You have $106,000 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 11 percent and that has only 65 percent of the risk of the overall market. If X has an expected return of 28 percent and a beta of 1.8, Y has an expected return of 16 percent and a beta of 1.1, and the risk-free rate is 5 percent, how much money will you invest in Stock Y? (Do not round intermediate calculations. Round your answer to the nearest whole dollar.)

example solution from a similar practice problem

E[R_p] = 0.13 = w_X(0.31) + w_Y(0.20) + (1 w_X w_Y)(0.07)

_p = 0.76 = w_X(1.80) + w_Y(1.20) + (1 w_X w_Y)(0)

Solving these two equations in two unknowns gives:

w_X = -0.496296

w_Y = 1.37778

w_Rf = 0.11852

Amount of Stock Y to buy = 1.37778($138,000) = $190,134