There are two investments available: Vanguard S&P 500 Index Fund (VEINX) and a risk-free asset. The VFINX has an expected return of 12% and the standard deviation of 20%. The risk-free asset offers two rates: the lending rate is 2% while the borrowing rate is 8%. a. (10%) Assuming that investors are maximizing utility function U=E(r)-0.5A02 in making financial decisions, what is the range of risk aversion for which a client will always invest 100% in VFINX (i.e. neither borrowing nor lending)? b. (7%) Suppose now you have a target risk level (total return standard deviation) of 25% per year. How would you construct a portfolio of the VFINX and the riskless asset to attain this target level of risk? What is the expected rate of return on this constructed portfolio? c(8%) Assuming that investors are maximizing utility function U=E(r)-0.5A02 in making financial decisions, is the constructed portfolio in (b) optimal to a client with A = 2.0? (i.e. Can a client with A= 2.0 have the highest utility level by investing in this portfolio?)