You hold a diversified portfolio consisting of a $5,000 investment in each of 20 different common stocks. The portfolio beta is equal to 1.12. You have decided to sell a lead mining stock What is the new beta of the portfolio?
A) 1.1139
B) 1.1700
C) 1.2311
D) 1.2927
E) 1.3573

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the formula for the new portfolio beta after selling a single stock:

New Beta = (Total Portfolio Value - Value of Stock Sold) / (Total Portfolio Value * Old Beta)

First, we need to calculate the total portfolio value:

Total Portfolio Value = $5,000 * 20 = $100,000

Next, we need to calculate the value of the stock being sold. The problem doesn't give us this information, so we'll just assume it's also $5,000.

Now we can plug in the numbers:

New Beta = ($100,000 - $5,000) / ($100,000 * 1.12) = 0.942

However, this is the beta of the remaining 19 stocks. To get the new beta of the entire portfolio, we need to use the formula for portfolio beta:

Portfolio Beta = (Weight of Stock 1 * Beta of Stock 1) + (Weight of Stock 2 * Beta of Stock 2) + ... + (Weight of Stock 20 * Beta of Stock 20)

Since all 20 stocks were originally weighted equally, each had a weight of 1/20 = 0.05. After selling one stock, there will be 19 left, so each will have a weight of 1/19 = 0.0526.

We can use this to calculate the new beta:

Portfolio Beta = (0.0526 * 1.12 * 19) + (0.0526 * New Beta) = 1.170

Therefore, the answer is B) 1.1700.

You Hold a Diversified Portfolio Consisting of a $5,000 Investment