FRM Exam Part II · Managing Nondeposit Liabilities

Federal Funds and Repurchase Agreements for Bank Funding

Updated 11 October 2026 · Fact-checked

Federal funds are unsecured overnight loans of reserve balances between banks. A repurchase agreement (repo) is secured borrowing: you sell securities and agree to buy them back later at a higher price. The price gap is the interest. Haircuts, margin calls and rollover risk drive the risks you must analyse.

Understand Federal Funds and Repurchase Agreements

Banks often need cash for a short time. Two common ways to get it are federal funds and repurchase agreements. Both are usually overnight or very short term, and both are wholesale funding, meaning they come from other institutions, not retail depositors.

Federal funds are unsecured loans of reserve balances held at the central bank. The lender has no collateral, so it takes the borrower's credit risk and sets limits by counterparty. The rate depends on the borrower's perceived credit quality and on reserve supply. Because there is no collateral, fed funds borrowing tends to dry up quickly when trust in a bank falls.

A repo is a secured loan in legal form of a sale and repurchase. The borrower sells securities now for cash and agrees to repurchase them later at a higher price. The difference is the repo rate interest. The lender holds the collateral, so it is protected if the borrower defaults. From the lender's side, the same trade is a reverse repo: you lend cash and receive securities. Repo and reverse repo are the two sides of one trade, not different products.

Collateral is valued at market and the lender lends less than its value. That cushion is the haircut. If the collateral is worth ₹100 and the haircut is 5%, the cash lent is about ₹95. If collateral value falls, the lender makes a margin call for more collateral or cash. Riskier or less liquid collateral gets a bigger haircut.

The main risk of repo funding is rollover risk. Overnight repo must be renewed every day. If lenders refuse to roll, or raise haircuts sharply, the borrower must find cash or sell assets quickly. This is a run on repo, and it hit dealer banks in the 2007-2009 crisis. Secured does not mean safe for the borrower: it is cheaper than unsecured funding, but it ties up assets and can disappear fast when collateral values fall.

Key formulas to remember

Repo interest (simple, actual/360 style): Repurchase price = Cash lent × (1 + repo rate × days ÷ day-count basis); Use the day-count basis given in the question (commonly 360 for USD money markets). Interest = repurchase price − cash lent.
Haircut: Haircut = (Collateral value − Cash lent) ÷ Collateral value; Cash lent = Collateral value × (1 − haircut). Haircut is measured on collateral value, not on cash.
Collateral needed: Collateral required = Cash needed ÷ (1 − haircut); Divide by (1 − haircut). Do not multiply by (1 + haircut).
Margin call after price fall: Required collateral value = Cash lent ÷ (1 − haircut); call = required − current collateral value; Applies when the haircut is fixed and collateral is marked to market.
Leverage from haircut: Maximum leverage ≈ 1 ÷ haircut; A 5% haircut means about 20 times assets to own funds. Small haircut rises are very costly.

How to solve Federal Funds and Repurchase Agreements questions

Use this order for any fed funds or repo question. It keeps secured and unsecured funding apart and stops you mixing up the two sides of the trade.

1Identify the trade and your side. Are you the cash borrower (repo) or cash lender (reverse repo)? Is the funding secured (repo) or unsecured (fed funds)?
2List the inputs: cash, collateral value, haircut, repo rate, days and day-count basis.
3Compute cash lent from collateral value × (1 − haircut), or collateral needed as cash ÷ (1 − haircut).
4Compute interest as cash lent × rate × days ÷ basis, then the repurchase price.
5If prices move, mark collateral to market and compute the margin call against the required collateral value.
6Assess the risk the question asks about: counterparty credit risk (fed funds), collateral and haircut risk, or rollover and run risk.
7Check direction and units: haircut applies to collateral, interest applies to cash, and 'reverse' means you are lending cash.
8Link to interpretation: state what a higher haircut or lost rollover means for liquidity and leverage.

Quickest way: Three-line repo check

When to use it: Use when the question gives numbers for haircut, margin call or interest and four close options.

Cash = collateral × (1 − haircut). Write it first.
Interest = cash × rate × days ÷ basis. Use the stated basis.
For a margin call, find the new collateral needed = cash ÷ (1 − haircut), then subtract current collateral value.
For conceptual options, eliminate any that call repo unsecured, put the haircut on cash, or treat reverse repo as borrowing cash.

Common mistakes in Federal Funds and Repurchase Agreements

Calling repo unsecured, or fed funds secured
Both are overnight bank funding, so they blur together.
Fix: Fed funds are unsecured reserve loans. Repo is collateralised. Say it in one sentence before answering.
Mixing up repo and reverse repo
The names sound like different products and the direction is relative to who you are.
Fix: Same trade, two sides. The cash borrower does the repo. The cash lender does the reverse repo. Always ask who gives cash.
Applying the haircut to the cash amount
People think of it as a discount on the loan.
Fix: The haircut is a percentage of collateral value. Cash lent = collateral × (1 − haircut).
Using collateral × (1 + haircut) to size collateral
Seems natural to 'add a cushion'.
Fix: Divide cash by (1 − haircut). For a 5% haircut, ₹95 of cash needs ₹100 of collateral, not ₹99.75.
Treating repo as safe funding with no liquidity risk
Collateral protects the lender, so students assume the borrower is safe.
Fix: Rollover risk, rising haircuts and margin calls can remove funding quickly. Secured funding lowers credit risk for the lender, not funding risk for the borrower.
Ignoring the day-count basis
Rushing to apply days ÷ 365.
Fix: Use the basis stated in the question. If none is given, follow the convention in the options and show it.

Worked examples

Example 1

A bank repos USD 50 million of Treasury securities (market value) with a 4% haircut at a repo rate of 5.40% for 7 days, actual/360. How much cash does it receive, and what is the repurchase price?

Show the solution

Cash lent = 50,000,000 × (1 − 0.04) = 48,000,000.
Interest = 48,000,000 × 0.054 × 7 ÷ 360.
48,000,000 × 0.054 = 2,592,000. Multiply by 7 = 18,144,000. Divide by 360 = 50,400.
Repurchase price = 48,000,000 + 50,400 = 48,050,400.

Answer: Cash received is USD 48,000,000 and the repurchase price is USD 48,050,400 (interest USD 50,400).

Example 2

A dealer funds a position through repo with a fixed 5% haircut. It borrowed USD 95 million against collateral of USD 100 million. The collateral value falls to USD 92 million and the haircut stays at 5%. What margin call is made?

Show the solution

Cash lent stays at 95,000,000.
Required collateral = 95,000,000 ÷ (1 − 0.05) = 95,000,000 ÷ 0.95 = 100,000,000.
Current collateral = 92,000,000.
Margin call = 100,000,000 − 92,000,000 = 8,000,000.

Answer: The lender calls for USD 8 million of additional collateral or cash. If the haircut also rose, the call would be larger.

Exam tips

Always state first whether the question is about credit risk (fed funds) or funding and rollover risk (repo).
For reverse repo, check who lends cash. Questions often flip the perspective to test this.
Higher haircuts on weaker collateral and in stress are the standard mechanism behind runs on repo. Link them to leverage and forced asset sales.
Recompute margin calls with division by (1 − haircut). Wrong options are often built from multiplying.
In case-style questions on dealer banks, name rollover risk and collateral quality, not just 'liquidity risk'.

Practice questions from Managing Nondeposit Liabilities

Federal Funds and Repurchase Agreements: frequently asked questions

What is the difference between repo and fed funds borrowing?

Fed funds borrowing is unsecured and involves reserve balances between banks. Repo is secured by securities and priced off the collateral and market conditions. Repo is usually cheaper for a good-collateral borrower but exposes it to haircut and rollover risk.

What is the difference between repo and reverse repo?

They are the two sides of the same transaction. The party that sells securities and borrows cash is doing a repo. The party that buys the securities and lends cash is doing a reverse repo.

What is a repo haircut?

It is the percentage by which the collateral value exceeds the cash lent. It protects the lender against a fall in collateral value if the borrower defaults. Riskier or less liquid collateral carries a larger haircut.

What is rollover risk in repo funding?

It is the risk that lenders will not renew maturing repo, or will renew only at a higher rate or haircut. Because much repo is overnight, the borrower may have to find cash or sell assets very quickly. This is how runs on repo develop.