Final answer:
The portfolio's beta is calculated as a weighted average of individual stocks' betas and it is found to be 1.20.
Step-by-step explanation:
To calculate the portfolio's beta, one must take a weighted average of the betas of the individual stocks in the portfolio. The formula to calculate portfolio beta (βp) is given by:
βp = (x₁ * β₁) + (x₂ * β₂)
where x₁ and x₂ represent the proportion of the total portfolio value invested in Stock X and Stock Y respectively, and β₁ and β₂ are the beta values for Stock X and Stock Y.
In this case:
- $62,500 is invested in Stock X, which represents (62500/100000) or 62.5% of the portfolio.
- The remainder, which is $37,500, is invested in Stock Y, representing (37500/100000) or 37.5% of the portfolio.
- Stock X has a beta of 1.50.
- Stock Y has a beta of 0.70.
Using the formula:
βp = (0.625 * 1.50) + (0.375 * 0.70)
βp = 0.9375 + 0.2625
βp = 1.20
Therefore, the portfolio's beta is 1.20, which corresponds to option a.