Open Market Operations Explained, With a Worked Example

Open market operations are the Federal Reserve's purchases and sales of government securities, usually U.S. Treasury bonds and bills, to change the amount of reserves in the banking system. When the Fed buys securities, bank reserves rise, the money supply expands, and short-term interest rates such as the federal funds rate fall; when it sells securities, reserves fall, the money supply contracts, and rates rise. This guide walks through the mechanics, the two graphs AP Macro uses to show them, and a full worked example with a $10 million purchase and a 10% reserve requirement.

See it move

Make it move

The money market: money supply and money demand set the nominal interest rate. Tap it to drag the curves, open the full version, or put it on your own site free, or turn it into a five-minute class activity.

What the Fed actually buys and sells

An open market operation is a trade in the ordinary bond market, which is where the "open market" name comes from. The Fed does not lend to the government directly in these trades. It buys and sells Treasury securities that already exist and trade between investors, banks, and securities dealers.

The key detail is how the Fed pays. When it buys a $10 million Treasury bond from a bank, it does not hand over cash from a vault. It credits $10 million to the reserve account that bank holds at the Fed. Those reserves did not exist before the purchase, so the trade adds new reserves to the banking system. When the Fed sells a bond, the process runs in reverse: the buyer's bank pays with reserves, and those reserves leave the banking system.

That gives the rule every AP student memorizes:

A memory trick some teachers use: "buy big, sell small." Buying bonds makes the money supply bigger, and selling bonds makes it smaller.

From reserves to the federal funds rate

The federal funds rate is the interest rate banks charge each other for overnight loans of reserves. A bank that ends the day short of reserves borrows from a bank that has extra.

When reserves are limited, treat them like any other good. If the Fed's purchase leaves banks holding more reserves than before, fewer banks need to borrow and more banks have reserves to lend, so the price of borrowing reserves, the federal funds rate, falls. A sale makes reserves scarcer and pushes the rate up.

In the years before 2008, this is how the Fed hit its federal funds rate target: it set a target (announcing it publicly from the mid-1990s on) and then used open market operations to adjust the supply of reserves until the market rate settled there. A lower federal funds rate then passes through to other short-term rates, to the rates banks charge on loans, and eventually to spending.

The two graphs

AP Macro shows open market operations on two related graphs. Practice both in the money market sandbox and the reserve market sandbox.

The money market. The vertical axis is the nominal interest rate and the horizontal axis is the quantity of money. Money demand slopes down. The money supply is a vertical line, because the central bank sets the quantity. An open market purchase shifts the money supply to the right, and the equilibrium nominal interest rate falls. An open market sale shifts it to the left, and the rate rises. The money market guide covers what shifts money demand and how to label the graph.

The reserve market. The vertical axis is the federal funds rate and the horizontal axis is the quantity of reserves. In a limited reserves framework, the demand for reserves slopes down, and the supply of reserves is vertical at the quantity the Fed provides. An open market purchase shifts the supply of reserves to the right, moving down the demand curve to a lower federal funds rate. A sale shifts it left to a higher rate. Under ample reserves the supply line crosses a flat section of demand, so the shift barely moves the rate; see ample vs limited reserves.

Both graphs tell the same story at different levels: the reserve market shows the rate banks pay each other, and the money market shows the broader nominal interest rate across the economy.

Worked example: a $10 million purchase with a 10% reserve requirement

The Fed buys $10 million of Treasury securities from a commercial bank. The required reserve ratio is 10%. Assume banks lend out all excess reserves and borrowers redeposit every dollar they receive.

Step 1: the bank's balance sheet. The bank gives up $10 million of securities and gains $10 million of reserves. Its deposits have not changed, so its required reserves have not changed either. The entire $10 million is excess reserves, money the bank is free to lend. Write the T-account change like this:

Step 2: the money multiplier.

Money multiplier = 1 / required reserve ratio = 1 / 0.10 = 10

Step 3: the maximum change in the money supply.

Maximum change = new excess reserves × money multiplier = $10 million × 10 = $100 million

Step 4: check the chain. The first bank lends $10 million. That loan is deposited at a second bank, which keeps 10% ($1 million) as required reserves and lends $9 million. The next bank keeps $0.9 million and lends $8.1 million, and so on:

$10 million + $9 million + $8.1 million + $7.29 million + ... = $10 million × (1 / 0.10) = $100 million

A variation the exam likes. Suppose the Fed instead buys the $10 million of bonds from a member of the public, who deposits the Fed's payment in a checking account. Now the seller's deposit itself is $10 million of new money, since a bond is not money but a checking deposit is. The bank must hold 10% of the new deposit, $1 million, as required reserves, so its excess reserves are $9 million. That $9 million supports up to $9 million × 10 = $90 million in new loans and deposits across the system. Total maximum change: $10 million + $90 million = $100 million, the same total by a different route. The difference is in what the first bank can lend: $10 million in the first case, $9 million in the second.

The reverse. A $10 million sale with the same 10% requirement drains $10 million of reserves and can shrink the money supply by up to $100 million.

You can check numbers like these with the money multiplier calculator and the maximum checkable deposit expansion calculator.

Why AP uses the money multiplier here

The $100 million figure is a maximum. Real banks keep some excess reserves instead of lending all of them, and borrowers keep some loan proceeds as cash, so the actual expansion is smaller. The money multiplier explainer covers those leakages.

There is a bigger reason the textbook number differs from today's Federal Reserve. The Fed set reserve requirements to zero in March 2020, and the banking system now holds far more reserves than banks are required to keep. In that setting, adding reserves through a purchase does not set off a predictable chain of lending, and the Fed moves the federal funds rate mainly by changing the interest rate it pays on reserves. AP Macro covers that ample reserves framework as well, and the monetary policy overview compares every tool.

The course still teaches open market operations through the money multiplier because it isolates the core logic of fractional reserve banking: reserves support a multiple of deposits, and the reserve ratio sets that multiple. When a question gives you a reserve requirement and a bond purchase, it is asking for that model, so use 1 / reserve ratio and give the maximum.

Open market operations vs other tools

Open market operations are one of several tools covered in AP Macro topic 4.6:

• The discount rate is the rate the Fed charges banks that borrow directly from it. See discount rate vs open market operations.
• The required reserve ratio sets the fraction of deposits banks must hold, and therefore the size of the multiplier.
• Quantitative easing is large scale buying of longer-term securities when short-term rates are already near zero. It works through the same purchase mechanics but on a much larger scale and with different goals. Compare them at open market operations vs quantitative easing, or read the quantitative easing explainer.

How it shows up on the AP exam

Expect questions that ask you to:

• Name the action. Given a goal (fight a recession, reduce inflation), state the open market operation: buy securities to expand, sell to contract.
• Show it on a graph. Shift the money supply or the supply of reserves in the correct direction and show the new interest rate.
• Trace the effects. Go from the purchase to reserves, the money supply, the interest rate, investment and interest-sensitive consumption, aggregate demand, real output, and the price level, one link at a time.
• Do the arithmetic. Find a bank's excess reserves, the amount a single bank can lend, the money multiplier, and the maximum change in the money supply.

Common mistakes:

• Reversing buy and sell. Buying puts reserves into banks; selling pulls them out.
• Multiplying the wrong number. When the purchase comes from the public, the loan chain starts from the $9 million of excess reserves, not the full $10 million deposit.
• Saying a single bank can lend the whole multiplied amount. One bank lends only its own excess reserves; the multiple comes from the whole banking system.
• Shifting money demand instead of money supply. Open market operations move the supply curve.
• Labeling the money market's vertical axis as the real interest rate. It is the nominal rate.

Key takeaways

• An open market purchase adds reserves, expands the money supply, and, when reserves are limited, lowers the federal funds rate and other short-term rates.
• An open market sale does the opposite.
• With a 10% reserve requirement, a $10 million purchase from a bank can raise the money supply by up to $100 million.
• On the graphs, shift the vertical supply curve, never the demand curve.