Could you please provide a detailed explanation for this question and the relevant formulas that are required in answering this question. Thank You.

Suppose we have two risky assets, Stock I and Stock J, and a risk-free asset. Stock I has an expected return of 25% and a beta of 1.5. Stock J has an expected return of 20% and a beta of 0.8. The risk-free asset's return is 5%.

a.Calculate the expected returns and betas on portfolios with x% invested in Stock Iand the rest invested in the risk-free asset, where x% = 0%, 50%, 100%, and 150%.

b. Using the four portfolio betas calculated in part (a), reverse engineer (i.e., derive mathematically) the portfolio weights for a portfolio consisting of only Stock J and the risk-free asset.