Question

A bank wants to use direct refinancing to manage its duration gap, D_G. Currently, for its assets, loans = $22 million and cash = $6 million. Equity = $4 million. Average D_A = 2.75 years, and average D_L = 4 years.

a) Should the bank buy loans with cash or sell existing loans for cash to reduce its interest risk?

b) What is the duration of the bank's existing loans?

c) How much cash will be used to eliminate the bank's interest rate exposure, if the loan available on the market has a duration of 7.6 years?

Answer 1

a) Average D_A = 2.75 years, Average D_L = 4 years

As Average D_L > Average D_A

So ,to reduce its inerest risk risk, the bank must buy more Loan.

b) Average D_A = 2.75 years, DCash = 0

Loan Amount = $22 million

Cash = $6 million

Assets = Loan Amount + Cash

= $22 million + $6 million

= $28 million

So Average D_A = (Loan / Assets) * D_Loan + (Cash / Assets) * D_Cash

=> 2.75 = (22 / 28) * D_Loan + (6 / 28) * 0

=> D_Loan = (2.75 * 28) / 22

= 3.5 years

So,  the duration of the bank's existing loans = 3.5 years

c) D_{Market Loan} = 7.6 years = D_{New Loan}

To eliminate the bank's interest rate exposure, we need to make duration of assets equal to the duaration of loan

i.e D_A should be equal to DL = 4 years

Now let new loan taken is $x miilion

D_A = (Loan / Assets) * D_Loan + (Cash / Assets) * D_Cash + (New Loan / Assets) * D_{New Loan}

=> 4 = [(22 / 28) * 3.5] + [(6 / 28) * 0] + [(x / 28) * 7.6]

=> 4 = 2.75 + 0 + (7.6x/28)

=> x = (4 - 2.75) * (28/7.6)

=> x = 4.60

So cash used to eliminate the bank's interest rate exposure = $4.6 million