QUESTIONS AND PROBLEMS
5.2. The term structure is upward sloping. Put the following in order of magnitude:
a. The five-year zero rate
b. The yield on a five-year coupon-bearing bond
c. The forward rate corresponding to the period between 5 and 5.25 years in the future
What is the answer to this question when the term structure is downward sloping?
5.3. The six-month and one-year zero rates are both 10% per annum. For a bond that lasts 18
and pays a coupon of 8% per annum (with a coupon payment having just been made), the yield is
10.4% per annum. What is the bond's price? What is the 18-month zero rate? All rates are quoted
with semiannual compounding.
5.4. It is January 9, 2003. The price of a Treasury bond with a 12% coupon that matures on
2009, is quoted as 102-07. What is the cash price?
5.5. The price of a 90-day Treasury bill is quoted as 10.00. What continuously compounded
return (on an actual/365 basis) does an investor earn on the Treasury bill for the 90-day period?
5.6. What assumptions does a duration-based hedging scheme make about the way in which the
term structure of interest rates moves?
5.7. It is January 30. You are managing a bond portfolio worth $6 million. The duration of the
portfolio in six months will be 8.2 years. The September Treasury bond futures price is currently
108-15, and the cheapest-to-deliver bond will have a duration of 7.6 years in September. How
should you hedge against changes in interest rates over the next six months?
5.8. Suppose that 6-month, 12-month, 18-month, 24-month, and 30-month zero rates are 4%,
4.2%, 4.4%, 4.6%, and 4.8% per annum with continuous compounding respectively. Estimate the
cash price of a bond with a face value of 100 that will mature in 30 months pays a coupon of 4%
per annum semiannually.
5.9. A three-year bond provides a coupon of 8% semiannually and has a cash price of 104. What
is the bond yield?
5.10. Suppose that the 6-month, 12-month, 18-month, and 24-month zero rates are 5%, 6%, 6.5%,
and 7%, respectively. What is the two-year par yield?
5.11. The cash prices of six-month and one-year Treasury bills are 94.0 and 89.0. A 1.5-year
bond that will pay coupons of $4 every six months currently sells for $94.84. A two-year bond
that will pay coupons of $5 every six months currently sells for $97.12. Calculate the 6-month, 1-
year, 1.5-year, and 2-year zero rates.