Your broker mailed you your year-end statement. You have $25,000 invested in Amazon, $18,000 tied up in Boeing, $36,000 in Caterpillar stock, and $11,000 in DuPont. The betas for each of your stocks are 1.43 for Amazon, .79 for Boeing, 1.37 for Caterpillar, and 1.71 for DuPont. What is the beta of your portfolio?
A) 1.33
B) 1.31
C) 1.00
D) 5.30

Question

Quizplus · Accepted Answer

To find the beta of the portfolio, we need to weigh the betas of each stock by the proportion of the total investment that each stock represents.

Weighted beta = (weight of Amazon * beta of Amazon) + (weight of Boeing * beta of Boeing) + (weight of Caterpillar * beta of Caterpillar) + (weight of DuPont * beta of DuPont)

Weight of Amazon = $25,000 / ($25,000 + $18,000 + $36,000 + $11,000) = 0.311
Weight of Boeing = $18,000 / ($25,000 + $18,000 + $36,000 + $11,000) = 0.224
Weight of Caterpillar = $36,000 / ($25,000 + $18,000 + $36,000 + $11,000) = 0.447
Weight of DuPont = $11,000 / ($25,000 + $18,000 + $36,000 + $11,000) = 0.018

Plugging in the values:

Weighted beta = (0.311 * 1.43) + (0.224 * 0.79) + (0.447 * 1.37) + (0.018 * 1.71) = 1.31

Therefore, the beta of the portfolio is 1.31.

Your Broker Mailed You Your Year-End Statement