Question

You have $96433 to invest in two stocks and the risk-free security. Stock A has an expected return of 12.84 percent and Stock B has an expected return of 10.23 percent. You want to own $30572 of Stock B. The risk-free rate is 4.69 percent and the expected return on the market is 12.04 percent. If you want the portfolio to have an expected return equal to that of the market, how much should you invest (in $) in the risk-free security? Answer to two decimals. (Hint: A negative answer is OK - it means you borrowed (rather than lent or invested) at the risk free rate.)

Answer 1

Expected return of Stock A = E(A) = 12.84%, Expected return of Stock B = E(B) = 10.23%, Risk free rate = Rf = 4.69%

Total amount invested in 2 stocks and risk free security = Total amount of portfolio = 96433

Amount invested in stock B = 30572

Amount invested in stock A and risk free security = Total amount invested in 2 stocks and risk free security - Amount invested in stock B = 96433 - 30572 = 65861

Expected return of portfolio = Expected return on market = 12.04%

Let w be the amount invested in risk free security and then

Amount invested on Stock A = Amount invested in stock A and risk free security - amount invested in risk free security = 65861 - w

Weight of Stock A in portfolio = W(A) = Amount invested in stock A / Total Amount of portfolio = (65861 - w) / 96433

Weight of Stock B in portfolio = W(B) = Amount invested in stock B / Total Amount of portfolio = 30572 / 96433

Weight of risk free security in portfolio = W(R) = Amount invested in risk free security / Total Amount of portfolio = w / 96433

Expected return of portfolio = E(P) = W(A) x E(A) + W(B) x E(B) + W(R) x Rf

96433 x 12.04% = 12.84% x 65861 - 12.84% x w + 10.23% x 30572 + 4.69% x w

11610.5332 = 8456.5524 - 0.1284w + 3127.5156 + 0.0469w

0.0815w = -26.4652

w = -26.4652 / 0.0815 = -324.7263

Amount invested in Risk free security = -324.73

Negative sign represents this amount of money was borrowed