An FI has $500 million of assets with a duration of ten years and $450 million o

Question

An FI has $500 million of assets with a duration of ten years and $450 million of liabilities with a duration of three years. The FI wants to hedge its duration gap with a swap that has fixed-rate payments with a duration of seven years and floating-rate payments with a duration of two years.

a. What is the optimal amount of the swap necessary to effectively macrohedge against the adverse effect of a change in interest rates on the value of the FI’s equity?

b. What is the exact number of swap contracts that the FI should enter into, assuming that each swap contract is $100,000 in size?

Explanation / Answer

Part a)

The optimal amount of swap necessary to effectively macrohedge against the adverse effect of a change in interest rates on the value of the FI’s equity is calculated as below:

Optimal Amount = (DA - kDL)*Assets/(DFixed - DFloating)

Here, DA = 10, k = .9, DL = 3, Assets = 500, DFixed =7 andDFloating = 2

Using these values in the above formula, we get,

Optimal Amount = ((10 - .9*3)*500)/(7 - 2) = $730 million or $730,000,000

_____

Part b)

The exact number of swap contracts is determined as below:

Exact Number of Swap Contracts = Optimal Amount/Contract Size = 730,000,000/100,000 = 7,300 contracts

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.