Interest income less interest expense, over the assets that earn interest. The formula is one line; what moves it is which side of the balance sheet reprices first.
Net interest margin is net interest income, interest earned less interest paid, divided by average earning assets. An illustrative bank earning 246,192 and paying 34,657 on 7,700,000 of earning assets has a NIM of 2.75 per cent. After a 425 basis point rise in market rates the same balance sheet earns a NIM of 2.21 per cent: income rises by 86,275 but interest expense rises by 128,010, because more of its funding reprices than its assets.
Worked in full in Bank Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The definition is not where analysts go wrong. The denominator is, and so is the reading: a falling NIM in a rising-rate year says something specific about the balance sheet, and the arithmetic shows exactly what.
Sagebrook National Bank is the fictional bank of the case, in thousands of dollars. Balances are held constant over the year, so year-end and average balances coincide. The market rate starts at 1.55 per cent and rises 425 basis points, to 5.80. Each line reprices by its beta times the shock: 100 per cent for cash, floating loans and FHLB advances, 35 per cent for savings, 85 per cent for time deposits, nothing for fixed-rate assets and current accounts.
| Line | Balance | Rate, year 0 | Rate, after shock |
|---|---|---|---|
| Cash and equivalents | 420,000 | 1.55% | 5.80% |
| Securities, available for sale | 1,180,000 | 1.72% | 1.72% |
| Securities, held to maturity | 1,640,000 | 1.94% | 1.94% |
| Loans, fixed rate | 2,850,000 | 4.35% | 4.35% |
| Loans, floating (index + 2.40%) | 1,610,000 | 3.95% | 8.20% |
| Earning assets | 7,700,000 | ||
| Deposits, non-interest-bearing | 1,760,000 | 0.00% | 0.00% |
| Deposits, savings | 3,240,000 | 0.18% | 1.67% |
| Deposits, time | 1,480,000 | 0.85% | 4.46% |
| FHLB advances | 620,000 | 1.35% | 5.60% |
| Subordinated debt | 150,000 | 5.25% | 5.25% |
The balance sheet totals 8,000,000; the other 300,000 of assets, including goodwill, earn nothing and stay out of the denominator.
NIM = (interest income − interest expense) ÷ average earning assets
Net interest spread = yield on earning assets − cost of interest-bearing liabilities
In Excel, with balances in B and rates in C: =(SUMPRODUCT(Assets_B,Assets_C)-SUMPRODUCT(Liabs_B,Liabs_C))/SUM(Assets_B).
Step 1: interest income. Multiply each earning asset by its yield: 6,510 on cash, 20,296 and 31,816 on the two securities books, 123,975 on fixed-rate loans and 63,595 on floating. Total 246,192, a yield on earning assets of 3.20 per cent.
Step 2: interest expense. 5,832 on savings, 12,580 on time deposits, 8,370 on FHLB advances and 7,875 on the subordinated debt. Total 34,657, a cost of 0.63 per cent on the 5,490,000 of interest-bearing liabilities.
Step 3: divide. Net interest income is 211,535. Over 7,700,000 of earning assets the NIM is 2.7472 per cent, 2.75 rounded.
Step 4: the shock year. Reprice every line and repeat. Income rises to 332,467, expense to 162,667, net interest income falls to 169,800, and the NIM to 2.21 per cent: 54 basis points lower, with net interest income down 19.7 per cent.
| Measure | Year 0 | After +425 bp |
|---|---|---|
| Yield on earning assets | 3.20% | 4.32% |
| Cost of interest-bearing liabilities | 0.63% | 2.96% |
| Net interest spread | 2.57% | 1.35% |
| Contribution of free funding | 0.18% | 0.85% |
| Net interest margin | 2.75% | 2.21% |
Only 2,030,000 of assets reprice fully: cash and floating loans. On the other side, the betas make 1,134,000 of savings, 1,258,000 of time deposits and 620,000 of advances reprice, 3,012,000 in all. The bank is liability-sensitive by 982,000, so each 100 basis points of rise costs 9,820 of net interest income, about 12.8 basis points of margin. The fixed-rate loans and the securities, more than two thirds of earning assets, earn the same 4.35, 1.72 and 1.94 per cent whatever the market does.
The gap between NIM and spread is the value of funding that costs nothing: 1,760,000 of current accounts plus equity. At low rates it adds 0.18 points; at 5.80 per cent it adds 0.85. That is the deposit franchise appearing in the income statement, and it is why NIM falls less than the spread.
| Rise, bp | Interest income | Interest expense | NII | NIM |
|---|---|---|---|---|
| 0 | 246,192 | 34,657 | 211,535 | 2.75% |
| 100 | 266,492 | 64,777 | 201,715 | 2.62% |
| 200 | 286,792 | 94,897 | 191,895 | 2.49% |
| 300 | 307,092 | 125,017 | 182,075 | 2.36% |
| 425 | 332,467 | 162,667 | 169,800 | 2.21% |
With constant betas the response is a straight line. In practice betas rise as a cycle goes on, so the later steps cost more than the first. Which deposits the beta is measured on changes the answer a great deal: see how to calculate a deposit beta, and on which deposits.
Net interest income over earning assets: 2.75 per cent for this bank, 2.21 after a 425 basis point rise. The calculation takes a minute; the useful part is splitting it into asset yield, funding cost and free funding, because that shows which side moved. Bank Management carries this bank through four readings of its capital, and the free workbook for this case computes the margin before and after the shock, line by line.
Spread is the yield on earning assets less the cost of interest-bearing liabilities. NIM divides net interest income by earning assets, so it also captures funding that costs nothing, such as current accounts and equity. On an illustrative bank the spread is 2.57 per cent and NIM 2.75; after a 425 basis point rise they are 1.35 and 2.21, the free funding worth 0.85 points.
Earning assets, averaged over the period: loans, securities and interest-bearing cash, excluding premises, goodwill and other non-earning assets. On an illustrative bank with 7,700,000 of earning assets inside 8,000,000 of total assets, net interest income of 211,535 is a NIM of 2.75 per cent, but only 2.64 per cent on total assets.
When more liabilities than assets reprice within the year. An illustrative bank has 2,030,000 of assets that reprice fully against 3,012,000 of liabilities once deposit betas are applied, so each 100 basis points costs 9,820 of net interest income and about 13 basis points of margin; a 425 basis point rise takes NIM from 2.75 to 2.21 per cent.
Net interest income before and after the shock is worked in the workbook for chapters 3 to 8 of Bank Management. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
Get the book on Amazon →Free companion files
Also on Amazon UK · Amazon Germany · Amazon France · Amazon Canada
Reading guide: regulation, compliance and banking → · All 681 articles →
If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.