Analyzing a Portfolio: You have $100,000 to invest in a portfolio cont

QUESTION

Analyzing a Portfolio: You have $100,000 to invest in a portfolio containing Stock X and Stock Y. Your goal is to create a portfolio that has an expected return of 18.5 percent. If Stock X has an expected return of 17.2 percent and a beta of 1.4, and Stock Y has an expected return of 13.6 percent an
According to the given information,Total investment = $100,000Portfolio expected return = 18.5%Expected return of Stock-X = 17.2ta of stock-X = 1.4Expected return of Stock-Y = 13.6ta of Stock-Y = 0.95We know that, Wx Wy = 1 Wy = 1 Wxa) The formula for calculating the portfolio expected return is Portfolio expected return = [Wx * E(Rx)] [Wy * E(Ry)] 0.185 = [Wx * 0.172] [(1-Wx) * 0.136] 0.185 = Wx (0.172 0.136) 0.136 0.185 = Wx (0.036) 0.136 0.185 0.136 = Wx(0.036) 0.049 = Wx (0.036) Wx = 0.049 / 0.036 = 1.36Here the weight of stock-X is 136%.b) One thing you might wonder is about whether it is possible for the percentage invested in Stock-X to exceed 100%. The

nswer is yes. This can happen if the investor borrows at the risk-free rate. The total investment in Stock-X would be 136% of the investors wealth. The weight of Stock-Y would be Weight of Stock-Y = (1-Weight of Stock-X) = (1 1.36) = -0.36 or -36%c) The formula for calculating the Portfolio beta is Portfolio beta = (Wx * Beta of X) (Wy * beta of Y) = (1.36 * 1.4) (-0.36 * 0.95) = 1.904 0.342 = 1.56Therefore, the value of Portfolio beta is 1.56

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