You own $8,000 of City Steel stock that has a beta of 2.1. You also own $12,000 of Rent-N-Co (beta = 1.75) and $5,000 of Lincoln Corporation (beta = 0.50). What is the beta of your portfolio?
A) 1.45
B) 1.61
C) 2.10
D) 4.35

Question

Quizplus · Accepted Answer

The beta of the portfolio is calculated as the weighted average of the individual betas, weighted by the proportion of the total investment in each stock. The calculation is as follows:$$ \text{Portfolio Beta} = \left( \frac{8000}{8000+12000+5000} \times 2.1 \right) + \left( \frac{12000}{8000+12000+5000} \times 1.75 \right) + \left( \frac{5000}{8000+12000+5000} \times 0.50 \right) $$$$ = \left( \frac{8000}{25000} \times 2.1 \right) + \left( \frac{12000}{25000} \times 1.75 \right) + \left( \frac{5000}{25000} \times 0.50 \right) $$$$ = (0.32 \times 2.1) + (0.48 \times 1.75) + (0.20 \times 0.50) $$$$ = 0.672 + 0.84 + 0.10 $$$$ = 1.612 $$Rounded to two decimal places, the portfolio beta is 1.61.

You Own $8,000 of City Steel Stock That Has a Beta