Question

Suppose you hold a portfolio consisting of a $10,000 investment in each of 8 different common stocks. The portfolio's beta is 1.25. Now suppose you decided to sell one of your stocks that has a beta of 1.00 and to use the proceeds to buy a replacement stock with a beta of 1.35. What would the portfolio's new beta be?

Answer 1

Answer:

1.29375

Explanation:

Data provided in the question:

Total investment = $10,000

Number of different common stock = 8

Portfolio's beta = 1.25

Beta of a stock sold = 1.00

Beta of the replacement stock = 1.35

Now,

Change in portfolio beta = weight × (change in security beta)

also,

change in security beta

= Beta of the replacement stock - Beta of a stock sold

= 1.35 - 1

= 0.35

and,

Weight = Beta ÷ Number of different common stock

= 1 ÷ 8 = 0.125

Therefore,

Change in portfolio beta = 0.125 × 0.35

= 0.04375

thus,

New portfolio beta = Portfolio's beta + Change in portfolio beta

= 1.25 + 0.04375

= 1.29375