Nancy is analyzing a bank’s income exposure to interest rate risk using the repricing model. She 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

3-Month Treasury Bills: 125 Savings Accounts: 630

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

6-Month Consumer Loans: 568 6-Month CDs: 315

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

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

Total Assets: 3150 6-Month Commercial Paper: 315

Total Liabilities and Equity: 3150

When implementing her analysis, she also decided to make the assumptions below.

A 1 percentage point increase in the market interest rate leads to a 0.4 percentage point increase in the rate paid on savings deposits.
A 1 percentage point increase in the market rate leads to a 0.7 percentage point increase in the rate paid on new time deposits.
A 1 percentage point increase in the market rate leads to a 1 percentage point increase in the rate paid on all other rate-sensitive liabilities (RSLs) and rate-sensitive assets (RSAs).

Following this approach, determine how a 0.5 percentage point increase in the market interest rate affects the net interest income (NII) over a one-year time horizon.

Question

Nancy is analyzing a bank’s income exposure to interest rate risk using the repricing model. She 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

3-Month Treasury Bills: 125                                                     Savings Accounts: 630

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

6-Month Consumer Loans: 568                                               6-Month CDs: 315

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

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

Total Assets: 3150                                                                        6-Month Commercial Paper: 315

Total Liabilities and Equity: 3150

When implementing her analysis, she also decided to make the assumptions below.

A 1 percentage point increase in the market interest rate leads to a 0.4 percentage point increase in the rate paid on savings deposits.
A 1 percentage point increase in the market rate leads to a 0.7 percentage point increase in the rate paid on new time deposits.
A 1 percentage point increase in the market rate leads to a 1 percentage point increase in the rate paid on all other rate-sensitive liabilities (RSLs) and rate-sensitive assets (RSAs).

Following this approach, determine how a 0.5 percentage point increase in the market interest rate affects the net interest income (NII) over a one-year time horizon.

BlackTom AI · Accepted Answer

ΔNII is driven by the repricing gap over the one-year horizon and the assumed sensitivities (betas) of instruments to a change in market rates. Use ΔNII = Δr × [sum(RSA × beta_RSA) − sum(RSL × beta_RSL)]. For a 0.5 percentage point (0.005) market increase, betaRSA = 1 for all RSAs; savings have beta = 0.4; new time deposits (CDs and short-term negotiated paper) have beta = 0.7; other RSLs (fed funds borrowings) have beta = 1.

1) Identify RSAs repricing within 1 year and their amounts:
- Fed funds (asset): 158 (beta = 1)
- 3-month T-bills: 125 (beta = 1)
- 6-month consumer loans: 568 (beta = 1)
Sum RSA = 158 + 125 + 568 = 851

2) Identify RSLs repricing within 1 year and apply betas:
- Savings accounts: 630 (beta = 0.4)
- Time deposits repricing ≤1 year: 3-month CDs 158, 6-month CDs 315, and 6-month commercial paper 315 — treat these short-term negotiated liabilities as “new time” type for this model (beta = 0.7). Sum time deposits = 158 + 315 + 315 = 788
- Other RSLs: Fed funds (liability) 62 (beta = 1)
Compute weighted RSL exposure:
- Savings effect per 1% change: 630 × 0.4 = 252 (for 1%); for Δr = 0.5% use 252 × 0.005 = 1.26
- Time deposits effect (1%): 788 × 0.7 = 551.6; for 0.5%: 551.6 × 0.005 = 2.758
- Other RSLs (1%): 62 × 1 = 62; for 0.5%: 62 × 0.005 = 0.31
Total RSL expense increase = 1.26 + 2.758 + 0.31 = 4.328

3) RSA income increase for 0.5%: RSA sum 851 × 1 × 0.005 = 4.255

4) Net change in NII = RSA income increase − RSL expense increase = 4.255 − 4.328 = −0.073

Why the correct answer is 0.0: The computed change is −0.073 (in the same units as the balance-sheet amounts); rounding to one decimal place (as per the multiple-choice answer format) gives 0.0. Other choices are incorrect: -0.5 would result if the 6-month commercial paper were treated as an “other RSL” with beta = 1 (giving −0.545 ≈ −0.5); −1.6 and −3.1 are much larger magnitudes and inconsistent with the small repricing gap; +1.0 is wrong sign and magnitude. Therefore the correct rounded answer is 0.0, matching the provided answer.

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