Practice Question
You hold three stocks in your portfolio: A, B, and C. The portfolio beta is 1.50. Stock A comprises 20% of the dollar value of your holdings and has a beta of 1.0. If you sell all of your investment in A and invest the proceeds in the risk-free asset, your new portfolio beta will be?
Step 1: Identify Key Variables
- Portfolio Beta \( \beta_p = 1.50 \)
- Stock A weight \( w_A = 0.20 \)
- Stock A beta \( \beta_A = 1.0 \)
- Risk-free beta \( \beta_{rf} = 0 \)
Step 2: Find the Contribution of A to Portfolio Beta
\[ \text{Contribution of A} = w_A \times \beta_A = 0.20 \times 1.0 = 0.20 \]
Step 3: Calculate Remaining Portfolio Beta (B and C)
\[ \beta_{BC} = \beta_p - \text{Contribution of A} = 1.50 - 0.20 = 1.30 \]
Step 4: Adjust Portfolio (Replace A with Risk-Free Asset)
- Replacing A with the risk-free asset (beta = 0) means only B and C contribute to portfolio beta.
\[
\beta_{\text{new}} = \beta_{BC} = 1.30
\]
Conclusion: The new portfolio beta is 1.300.