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? 4. Compute the market beta i of asset i defined by M2con(i,lM). 5. 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 - What is ui in terms of ei ? - Show that cov(RM,Ri)=0. This implies that the i from regression of Ri on RM is unbiased. - Compute, for i=j,cov(ui,uj), which is non-zero, thus the residuals of marker regression model is correlated. This implies that the market regression model is not an index model which require residuals of different stocks to be uncorrelated. 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? 4. Compute the market beta i of asset i defined by M2con(i,lM). 5. 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 - What is ui in terms of ei ? - Show that cov(RM,Ri)=0. This implies that the i from regression of Ri on RM is unbiased. - Compute, for i=j,cov(ui,uj), which is non-zero, thus the residuals of marker regression model is correlated. This implies that the market regression model is not an index model which require residuals of different stocks to be uncorrelated