linear factor pricing models are most popular
models of this sort in finance;
• They dominate discrete-time empirical work.
Factor pricing models
• Factor pricing models replace the consumption-based expression for
marginal utility growth with a linear model of the form
mt+1 = a + b' ft+1
• The key question: what should one use for factors ft+1
Capital asset pricing model (CAPM)
w
• CAPM is the model m = a + bR , R w is the wealth portfolio return.
• Credited Sharpe (1964) and Linterner (1965), is the first, most famous,
and so far widely used model in asset pricing.
• Theoretically, a and b are determined to price any two assets, such as
market portfolio and risk free asset.
• Empirically, we pick a,b to best price larger cross section of assets;
• We don’t have good data, even a good empirical definition for wealth
portfolio, it is often deputed by a stock index;
• We derive it from discount factor model by
•(1)two-periods, exponential utility, and normal returns;
•(2) infinite horizon, quadratic utility, and normal returns;
•(3) log utility
•(4) by seeing several derivations, you can see how one assumption can
be traded for another. For example, the CAPM does not require normal
distributions, if one is willing to swallow quadratic utility instead.
Two-period quadratic utility
• Investor have a quadratic preferences and live only for two
periods; β
1 1
U (c ,c ) = −(c − c*)2 −βE[(c − c*)2 ]
t t+1 2 β t 2 t+1
β U '(c ) c − c*
m = t+1 = t+1
t+1 U '(c ) c − c*
t t β
w
Rt+1(wt − ct ) − c* − c* β(wt − ct ) w
= = + Rt+1
ct − c* ct − c ct − c*
w
= at + bt Rt+1
Exponential utility, Normal distributions
• We present a model wi