Question

# You have \$110,000 to invest in a portfolio containing Stock X, Stock Y, and a risk-free...

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? (Do not round intermediate calculations. Round your answer to the nearest whole dollar.

Solution :

Here,

Let Weight of Stock X , Wx = x

Weight of Stock Y , Wy = y

Weight of Risk-free assets = 1 - x - y

Then,

Expected return of Portfolio = 0.10

x * 0.30 + y * 0.20 + ( 1 - x - y ) * 0.04 = 0.10

0.30 * x + 0.20 * y + 0.04 - 0.04 * x - 0.04 * y = 0.10

0.26 x + 0.16 y = 0.06

Now,

Risk = 0.74

x * 2.0 + y * 1.2 + ( 1 - x - y ) * 0 = 0.74

2.0 x + 1.2 y = 0.74

Solving the above two equations, we get

x = 5.8 and

y = - 9.05

So,

Weight of Risk-free assets = 1 - 5.8 + 9.05 = 4.25

Therefore,

Investment in Stock Y = -9.05 * 110,000

Investment in Stock Y = -\$995,500

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