Consider $2$ put options written on a non$-$dividend paying stock that matures in $6$ months. One of the options has a strike price of $$20$ and costs $$3,$ the other option has a strike of $$25$ and costs $6$$$.$

a$)$ Explain what positions should be taken in the options to achieve a long "Bear Spread".

b$)$ Draw a profit diagram of the long "Bear Spread".

c$)$ What is the maximum and the minimum profit of the Bear Spread?

d$)$ What is the break$-$even stock price?

e$)$ Explain under what market views an investor would take on such position if today$$s stock price is $$20$