An investor invests $30\%$ of his funds in risk free asset and the remaining $70\%$ of funds in an index fund that represents the market. The risk$-$free return is $8\%.$ The index fund is expected to give a return of $21\%.$ Using the CAPM Model.

a$.$ What is the expected return from the portfolio of the investor? The standard deviation of returns from the index funds is $9\mathrm{.}80.$ What is the Standard Deviation of the portfolio return?

b$.$ If the investor withdraws his investment in the risk free security and invests the same also in the index fund, what is the expected return? What is the portfolio risk?