- 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
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Get Help Now!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%
- Calculate the yield to maturity, duration (in years), and modified duration (in semi-annual periods) for each bond.
- 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?
- 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?
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