Ask Question
13 July, 04:16

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?

+4
Answers (1)
  1. 13 July, 04:23
    0
    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
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “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 ...” in 📗 Business if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers