You Are a Young Investment Banker Considering the Issuance of a Guaranteed

question 3

Essay

You are a young investment banker considering the issuance of a guaranteed note with stock index participation for a client. The current yield curve is flat at 8% for all maturities. Long-term at-the-money options on the stock market index are traded by banks. Two-year at-the-money calls trade
at 17.84% of the index value; three-year at-the-money calls trade at 20% 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. Your boss asks you to compute the "fair" participation rate that would be feasible for various guaranteed coupon rates and maturities. In other words, based on the current market conditions (as described above), 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%.

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Definitions:

Population Standard Deviation

A measure that quantifies the amount of variation or dispersion of a set of values in a total population.

Set of Data

A set of data refers to a collection of numbers or values that relate to a particular subject or experiment.

Parameter

Numeric characteristic of a population.

Population

The entire aggregation of items or individuals from which samples can be drawn for statistical analysis.