Problem Set 3
Problem Set 3
Problem Set 3
Suppose you observe that a three-year, default-free security with an annual coupon rate of
10% and a face value of $1000 has a price today of $1183.95. Is there an arbitrage
opportunity? If so, show specifically how you would take advantage of this opportunity. If
not, why not?
Problem 2
Suppose you are given the following information about the default-free, coupon-paying yield
curve:
Problem 3
Suppose that the prices of zero-coupon bonds with various maturities are given in the
following tables. The face value of each bond is $1,000.
Problem 4
a) Suppose the yield to maturity on both bonds increases to 9%. What will be the actual
percentage capital loss on each bond? What percentage capital loss would be predicted by
the duration-with-convexity rule?
b) Repeat part a), but this time assume the yield to maturity decreases to 7%.
c) Compare the performance of the two bonds in the two scenarios, one involving an
increase in rates, the other a decrease. Based on the comparative investment performance,
explain the attraction of convexity.
d) In view of your answer to c), do you think it would be possible for two bonds with equal
duration but different convexity to be priced initially at the same yield to maturity if the
yields on both bonds always increased or decreased by equal amounts, as in this example?
Would anyone be willing to buy the bond with lower convexity under these
circumstances?
Problem 5
A newly issued bond has a maturity of 10 years and pays a 7% coupon rate (with coupon
payments coming once annually). The bond sells at par value.