Practice Question
Suppose you hold a diversified portfolio consisting of a $100 investment in each of 10 different common stocks. The portfolio’s beta is 1.2. You decide to sell one of the stocks that has a beta of 1.5, and use the proceeds (i.e., $100) to buy a replacement stock with a beta of 0.9. What would be your new portfolio’s beta?
Step 1: Calculate Total Initial Beta
\[ \text{Total Initial Beta} = \text{Portfolio Beta} \times \text{Number of Stocks} = 1.2 \times 10 = 12 \]
Step 2: Adjust for Stock Sale
\[ \text{Beta After Selling One Stock} = 12 - 1.5 = 10.5 \]
Step 3: Add New Stock
\[ \text{New Total Beta} = 10.5 + 0.9 = 11.4 \]
Step 4: Compute New Portfolio Beta
\[ \text{New Portfolio Beta} = \frac{11.4}{10} = 1.14 \]
Conclusion
The new portfolio beta is 1.140. This reflects a slightly less risky portfolio after replacing the higher-beta stock.