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 returns that each one will generate aredistributedwithameanof1%andastandard``deviationof9%.Afterhearingdescriptions of their strategies, you believe that it is reasonable to assume that the returns on their assets will be uncorrelated.

a) Your colleague says that since all managers are basically equivalent there is no point to hiring more than one.Prove mathematically that a portfolio that is 50% investedinonemanager("manager1")and50%investedinanothermanager("manager 2") would be strictly preferred by a risk-averse investor over an investment in either one individually.

b) What is the correlation of the return on the 50/50 portfolio with the return of manager 1?