!!! Please ignore the intermediation service question for 2.1.3, I only need to know the structure of the portfolio !!!

PROBLEM 2.1. Consider two stocks, Stock X and Stock Y, and following information. (1) The expected rate of return and the standard deviation of stock X are rX=0.13 and X=0.2. (2) The expected rate of return and the standard deviation of stock Y are rY=0.1 and Y=0.15. (3) The covariance between the rates of return is X,Y=0.01. There is also a risk-free asset whose rate of return is rF=0.02. 2.1.1. Suppose that a "mean-variance" investor who can only invest his or her funds in Security X and in the risk-free asset wishes to construct a portfolio with standard deviation equal to 0.15. Which portfolio should the investor construct, and which would be its expected rate of return? 2.1.2. It is possible to show that in the "market portfolio" for this scenario, the weights of securities X and Y should respectively be equal to a and to 1a, where 1 a=(rXrF)Y2(rY+rX2rF)XY+(rYrF)X2(rXrF)Y2(rYrF)XY. Calculate the values of the weights, as well as the expected rate of return of the market portfolio and its standard deviation. 2.1.3. We plan to offer to the investor in 2.1.1 a portfolio that outperforms the portfolio that he or she is planning to construet, in expectation. What portfolio could we construct on the investor's behalf? What is the greatest percentage of the capital invested that we should expect the investor to be willing to pay as a fee for our intermediation service, for such portfolio