Question

You have $10,000 to invest in a portfolio containing Stock R, Stock S, and a risk-free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 15% and that has only 120% of the risk of the overall market. If Stock R has an expected return of 25% and a beta of 1.6, Stock S has an expected return of 17.5% and a beta of 1.3, and the risk-free rate is 6%, how much money will you invest in Stock R? Explain your answer.    

Answer 1

Let investment in R be x, S be y and risk free asset be 10000-x-y

From expected return:
x*25%+y*17.5%+(10000-x-y)*6%=15%*10000

From beta:
x*1.6+y*1.3+(10000-x-y)*0=1.2*10000

Solving the two we get
x=-3333.33
y=13333.33
10000-x-y=0

Investment in Stock R is -3333.33
i.e., Short/Sell Stock R worth 3333.33