You have a $4 million portfolio consisting of a $100,000 investment in each of 20 different stocks. The portfolio has a beta of 1.1. You are considering selling $100,000 worth of one stock with a beta of 0.9 and using the proceeds to purchase another stock with a beta of 1.4. What will the portfolio's new beta be after these transactions?

Answer: 1.112375

Explanation:

Number of stocks = 20

Portfolio beta (Bp) = 1.1

Worth of stock to be sold (Ss) = 100,000

Portfolio worth (Wp) = 4,000,000

Beta of stock to be sold (Bs) = 0.9

Beta of other stock to be purchased (Bo) = 1.4

Therefore, new worth of portfolio (Np):

(4,000,000 - 100,000) = 3,900,000

Bp = (Ss / Wp) Bs + (Np / Wp) Br

Where Br = Beta of what is left after the sale of the $100,000 stock

1.1 = (100,000 / 4,000,000) 0.9 + (3,900,000/4,000,000) Br

1.1 = (0.025 * 0.9) + (0.975) Br

1.1 = 0.0225 + 0.975Br

1.1 - 0.0225 = 0.975Br

Br = 1.0775 / 0.975

Br = 1.105

New beta (Bn):

(Ratio of sold stock * Bo) + (ratio of stock left * Br)

(100,000/4000000) 1.4 + (3900000/4000000) 1.105

Bn = (0.025 * 1.4) + (0.975 * 1.105)

Bn = 0.035 + 1.077375

Bn = 1.112375