Reserve Scarcity and the Demand Curve for Reserves

A bank does not keep its spare cash under a mattress. It keeps it as a deposit at the central bank, called a reserve balance, and it uses that balance to settle payments with every other bank in the country. Every wire, every cheque, every interbank loan clears through those accounts. Run the balance too low on a busy day and a payment can fail; hold too much and you are sitting on an asset that pays close to nothing while your loan book could have been earning far more. That tension between "enough to be safe" and "not so much it's wasted" is what draws a demand curve for reserves — and where the total supply of reserves in the banking system lands on that curve determines whether overnight rates trade calmly near the policy target or lurch around unpredictably.

The shape of the curve

Plot the interbank overnight rate on the vertical axis and total reserves in the banking system on the horizontal axis, and the demand curve for reserves looks like a backwards L.

• Scarce reserves. When aggregate reserves are low relative to what banks need for payments and regulatory buffers, the curve is steep. A small drop in supply forces banks to bid aggressively for the reserves that remain, because being short is expensive — an overdraft, a rushed uncollateralized loan, or in the worst case a trip to the discount window, which carries a stigma of looking weak. Rates spike well above target.
• Ample reserves. Add more reserves and the curve flattens. Banks are no longer fighting over scarce balances; a bank a little short can borrow calmly from one a little long, near the target rate, without drama.
• Abundant reserves. Add even more and the curve goes essentially flat and low. Reserves are now so plentiful that no bank values the marginal dollar much above the rate the central bank pays on the balances directly — the interest on reserve balances (IORB) rate. Extra reserves just sit there.

Worked example: a shrinking balance sheet meets a steep curve

This is close to what happened in the United States in September 2019. Bank reserves had been drawn down for over a year as the central bank ran off its balance sheet, while at the same time corporate tax payments and Treasury settlements pulled cash out of the system on a single day. Suppose reserves that had been comfortably in the ample zone at roughly $1.5 trillion fell, on that day, to an effective level the market treated as scarce for a few hours. Overnight repo rates, which normally sit within a few basis points of the fed funds target, spiked from around 2.25 percent to as high as 10 percent intraday — a move of roughly 775 basis points in a market where a 10-basis-point wobble is normally news. Nothing about the policy rate had changed; only the position on the demand curve had.

The lesson generalizes: a system can sit in the ample zone for years, look stable, and then a single settlement day pushes the marginal reserve balance into the steep part of the curve, and rates convulse.

Worked example: reading the elasticity

Reserve demand elasticity is often summarized as the percentage change in the rate spread over IORB for a given percentage change in aggregate reserves. Suppose reserves fall by 2 percent and the fed funds rate rises 15 basis points above IORB, from 5 basis points above to 20 basis points above. That is a large rate move for a small quantity move — evidence the system was near the steep, scarce part of the curve. If the same 2 percent drop in reserves instead moved the spread by only 1 basis point, that would be evidence of sitting comfortably in the flat, abundant part.

Where you meet it in practice

The demand curve for reserves is the reason repo markets, the fed funds market, and IORB policy are really one system, not three. A repo trading desk watching September 2019-style spikes is watching reserve scarcity in real time; a central bank running quantitative tightening is deliberately walking supply down the curve and has to stop before it hits the steep part. For a quant, the practical takeaway is that "the policy rate" is a target the central bank hits by managing quantity, not a lever it pulls directly — and the demand curve is what translates quantity into price.