Stock J has a beta of 1.3 and an expected return of 13.66 percent, while Stock K

Question

Stock J has a beta of 1.3 and an expected return of 13.66 percent, while Stock K has a beta of 0.85 and an expected return of 10.6 percent. You want a portfolio with the same risk as the market.

Requirement 1: What is the portfolio weight of each stock? (Do not round intermediate calculations. Round your answers to 4 decimal places)

Requirement 2: What is the expected return of your portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places)

Explanation / Answer

you have to assume that the weight of each stock is equal to the weight of the entire portfolio (meaning your portfolio contains only these two stocks). So, let's call w(j) and w(k) the weight of j and k, respectively.

We know w(j)+w(k)=1 (the weight of j and k equals 1 because it makes up the whole portfolio 1=100%)
We also know that 1.3(w(j))+.85(w(k))=1 because the weight of each stock's beta equals to a beta of 1 (if you want risk to be the same as the market, beta has to equal 1).

So you can solve for w(k) by setting w(j) = 1 - w(k). Then plug in this for the weighted beta formula. I got w(k) = 2/3 (67%) and thus w(j) = 1/3 (33%).

Then, use these weights to solve for the overall rate of return. So .1366*(.33)+.106*(.67) and I got 11.62% for the expected return of the portfolio.

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