Lecture 9: time and assets market
Lecture 9: time and assets market
Contents Inter-temporal preferences TWo periods Several periods Asset market CAPM APT Complete market Pure arbitrage
Contents • Inter-temporal preferences – Two periods – Several periods • Asset market – CAPM – APT – Complete market – Pure arbitrage
Inter-temporal preferences Utility function of inter-temporal U(c(…c)=∑。h(c) Every period consumption c, depend on how much he consumed and invested in period t-1
Inter-temporal preferences • Utility function of inter-temporal • Every period consumption ct depend on how much he consumed and invested in period t-1. 1 1 1 ( ) ( ) T t T t t U c c u c − = =
Inter-temporal preferences Two periods model In the case with out any uncertainty max(co, CD=u(co)+du(c) St.(v-c0)(1 0 +r)=c1 First order condition u(c n)=6(+r) u(c If Co=c, means 8 1+r
Inter-temporal preferences • Two periods model : • In the case with out any uncertainty • First order condition: • If means 0 1 0 1 0 1 max ( , ) ( ) ( ) . . ( )(1 ) U c c u c u c s t w c r c = + − + = 0 1 ( ) (1 ) ( ) u c r u c = + 1 1 r = + 0 1 c c =
Inter-temporal preferences TWO periods model with uncertainty investment Endowment wealth w Period 1: consume c, invest the rest wealth in two assets,(1-x) percentage has a certain return of Ro and x pays a random return of R Period2: C2=W2=(W-C[RX+Ro(1-x)]=(w-CR Utility function: U(, C2)=u(C)+DEu(C2)
Inter-temporal preferences • Two periods model with uncertainty investment. – Endowment wealth w. – Period1: consume c1 , invest the rest wealth in two assets, (1-x) percentage has a certain return of R0 and x pays a random return of – Period2: – Utility function: R1 2 2 1 1 0 1 c w w c R x R x w c R = = − + − = − ( )[ (1 )] ( ) 1 2 1 2 U c c u c Eu c ( , ) ( ) ( ) = +