Question

A commercial bank calculates that the duration of its liabilities (excluding net worth) averages one year while the duration of its assets averages 5 years. Assume that this bank has $100mn of assets and $25mn of capital. Also assume that assets and liabilities (excluding net worth) are interest rate sensitive and enter the balance sheet at market value.

a) If interest rates rose by 2% what would happen to the value of the bank's assets? What would happen to the value of their debts?

b) What happens to the leverage ratio?

d) If the bank wanted to neutralize (immunize) the impact of interest rate shifts through the futures market, should it buy or sell interest rate futures?

e) On the assumption that the bank deals in 3 mouth Eurodollar futures with one contract having a principle value of $1mn, how many contracts would be needed for full hedging?

Answer 1

Part 1) let us first understand what does duration say, if duration of any amount is D then it means that if interest goes up by 1% then that amount will go down by D * 1% = D % that is why it is known as interest rate sensitivity.

Part a

Bank's asset duration is 5 and liability duration is 1

Its assets are $100 mn and capital is $ 25 million which means that its liabilities are $ 75 mn ( using the relationship of Assets = capital + liabilities)

And interest rates are rising by 2% which means that bank's assets will go down by 5 * 2%= 10% and liabilities will go down by 1 * 2% = 2%

So the new value of assets would be = $100 * (1- .10) = $90 mn

And assuming its liabilities are comprised of only debt, the new value of debt would be = $75 ( 1-.02) = $73.5 mn

Part b

Leverage ratio = tier1 capital/ total exposure

Where

Tier1 capital = comman stock + disclosed reserves (which are unaffected by interest rates changes)

Total exposure = total value of risky assets and since the rise of interest rates lead to falling in the value of all assets, leverage ratio will go down. However it should not go below the minimum benchmark of 3% as provided by basel norms.

Part c

Bank need not to worry about interest rate falling because in case interest rates fall, assets will rise much faster( 5times faster) then the liabilities as their duration ratio is 5:1, however if the interest rates rises assets will fall 5 times faster then liabilities so we need to protect this only and to hedge the risk of interest rates rise we need to buy interest rates futures

Part c

We will hedge the downside risk of assets only as the fall in liabilities is not a matter of concern. So if the contract value os $1 mn then to hedge the portfolio of $100 mn we need to buy 100 contracts.

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