1/. Assume that Blue Sunday Bank has $200 million of assets with an average dura
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Question
1/. Assume that Blue Sunday Bank has $200 million of assets with an average duration of 1.6 years and liabilities of $100 million with an average duration of 1.95 years. Compute the current duration gap of this bank. Assuming that U.S. Treasury bonds with a duration of 1.2 years are currently quoted in the market at 98-16, explain the position (buy or sell) in a futures contract (including the number of contracts) that the bank manager should take to eliminate interest rate risk.
Duration Gap
Formula =
Dollar Weighted Duration of Asset Portfolio – Dollar Weighted Duration of Liabilities Portfolio
x
Asset Duration =1.6
Liabilities Duration = 1.95
Total Assets =200,000,000
Total Liabilities =100,000,000
100,000,000/200,000,000=.05 x 1.95=.975
1.6-.975=.625
Duration Gap
Formula =
=1.6
= 1.95
Total Assets or TA =200,000,000
Total Liabilities or TL =100,000,000
Duration of the underlying security
named in the futures contract or D = 1.2
Price of futures contract or = 98,500
100,000,000/200,000,000=.05 x 1.95=.975
1.6-.975=.625x200,000,000=125,000,000
1.2x98500-118200
125,000,000/118200 = 1057.5 or 1056
Blue Sunday should purchase futures contracts as they are in a positive duration gap and thus sensitive to a rise in interest rates.
Are my calculations correct? Does it appear as if I am missing anything?
Duration Gap
Formula =
Dollar Weighted Duration of Asset Portfolio – Dollar Weighted Duration of Liabilities Portfolio
x
Asset Duration =1.6
Liabilities Duration = 1.95
Total Assets =200,000,000
Total Liabilities =100,000,000
100,000,000/200,000,000=.05 x 1.95=.975
1.6-.975=.625
Explanation / Answer
Answer:
Duration Gap
Formula =
Dollar Weighted Duration of Asset Portfolio – Dollar Weighted Duration of Liabilities Portfolio
x
Asset Duration =1.6
Liabilities Duration = 1.95
Total Assets =200,000,000
Total Liabilities =100,000,000
100,000,000/200,000,000=.05 x 1.95=.975
1.6-.975=.625
Duration Gap
Formula =
=1.6
= 1.95
Total Assets or TA =200,000,000
Total Liabilities or TL =100,000,000
Duration of the underlying security
named in the futures contract or D = 1.2
Price of futures contract or = 98,500
100,000,000/200,000,000=.05 x 1.95=.975
1.6-.975=.625x200,000,000=125,000,000
1.2x98500-118200
125,000,000/118200 = 1057.5 or 1056
All calculations are correct and complete.
Duration Gap
Formula =
Dollar Weighted Duration of Asset Portfolio – Dollar Weighted Duration of Liabilities Portfolio
x
Asset Duration =1.6
Liabilities Duration = 1.95
Total Assets =200,000,000
Total Liabilities =100,000,000
100,000,000/200,000,000=.05 x 1.95=.975
1.6-.975=.625
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