3. Suppose that your job is to hire portfolio managers and let each one of them run his own investment strategy independently. Unfortunately, you know little about these managers, and have no better guess than to assume that the monthly retums that each one will generate are distributed with a mean of 1% and a standard deviation of 9%. After hearing descriptions of their strategies, you believe that it is reasonable to assume that the returns on their assets will be uncorrelated. a) (5 points) Your colleague says that since all managers are basically equivalent there is no point to hinng more than one Prove mathematically that a portfolio that is 50% invested in one manager ("manager 1") and 50% invested in another manager ("manager 2") would be strictly preferred by a risk-averse investor over an investment in cither one individually b) (5 points) What is the corelation of the return on the 50 50 portiolo with the retum of manager 13