Final answer:
To calculate the change in portfolio beta after replacing stock C with stock E, the student must calculate the weighted average beta of the portfolio before and after the change, then find the difference between the two.
Step-by-step explanation:
The question pertains to portfolio beta calculation, a concept in finance that measures the overall risk of an investment portfolio relative to the market as a whole. The student wishes to know how the beta of the portfolio changes when one stock with a certain beta is sold and replaced with another stock with a different beta. To find the change in the portfolio's beta, we need to calculate the weighted average beta of the portfolio before and after the exchange of stock C with stock E.
The existing portfolio beta is calculated by adding the products of the investment amounts and their respective betas, then dividing by the total portfolio value. Initially, the weighted average beta of LeBron's portfolio is:
- ((100,000 × 1.40) + (100,000 × 0.70) + (200,000 × 1.20) + (200,000 × 2.00)) / 600,000
After selling stock C and buying stock E, the new portfolio beta will be:
- ((100,000 × 1.40) + (100,000 × 0.70) + (200,000 × 0.80) + (200,000 × 2.00)) / 600,000
The change in the portfolio beta is the difference between the new portfolio beta and the original portfolio beta.