Question

You have $99,445 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 11 percent. You want to own $30,372 of Stock B. The risk-free rate is 3.03 percent and the expected return on the market is 10.49 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 on portfolio = Expected return on market = 10.49%

let the amount invested in stock A be"X ". So amount invested in risk free asset =Total amount- amount invested in A -amount invested in B

              = 99445 -X -30372

              = 69073 -X

	Return	Amount invested	Weight	Return *Weight
Stock A	13.34%	X	X/99445	13.34*X/99445
Stock B	11%	30372	30372/99445	11*30372/99445
Risk free asset	3.03%	69073-X	(69073-X)/99445	3.03*(69073-X)/99445
Total		99445
Expected return of portfolio				10.49%

10.49 = [13.34*X /99445] +[11*30372/99445]+[3.03*(69073-X)/99445]

          = .000134 X + 3.35957 + [(209291.19 - 3.03 X )/99445]

          = .000134X + 3.35957 + 2.104592 - .00003047 X

10.49 = .00010353 X + 5.464162

10.49-5.464162 = .00010353 X

X = 5.025838/.00010353

     = 48545

Amount invested in stock A= 48545

Amount invested in risk free asset = 69073-48545= 20528

Amount invested in risk free asset = 20528