Consider portfolios of two uncorrelated assets A and B with weights w and 1 – w, returns ???????? and ????????, and risks σA and σB, respectively. (a) Find an expression for portfolio risk as a function of ????,????????,???????? only. (b) Show that the minimum-risk portfolio has investment weights ????∗,1−????∗ with ????∗ = ????????2 ????????2+????????2. Hint: The squared risk of the portfolio is a parabolic function of the form ????(????)=???? ????2 +???? ????+c. Find ????,????,c then find the vertex. Alternatively, you can use first-order calculus to find the minimum.
