As a fund manager for Star Invest Inc., you are currently helping a client with her investment portfolio. Diversification strategy recommended by Star Invest requires any portfolio to be split across three different mutual funds while respecting the following limits: o Between 20% and 30% to be allocated within Growth Fund. o Between 20% and 50% to be allocated within Income Fund. o No less than 30% to be allocated within Money Market Fund. Current estimates of the risk factors are: 10% for the Growth Fund, 7% for the Income Fund, and 1% for the Money Market Fund. All the estimates are given in terms of a percentage of each pound invested and they are all considered to be rather stable figures. Much less stable figures are the forecast net yields estimated to be 18% for the Growth Fund, 12.5% for the Income Fund and 7.5% for the Money Market Fund. The client is willing to invest up to 800,000 but only if you manage to produce a well-designed investment plan. Her risk profile indicates the acceptable average risk level of 5.5%, but considering a non-exact nature of the way the acceptable average risk level is estimated, suggesting the investment plan with a slightly lower or slightly larger risk level is acceptable. A mathematical model formulated for this problem using 5.5% as the maximum acceptable average risk level is shown below and also modelled in the Excel file. : 1) Propose the investment plan, i.e., how much to invest into each of the three mutual funds and what is the expected total gain? 2) Why the investment plan you proposed is the best plan for the given set of limitations? 3) For the plan you proposed, what is the overall net yield expected for any additional pound invested? 4) How sensitive is your proposed investment plan to possible future changes in net yields estimates of the three funds? 5) Which one or which ones of the three estimated yields need to be closely monitored and why? 6) What are the consequences of changing the acceptable average risk level? Examine changes in both directions! 7) What is the maximum possible risk level of any portfolio given the diversification strategy limits set by Star Invest? While performing your analysis you will realise that even without changing acceptable average risk level, there is a way to increase the clients expected total gain if you were allowed to change one of the diversification strategy limits imposed by Star Invest. 8) Inform the client which particular limit set by Star Invest is preventing you from achieving even higher gains. 9) How much extra the client could expect to gain if you get the senior management of Star Invest to agree on relaxing that limit by 5%?