Question

You hold a diversified portfolio consisting of a $10,000 investment in each of 20 different common stocks (that is, your total investment is $200,000). The portfolio beta is equal 1.2. You have decided to sell one of your stocks that has a beta equal to 0.7 for $10,000. You plan to use the proceeds to purchase another stock that has a beta equal to 1.4. What will be the beta of the new portfolio? a. 1.165 b. 1.235 c. 1.250 d. 1.284 e. 1.333

Answer 1

Answer:

new beta of the portfolio= 1.235

so correct option is  b. 1.235

Explanation:

given data

investment  = $10,000

common stocks = 20

total investment = $200,000

portfolio beta = 1.2

sell one stocks  beta = 0.7

sell = $10,000

purchase another stocks beta = 1.4

to find out

What will be the beta of the new portfolio

solution

we first find increment in beta that is express as

increment in beta = investment × ( purchase stocks beta - sell stocks  beta) ÷ total investment     .............................1

put here value we get

increment in beta = $\frac{10000*(1.4-0.7)}{200000}$

increment in beta =  0.035

so

new beta of the portfolio will be

new beta of the portfolio = 1.2 + 0.035

new beta of the portfolio= 1.235

so correct option is  b. 1.235