a Derive the optimal portfolio weights, w 1 , w 2 , w 3 for 3 asset case Hint Solve the following constraint optimization problem min 2 p w 2 1 2 1 w 2 2 2 2 w 2 3 2 3 2w 1 w 2 12 2w 1 w 3 13 2w 2 w 3 23 s t (l) w 1 E(r 1 ) w 2 E(r 2 ) w 3 E(r 3 ) E(r p ) (g) w 1 w 2 w 3 1 b Derive the optimal portfolio variance, p 2

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a.Derive the optimal portfolio weights, {w 1 , w 2 , w 3 } for 3-asset case. Hint: Solve the following constraint optimization problem: min

a.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

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

(g) w₁+ w₂+ w₃= 1

b.Derive the optimal portfolio variance, _p^2*

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