# Practice Problems for Lecture 4

1. Consider the following situation. Today you are looking at a Treasury bond with a coupon of 10% paid semiannually and a face value of \$100 which is one year from maturity and is currently trading at \$99.10 after this period's coupon has already been paid. (In truth, if the coupon has not been paid it does not matter, since the amount of accrued interest, now the entire coupon, is added to the price.) You have also obtained prices of Treasury STRIPs -- one that matures in 6 months and is currently trading at \$95.24 with a face of \$100 and another one maturing in a year with a price of \$89.85 with a face of \$100.

(A) What is the implied forward rate for borrowing and lending 6 months from today?

(B) What is the bond-equivalent yield of the Treasury bond?

(C) What is the Macaulay duration of the Treasury bond with respect to its own yield?

(D) What is the Macaulay duration of the Treasury bond with respect to the discount factors in the economy?

(E) What is the effective duration of the Treasury bond with respect to the discount factors in the economy?

2. Consider a fixed income security which pays one half of its value in 20 years, one quarter in 10 years and one quarter in 5 years.

(A) What is the Macaulay duration of this security?

(B) What is the effective duration of this security?