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%)

g) Calculate the utility of holding the market portfolio.

h) Show that investor 2 has, on average, a negative alpha but may be active if asset

management is not so costly.

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%