Suppose that financial markets consist of 2 risky assets and one risk-less asset. Let Rf=1% and there be four investors each of whom has different beliefs for the expected returns of the 2 risky assets as follows: ^1= (6% 1%), ^2= (3% 2%), ^3=(2% 3%)and ^4 =(1% 5%). The investors all have the same degree of risk aversion in the mean-variance preferences, p^1= p^2 = p^3 = p^4 = 2, and their wealth levels to be invested are all the same as well w^1= @^2= w^3 = w^4 = 10. The variance-covariance matrix and the true expected returns of the risky assets are given by

COV (2% 0%

0% 2%)

And = (2% 2%)

c) Calculate the market portfolio weights by calculating the proportions of wealth invested in

asset 1 and assets 2 by the individual investors in a). Check that it is the same as the tangent

portfolio corresponding to the average market belief.

d) Calculate the betas and the alphas of the assets using the risky assets of the market portfolio

(corresponding to the average market belief).

3.5. Suppose that financial markets consist of 2 risky assets and one risk-less asset. Let R = 1% and there be four investors each of whom has different beliefs for the expected returns of the 2 risky assets as follows: ut 6% 1% 3% 2% (2% 3% and je 1% 5% The investors all have the same degree of risk aversion in the mean-variance preferences, pl = p2 = p = p4 = 2, and their wealth levels to be invested are all the same as well wo = w = w;= w; = 10. The variance-covariance matrix and the true expected returns of the risky assets are given by COV = 2% 0% 0% 2% and h = 2% 2% 3.5. Suppose that financial markets consist of 2 risky assets and one risk-less asset. Let R = 1% and there be four investors each of whom has different beliefs for the expected returns of the 2 risky assets as follows: ut 6% 1% 3% 2% (2% 3% and je 1% 5% The investors all have the same degree of risk aversion in the mean-variance preferences, pl = p2 = p = p4 = 2, and their wealth levels to be invested are all the same as well wo = w = w;= w; = 10. The variance-covariance matrix and the true expected returns of the risky assets are given by COV = 2% 0% 0% 2% and h = 2% 2%