You hold a portfolio consisting of a $5,000 investment in each of 20 different stocks.The portfolio beta is equal to 1.12.You have decided to sell a coal mining stock (b = 1.00) at $5,000 net and use the proceeds to buy a like amount of a mineral rights company stock (b = 2.00).What is the new beta of the portfolio?
A) 1.1139
B) 1.1700
C) 1.2311
D) 1.2927
E) 1.3573

Question

Quizplus · Accepted Answer

The new beta of the portfolio is calculated by removing the impact of the sold stock and adding the impact of the purchased stock. The original portfolio beta is 1.12, and the total value is $100,000 ($5,000 x 20). Removing the coal stock with a beta of 1.00 decreases the weighted average beta slightly, but adding the mineral rights company stock with a beta of 2.00 increases it. The calculation is as follows: New Portfolio Beta = 1.12 + (1/20)*(2.00 - 1.00) = 1.12 + 0.05 = 1.17.

You Hold a Portfolio Consisting of a $5,000 Investment in Each