Question

You own $33,200 of Olympic Steel stock that has a beta of 2.90. You also own $24,568 of Rent-a-Center (beta = 1.93) and $8,632 of Lincoln Educational (beta = 0.98). What is the beta of your portfolio?

Answer 1

To calculate the beta of a portfolio, you need to multiply the beta of each stock by the proportion of the stock's value in the portfolio and then sum up these values. In this case, the beta of the portfolio is 2.29.

Step-by-step explanation:

To calculate the beta of a portfolio, you need to multiply the beta of each stock by the proportion of the stock's value in the portfolio and then sum up these values. In this case, you own three stocks: Olympic Steel, Rent-a-Center, and Lincoln Educational. The beta of Olympic Steel is 2.90, the beta of Rent-a-Center is 1.93, and the beta of Lincoln Educational is 0.98. The total value of your portfolio can be calculated as $33,200 + $24,568 + $8,632 = $66,400. Now, let's calculate the weight of each stock in the portfolio:

Weight of Olympic Steel = $33,200 / $66,400 = 0.50

Weight of Rent-a-Center = $24,568 / $66,400 = 0.37

Weight of Lincoln Educational = $8,632 / $66,400 = 0.13

Now, multiply each stock's beta by its weight:

Weighted Beta of Olympic Steel = 2.90 * 0.50 = 1.45

Weighted Beta of Rent-a-Center = 1.93 * 0.37 = 0.71

Weighted Beta of Lincoln Educational = 0.98 * 0.13 = 0.13

Finally, sum up the weighted betas:

Beta of the Portfolio = 1.45 + 0.71 + 0.13 = 2.29

Therefore, the beta of your portfolio is 2.29.