Please show your work 1. Suppose a bank has an asset duration of 4 years and a l
ID: 2818612 • Letter: P
Question
Please show your work
1. Suppose a bank has an asset duration of 4 years and a liability duration of 2.75 years. This bank has $1,050 million in assets and $780 million in liabilities. They are planning on trading in a Treasury bond future which has a duration of 7.5 years and which is selling right now for $98,500 for a $100,000 contract. How many futures contracts does this bank need to fully hedge itself against interest rate risk?
2. Suppose a Eurodollar time deposit futures contract has a duration of .6 years and has a current market price of $965,000. Market interest rates are 7.5 percent and are expected to fall to 6.5 percent. What is the change in this futures contract's market price from this change in interest rates?
3. An investor purchases one September T-bond futures contract at 116-210. The settlement price for the contract on next day is 118-120. What is the marked-to-market gain/loss for the investor?
Explanation / Answer
(1) Asset Duration = 4 years = D(a) and Liability Duration = 2.75 years = D(l)
Asset Size = $ 1050 million and Liability Size = $ 780 million
k = Ratio of Liabilities to Assets = (780 / 1050) = 0.7428 ~ 0.743
As D(a) > k x D(l) = 4 > 0.743 x 2.75, the duration gap is positive which implies that an increase in the interest rate erodes asset value by a greater amount than it erodes liability values, thereby leading to a reduction in equity. The opposite happens in case of interest rate decrease. Assets gain more in value than liabilities, thereby elevating equity. A positive duration gap is hedged by taking a position in the T-bond futures that benefits from a rise in interest rates (as positive duration gaps face the risk of shrinking equity (assets - liabilities) when interest rates rise).Such a position would entail selling short the T-bonds so that a negative (decrease) in equity owing to interest rate rise is compensated by the difference between the selling and buying price of the T-Bond Future contracts.
Price of each contract = $ 98500, Face Value of Contract = $ 100000 and Duration of Futures = 7.5 years
Number of Futures Required = [D(a) - k x D(l)] x Asset Value / Duration of Futures x Price of Futures
= [4 - (780/1050) x 2.75] x 1050 / [7.5 x (98500/100000)] = 278.17 ~ 278 contracts as contract number can't be a decimal number.
NOTE: Please raise separate qeuries for solutions to the remaining unrelated questions.