Question

4c. A bank has assets with a total value of $14.260 billion; $14.170 billion of which are rate sensitive. The bank’s liabilities total $13.905 billion; all are rate sensitive. If the average duration of its asset portfolio is 5.175 years and its liabilities have a 3.105-year average duration.

What is the expected dollar change in the value of the bank’s equity if the average interest rate increases from 3.25% to 3.55%?

Answer 1

Total Assets = $ 14.26 billion and Rate Sensitive Assets = $ 14.17 billion

Non-Rate Sensitive Asset = A(NR) = 14.26 - 14.17 = $ 0.09 billion

Total Liabilities = $ 13.905 billion

Average Duration of Assets = 5.175 years and Average Duration of Liabilities = 3.105 years

Change in Interest Rate = (3.55 - 3.25) = 0.3 %

It must be noted that a rise in interest rates depresses the value of assets and liabilities and vice-versa.

% Change in Value of Rate-Sensitive Assets = - 5.175 x 0.003 = - 0.0155 or -1.55 %

New Value of Assets = 0.09 + 14.17 x (1-0.0155) = $ 14.04 billion

% Change in Value of Liabilities = - 3.105 x 0.003 = - 0.00932 or - 0.932 %

New Value of Liabilities = (1-0.00932) x 13.905 = $ 13.7755 billion

New Value of Equity = 14.04 - 13.7755 = $ 0.26454 billion

Original Value of Equity = 14.26 - 13.905 = $ 0.355 billion

Change in $ Value of Equity = 0.355 - 0.26454 = $ 0.09046 billion