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An FI is planning the purchase of a $5 million loan to raise the existing average...

An FI is planning the purchase of a $5 million loan to raise the existing average duration of its assets from 3.5 years to 5 years. It currently has total assets worth $20 million, $5 million in cash (0 duration) and $15 million in loans. The FI’s liabilities have an average duration of 5 years. All the loans are fairly priced.

a. Assuming it uses the cash to purchase the loan, should the FI purchase the

loan if its duration is seven years?

b. What asset duration loans should the FI purchase to raise its average duration

to five years?

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Answer #1

a: Duration of the existing loan =  0 + (15/20) * X = 3.5 years

X = Loan duration = 4.667 years

New duration of portfolio = (5/20)*7 + (15/20)*4.667 = 5.2 years

The average duration will rise more than the duration of liabilities required which is 5 years. Hence it should not be purchased.

b: Let the Asset duration be X

(5/20)*X  + (15/20)*4.667 = 5

Hence

X = 6

Asset duration loans purchased to raise its average duration to five years = 6 years

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