Question

You have $84,174 to invest in two stocks and the risk-free security. Stock A has an expected return of 13.34 percent and Stock B has an expected return of 9.55 percent. You want to own $26,193 of Stock B. The risk-free rate is 4.84 percent and the expected return on the market is 11.97 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

Let Ia be the investment in stock A, Ib the investment in Stock B and Irf be the investment in Risk free security.

Given that investment in B = 26,193, So Weight of Investment in B , Wb = 26,193/84,174 = 31.12 %

Investible surplus after investment in B = (84,174 - 26,193) = $ 57,981

So , Ia = (57981 - Irf), Wa = (57981-Irf)/ 84,174

Wrf = Irf/ 84,174

Given Expected return of A, Ra = 13.34%, Rb = 9.55%, Rf = 4.84%

Expected return on portfolio = 11.97% = Ra * Wa + Rb * Wb + Rf * Wrf

11.97% = 13.34% * [(57,981- lrf)/ 84,174] + 9.55% * 31.12% +4.84% lrf/84,174

8.99% = 13.34% * [(57,981- lrf)/ 84,174] + lrf/84,174 * 4.84%

7574.01 = 7734.66 - 0.1334 lrf +0.0484lrf

160.65 = 8.5% lrf

lrf = $ 1,890 is the investment in risk free security.