Problem 2 (20 marks)

Bond Coupon Rate Maturity Market Price

A 3 % PAID ANNUALLY 1 YR 998.06

B 4 % PAID ANNUALLY 2 YR 1011.49

C 7 % PAID ANNUALLY 3 YR 1094.68

1. Assume the pure expectations hypothesis (PEH) holds, and estimate the term structure for the next three years (i.e. calculate the spot rate for the first year, and the forward rates for the second, and third years).
2. Now assume (setting aside the information in question (1)) that the spot rate for the first year, the forward rate for the second year, and the forward rate for third year are 4.2%, 4.4%, and 4.5%, respectively. What must the price of a three-year Government of Canada noncallable bond with an annual coupon of 6% be?

3.Assume that the term structure of forward rates is that given in question (2). Suppose that XYZ Inc. issued a new $1,000 face value retractable (puttable) bond with 3 years to maturity, carrying a 5% annual coupon, paid annually. This bond is retractable (puttable) according to the following schedule:

Puttable in 1 year for $975

Puttable in 2 years for $990

Assume that the Pure Expectations Theory of the term structure holds, and that there are no costs involved in issuing new bonds. Also assume that XYZ's bonds are traded with a 2% yield spread over the Government of Canada forward rates. Note that XYZ bondholders can only retract (put) the bond in one year or in two years. Assume that XYZ bondholders choose the retraction date so that their retraction profit is maximized. When do you expect XYZ bondholders to retract (put) the new bond?

Hint: To solve this problem, calculate the expected bond prices in Year 1 and Year 2 using the Pure Expectations theory formulas.

Expected value of the bond one year from now:

Expected value of the bond two years from now:

Then compare the expected bond prices with the exercise price on the "put option" on the bonds for the decision to retract the bonds or not.