a) Suppose that you are the manager of a bank whose $100 billion of assets have
ID: 2451970 • Letter: A
Question
a) Suppose that you are the manager of a bank whose $100 billion of assets have an average duration of four years and whose $90 billion of liabilities have an average duration of six years. Conduct a duration analysis for the bank, and show what will happen to the net worth of the bank if interest rates rise by 2 percentage points. What actions could you take to reduce the bank’s interest rate risk?
b) Suppose that you are the manger of a bank that has $15 million of fixed-rate assets, $30 million of rate-sensitive assets, $25 million of fixed-rate liabilities, and $20 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. What actions could you take to reduce the bank’s interest-rate risk?
Explanation / Answer
Answer:a) (a) what will happen to the market value of assets
The market value of assets will fall by $8 billion.
% change in market value of the assets – % change in interest rate x duration in years
% change in market value of the assets – 2% x 4 years = – 8%
The change in the market value of assets = $100 billion x (– 8%) = – $8 billion
(b) what will happen to the market value of liabilities
The market value of liabilities will fall by $10.8 billion.
% change in market value of the liabilities – % change in interest rate x duration in years
% change in market value of the liabilities – 2% x 6 years = – 12%
The change in the market value of liabilities = $90 billion x (– 12%) = –$10.8 billion
(c) what will happen to the net worth of the bank.
Net worth of the bank will rise by $2.8 billion
Net worth = – $8 billion – (– $10.8 billion) = – $8 billion + $10.8 billion = + $2.8 billion
(d) Describe one action you could take to reduce the bank’s interest-rate risk.
Any one of the following:
a. shortening the maturity of liabilities to a duration of 4 years
b. lengthening the maturity of assets to a duration of 6 years
c. engaging in interest rate swap ( swap interest rate earned on this bank’s assets with interest on another bank’s assets that have a duration of 6 years).
Answer:b) Short cut method: GAP = $30 m - $20 m = $10 m
change in profits = 5%*(30-20) = $0.5 m
Explanation:
Liabilities
RSA $30 RSL $20
FRA $15 FRL $25
GAP = RSA – RSL = + $5 million. Profits will increase by $500,000 if interest rates rise by 5 percentage points. Interest income increases by $1,500,000 and interest expense increases by $1,000,000.
$1,500,000 - $1,000,000 = +$500,000
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