Please answer all of them with all explanations

A.2. A US investor is considering the possibility of building a portfolio combining the risk-free asset and a portfolio that replicates the S\&P500. The Treasure Bills (T-bills) rate of return is 5%, the risk of the S&P500 is 22% and its expected return is 11%. (a) How much of his wealth does he need to invest in the risk-free asset (w) to obtain a portfolio with a risk of 12% ? (b) Write down the mathematical expression for the equation that relates risk and return for the portfolio derived in the previous question. (c) This investor can choose between investing in a portfolio that replicates the S&P500 and investing in an investment fund that follows the Dow Jones Industrial Average (DJIA) whose expected return and risk are 13% and 32% respectively. Write down the mathematical expression for the equations that relate risk and return in both cases. Which investment strategy should he choose if he wants to maximize utility? (d) Look up information about the S\&P500 and the DJIA indexes