Question

You hold a diversified portfolio consisting of a $10,000 investment in each of 15 different common stocks (i.e., your total investment is $150,000). The portfolio beta is equal to 1.2 . You have decided to sell one of your stocks which has a beta equal to 1.4 for $10,000. You plan to use the proceeds to purchase another stock which has a beta equal to 1.3 . What will be the beta of the new portfolio? Show your answer to 2 decimal places.

Answer 1

1.19

Step-by-step explanation:

The beta of a portfolio can be simply determined by a weighted average of each individual investment's beta. Thus, the portfolio beta after selling $10,000 of a stock with beta equal to 1.4 is:

`B_1 = (150,000*1.2-10,000*1.4)/(140,000)\\B_1 =1.185714`

The beta of a new portfolio after purchasing $10,000 worth of a new stock with beta equal to 1.3 is:

`B_2 =(1.185714*140,000+1.3*10,000)/(150,000)\\B_2=1.1933`

The beta of the new portfolio is 1.19.