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%)

a) Calculate the optimal portfolios of the investors based on their beliefs. Also, calculate the

tangent portfolios.

b) Calculate the average market belief (weighted with wealth) of the expected returns.

Calculate the optimal portfolio corresponding to the average market belief and the related

tangent portfolio.

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%