Question

Your retirement fund consists of a $5,000 investment in each of 15 different common stocks. The portfolios beta is 1.20. Suppose you sell one of the stocks with a beta of 0.8 for $5,000 and use the proceeds to buy another stock whose beta is 1.6.
Calculate your portfolios new beta.

(Please show all steps and you can use a financial calculator as well).

Answer 1

Total number of common stocks within the portfolio = 15

All the stocks within the portfolio have equal investment of $5000

Therefore,weight of each stock within the portfolio = 1/15

Portfolio beta = 1.20

Beta of stock to be sold = 0.8

Beta of new stock to be purchased = 1.6

After replacement,

Portfolio new beta = Previous portfolio beta - (Weight * Beta of sold stock) + (Weight * Beta of purchased stock)

New portfolio beta = 1.20 - [(1/15) * 0.8] + [(1/15) * 1.6]

= 1.20 - 0.05333 + 0.10667

= 1.25334

≈ 1.25

Hence,the new portfolio beta is 1.25