Question: 7. (10 points) Consider a 1-year inverse floater, face value $1000, issued by a risk-free borrower, paying a floating rate equal to 10% minus the

7. (10 points) Consider a 1-year inverse floater, face value $1000, issued by a risk-free borrower, paying a floating rate equal to 10% minus the 6-month Treasury rate. (a) Briefly explain how the above inverse floater can be created by a portfolio of the following two securities, both with one year to maturity, a face value of $1000, and both issued by the same risk-free borrower: . Security A: a bond paying a fixed semi-annual coupon rate of 5% P.A. . Security B: an FRN paying a floating coupon rate equal to the 6-month Treasury rate. (b) The 6-month Treasury rate is 5% p.a. The yield to maturity of security A is 6% p.a. Both rates are semi-annual compounding. Compute the price and the duration of the inverse floater. (Hint: duration of a portfolio is the weighted average of the durations of individual assets in the portfolio with the weights being the corresponding asset values.)

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