Question

You have $134,000 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 13 percent and that has only 72 percent of the risk of the overall market. If X has an expected return of 32 percent and a beta of 1.6, Y has an expected return of 20 percent and a beta of 1.2, and the risk-free rate is 7 percent, how much money will you invest in Stock Y? (Do not round intermediate calculations. Round your answer to the nearest whole dollar.)

Answer 1

Given:
Total amount to be invested = $134000
Expected rate of return of the portfolio E(P) = 13%
Expected rate of return of stock X E(X) = 32%
Expected rate of return of stock Y E(Y) = 20%
Risk free rate Rf = 7%
beta for stock X beta(X) = 1.6
beta for stock Y beta(Y) = 1.2
Expected beta beta(P) = 0.72
First equation:
E(P) = wx * E(X) + wy * E(Y) + (1 - wx - wy) * Rf

where, wx = weight of stock X
wy = weight of stock Y

0.13 = wx * 0.32 + wy * 0.20 + (1 - wx - wy) * 0.07

Second equation for risk
beta (P) = wx * beta(X) + wy * beta(Y) + (1 - wx- wy)* 0
0.72 = wx * 1.6 + wy * 1.2 + 0

solving both the equation
we get wy = 0.913
           wx = - 0.235

Therefore, we will invest 0.913 * 134000 = $122348

In Stock Y we will invest $122348