There are just three risky assets with expected rates of return E(r₁) = 15, E(r₂) = 5 and E(r₃) = 10, respectively, and variances of the returns ₁²=10, ₂²=15, and₃²=20. Assume that the returns of these assets are uncorrelated.

(Keep all your answers to 4 decimal places.)

(a) Find the minimum-variance portfolio, and then determine the mean and standard deviation of the return on the portfolio.

w₁: _______ w₂: _______

E(r): _______ : ________

(b) Find another efficient portfolio by setting = 1 and = 0 in the equations of Markowitz model, and then determine the mean and standard deviation of the return on the portfolio.

w₁: _______ w₂: _________

E(r): _______ : ________

(c) Assume in addition that there is a risk-free asset with rate r_f = 0.5. (Shorting is allowed.) Find the efficient portfolio of risky assets.

w₁: ______ w₂: _______