(Please do by hand, not on excel)

You manage a fund with a perpetual annual obligation of $5m. The current YTM is 10%.

a). Create a strategy using zero-coupon bonds to immunize your portfolio from interest movements.

b). How many zero-coupon bonds with a par value of $1,000 will you need to purchase to meet your obligations?

c). If the convexity of a zero-coupon bond with a duration of 5 years and par value of $1,000 and YTM of 10% is 24.79, estimate the new price of the zero-coupon bond if YTM decreases by 5% using the bonds duration and convexity. What is the difference between your estimated price and the actual new price?