Question

You have $10636 to invest in a stock portfolio. Your choices are Stock X with an expected return of 13.35 percent and Stock Y with an expected return of 10.69 percent. If your goal is to create a portfolio with an expected return of 11.81 percent, how much money (in $) will you invest in Stock X? Answer to two decimals, carry intermediate calcs. to four decimals.

Answer 1

Expected return of portfolio = (W₁ x r₁) + (W₂ x r₂) +…. (W_n x r_n)

W ₁, W₂… W _n = Weight of stock 1, 2 … n etc.

r ₁, r ₂… r _n = Return of stock 1, 2 … n etc.

Suppose weight of stock X is W_X and that of stock Y is W_Y

W_X + W _y = 1

W _y = 1 - W_X

Expected return of portfolio = (W_X x r_X) + (W_Y x r_Y)

                                11.81 % = (W_X x 13.35 %) + (W_Y x 10.69 %)

                                0.1181 = (W_X x 0.1335) + (W_Y x 0.1069)

                                0.1181 = (W_X x 0.1335) + [(1-W_X) x 0.1069]

                               0.1181 = 0.1335 W_X - 0.1069 W_X + 0.1069

                              0.1181 = 0.0266 W_X + 0.1069

                              0.0266 W_X = 0.1181 - 0.1069

                              0.0266 W_X = 0.0112

                              W_X = 0.0112/0.0266 = 0.421052631578947 or 0.4211

Amount to invest in stock X = 0.4211 x $ 10,636 =$ 4,478.8196 or $ 4,478.82

$ 4,478.82 needs to invest in stock X.