Question

The duration of the assets of your bank is 5.3 years and the duration of your liabilities is 2.1 years. Your bank has $320,000 in assets, $300,000 in liabilities and $20,000 in equity. Suppose the current fed funds rate is 2% and the Fed decides to increase the interest rate by 50 basis points. What is the new equity value of your balance sheet?

Answer 1

Assets: Asset Value = $ 320000 and Duration = 5.3 years

Change in Fed Funds Rate = 0.5 %

% Change in Asset Value = - Duration x % Change in Fed Funds Rate = - 5.3 x 0.005 = - 0.0265 or - 2.65 %

New Value of Assets = (1-0.0265) x 320000 = $ 311520

Liabilities: Liability Value = $ 300000, Duration = 2.1 years

Change in Feds Fund Rate = 0.5 %

% Change in Liability Value = - Duration x % Change in Feds Fund Rate = - 2.1 x 0.005 = - 0.0105 or - 1.05 %

New Liability Value = (1-0.0105) x 300000 = $ 296850

Initial Equity Value = $ 20000

New Equity Value = 311520 - 296850 = $ 14670