Bond A is currently trading at a price of 114.51, has a face value of 100 and 25% coupon and three years to maturity.
Bond B is currently trading at a price of 117.42, has a face value of 100 and 25% coupon and two years to maturity.
Finally, Bond C is currently trading at a price of 113.63, has a face value of 100 and 25% coupon and 1 year to maturity.
(A) First, find the zero-coupon discount factors for one, two and three years out (i.e. find D(0,1), D(0,2) and D(0,3)).
Hint: D(0,1) is easy to find just from the information about Bond C. For D(0,2) you need to construct a portfolio of Bond C and Bond B that has a zero payoff 1 year from now. Finally, to get D(0,3) you need to construct a portfolio of all three bonds that has zero payoffs in both 1 and 2 years from now. This is a similar tack to the one used in the in-class exercise on page/slide 5 in Lecture 4.
(B) Next, compute the zero-coupon yields for one, two and three years out (i.e. z(0,1), z(0,2) and z(0,3)).
(C) Compute the forward rates implied by the prices of these bonds for one, two and three years out (i.e. f(0,1), f(0,2) and f(0,3)).
(D) Finally, compute the par coupon bond yields for one, two and three years out (see the last two slides in Lecture 2).
Following the previous problem, but consider only two-year horizon. Assume that the one-year spot rate is the same as the forward rate f(0,1)(10%). Furthermore, you believe/know that in year 1 you can borrow at a rate of 15%.
A. Is there any arbitrage opportunity?
B. If there is an arbitrage opportunity, try to construct a strategy using one-year and two-year zero-coupon bonds.
C. (optional) Try to construct a strategy using spot borrowing, Bond B and Bond C from the previous problem.
Note: Please refer to the previous problem for forward rates, discount factors, and coupon bond prices.