Banks & Risk Management A commercial bank calculates that the durations of its l

Question

Banks & Risk Management A commercial bank calculates that the durations of its liabilities (excluding net worth) averages six months while the duration of its assets averages 2 years. Assume that this bank has $100m of assets and $10m of capital. Also assume that assets and liabilities (excluding net worth) are interest rate sensitive and enter the balance sheet at market value (marked to market) a) If interest rates rose by 2% (200bp) what would happen to the value of this bank's assets and liabilities (excluding net worth)? b) Further to your answer above, what happens to this bank's leverage ratio? c) If the bank wanted to neutralize (immunise) the impact of interest rate shifts through the futures market, should it buy or sell interest rate futures? d) On the assumption that the bank deals in 3mth Eurodollar futures with one contract having a principal value of $1m, how many contracts would be needed for full hedging?

Explanation / Answer

a)

Value of bank Asset:

Duration=2 years

Change in interest rate=2%

% change=-2*0.02/(1+0.10)

=-0.03636 or -3.63%

With a total asset value of $100 million, the market value of assets falls by $3.63 million($100 million*0.0363)=3.63 .

With a total liabilities value of $90 million, the market value of liabilities falls by $9.819 million ($90 million*10.91%)=9.819 .

Duration=6 years

Change in interest rate=2%

% change=-6*0.02/(1+0.10)

=-0.1091 or -10.91%

b)

Leverage ratio=Bank capital/Bank assets

=$10+9.819/96.37

=0.2056

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