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 (marked to market). If interest rates rose by 200bp what would be the impact on this bank’s leverage ratio?

a. falls to 20% exactly

b. rises to 27% exactly

c. falls to just over 18%

d. rises to just over 26%

Further to Question 6, if the bank had wanted to neutralise (immunise) the balance sheet impact of any interest rate shifts through the futures market, what would be the best strategy?

a. Buy 1200 Treasury Bond futures contracts

b. Sell 1700 3mth Eurodollar futures contracts

c. Buy 850 3mth Eurodollar futures contracts

d. Sell 1250 6mth Euroyen futures contracts

Answer 1

Duration of Liability excluding networth(in years)	1
Duration of Asset(in years)	5
Assets Value ($million)	100
Capital Value($million)	25
Liability Value (Normal equation is Assets = Liabilities + Capital, thus liabilities = Assets - Capital) (100-25) ($million)	75
Leverage ratio = Capital / Assets (25/100)	0.25

Increase in interest rate = 200 bp(basis points) or 2%

Thus, value of asset with average duration of 5 years will fall by = 2% * 5 = 10% (since bank's assets are predominantly loans given, increase in interest will increase the exposure of assets resulting in reduction in assets value)

Thus, revised asset value = $100 Milliion * (100%-10%) = $90 Million

Thus, value of liability with average duration of 1 years will fall by 2% (since bank's liabilities are predominantly loans borrowed, increase in interest reduces the banks exposure of liabilities and thus results in reduction in liabilities value)

Thus, revised liability value = $75 Milliion * (100%-2%) = $73.5 Million

Revised capital value (Assets - Liabilities) = $90 Million - $73.5 Million = $16.5 Million

Revised Leverage ratio = Revised Capital value / revised assets value = $16.5 Million / $90 Million = 18.33%

Thus, an increase in interest by 200 basis points makes the leverage ratio to fall to just over 18%

b. if the bank had wanted to neutralise (immunise) the balance sheet impact of any interest rate shifts through the futures market, what would be the best strategy

The best strategy would be to buy 1200 Treasury Bond futures contracts. These treasury (government) bonds comes at a certain fixed interest rate and it will help the bank to neutralise the impact of any interest rate in the balance sheet to the extent of fixed interest rate of the treasury bond.

The other alternatives given are linked to currency futures. Movement in one currency will not impact or mirror the movement in interest rates at large (since movement in interest rate are impacted by multiple economic parameters like liquidity, slowdown in economy, etc). Hence these strategies will not help the bank to immunise the impact of interest rate in balance sheet