Question

Bond	Coupon Rate	Maturity	Market Price
A	4% Paid annually	1 Year	998.06
B	4% Paid annually	2 years	1011.49
C	7% Paid annually	3 years	1094.68

1. Assume the pure expectations hypothesis 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 the third year are 4.25%, 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 given in question 2. Suppose that XYZ issued a new $1,000 fane 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?

Answer 1