1. Derive the optimal portfolio weights, {w₁, w₂, w₃} for 3-asset case.

Hint: Solve the following constraint optimization problem:

min ²_p = [w²₁²₁ + w²₂²₂ + w²₃²₃] + 2w₁w₂₁₂ + 2w₁w₃₁₃ + 2w₂w₃₂₃

w₁,w₂,w₃

(l) w₁E(r₁) + w₂E(r₂) + w₃E(r₃) = E(r_p)

s.t (g) w₁ + w₂ + w₃=1

2. Derive the optimal portfolio variance, *_p²