You hold a portfolio consisting of a $5,000 investment in each of 20 different stocks. The portfolio beta is equal to 1.12. You have decided to sell a coal mining stock (b = 1.00) at $5,000 net and use the proceeds to buy a like amount of a mineral rights company stock (b = 2.00). What is the new beta of the portfolio?

The new beta of the portfolio 1.17

Explanation:

Portfolio beta is sum of weighted beta of all stocks consisting of it.

Portfolio beta = 1.12

Weight of each portfolio = 5,000

All weight or Amount = 5,000 * 20 = 100,000

Weight of one stock = 5,000 / 100,000 = 0.05

Foregone beta or beta of sold stock = 1

Acquired beta or beta of purchased stock = 2

Weight of both are same = 0.05

New beta = Portfolio beta - (foregone beta * weight) + (Acquired beta * weight)

New beta = 1.12 - (1 * 0.05) + (2 * 0.05)

New beta = 1.12 - 0.05 + 0.1

New beta = 1.17

So New portfolio beta is 1.17

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