Question

You have $110,000 to invest in a portfolio containing Stock X, Stock Y, 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 10 percent and that has only 74 percent of the risk of the overall market. If X has an expected return of 30 percent and a beta of 2.0, Y has an expected return of 20 percent and a beta of 1.2, and the risk-free rate is 4 percent, how much money will you invest in Stock Y?

Answer 1

Let amount invested in Stock X, Stock Y and Risk free asset be denoted by
X, Y and R
There are three equations to be solved
X + Y + R = 110000
30X+20Y+4R=10*(X+Y+R)
2X+1.2Y=0.74
Solving this three equations we have
X	-989985
Y	1649976
R	-549991