You have $100,000 to invest in a portfolio containing Stock X and Stock Y. Your goal is to create a portfolio that has an expected return of 12.7 percent.

Stock X has an expected return of 11.4 percent and a beta of 1.25, and Stock Y has an expected return of 8.68 percent and a beta of. 85.

a. How much money will you invest in Stock Y? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.)

b. What is the beta of your portfolio? (Do not round intermediate calculations and round your answer to 3 decimal places, e. g., 32.161.)

a.)

The expected return of a portfolio (P) is the sum of the weighted average of the two assets.

rP = wX*rX + (1-wX) * rY

w is weight of ...

r is the return of ...

0.127 = (wX*0.114) + (1-wX) * 0.0868

0.127 = 0.114wX + 0.0868 - 0.0868wX

Collect like terms and subtract 0.0868 from both sides;

0.127 - 0.0868 = 0.0272wX

0.0402 = 0.0272wX

Divide both sides by 0.0272;

0.0402/0.0272 = wX

Weight of X; wX = 1.4779 or 147.79%

Weight of Y = 1-wX = 1 - 1.4779 = - 0.4779 or - 47.79%

Money invested in Y = - 0.4779 * $100,000 = - $47,794.12

A negative value means that you are borrowing or short selling stock Y at an amount of - $47,794.12.

b.)

Beta of a portfolio measures the volatility of the portfolio in comparison to the market index. It measures the systematic risk which cannot be diversified away like inflation. It is also calculated by finding the sum of the weighted average of individual asset betas in the portfolio as shown below;

bP = wX*bX + wY*bY

whereby b = beta of ...

w = weight of ... (found on part a above)

bP = (1.4779*1.25) + (-0.4779 * 0.85)

bP = 1.8474 - 0.4062

bP = 1.44

Therefore, portfolio beta is 1.44