$1.$ Consider the following options portfolio: You write a January $2012$ expiration call option on IBM with exercise price $$170.$ You also write a January expiration IBM put option with exercise price $$165.$

a$.$ Graph the payoff of this portfolio at option expiration as a function of IBM$$s stock price at that time.

b$.$ What will be the profit$/$loss on this position if IBM is selling at $$167$ on the option expiration date? What if IBM is selling at $$175?$ Refer to Figure $15\mathrm{.}1.$

c$.$ At what two stock prices will you just break even on your investment?

d$.$ What kind of $$bet$$ is this investor making; that is$,$ what must this investor believe about IBM$$s stock price in order to justify this position?