You are an investment banker considering the issuance of a guaranteed note with stock index participation for a client. The current yield curve is flat at 8 percent for all maturities. Two-year at-the-money calls trade at 17.84 percent of the index value; three-year at-the-money calls trade at 20 percent of the index value. You are hesitant about the terms to set in the structured note. You know that if you guarantee a higher coupon rate, the level of participation in the stock appreciation will be less.
a. Your supervisor asks you to compute the "fair" participation rate that would be feasible for various guaranteed coupon rates and maturities. Based on the current market conditions (as described), estimate the participation rates that are feasible with a maturity of two or three years and a coupon rate of 0, 1, 2, 3, 5, and 7 percent.
b. Explain the relationship between the amount of the guaranteed coupon and the participation rate that can be offered.