Answer Happy

Consider the following problem:
Suppose that you hold a £1 million portfolio of 5-year maturity
bonds with modified duration 4.5 years and desire to hedge your
interest rate exposure with Treasury-bond futures. Treasury-bond
futures have 20 years to maturity and modified duration 9 years and
are currently sold at F0 =£90. The futures contract size is
£100,000 par value. Suppose that all bonds in the bond and futures
markets have £100 par value.
(i) You estimate that the yield on 20-year bond changes by 10
basis points for every 15-basis-point move in the yield on 5-year
bonds. How many futures contracts should you sell?
(ii) How would your answer to question (i) change if the yield
on 20-year bond changes by 10 basis points for every 10-basis-point
move in the yield on 5-year bonds?
(b) The following information is the balance sheet of Bank A.
All interest rates are fixed and paid annually.
Calculate the net interest margin. How is the bank exposed to
interest rate increases or decreases? Explain why.
Amount £7.5 million £75 million £17.5 million Asset Cash Loans Treasuries Liabilities and Equity Amount Time Deposits £35 million £57.5 million CDs Equity £7.5 million Rate 12% 9% Rate 7% 8% Duration 1.75 years 7.00 years Duration 1.75 years 2.50 years