A negative interest rate is a nominal interest rate below zero. When a contract applies that rate to a positive principal, interest accrues against the funds provider rather than adding to their balance. For a quant, the sign must survive the whole calculation: inserting an uncontracted zero floor changes the cash flows being valued.
The same sign can describe different things
| What is negative? | What the quote describes |
|---|---|
| A central-bank policy rate | A policy instrument. For an administered deposit-facility rate, eligible banks may be charged on balances subject to that rate and its exemptions. |
| A customer deposit rate | The rate specified for a particular account, balance tier and period. It is a separate contract from the central bank’s arrangement with banks. |
| A bond yield | A rate implied by the purchase price and the bond’s promised cash flows under a yield convention. A positive coupon can coexist with a negative yield if the purchase price is sufficiently high. |
| A real interest rate | An inflation-adjusted return. It can be negative even when the nominal rate is positive, because purchasing power is a different measurement. |
A negative bond yield does not require a negative coupon, and it is not a prediction of the return from selling the bond before maturity. Expected and realised real rates also differ: the Czech National Bank’s explanation distinguishes using expected inflation from using inflation that actually occurs.
A contract that pays back less
Consider a fictional simple-interest contract, expressed in currency units. Its principal is 1,000, its contractual annual nominal rate is −0.50%, and its contractual year fraction is 1. There are no fees, no zero floor and no interim cash flows. This is a toy contract, not an actual household deposit quote or a current policy observation.
For principal , decimal simple rate and year fraction , the interest is and the maturity amount is . Here:
The funds provider receives 995 at maturity, a nominal loss of 5 under the contract. The corresponding return is
A fictional contractual calculation, not a retail quote or current policy rate. Negative interest reduces the amount payable at maturity under these stated terms.
For an actual instrument, first read the rate convention, accrual period, floors, fees and payment terms. A negative quoted rate alone does not specify every cash flow. Conversely, an account can have a nonnegative quoted rate and still lose nominal value after fees; the ECB’s transmission analysis distinguishes those cases.
Why everyone does not switch to banknotes
Physical cash retains its face value, but large holdings require secure storage and are less convenient for payments. These costs and services help explain why some depositors can accept a modest negative rate. The ECB’s explainer discusses safe banknote storage; its transmission analysis treats cash and deposits as imperfect substitutes.
Those frictions do not imply unlimited scope to cut rates. The effective lower bound depends on institutions and transmission, whereas a strict zero lower bound imposes zero as the floor.
A negative policy rate does not mean every household deposit earns that same negative rate. Banks set customer terms separately. The RBA’s account of negative-rate episodes describes incomplete pass-through to households and smaller businesses. A policy scenario therefore needs separate assumptions for administered rates, market yields and customer contracts.
Sources
- RBA: Unconventional Monetary Policy, Negative interest rates. Historical episodes explain the mechanism; no present policy setting is asserted here.
- ECB: The ECB’s negative interest rate, questions on savings and banknote storage; updated July 2022.
- ECB: Negative rates and the transmission of monetary policy, cash substitution, deposit-rate stickiness and fees; Economic Bulletin, Issue 3/2020.
- Czech National Bank: What are nominal and real interest rates?, nominal versus purchasing-power returns and expected versus realised inflation.