Question

Suppose you heid a diversified portfolio consisting of a $7,500 investment in each of 20 different common stocks. The portfolio's beta is 0.75 . Now suppose you decided to sell one of the stocks in your portfolio with a beta of 1,0 for $7,500 and use the proceeds to buy another stock with a beta of 1.40 . What would your portfolio's new beta be? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

To find the portfolio's new beta, calculate the weighted average beta of the remaining stocks and add the new stock's beta. The portfolio's new beta will be 2.05.

Step-by-step explanation:

To find the portfolio's new beta, we need to calculate the weighted average beta of the remaining stocks in the portfolio, and then add the new stock's beta.

First, calculate the total value of the portfolio before selling the stock:

Total Value = $7,500 * 20 = $150,000

Next, calculate the portion of the portfolio's beta contributed by each stock:

Portfolio Beta = Average Beta * Total Value / Stock Value

For the stock being sold (with a beta of 1.0), the contributed beta is:

Contribution of Stock Being Sold = 1.0 * $7,500 / $7,500 = 1.0

Now, calculate the new stock's contribution to the portfolio's beta:

Contribution of New Stock = 1.4 * $7,500 / $7,500 = 1.4

Finally, calculate the weighted average beta of the remaining stocks:

Remaining Beta = (Portfolio Beta - Contribution of Stock Being Sold) / (Total Value - Stock Value) * (Total Value - Stock Value) / Total Value

Substituting the known values:

Remaining Beta = (0.75 * $150,000 - 1.0) / ($150,000 - $7,500) * ($150,000 - $7,500) / $150,000

Simplifying the equation:

Remaining Beta = 0.65

Finally, the portfolio's new beta is:

New Beta = Remaining Beta + Contribution of New Stock = 0.65 + 1.4 = 2.05