Final answer:
The expected return on a portfolio equally invested in both assets is 8.175%. If a portfolio of the two assets has a beta of 0.85, the weights are 32% for the risk-free asset and 68% for the stock. The beta of a portfolio with an expected return of 11.5% is 0.985.
Step-by-step explanation:
When calculating the expected return on a portfolio with one stock having a beta of 1.25 and an expected return of 12.3 percent, and the other asset being a risk-free asset with a return of 4.05 percent, we must first find the average of the two returns. This is calculated by adding the expected return of the stock and the return of the risk-free asset and then dividing by 2.
The expected return on a portfolio equally invested in the two assets: (12.3% + 4.05%) / 2 = 8.175%
To find the portfolio weights if a portfolio has a beta of 0.85, we can use the formula for the portfolio beta, which is a weighted average of the individual betas. Assuming the weight of the risk-free asset is w and the weight of the stock is (1 - w), we solve for w given that 1.25(1 - w) = 0.85.
Finding the portfolio weights: 1.25(1 - w) = 0.85 1.25 - 1.25w = 0.85 1.25w = 1.25 - 0.85 w = 0.4 / 1.25 w = 0.32, or 32%
The weight of the stock in the portfolio would therefore be 1 - 0.32 = 0.68, or 68%. Finally, to find the beta of a portfolio with an expected return of 11.5 percent, we use the Capital Asset Pricing Model (CAPM), which can be rearranged to solve for beta given the expected return of the portfolio, the risk-free rate, and the expected return of the market.
Using CAPM to find the beta of the portfolio with an 11.5 percent return:
11.5% = 4.05% + beta(12.3% - 4.05%) Beta = (11.5% - 4.05%) / (12.3% - 4.05%) Beta = 0.985, or 98.5%