Bootstrap and Lock in Forward Rate:

(a) Imagine that currently in the market the following bonds are available:

Maturity Coupon Rate Price

0.5 0% $ 97.500

1.5 8% $101.500

1.5 0% $ 90.100

2.0 0% $ 85.200

Maturity is in years, coupons are paid semiannually but quoted annually on a bond equivalent basis, and prices are quoted per $100 face value. Construct a 2-year spot yield curve from this information. More precisely, calculate a spot rate for each six-month period. Report the rate on a bond equivalent basis.

(b) Assume the zero-coupon bonds from 1 year to 4 years are all available, and the current 1-year, 2- year, 3-year and 4-year spot rates are 4%, 5%, 6% and 7% accordingly. Interest rates are annually compounded. You want to lock in a 1-year interest rate beginning in 3 years, by using some of the zero coupon bonds above. Which zero-coupon bonds would you use? And what is the locked-in 1-year rate beginning in 3 years?