Mr. Banks is contemplating dividing his portfolio between two assets, a risky asset that has an expected return of 30% and a standard deviation of 10%, and a safe asset that has an expected return of 10% and a standard deviation of 0%.

a) If he invests percent of his wealth in the risky asset, what will his expected return be? What will the standard deviation be?

b) Solve for Mr Banks' budget constraint i.e. the expected return on his wealth as a function of the standard deviation

c) Mr. Banks' utility function is (_x, _x) = (_x, 30 2 ). What are his optimal values of _x and _x ?

d) What fraction of his wealth should Mr. Banks invest in the safe asset?