Benjamin and Sarah Redding, that we met earlier this semester, are considering building their investment portfolio and would like your expertise... Assume that there are three possible states of the world, a boom, a recession, and a normal economy moving forward. Experts believe that the chance of a boom economy is 45% and the chances of a recession is 15%. There stock options are an: 1. Stock A that will have a return of 20% during a boom economy, an -18% return during a recession, and a 12% return in a normal economy. 2. Stock B that will have a return of 8% during a boom economy, a 3% return during a recession, and a 3% return in a normal economy 3. Stock C that will have a return of 12% during a boom economy, a -2% return during a recession, and a 5% return in a normal economy There is also a mutual fund that is a proxy for the S&P 500. The expected return for this fund is 9% and its standard deviation is 15%. The treasury bill has a return of 4% and standard deviation of 1.75%. The beta of Stocks A, B, and C are 1.8, 0.65, and 1.1, respectively. The correlation coefficient between A and B is .56, between A and C is 1.0, between B and C is - .84 If the Reddings have a choice between constructing a portfolio equally divided between Stock A and Stock C and a portfolio where two-thirds is invested in Stock A and the remainder in Stock C, which portfolio will they choose and why? Your explanation should be based on mathematical calculation(s) and those calculations must be shown in order to receive credit