Question

(6 points) 3. The bank you own has the following balance sheet Liabilities with current interest rate Assets with current interest rate $5million $20 million Variable: 1% Checking Fixed: 0% Reserves deposits Savings Deposits $25 million Fixed: 2% $10 million Variable: 2% Government Securities Variable: 3 % $10 million Money Market Deposit Accounts $35 million Fixed: 6% Mortgage Loans Bank Capital To be To be $10 million Variable: 7% Short-Term determined determined Loans Business $20 million Fixed: 9% Loans $80 million Total Liabilities $80 million Total Assets B. Suppose short-term interest rates increased by 2% Given your bank's balance, is your bank rate sensitivity gap positive or negative? Explain why. a. b. Find the dollar value of your bank's rate sensitivity gap. Calculate the change in your bank's profit. C. d. List three things your bank could do to reduce the risk associated with the increase in the short- term interest rates

Answer 1

Solution

a.My bank's sensitive gap is negative since the liabilities are increasing more in comparison to the assets when the increased interest rates are applied.

b.Given that the short-term interest rates increase by 2%

Reserves	Fixed - 0	5	CD	V-1	20
Govt.securities	V- 2	10	SD	F-2	25
Mortgage loans	Fixed - 6	35	MMDA	V-3	10
Short-term loans	V -7	10	Bank Capital	To be determined	To be determined
Business loans	F - 9	20	-	-	-

Assets

Interest received on govt.securities and short-term loans will increase by 2 % each

Increase in interest received = (10 * 0.02) + ( 10* 0.02) i.e., 0.20 + 0.20 i.e., $0.40 million

If govt securities are assumed to consist of only only long-term securities like T-bills,T-bonds then they are to be excluded from this calculation.The resultant increase in the interest received is $0.20 million   

Note: Govt.securities can consist of both long-term and short-term securities.Here I assumed that it is only short-term securities

Liabilities

Interest payed on checking deposits and money market deposit accounts will increase by 2 % each

= (20 * 1.02 ) + ( 10 * 1.02) i.e., $0.40 + $0.20 i.e., $0.60 million

The liabilities are increasing by $0.60 million but the assets are increasing at most by $0.40 million .So,there is a negative sensitive gap of $0.20 million

c. Change in bank's profit

Before interest rate change

Total Interest received = (10 * 0.02) +(35 * 0.06 ) +(10 * 0.07) +(20 *0.09) i.e., 0.20 +2.10 +0.70 +1.80

= $4.80 million

Total interest payed = (20 * 0.01) +(25 * 0.02 ) +(10 * 0.03) )

= $1.0 million

Profit = $3.80 million

After interest rate change

Total Interest received = (10 * 0.04) +(35 * 0.06 ) +(10 * 0.09) +(20 *0.09)

= 0.4+2.10+0.9+1.80 i.e., $5.20 million

Total Interest payed = (20 * 0.03) +(25 * 0.02 ) +(10 * 0.05)

= $1.60 million

Profit = $3.60 million

Note: Even here I have considered that the govt.securities consist of only short-term financial instruments.In contrary to this if it consists of only long-term instruments then the profit after interest change will be at $3.40 million

d. 3 things that my bank can do to reduce the risk associated with the increase in the short-term interest rates:c.

1.Instead of charging the fixed rate of interest on the mortgage and business loans,my bank can make the interest rate as variable (if not fully variable,it can add some variable component ) and linked to the repo rates prevailing in the market.

2.My bank can convert the interest offered on the checking deposits and money market deposit accounts from variable to fixed.

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