Practice Question
Suppose you hold a diversified portfolio consisting of a $10,000 investment in each of 12 different common stocks. The portfolio's beta is 1.25. Now suppose you sell one of your stocks with a beta of 1.00 and use the proceeds to buy a stock with a beta of 1.34. What is the portfolio’s new beta? Assume the portfolio is equally weighted.
Step 1: Understand the Setup
- Initial beta \( \beta_p = 1.25 \)
- Number of stocks \( n = 12 \)
- Sold stock beta \( \beta_s = 1.00 \)
- New stock beta \( \beta_r = 1.34 \)
Step 2: Calculate Total Beta
\[ \text{Total Beta}_{\text{old}} = \beta_p \times n = 1.25 \times 12 = 15 \]
Step 3: Replace the Stock
\[ \text{Total Beta}_{\text{new}} = 15 - 1.00 + 1.34 = 15.34 \]
Step 4: Compute New Portfolio Beta
\[ \beta_{\text{new}} = \frac{15.34}{12} = 1.278 \]
Conclusion
The new portfolio beta is 1.278, meaning the portfolio is now slightly more volatile than before.