Question

You have $98,483 to invest in two stocks and the risk-free security. Stock A has an expected return of 10.18 percent and Stock B has an expected return of 11.04 percent. You want to own $25,007 of Stock B. The risk-free rate is 5.16 percent and the expected return on the market is 12.39 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

Weight of Stock B =25007/98483
Weight of Stock A =x
Weight of Risk free rate =1-25007/98483-x
Expected Return of Assets =Expected Return of Market
x*10.18%+25007/98483*11.04%+(1-25007/98483-x)*5.16% =12.39%
x*(10.18%-5.16%)=12.39%-5.16%+5.16%*25007/98483-25007/98483*11.04%
x =114.2816%
Weight of Risk free asset =1-25007/98483-114.2816% =-39.67%