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it has no factor risk, and it has a positive expected return. OneFactor Model and APT ? Pricing effects on arbitrage portfolio – The buyingandselling activity will continue until all arbitrage possibilities are significant reduced or eliminated – There will exist an approximately linear relationship between expected returns and sensitivities of the following sort: ii br 10 ?? ??OneFactor Model and APT – The equation is the asset pricing equation of the APT when returns are generated by one factor 171。The linear equation means that in equilibrium there will be a linear relationship between expected returns and sensitivities. 171。The expected return on any security is, in equilibrium, a linear function of the security’s sensitivity to the factor, bi OneFactor Model and APT – Any security that has a factor sensitivity and expected return such that it lies off the line will be mispriced according to the APT and will present investors with the opportunity of forming arbitrage portfolios. – Page 327: Figure OneFactor Model and APT ? Interpreting the APT pricing equation – Riskfree asset, rf – Pure factor portfolio, p* ififi brrrr 10 ?? ????11 ?? ???? ?? fpfp rrrr? ? iffip brrrr ???? ? 11 :l e t ??TwoFactor Model And APT ? The twofactor model ? Arbitrage portfolios – A market value of zero – No sensitivity to any factor – A positive expected return iiiii eFbFbar ???? 221122110 iii bbr ??? ???TwoFactor Model And APT ? Pricing effects 221102211r a t e r i s k f r e e)()(??????????????????fffififfirrrbrbrrrTwoFactor Model And APT –?1 is the expected return on the portfolio which is known as a pure factor portfolio or pure factor play, because it has: 171。Unit sensitivity to one factor (F1, b1=1) 171。No sensitivity to any other factor (F2, b2=0) 171。Zero nonfactor risk 171。This portfolio is a welldiversification portfolio that has unit sensitivity to the first factor and zero sensitivity to the second factor. TwoFactor Model And APT – It is the same with ?2 . It is the welldiversification portfolio that has zero sensitivity to the first factor and unit sensitivity to the second factor, meaning that it has b1=0 and b2=1. – Such as a portfolio that has zero sensitivity to predicted industrial production and unit sensitivity to predicted inflation would have an expected return of 6%. ? Multiplefactor model ? The APT pricing equation MultipleFactor Model And APT ikikiiii eFbFbFbar ?????? ?2211ikkiii bbbr ???? ????? ?22110ikfkiffi brbrrr )()( 11 ?????? ?? ?The APT And The CAPM ? Common point – Both require equilibrium – Both have almost similar equation ? Distinctions – Different equilibrium mechanism 171。Many investors . Few investors – Different Portfolio 171。Market portfolio . Welldiversifyed P. Summary ? The Factor Models – Onefactor models – Multifactor models ? Factor models and equilibrium ? Arbitrage opportunity and portfolio ? The arbitrage pricing equation – Onefactor equation – Multifactor equation Assignments For chapter 8 ? Readings – Page 282 through 301 – Page 308 through 321 ? Exercises – Page 304: 14,15。 Page 323: 4, 13 ? Q/A: – Page 302: 3 – Page 324: 8