Fenner Smith 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 Mr. Smith invests x percent of his wealth in the risky asset, what will be his expected return?
(b) If Mr. Smith invests x percent of his wealth in the risky asset, what will be the standard deviation of his wealth?
(c) Solve the above two equations for the expected return on Mr. Smith’s wealth as a function of the standard deviation he accepts.
(d) Plot this “budget line” on the graph below.
(e) If Mr. Smith’s utility function is u (rx, σx) = min {rx, 30 − 2σx}, then Mr. Smith’s optimal value of rx is ______, and his optimal value of σx is ______. (You will need to solve two equations in two unknowns. One of the equations is the budget constraint.)
(f) Plot Mr. Smith’s optimal choice and an indifference curve through it in the graph.
(g) What fraction of his wealth should Mr. Smith invest in the risky asset?