Question

You have a $2 million portfolio consisting of a $100,000 investment in each of 20 different stocks. The portfolio has a beta of 1.05. You are considering selling $100,000 worth of one stock with a beta of 1.15 and using the proceeds to purchase another stock with a beta of 1.3. What will the portfolio's new beta be after these transactions? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

Answer:

As given in question

(a)	Total amount of Portfolio	$2,000,000
(b)	No. of stocks	20
(c)	Amount invested in each stock	$100,000
(d)	Beta of portfolio	1.05
(e)	Beta of selling stock	1.15
(f)	Weightage of selling stock (c)/(a)	0.05
(g)	Beta of new purchasing stock	1.3
(h)	Weightage of selling stock (c)/(a)	0.05

Beta of a portfolio is calculated with the below formula:

Beta of Portfolio = (Beta of stock1 x Weightage of stock1) + (Beta of stock2 x Weightage of stock2) + (Beta of stock3 x Weightage of stock3) so on…………..

Therefore, we will deduct the beta of selling stock from the beta of old portfolio and add the beta of new purchasing stock to the beta of old portfolio.

Beta of new portfolio = Beta of old portfolio – (Beta of selling stock x weightage of selling stock) + (Beta of new purchasing stock x weightage of new purchasing stock)

                                                = 1.05 – (1.15 x 0.05) + (1.3 x 0.05)

                                                = 1.0575 or 1.06