Answer:
number of contracts needed to hedge is 3714
Explanation:
given data
asset duration = 5 years
liability duration = 2.5 years
assets = $1,000 million
liabilities = $750 million
time = 8.5 years
currently selling = $99,000
contract = $100,000
to find out
How many futures contracts does the bank need to fully hedge itself against interest rate risk
solution
we get here no of contract that is express as
no of contract = (DA - k × DL) A ÷ (DF × PF) .......................1
here DA is asset duration and DL is liability duration and A is assets and DF is time and PF is currently selling and
here K is
k =
k = 0.75
so now put all value in equation 1
no of contract = (DA - k × DL) A ÷ (DF × PF)
no of contract = (5 -0.75 × 2.5) 1000 ÷ (8.5 × 99000)
no of contract = 3714
so number of contracts needed to hedge is 3714