FRM Exam Part II · Repurchase Agreements and Financing

Repo Financing and Collateral Use Explained

Updated 11 October 2026 · Fact-checked

A repo is a sale of securities with an agreement to buy them back later at a higher price. Dealers and hedge funds use it to borrow cash against securities, take leverage, or borrow a specific security to short. To solve questions, find the cash lent, the haircut, the equity needed and the repo rate cost.

Understand Repo Financing and Collateral Use

A repurchase agreement (repo) is a secured loan in form of a sale and buyback. One party sells a security today for cash and agrees to repurchase it at a fixed future date for a higher price. The price difference is interest, quoted as the repo rate. The cash lender holds the security as collateral. The same trade seen from the lender's side is a reverse repo.

The cash lender rarely lends the full market value. It applies a haircut: cash lent = collateral market value × (1 − haircut). The borrower must fund the haircut from its own capital. That is why the haircut sets the maximum leverage. With a 5% haircut, ₹100 of securities needs ₹5 of equity, so assets ÷ equity = 20.

Dealers use repo to finance their securities inventory. They hold bonds to make markets and fund most of them overnight or short term through repo. Hedge funds use repo to buy more bonds than their capital allows: buy the bond, repo it out for cash, use the cash to buy more, and repeat. Both depend on lenders rolling the funding every day, so this is rollover (funding liquidity) risk.

Repo also sources securities. To short a bond, you borrow it by doing a reverse repo (you lend cash, receive the bond), then sell the bond in the market. You must later buy it back and return it. When the bond is in demand, the cash lender who receives it accepts a lower rate on its cash, so the reverse repo rate you earn is below the general rate. The borrower of cash who delivers the bond pays less. Such a bond is special and trades at a repo rate below the general collateral (GC) rate.

Repo differs from securities lending. In securities lending the lender gives out a security and usually receives collateral that may be cash or other securities, and a lending fee is paid. A repo is driven by cash: the security is collateral for a cash loan. Collateral received can often be reused. Rehypothecation means the receiver pledges the same collateral again to a third party. It lengthens collateral chains, raises interconnectedness, and can cause runs if haircuts jump when confidence falls.

Key formulas to remember

Cash lent: Cash lent = Collateral market value × (1 − haircut); Haircut is a percentage of collateral value. Use market value, not face value, unless told otherwise.
Equity required: Equity = Collateral value × haircut; This is the borrower's own capital in the position, ignoring other costs.
Maximum leverage: Leverage (assets ÷ equity) = 1 ÷ haircut; A 4% haircut gives 25 times. Add the repo rate cost to see the effect on return.
Repurchase price: Repurchase price = Cash lent × (1 + repo rate × days ÷ day-count basis); Check the basis: 360 is typical for USD repo, 365 for some currencies. Use the one given.
Levered return: Return on equity = [Asset return × Assets − Repo rate × Cash borrowed] ÷ Equity; Leverage multiplies both gains and losses.
Margin call trigger: Extra cash/collateral = Original cash lent − New collateral value × (1 − haircut); Applies when the collateral price falls and the haircut stays fixed. Use the original cash lent and the post-fall collateral value. The result is the cash to repay; extra collateral needed is this amount ÷ (1 − haircut). It equals required equity (new value × haircut) minus current equity (new value − original cash lent).

How to solve Repo Financing and Collateral Use questions

Use the same sequence for any repo financing or collateral question, from simple calculations to case-style judgement.

1Identify each party's role: who is the cash borrower (repo seller) and who is the cash lender (reverse repo buyer).
2Note the purpose: financing inventory, taking leverage, or sourcing a security to short.
3Compute cash lent from market value and haircut, then equity as value minus cash lent.
4Compute financing cost using the repo rate, days and the day-count basis given.
5Combine asset return and financing cost to get return on equity, or stress the price to find the margin call.
6Check for special collateral: a lower repo rate means the security is in demand.
7Name the risk precisely: rollover risk, haircut procyclicality, counterparty risk, or rehypothecation chain risk.
8Pick the option that matches both the number and the correct risk label.

Quickest way: Haircut-first shortcut

When to use it: Use this on calculation MCQs where time is short and options differ in leverage or equity.

Write haircut h. Leverage = 1 ÷ h.
Equity = value × h. Cash = value − equity.
For a price move of x%, equity change = x ÷ h in percentage of equity (before financing costs).
Subtract financing cost as repo rate × cash ÷ equity.
Eliminate options with the wrong sign or wrong leverage multiple.

Common mistakes in Repo Financing and Collateral Use

Treating the haircut as the amount of cash lent.
The word suggests the amount received, not the amount withheld.
Fix: Cash lent = value × (1 − haircut). The haircut is the borrower's equity share.
Confusing a repo with securities lending.
Both move securities against collateral.
Fix: Repo is a cash loan with securities as collateral. Securities lending is a loan of a security, usually against collateral, with a fee.
Applying the wrong day-count basis.
Students default to 365.
Fix: Use the basis in the question. If none is given, state your assumption and follow the stem.
Saying special collateral has a higher repo rate.
Demanded assets feel more expensive.
Fix: A special security trades at a lower repo rate. The cash lender who receives it accepts a lower rate on its cash, so the borrower of cash who delivers it pays less.
Ignoring that haircuts can rise in stress.
Haircuts are treated as constants.
Fix: A higher haircut cuts cash lent per unit of collateral, forces deleveraging and fire sales, and makes funding procyclical.
Treating rehypothecation as risk-free efficiency.
The benefit of lower funding cost is emphasised.
Fix: Reuse lengthens collateral chains. If one party fails, recovering the collateral can be delayed or lost.

Worked examples

Example 1

A hedge fund buys USD 50 million of Treasuries and finances them in repo at a 4% haircut and a 5.00% repo rate (actual/360). It holds the position for 30 days. The bonds rise 0.40% in price over that period; ignore coupons. What is the fund's return on equity over the 30 days?

Show the solution

Equity = 50 million × 4% = USD 2 million.
Cash borrowed = 50 − 2 = USD 48 million.
Interest = 48 million × 5.00% × 30 ÷ 360 = USD 0.2 million.
Price gain = 50 million × 0.40% = USD 0.2 million.
Net profit = 0.2 − 0.2 = USD 0.
Return on equity = 0 ÷ 2 million = 0%.

Answer: 0%. The price gain exactly offsets the repo interest, so equity earns nothing.

Example 2

A dealer holds EUR 200 million of bonds financed at a 5% haircut. The bond price falls 3% and the lender still applies a 5% haircut to the new value. The dealer's cash borrowed was fixed at the original level. How much additional cash or collateral must the dealer provide to restore the haircut?

Show the solution

Original cash borrowed = 200 × (1 − 0.05) = EUR 190 million.
Original equity = 200 − 190 = EUR 10 million.
New collateral value = 200 × (1 − 0.03) = EUR 194 million.
Price loss = 200 − 194 = EUR 6 million. This cuts the dealer's equity from EUR 10 million to 194 − 190 = EUR 4 million.
Required equity at a 5% haircut on the new value = 194 × 0.05 = EUR 9.7 million.
Shortfall = 9.7 − 4 = EUR 5.7 million.
Check: the cash the lender will now support = 194 × 0.95 = EUR 184.3 million, and 190 − 184.3 = EUR 5.7 million. Also 6 × 0.95 = EUR 5.7 million.
If the dealer posts extra collateral instead of cash, it needs 5.7 ÷ 0.95 = EUR 6 million of collateral value.

Answer: EUR 5.7 million of cash repayment, or EUR 6 million of extra collateral value. The EUR 6 million price loss cuts the dealer's equity from EUR 10 million to EUR 4 million. At a 5% haircut on EUR 194 million, the dealer needs EUR 9.7 million of equity, so the shortfall is 9.7 − 4 = EUR 5.7 million.

Exam tips

Always write haircut, cash lent and equity as three separate lines before reading options.
Questions often test leverage as 1 ÷ haircut. Check whether the stem gives haircut or margin ratio.
Read for the purpose: a short-selling question points to reverse repo and special collateral, not a funding calculation.
For risk labels, link haircut jumps and failed rollover to funding liquidity risk and procyclicality.
If options include the same quantity in two forms, recompute rather than guess the format.

Practice questions from Repurchase Agreements and Financing

Repo Financing and Collateral Use: frequently asked questions

How do hedge funds use repo for leverage?

They buy a bond, then repo it out to get cash. The haircut is their equity. They use the cash to buy more bonds and repeat. Leverage is capped at about 1 ÷ haircut, and the repo rate is their funding cost.

What is the difference between repo and securities lending?

A repo is a cash loan secured by a security, priced by the repo rate. Securities lending is a loan of a security, usually against collateral, with a lending fee. The trade motive differs: repo raises cash, securities lending sources a particular security.

What is rehypothecation?

It is the reuse of received collateral by pledging it again to another party. It lowers funding costs and supports market liquidity. It also creates long collateral chains and raises risk if a link fails or confidence drops.

How is a short sale done using repo?

The short seller does a reverse repo: it gives cash and receives the bond. It sells the bond in the market. Later it buys the bond back and returns it to close the reverse repo and recover the cash.