What Interest-Rate Pass-Through Measures
A change in a market interest rate does not automatically produce an equal change in every rate faced by households and businesses. A floating-rate loan may be linked to a market benchmark, while a deposit rate may be set by a bank in response to funding needs and competition. The central question is how much of a market-rate change reaches a particular customer rate, and how quickly it arrives.
To compare rates, use rates measured over the same period and on the same basis. In the definitions below, \(m\) is a market reference rate, \(r^L\) is a borrower’s loan rate, and \(r^D\) is a saver’s deposit rate. Changes are measured in percentage points or basis points, not as percentage changes in the rate level.
For example, if a market rate rises by 100 basis points and a loan rate rises by 60 basis points, the measured loan pass-through is \(60/100=0.60\). Here, 100 basis points (bp) equal 1 percentage point. A coefficient below 1 is not necessarily evidence that the customer rate will never change further: the comparison may capture only an initial response, or the contract may permit repricing later.
Changes in Rates and Changes in Spreads
A customer rate can be understood as a market rate plus or minus a gap that reflects the product and its pricing. For a loan, define the observed spread over the reference rate as \(s^L=r^L-m\). This spread may reflect the product’s credit risk, contract terms, and other pricing factors. For a deposit, define the gap below the market rate as \(g^D=m-r^D\). These are accounting definitions; neither gap must stay constant.
This identity follows by subtracting the market-rate change from the loan-rate change. If a market rate rises and a loan rate rises by less, the loan spread over that benchmark narrows during the comparison period. Similarly, \(\Delta g^D=\Delta m-\Delta r^D=(1-\beta^D)\Delta m\). If the market rate rises more than the deposit rate, the deposit gap below the market rate widens. Such calculations describe the change in the gap; they do not, by themselves, establish why it changed.
The benchmark must be a sensible comparison. A short-term market rate is not necessarily the right reference for a long-term fixed-rate product. A customer rate may also change because its risk or contractual spread changes, not just because the reference rate moves. Comparing rates without checking the product, period, and reference can therefore give a misleading pass-through estimate.
Worked Example: Comparing Loan and Deposit Pass-Through
A hypothetical bank’s relevant market reference rate rises from 4.00% to 5.25%. Over the same comparison period, a business loan rate rises from 6.20% to 7.075%, while a household deposit rate rises from 2.00% to 2.50%. Find each product’s pass-through and describe the change in its gap from the market rate.
Method. Calculate each rate change in percentage points, divide by the market-rate change, and then compare the product’s gap with the benchmark before and after. This avoids comparing relative percentage changes in rate levels.
The market rate change is \(5.25\%-4.00\%=1.25\) percentage points, or 125 bp. The loan rate change is \(7.075\%-6.20\%=0.875\) percentage points, or 87.5 bp. Therefore,
The loan rate passed through 70% of the market-rate increase during this period. Its initial spread was \(6.20\%-4.00\%=2.20\) percentage points. Its final spread was \(7.075\%-5.25\%=1.825\) percentage points. The spread therefore narrowed by \(2.20-1.825=0.375\) percentage points, or 37.5 bp.
The deposit rate change is \(2.50\%-2.00\%=0.50\) percentage points, or 50 bp. Its pass-through is
The initial market-rate gap for the deposit is \(4.00\%-2.00\%=2.00\) percentage points. The final gap is \(5.25\%-2.50\%=2.75\) percentage points, so it widened by 0.75 percentage points, or 75 bp. Check: the loan spread change is \(87.5-125=-37.5\) bp, and the deposit gap change is \(125-50=75\) bp, consistent with the before-and-after calculations. The common mistake avoided here is treating the 0.875-point loan increase as a percentage increase in the original loan rate; pass-through uses changes in rates, not percentage changes in their levels.
Pass-Through Can Be Delayed
A single before-and-after coefficient summarizes the size of a response over a chosen window, but it does not reveal when the response occurred. To represent timing, suppose a market-rate change persists and the customer rate adjusts in several periods. Let \(\beta_k\) be the portion of a market-rate change passed through after \(k\) periods. For an isolated market-rate change, the customer-rate change in period \(t\) can be represented as a sum of current and earlier market-rate changes:
This expression says that the customer rate may respond both to a market-rate change in the current period and to market-rate changes that occurred earlier. For one isolated change, the cumulative pass-through through period \(K\) is \(\sum_{k=0}^{K}\beta_k\). This is a short-run description under the specified timing model. Its coefficients need not be equal across products, and the formula should not be used as a contractual rule unless the product’s terms actually imply that pattern.
Worked Example: Calculating a Staged Rate Adjustment
A hypothetical lender tracks a floating-rate product after a permanent 100 bp increase in its reference rate. Its pricing process passes through 25% of the reference-rate change in the first month, a further 35% in the second month, and a further 20% in the third month. The customer rate is initially 5.00%. Find the rate after each adjustment and the cumulative pass-through after three months.
Method. Treat each percentage as a share of the original 100 bp market-rate change, and add the resulting customer-rate changes period by period. This avoids mistaking a further adjustment for a percentage of the already-adjusted customer rate.
In month one, the adjustment is \(0.25\times100=25\) bp, or 0.25 percentage points. The customer rate becomes \(5.00\%+0.25\%=5.25\%\).
In month two, the further adjustment is \(0.35\times100=35\) bp, or 0.35 percentage points. The rate becomes \(5.25\%+0.35\%=5.60\%\).
In month three, the further adjustment is \(0.20\times100=20\) bp, or 0.20 percentage points. The rate becomes \(5.60\%+0.20\%=5.80\%\). The cumulative customer-rate increase is \(25+35+20=80\) bp. Thus cumulative pass-through is \(80/100=0.80\), or 80%. Check: the rate rose from 5.00% to 5.80%, an increase of 0.80 percentage points, matching the 80 bp cumulative change. The stated adjustment pattern stops after month three; the example does not assume any further response.
Why Products Have Different Pass-Through
Pass-through varies because the connection between a market rate and a customer rate depends on how the product is priced and when it can be repriced. A market-rate movement may affect one product quickly but have little immediate effect on another. The following features help explain differences; none alone determines a universal pass-through coefficient.
- Contractual repricing terms. A variable-rate contract may specify a reference rate and reset dates, while a fixed-rate contract may hold the customer’s rate unchanged until refinancing or renewal. Caps, floors, or delayed reset dates can limit or postpone a response.
- Market reference and maturity. A product linked to a short-term benchmark need not move in the same way as one priced from longer-term borrowing costs. A rate comparison is informative only if the benchmark reasonably matches the product’s pricing horizon.
- Changes in product spreads. The customer rate can reflect more than the market benchmark. If a lender changes a risk-related or other spread at the same time, the observed change in the customer rate combines benchmark pass-through with that spread movement.
- Deposit competition and alternatives. A bank may adjust deposit rates differently across account types and customer groups. The willingness of savers to move funds, and the availability of alternative places to save, can affect how a bank responds.
- Adjustment costs and pricing choices. Providers may not change every customer rate immediately after a market movement. Operational schedules, product strategy, and competition can contribute to differences in both the size and timing of adjustments.
Consequently, loan pass-through and deposit pass-through need not be equal, even when both are compared with the same market-rate change. They also need not be symmetric across increases and decreases. A coefficient measured during a rate increase is not sufficient evidence that a similar-sized decrease would produce the same customer-rate response.
Worked Example: Translating Pass-Through Into Annual Cash Flows
A hypothetical household has a variable-rate loan balance of $240,000 at 6.40% and a savings balance of $80,000 earning 2.10%. Both rates are annual rates. A relevant market rate rises by 0.75 percentage points. Assume the loan passes through 80% of that change and the deposit passes through 40%. For a simple annual comparison, assume both balances remain constant and the new rates apply for a full year. Find the change in annual loan interest, deposit interest, and net interest outflow.
Method. First calculate each customer-rate change from its pass-through coefficient. Then multiply the change in annual rate by the relevant balance. This is a simple-interest cash-flow comparison, not a calculation of compounded returns.
The loan-rate increase is \(0.80\times0.75=0.60\) percentage points, so the new loan rate is \(6.40\%+0.60\%=7.00\%\). Initial annual loan interest is \(240{,}000\times0.064=\$15{,}360\). At the new rate it is \(240{,}000\times0.070=\$16{,}800\). The annual increase is \(\$16{,}800-\$15{,}360=\$1{,}440\).
The deposit-rate increase is \(0.40\times0.75=0.30\) percentage points, so the new deposit rate is \(2.10\%+0.30\%=2.40\%\). Initial annual deposit interest is \(80{,}000\times0.021=\$1{,}680\). At the new rate it is \(80{,}000\times0.024=\$1{,}920\). The annual increase is \(\$1{,}920-\$1{,}680=\$240\).
Net interest outflow, defined here as loan interest paid minus deposit interest received, initially equals \(\$15{,}360-\$1{,}680=\$13{,}680\). After repricing it equals \(\$16{,}800-\$1{,}920=\$14{,}880\). The increase in net outflow is \(\$14{,}880-\$13{,}680=\$1{,}200\), also equal to \(\$1{,}440-\$240\). Check: the loan cost rises by more than the deposit return, so net outflow increases. The common mistake avoided is comparing the two pass-through percentages alone without accounting for the different balances.
Common Mistake: Dividing Rate Levels Instead of Rate Changes
Suppose a market rate rises from 4.00% to 5.00%, while a customer loan rate rises from 6.00% to 6.60%. A tempting but incorrect calculation is to divide the customer rate’s relative increase by the market rate’s relative increase: \((0.60/6.00)/(1.00/4.00)=0.10/0.25=0.40\). That is not the pass-through coefficient, because it compares percentage changes in two different rate levels.
The correct calculation uses the rate changes themselves: the market rate increases by 1.00 percentage point, and the customer rate increases by 0.60 percentage points. Therefore, pass-through is \(0.60/1.00=0.60\), or 60%. Exam check: convert both changes to basis points if the units are unclear, then divide customer-rate basis points by market-rate basis points.
Check Your Understanding
For each problem, calculate with rate changes rather than relative percentage changes in rate levels.
- A hypothetical equipment loan rate rises from 5.80% to 6.25% when its market reference rises from 3.30% to 4.05%. Find loan pass-through and the change in the loan spread over the reference rate. (Answer: pass-through \(=0.60\); spread narrows by 30 bp.)
- A deposit rate rises by 18 bp after a market reference rate rises by 60 bp. Find the deposit pass-through and the change in the market-rate gap above the deposit rate. (Answer: pass-through \(=0.30\); the gap widens by 42 bp.)
- After a permanent 80 bp market-rate increase, a product passes through 15% of the change in the first period and a further 45% in the second. If its initial rate is 4.20%, find its rate after each period and cumulative pass-through after the second period. (Answer: first period 4.32%; second period 4.68%; cumulative pass-through \(=0.60\), or 60%.)
- A borrower has a constant $150,000 balance at 5.50%. The market rate rises by 0.40 percentage points, and loan pass-through is 75%. Assuming the new rate applies for a full year, find the new loan rate and the change in annual interest. (Answer: new rate \(=5.80\%\); annual interest increases by $450.00.)
- A market rate rises by 50 bp. A loan rate rises by 35 bp in the first month and a further 10 bp in the second month. Find the cumulative pass-through after two months and the loan’s remaining shortfall from a one-for-one response. (Answer: cumulative pass-through \(=0.90\), or 90%; shortfall \(=5\) bp.)