Question

b) Suppose that you are the manager of a bank that has K15 million of fixed-rate assets,
K30 million of rate sensitive assets, K25 million of fixed-rate liabilities, and K20
million of rate-sensitive liabilities. Conduct a gap analysis for the bank, and show what
will happen to bank profits if interest rates rise by 5 percentage points. Mention three
actions you could take to reduce the bank’s interest-rate risk?
c) A bank manager wants to know what happens when interest rates rise from 10% to 11%.
The total asset value is K100 million, and the total liability value is K95 million. The
bank manager gets a figure for the average duration of the assets of 2.70 years and an
average duration of liabilities of 1.03 years. Calculate the change in the market value of
the assets and liabilities.

Answer 1

Hi,

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Question:

Answer:

b). Answer:

Fixed-rate assets = K15 million

Rate sensitive assets = K30 million

Fixed-rate liabilities= K25 million

Rate-sensitive liabilities = K20 million

If interest rates rise by 5 percentage points-

Then Rate sensitive assets K30 million will increased by K31.5 million

(K30 million +  K30 million*5% =  K30 million + K1.5 million = K31.5 million)

Rrate-sensitive liabilities K20 million will increased by  K21 million

(K20 million + K20 million *5% =  K20 million +  K1 million =  K21 million)

Bank profit after interest rate change = Total Assets - Total Liabilities

=  (K15 million +  K31.5 million) - ( K25 million + K21 million)

K46.5 million - K46 millions = K0.5 million (Profit).

Bank will earn the profit of K0.5 million (Profit).

Three actions you could take to reduce the bank’s interest-rate risk:

1). The interest rate risk can be reduced by shortening the maturity of the assets or by lengthening the maturity of the liabilities.

2) You could engage in an interest-rate swap, in which you swap the interest earned on your assets with the interest on another bank's assets that have a duration of 2.5 years.

3). Interest rate hedging .

c). Answer:

Interest rates rise from 10% to 11%.

The total asset value is K100 million.

The total liability value is K95 million.

The average duration of the assets of 2.70 years.

The average duration of liabilities of 1.03 years.

The change in the market value of the assets and liabilities =

FV = PV(1+r)^n

PV = present value

r = interest rate

n = time

At 115 interest rate:

FV of assets = K100 million(1+11%)^2.70

= K100 million(1.11)^2.70

= K134 million

FV of liabilities = K95million(1+11%)^1.03

= K95million(1.11)^1.03

= K106. 34 million.

At 10 % interest rate:

FV of assets = K100 million(1+10%)^2.70

= K100 million(1.1)^2.70 = K130.84

FV of liabilities = K95 million(1+10%)^1.03

= K105.26

So, we can see that assets will be increased by K3.16 (K134 - K130.84) and liabilities will reduced by K1.08 million ( K106.34 - K105.26).

Thank You