A financial investor builds a portfolio that is worth an expected $35$mil. The investor knows that his analysts can build a model to boost the potential return from the portfolio investment. The additional return has a Normal Distribution with mean $3$mil and standard deviation $0\mathrm{.}5$mil. The investor wishes to sell his financial services at a price that guarantees his expected profit will be $5\%$ of the total return from the portfolio.

A$)$ What should the price of his financial service be$?$

B$)$ Simulate $($with a min of $200$ repetitions$)$ the average and the standard deviation of the profit the financial advisor realizes when setting the price for his services between $1\%$ and $10\%$ of

the total expected return from the portfolio. Then discuss your findings.

C$)$ Now assume the financial advisor knows that another advisor will offer a competitive portfolio. Based on historical data, he knows this competitive portfolio$$s total return follows a normal distribution with mean $36$mil and standard deviation of $2$mil and is priced at $5\%$ of total return. Clients will naturally choose the advisor which offers the portfolio with the highest net return. How does the distribution of profit over the range of financial prices considered in part B$)$ changes, when the competitor is considered?