Suppose you observe a three-year, AA-rated corporate bond with an annual coupon rate of 4% and a face value of $1000. The following table summarizes the yield to maturity for three-year (annual-pay) coupon corporate bonds of various ratings: Rating YTM AAA 3.7% AA 3.9% Maturity (years) Zero-coupon YTM A 4% a) Calculate the price of the three-year 4% bond. (3 marks) b) Assuming that the yield did not change, what would this bond's price be next year? How about at the maturity date? (1 mark) c) What must the rating of the bonds be for them to sell at par? (1 mark) d) What is the credit spread on an AA-rated corporate bond? (1 mark) e) If the three-year bond has been upgraded to an AAA-rated corporate bond. Do you expect the return of the bond to be higher or lower than the current bond yield? (2 marks) What is the percentage change in the price of this bond, if the yield to maturity is to decrease to 3.7%? (2 marks) f) 1 3.6% BBB 4.7% Assume zero-coupon yields on default-free securities are as summarized in the following table: 2 3.8% BB 5.1% 3 4% g) Is there an arbitrage opportunity? If so, describe how would you take advantage of this opportunity? If not, why not? (7 marks)