Question

Please provide the work and explanations so that I can understand the problem.

Your friend wants to invest in a portfolio that includes two stocks and the risk free investment. Stock G has a beta of 2.5 and an expected return of 10%, Stock E has a beta of 0.5 and an expected return of 5% and the risk free rate is 2%. Your friend comes to you asking for help in creating a portfolio with an expected return of 9% and a market risk of 1.5. If your friend has $20,000 to invest how much of it should she put in Stock G?

Answer 1

Lets consider this is as a two asset problem: First asset is portfolio (which includes Stock E and Stock G only) and second asset is risk free asset

beta of risk free asset is zero

Portfolio beta=proportion in stock 1*beta of stock 1+proportion in stock 2*beta of stock 2+proportion in risk free asset*beta of risk free asset

market risk of 1.5 means beta of 1.5

Let proportion in Stock G be x and proportion in Stock E be y and in risk free asset be 1-x-y

Hence,
x*2.5+y*0.5=1.5

Now

Portfolio expected returns=proportion in stock 1*returns of stock 1+proportion in stock 2*returns of stock 2+proportion in risk free asset*returns of risk free asset

=>9%=x*10%+y*5%+(1-x-y)*2%

=>x*8%+3%*y=7%

Solving the two equations simultaneously we get

x=0.285714, y=1.57143

Hence, invest 0.285714 of your wealth in Stock G=20000*0.285714=5714.28