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?

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

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