You are analyzing a bank’s income exposure to interest rate risk using the simple version of the repricing model, where assets and liabilities are simply classified as rate sensitive or not. You collected the information below on the bank’s balance sheet.

Assets Liabilities and Equity

Cash (no interest payments): 315 Equity: 378

Fed Funds (overnight): 158                                                       Demand Deposits: 977

6-Month Treasury Bills: 125 Savings Accounts: 630

3-Year Treasury Notes: 190 6-Month CDs: 158

3-Month Consumer Loans: 568                                                9-Month CDs: 315

4-Year Business Loans: 282 2-Year CDs   315

30-Year Fixed-Rate Mortgages: 1512                                       Fed Funds (overnight): 62

Total Assets: 3150 3-Month Commercial Paper: 315

Total Liabilities and Equity: 3150

You decided to assume that savings deposits are rate sensitive and determined that the bank’s tax rate is equal to 25%.

Following this approach, determine how a 0.3 percentage point increase in the market interest rate affects the bank’s return on assets (ROA) over a one-year time horizon.

Question

You are analyzing a bank’s income exposure to interest rate risk using the simple version of the repricing model, where assets and liabilities are simply classified as rate sensitive or not. You collected the information below on the bank’s balance sheet.

Assets                                                                                              Liabilities and Equity

Cash (no interest payments): 315                                            Equity: 378

Fed Funds (overnight): 158                                                       Demand Deposits: 977

6-Month Treasury Bills: 125                                                      Savings Accounts: 630

3-Year Treasury Notes: 190                                                       6-Month CDs: 158

3-Month Consumer Loans: 568                                                9-Month CDs: 315

4-Year Business Loans: 282                                                       2-Year CDs   315

30-Year Fixed-Rate Mortgages: 1512                                       Fed Funds (overnight): 62

Total Assets: 3150                                                                          3-Month Commercial Paper: 315

Total Liabilities and Equity: 3150

You decided to assume that savings deposits are rate sensitive and determined that the bank’s tax rate is equal to 25%.

Following this approach, determine how a 0.3 percentage point increase in the market interest rate affects the bank’s return on assets (ROA) over a one-year time horizon.

BlackTom AI · Accepted Answer

Liability sensitivity (negative repricing gap) means a rise in market rates will reduce the bank’s net interest income and hence ROA. Compute the one-year repricing gap, the dollar change in net interest income from a 0.3 percentage-point (=0.003) rate increase, apply taxes, and convert to a percent of assets.

1) Classify and sum rate-sensitive items (repricing within one year)
- Rate-sensitive assets: Fed Funds (overnight) 158 + 6-month T-bills 125 + 3-month consumer loans 568 = 158 + 125 + 568 = 851
  (Cash pays no interest → excluded; 3-year, 4-year, 30-year assets repricing >1 year → excluded)
- Rate-sensitive liabilities: Savings 630 + 6-month CDs 158 + 9-month CDs 315 + Fed Funds (liab) 62 + 3-month commercial paper 315
  = 630 + 158 + 315 + 62 + 315 = 1,480
  (Demand deposits, 2-year CDs, and equity are treated as non-rate-sensitive)

2) Repricing gap (RSA − RSL)
- Gap = 851 − 1,480 = −629 (negative means liability-sensitive)

3) Change in net interest income (NII) before tax from a Δr = +0.003
- ΔNII_before_tax = Gap × Δr = (−629) × 0.003 = −1.887 (dollars of income loss)

4) After-tax effect on net income (tax rate = 25%)
- ΔNII_after_tax = ΔNII_before_tax × (1 − tax) = −1.887 × 0.75 = −1.41525

5) Convert to change in ROA (divide by total assets = 3,150)
- ΔROA = ΔNII_after_tax / Total assets = −1.41525 / 3,150 = −0.0004491 = −0.04491%
- Rounded to two decimal places: −0.04%

Why this is correct and others are wrong:
- Positive options (0.02%, 0.04%) have the wrong sign; a liability-sensitive bank loses NII when rates rise.
- −0.02% likely ignores tax or misdivides by assets (half the correct magnitude).
- −0.11% is much too large; it corresponds to using the full pre-tax loss or failing to divide by assets properly.
Conclusion: the one-year ROA falls by approximately −0.04%, which matches the provided correct answer.

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