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

Issuer Years to Maturity Coupon Price (% of FV)

Cablevision 5 5.875% 92.750

3M Co. 5 2.00% 98.689

IBM 15 5.875% 124.843

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.

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 (5 years). For each bond, consider a rise in semi-annual yields of 15 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 15 basis points. Using modified duration to estimate the rate of capital gain, which bond has the highest rate of capital gain? Why is duration a better measure than maturity when calculating a bonds sensitivity to changes in interest rates?

3. Consider the bonds with the same coupon rate. For each bond, consider an increase in semi-annual yields of 15 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 15 basis points. Using modified duration to estimate the rate of capital gain, which bond has the highest rate of capital gain?