There is the last week's homework.

8.What is the risk premium of any portfolio in Identical Idiosyncrasy Economy of last week's homework? If not zero, it is a violation APT, because there is not factor and the APT risk premium is 0 . In an economy named Identical Idiosyncrasy, there are n stocks. The excess return of all stocks are independent and identically distributed, for i=1,,n, Ri=i+ei, where constant, i is the risk premium and ei are mean-0 IID random variables with standard deviation of . The investors in this economy all use mean-variance theory to make portfolio choice and all have the same risk aversion coefficient A. The market cap of all the stocks are the same. 1. Does CAPM hold in this economy? 2. What is the market portfolio return RM in terms of ei ? 3. What is the market risk premium, given CAPM? 4. Compute the market beta i of asset i defined by M2cov(Ri,RM). 5. Does asset i have systematic risk defined in the index model? Does the market portfolio have systematic risk in the sense that its total variance does not go to 0 when n goes to infinity? 6. What is i according to CAPM? 7. Define ui=RiiRM, consider the market regression model Ri=iRM+ui. (a) What is ui in terms of ei ? (b) Show that cov(RM,ui)=0. This implies that the i from regression of Ri on RM is consistent. (c) Compute, for i=j,cov(ui,uj), which is non-zero, thus the residuals of marker regression model is correlated. (d) The above market regression model looks like an index model and smells like an index model. Is it an index model