You own $9,000 of Olympic Steel stock that has a beta of 2.5. You also own $7,000 of Rent-a-Center (beta = 1.2) and $8,000 of Lincoln Educational (beta = 0.4). What is the beta of your portfolio?
A) 1.18
B) 1.07
C) 1.42
D) 1.53

Question

Quizplus · Accepted Answer

The beta of the portfolio is calculated as the weighted average of the individual betas, based on the proportion of each investment in the total portfolio. The calculation is as follows: $$ \text{Portfolio Beta} = \left( \frac{9000}{9000+7000+8000} \times 2.5 \right) + \left( \frac{7000}{9000+7000+8000} \times 1.2 \right) + \left( \frac{8000}{9000+7000+8000} \times 0.4 \right) $$$$ = \left( \frac{9000}{24000} \times 2.5 \right) + \left( \frac{7000}{24000} \times 1.2 \right) + \left( \frac{8000}{24000} \times 0.4 \right) $$$$ = (0.375 \times 2.5) + (0.2917 \times 1.2) + (0.3333 \times 0.4) $$$$ = 0.9375 + 0.35 + 0.1333 $$$$ = 1.421 $$Rounded to two decimal places, the beta of the portfolio is 1.42.

You Own $9,000 of Olympic Steel Stock That Has a Beta