You have S100.000 to invest in a portfolio containing Stock X, Stock thalt Y, an

Question

You have S100.000 to invest in a portfolio containing Stock X, Stock thalt Y, and a risk-free asset. You must invest all of your money. Your goal is to create a portfolio has an expected return of 13.5 percent and that has only 70 percent of the risk of the overall market. I X has an expected return of 3 percent and n beta of 1.8, Y has an expected return of 20 percent and a beta of 1.3, and t iavest in Stock X? How do you interpret your answer? he risk-free rate is 7 percent, how much money will you

Explanation / Answer

Let Weight of Stock X in portfolio be x, Weight of Stock Y be y and Weight of Risk-free Asset be (1-x-y)

Expected Return of Portfolio = 13.50%
x*31% + y*20% + (1-x-y)*7% = 13.50%
0.31x + 0.20y + 0.07 - 0.07x - 0.07y = 0.1350
0.24x + 0.13y + 0.07 = 0.135
0.24x + 0.13y = 0.065                                                       .... (1)

Beta of Portfolio = 0.70
x*1.8 + y*1.3 + (1-x-y)*0 = 0.70
1.8x + 1.3y = 0.70                                                              .... (2)

Solving (1) and (2), we get
x = -0.0833, y = 0.6538

Weight of Stock X = -0.0833
Weight of Stock Y = 0.6538
Weight of Risk-free Asset = 1 - (-0.0833) - 0.6538
Weight of Risk-free Asset = 0.4295

Investment in Stock X = -0.0833 * $100,000
Investment in Stock X = -$8,330

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