Why a Policy Rate Can Fall Below Zero
A central bank can set a negative interest rate on certain balances that commercial banks hold with it. For a bank subject to that rate, holding those reserves has a direct cost rather than earning interest. The policy can lower short-term market rates and change banks’ incentives, but its effects depend on the rules for reserve remuneration, banks’ funding costs, and the availability of alternatives such as physical cash.
A negative policy rate does not mean that every bank deposit or loan has a negative interest rate. A central bank may apply the negative rate only to a specified class or portion of reserve balances. Banks may also be reluctant to charge negative rates on many customer deposits, while lending rates reflect credit risk, operating costs, and other factors in addition to the policy rate. These distinctions are important when assessing how far monetary easing reaches in practice.
The analysis here is aligned with the SOA VEE Economics (Validation by Educational Experience) syllabus. The focus is on the mechanisms and constraints of negative policy rates, not on any claim that one policy arrangement applies in every economy.
The relevant rate may be a central-bank deposit-facility rate or another rate used to guide overnight market rates. The exact operating arrangement matters. A rate announced by the central bank is not automatically the rate paid on every reserve balance or charged on every customer account. Some systems apply different rates to different portions of a bank’s reserves; this is called tiering.
Reserve Charges and Tiering
Suppose an arrangement exempts a portion of each bank’s reserves from negative remuneration and applies a negative rate only to balances above that exemption. The bank’s annual charge depends on the balance that is actually subject to the rate, not simply its total reserve balance. Tiering can therefore reduce the burden on banks relative to charging the negative rate on every reserve dollar.
Worked Example: Calculating a Tiered Reserve Charge
A bank holds $200 million in eligible reserves. Under a hypothetical central-bank arrangement, the first $60 million earns 0%, and the remaining balance is remunerated at an annual rate of -0.40%. Assume the balance is constant for one year, there are no changes in the rules during the year, and the calculation uses simple annual interest. Calculate the bank’s charge and compare it with the charge if all reserves were subject to the negative rate.
Method. Separate the exempt balance from the balance subject to the negative rate. The amount charged is \(200-60=140\) million dollars.
The negative sign on the rate means the bank pays the charge. The first $60 million has no charge under the stated rules, so the bank pays $560,000 for the year.
If all $200 million were charged at 0.40%, the calculation would instead be \(200{,}000{,}000 \times 0.004=\$800{,}000\). Tiering reduces the charge by \(\$800{,}000-\$560{,}000=\$240{,}000\), which is also \(60{,}000{,}000 \times 0.004\), the charge avoided on the exempt tier.
Check. The charge on the $140 million subject to the rate is $560,000; adding a zero charge on the exempt $60 million leaves that total unchanged. The common mistake is to apply -0.40% to all $200 million even though the rules exempt the first $60 million.
A charge on reserves creates an incentive to consider other uses for funds, including loans or securities. It does not make lending automatic. A bank must still consider the expected return after credit losses, operating expenses, funding costs, and the costs of meeting capital and liquidity requirements. It may also lack suitable borrowers or acceptable lending opportunities. The negative reserve rate changes the comparison; it does not remove the other conditions.
Worked Example: Comparing a Loan With Charged Reserves
A bank has $20 million of reserves that would earn -0.40% for one year. It is considering a hypothetical one-year loan for the same amount, with an annual interest yield of 1.10%. For this simplified comparison, expected credit losses are 0.45% of the loan, servicing costs are 0.20%, and incremental funding and capital costs are 0.15%. Assume the stated rates are annual, the bank can make the loan for the full year, and there are no other costs or returns. Which option has the higher estimated contribution?
Method. First calculate the loan’s estimated return after the specified costs: \(1.10\%-0.45\%-0.20\%-0.15\%=0.30\%\). On $20 million, that is \(20{,}000{,}000 \times 0.003=\$60{,}000\).
Holding the reserves instead produces a charge of \(20{,}000{,}000 \times 0.004=\$80{,}000\), or a contribution of -$80,000. The estimated difference in favor of the loan is therefore \(\$60{,}000-(-\$80{,}000)=\$140{,}000\). Equivalently, the return difference is \(0.30\%-(-0.40\%)=0.70\%\), and \(20{,}000{,}000 \times 0.007=\$140{,}000\).
Check. Under these assumptions, the loan has the higher estimated contribution by $140,000. This is not a general prediction that a bank will lend: the comparison assumes an available borrower and omits costs or constraints not listed. A common mistake is to compare the 1.10% loan yield directly with -0.40% on reserves and ignore the loan’s stated costs.
Deposit Rates, Cash, and the Practical Lower Bound
A bank’s reserve rate and the rate paid on a customer’s deposit are different rates. A bank may pass some of a negative policy rate on to large or business depositors, but may hesitate to charge negative rates on ordinary household deposits. If customers can switch to cash, a sufficiently negative deposit return may lead them to withdraw funds. Yet cash is not costless to hold: storage, security, insurance, transportation, and the loss of convenient payment services can all matter.
The simple comparison below identifies the cash-substitution threshold under a deliberately narrow set of assumptions. Let \(r\) be the annual rate on a bank deposit and let \(c\) be the annual proportional cost of holding cash. Assume one-year simple returns, the same initial balance, and that the deposit and cash are equally suitable for the holder apart from the stated cost. The deposit grows to \(1+r\) per dollar. Cash retains \(1-c\) dollars of value after its holding cost. The deposit is at least as attractive as cash when \(1+r \geq 1-c\), or \(r \geq -c\). If the deposit rate falls below \(-c\), cash has the higher net return under these assumptions.
This derivation is a useful benchmark, not a universal prediction of when people will withdraw deposits. Holding costs vary across people and businesses, and deposits provide payment and account services that cash may not replicate. The comparison also leaves out taxes, account fees, safety considerations, and any differences in convenience or risk. Because these circumstances differ, there is no single cash-substitution threshold that applies to everyone.
Worked Example: Comparing a Negative Deposit Rate With Cash Costs
A customer has $80,000 in a hypothetical account paying -0.60% for one year. Holding the same amount in cash would cost 0.25% of the balance for storage and insurance over the year. Assume both rates are annual, costs and interest are calculated on the initial balance, and there are no fees, taxes, or other differences. Compare the dollar outcomes and find the threshold deposit rate.
Method. The account charge is \(80{,}000 \times 0.006=\$480\), so the account’s balance after the charge is $79,520. The cash-holding cost is \(80{,}000 \times 0.0025=\$200\), leaving $79,800 after that cost.
Cash therefore leaves the customer with \(\$79{,}800-\$79{,}520=\$280\) more over the year under the stated assumptions. The threshold is the negative of the cash cost rate: \(-0.25\%\). At a deposit rate of -0.25%, the account charge and cash cost would both be \(80{,}000 \times 0.0025=\$200\). At -0.60%, the account is less attractive in this simplified comparison.
Check. The calculated outcomes differ by $280, and the threshold is -0.25%. The comparison uses the stated cash cost, not zero; treating cash as a cost-free alternative would overstate the incentive to withdraw funds.
How Negative Rates Affect Bank Profitability
Negative policy rates can affect both sides of a bank’s balance sheet. The return on some reserve balances may fall, while loan yields may also decline as market rates and lending rates adjust. At the same time, if customer deposit rates are already near zero and are difficult to push lower, the bank may not receive an equal reduction in its funding costs. This can compress interest margins. The effect on a particular bank depends on its balance sheet and the extent to which each rate changes.
Worked Example: Separating Changes in a Bank’s Interest Income and Costs
A hypothetical bank holds $300 million of loans and $100 million of reserves. It funds these assets with $300 million of deposits and $100 million of wholesale funding. Initially, loans yield 4.20%, reserves earn 0%, deposits cost 0.20%, and wholesale funding costs 1.00%. After a policy-rate cut, assume loan yields fall to 3.90%, reserves are charged 0.40%, the deposit rate reaches 0%, and wholesale funding still costs 1.00%. Assume balances remain unchanged for one year and ignore fees, operating costs, credit losses, and taxes. Compare annual net interest income before and after the change.
Method. Calculate interest earned on each asset and interest paid on each funding source. Initially, loan income is \(300{,}000{,}000 \times 0.042=\$12{,}600{,}000\), and reserve income is zero. Deposit costs are \(300{,}000{,}000 \times 0.002=\$600{,}000\), while wholesale funding costs are \(100{,}000{,}000 \times 0.01=\$1{,}000{,}000\). Initial net interest income is \(\$12{,}600{,}000-\$600{,}000-\$1{,}000{,}000=\$11{,}000{,}000\).
After the change, loan income is \(300{,}000{,}000 \times 0.039=\$11{,}700{,}000\). The reserve charge is \(100{,}000{,}000 \times 0.004=\$400{,}000\), so reserve income is -$400,000. Deposit costs are zero, and wholesale funding costs remain $1,000,000. New net interest income is \(\$11{,}700{,}000-\$400{,}000-\$0-\$1{,}000{,}000=\$10{,}300{,}000\).
Net interest income falls by \(\$11{,}000{,}000-\$10{,}300{,}000=\$700{,}000\). The components reconcile: loan income falls by $900,000, the reserve charge worsens the result by $400,000, and removing the deposit cost improves it by $600,000. Thus the net change is \(-\$900{,}000-\$400{,}000+\$600{,}000=-\$700{,}000\).
Check. The total change agrees with both the before-and-after totals and the component calculation. This is net interest income under the stated assumptions, not total profit. A common mistake is to assume that the bank’s deposit cost falls by the same amount as its reserve return; here the deposit rate has limited room to fall while the reserve rate becomes negative.
Constraints on Deeper Rate Cuts
A negative policy rate can still ease financial conditions, but several constraints limit its effects. First, the pass-through from the policy rate to bank lending and deposit rates is incomplete. Banks may absorb some of the cost in their margins rather than passing it fully to customers. Second, if customer deposit rates are difficult to reduce, banks’ funding costs may not fall in line with the returns on loans and reserves. Third, cash offers an alternative for some holders, but the cost and inconvenience of holding it mean that substitution is neither immediate nor identical across depositors.
The lower bound is therefore effective, rather than necessarily zero. Lowering a policy rate further may still affect market rates or some spending decisions, but the benefits can diminish as costs to banks and incentives to hold cash grow. The point at which this happens depends on the monetary-policy framework and the structure of the financial system; it should not be treated as a fixed universal rate.
Common Exam Traps
- Applying the rate to the wrong reserve balance. If an arrangement exempts a tier, calculate the charge only on the portion subject to the negative rate.
- Equating the policy rate with every customer rate. Reserve remuneration, deposit rates, and loan rates are distinct; their changes need not match.
- Treating cash as costless. Storage and security costs can make a small negative deposit rate preferable to holding cash.
- Assuming a negative reserve rate guarantees more lending. A bank still evaluates expected returns, risks, costs, and lending opportunities.
- Calling net interest income total profit. A calculation that excludes operating costs, losses, and taxes cannot establish the change in overall profit.
Check Your Understanding
Use the stated assumptions in each problem; answers are included so you can check the calculation.
- A bank holds $90 million in eligible reserves. The first $30 million is exempt, and the remaining balance is charged 0.25% annually. Assuming a constant balance for one year, what is the charge? (Answer: $150,000)
- A customer has $40,000 in an account paying -0.40% for one year. Cash holding costs 0.15% of the balance for that year. Using simple annual rates and ignoring all other differences, calculate each cost and identify the preferred option. (Answer: Account charge $160; cash cost $60; cash leaves $100 more.)
- A bank compares a $10 million one-year loan yielding 0.90% with reserves charged 0.20%. For the loan, expected credit losses are 0.30%, servicing costs are 0.20%, and incremental funding and capital costs are 0.10%. Which option has the higher estimated contribution, and by how much? (Answer: The loan’s net return is 0.30%, or $30,000; reserves contribute -$20,000; the loan is higher by $50,000.)
- A bank has $200 million of loans yielding 3.50% and $50 million of reserves charged 0.30%. It funds these with $180 million of deposits costing 0.10% and $70 million of wholesale funding costing 1.00%. With balances constant for one year and no other income or costs, calculate net interest income. (Answer: Loan income $7,000,000; reserve charge $150,000; deposit cost $180,000; wholesale cost $700,000; net interest income $5,970,000.)
- A colleague says, “If the policy rate is -0.50%, every bank must charge depositors -0.50%, every loan rate must also be negative, and all depositors will switch to cash.” Identify the errors in this statement. (Answer: None of those outcomes follows automatically. Banks can face different reserve rules and deposit-rate constraints; loan rates also reflect other costs and risks; cash has holding costs, so the response varies across depositors.)