What does the complete portfolio look like for the investor

Question

In a world of one risk-free and one risky asset, an investor faces the following values:

Expected return on risky portfolio E(r_P) = 0.12

SD of risky portfolio                              σ_P   = 0.25

Risk-free rate                                           rf     = 0.05

In what follows the notation is such that:

y = fraction of the complete portfolio in the risky portfolio E(r_C) = return on the complete portfolio σ_C= SD of the complete portfolio

a) What does the complete portfolio look like for the investor who says, "I won't

accept more than σ_C =10% (SD in my complete portfolio)?" In other words what is y(the percentage of risky asset), and what is 1-y (the percentage of the risk free asset) for this investor? Show your work.

b) What is E(r_C) for this investor? Show your work.

c) What does the complete portfolio look like for the investor who says, "I want to achieve a 15% expected return, at minimum risk of course."

In other words, what is y and (1-y) for this investor? Show your work. (Hint: Don't be discouraged if y>1 and thus (1-y) is negative. Remember an investor can borrow money at risk free rate)