A financial institution has to pay $1,000 after 2 years and $2,000 after 4 years. The

current market interest rate is 10%, and the yield curve is assumed to be flat at any

time. The institution wishes to immunize the interest rate risk by purchasing zero-

coupon bonds which mature after 1, 3 and 5 years. One member in the risk

management team of the institution,

Alan, devised the following strategy:

Purchase a 1-year zero-coupon bond with a face value of $44.74,

Purchase a 3-year zero-coupon bond with a face value of $2,450.83,

Purchase a 5-year zero-coupon bond with a face value of $500.00.

(a) Find the present value of the liability.

(b) Show that Alan's portfolio satisfies the conditions of the duration matching strategy.

(c) Define surplus S = V A V L , calculate S when there is an immediate one-time change

of interest rate

10% to (i) 9%, (ii) 11%,

(d) Find the convexity of the portfolio of assets and the portfolio of liabilities at i = 10%.

(e) Did Alan's portfolio satisfy the Conditions of Redington's Immunization strategy?