1. Consider the following bonds with face values of $1,000. The coupon bonds make semi-annual coupon payments:

Issuer Years to Maturity Coupon Price (% of FV)

GAP Inc. 7 5.95% 113.647

European Investment Bank 7 2.50% 100.813

Raymond James 10 5.95% 116.409

In class, we calculated duration for a bond with semi-annual coupons. With semi-annual coupons, we transform duration from years to semi-annual periods. For example, if a bond with semi-annual coupons has a yield to maturity of 2.48% and a duration of 1.956 years, we transform the duration to 1.956*2 = 3.912 semi-annual periods. Since the semi-annual yield on the bond is 2.48/2 = 1.24%, modified duration, D* = 3.912/1.0124 = 3.864 semi-annual periods. Then, if the semi-annual yield rises by 10 basis points, the change in the price of the bond is

-3.864*.001 = -.00386 = -.386%

1. Calculate the yield to maturity, duration (in years), and modified duration (in semi-annual periods) for each bond.
2. Consider the two bonds with the same maturity (7 years). What explains the different durations of the 2 bonds? For each bond, consider a rise in semi-annual yields of 12 basis points. Using modified duration to estimate the rate of capital loss, which bond has the highest rate of capital loss? For each bond, consider a decline in semi-annual yields of 12 basis points. Using modified duration to estimate the rate of capital gain, which bond has the highest rate of capital gain?
3. Consider the bonds with the same coupon rate. For each bond, consider an increase in semi-annual yields of 12 basis points. Using modified duration to estimate the rate of capital loss, which bond has the highest rate of capital loss? For each bond, consider a decrease in semi-annual yields of 12 basis points. Using modified duration to estimate the rate of capital gain, which bond has the highest rate of capital gain?