Mr$.$ Pavamana Rao is an investment analyst at the New York branch of Citibank. He has invested in a portfolio consisting of $1500$ shares of Microsoft stock that is currently trading at $$320$ per share. He is concerned that the US stock market may be adversely impacted over the next $3$ months due to poor economic performance partly due to the policy changes initiated by the Biden administration. He notices that call options, with a strike price of $ $317,$ on Microsoft stock and expiring in $3$ months are trading at $$4\mathrm{.}50.$ He also notices that put options, with a strike price of $ $317$ on Microsoft stock and expiring in $3$ months are trading at $$2\mathrm{.}20.$ Mr$.$ Rao would like to implement a Portfolio Insurance strategy $($using options$)$ to protect against a potential sharp downturn in Microsoft stock. Given this situation, answer the following questions:

a$)$ What is meant by a Portfolio Insurance strategy? How can Mr$.$ Rao implement such a strategy $($using options$)?$ Explain succinctly in a few sentences.

b$)$ What is the maximum gain for Mr$.$ Rao's strategy?

c$)$ What is the maximum loss for Mr$.$ Rao's strategy?

d$)$ Compute the breakeven point for Mr$.$ Rao's strategy?

e$)$ Draw the Payoff diagram and Profit and Loss diagram for this strategy?