The current price of a non-dividend paying stock is $40 and the continuously compounded risk-free interest rate is 8%. You enter into a short position on 3 call options. Each call option has 3 months to maturity, a strike price of $35, and an option premium of $6.13. Simultaneously, you also enter into a long position on 5 call options. Each call option has 3 months to maturity, a strike price of $40, and an option premium of $2.78. You hold all 8 options in a portfolio until maturity.

a. How are options used to hedge risk? Explain.

b. What are the maximum possible profit and the maximum possible loss on the entire portfolio? Show your work.