Spoofer National Bank has created an instrument called a market participation CD (MPCD). The CD will mature in one year and at that time will pay either $50 or the value of one share of Megatronics stock, whichever is greater. However, in the fine print of the contract, it specifies that the payoff will never exceed $55, even if the stock price is above that amount. Thus the payoff for the market participation CD is:

State of market: MPCD pays:

S₁< 50 50

50 < S₁< 55 S₁

55 < S₁ 55

a. Diagram the payoff function for the MPCD. Be sure to label the critical values on the diagram including: maximum payoff, minimum payout, and the location of any kinks in the diagram.

b. Your boss at Spoofer NB has asked you to construct a portfolio that will provide the bank with exactly the amount needed to cover the payments it will be required to make on one MPCD in every state of the market. What instruments would you use to construct the portfolio? Please specify i) the type of instrument ii) including relevant parameters such as strike price, face value, etc., and iii) type of position (long or short).

c. Based on your answer to b, what is the fair marketvalue of an MPCD?