Chapter 13 Factor pricing model Fan longzhen
Chapter 13 Factor pricing model Fan Longzhen
Introduction The consumption-based model as a complete 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
Introduction • The consumption-based model as a complete 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 m=a+b'f+ The key question: what should one use for factors
Factor pricing models • Factor pricing models replace the consumption-based expression for marginal utility growth with a linear model of the form • The key question: what should one use for factors 1 1 ' t+ = + t+ m a b f t+1 f
Capital asset pricing model ( capm CAPM is the model m=a+bR, rw is the wealth portfolio return Credited Sharpe(1964)and Interner(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 dont 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 ()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
Capital asset pricing model (CAPM) • CAPM is the model , 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. w m = a + bR w R
Two-period quadratic utility Investor have a quadratic preferences and live only for two periods, U(c,c)=-( C C,-1-C R:(1-c) B*,B(w,-c,) C-C C-C b, R
Two-period quadratic utility • Investor have a quadratic preferences and live only for two periods; [( *) ] 2 1 ( *) 2 1 ( , ) 2 1 2 1 U c c c c E c c t t+ = − t − − β t+ − w t t t w t t t t t t t t w t t t t t t a b R R c c w c c c c c c R w c c c c c c U c U c m 1 1 1 1 1 1 * * ( ) * ( ) * * * '( ) '( ) + + + + + + = + − − + − − = − − − = − − = = β β β β β