1. Assume investors are choosing their portfolios according to the CAPM. Suppose the risk free net interest rate is 1%. The mean net return on the NYSE (a proxi for the market portfolio) is 16%. The standard deviation of the NYSE index is 1%. a) Suppose one of your clients has preferences represented by the following utility in the asset return, r: U(r) = r p2 She has an endowment of 100,000. How much would you recommend her to invest in the NYSE and how much in the risk-free asset? b) Consider the case in which the risk free net interest rate is now 2%. The mean net return on the NYSE now is 17%. The standard deviation of the NYSE index is 1%. Compute the optimal investment in such a case. How does it compare to your previous answer? Explain. c) Finally, consider the case in which the risk free net interest rate is 1%. The mean net return on the NYSE is 17%. The standard deviation of the NYSE index is 1%. Compute the optimal investment in such a case. How does it compare to your previous answers? Explain