FRM Part II · FRM Exam Part II

Repurchase Agreements and Financing: formula sheet

Full chapter guide

Key formulas

Cash lent with a haircut: Cash = Collateral market value × (1 − haircut); Haircut is a percentage of collateral value, not of cash.
Repurchase price: Repurchase price = Cash × (1 + repo rate × days ÷ 360); Use 365 for GBP and some other markets. Simple interest, not compounded, for a term repo.
Repo interest: Interest = Cash × repo rate × days ÷ day-count basis; Paid by the repo seller (cash borrower) to the cash lender.
Initial margin ratio: Margin ratio = Collateral value ÷ Cash lent = 1 ÷ (1 − haircut); A 5% haircut equals a margin ratio of about 105.26%.
Specialness: Specialness = GC repo rate − special repo rate; Positive for a security in demand. The special rate is lower than GC.
Repo interest: Interest = Cash lent × repo rate × days ÷ day-count basis; Use 360 for USD repo, 365 for GBP. Repurchase price = cash lent + interest.
Haircut: Haircut = (Collateral market value − Cash lent) ÷ Collateral market value; Equivalent view: Cash lent = Collateral value × (1 − haircut). Check which base the question uses.
Margin (over-collateralisation) ratio: Collateral required = Cash lent ÷ (1 − haircut); Collateral value must be at least this amount to keep the loan fully secured.
Structure rule: tri-party: Tri-party agent = settlement + collateral management, no credit guarantee; Counterparty risk stays between lender and borrower.
Structure rule: central clearing: Novation: CCP is counterparty to both sides, trades netted, margin and default fund apply; Counterparty risk moves to the CCP.
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).
Haircut: Haircut = (Collateral value − Cash lent) ÷ Collateral value; Cash lent = Collateral value × (1 − Haircut).
Borrower equity funding: Equity needed = Asset value × Haircut; Borrower must fund this from its own capital.
Maximum leverage from haircut: Maximum leverage = 1 ÷ Haircut; Assets ÷ equity. A 5% haircut gives 20 times; a 10% haircut gives 10 times.
Funding gap after a haircut rise: Gap = Asset value × (New haircut − Old haircut); Extra cash needed to keep the same assets funded, if the asset price is unchanged.
Margin spiral loop: Shock → higher volatility → higher haircut → forced sales → lower prices → losses → higher haircut; Qualitative rule; recall the sequence for conceptual questions.
LCR: LCR = Stock of HQLA ÷ Total net cash outflows over 30 days ≥ 100%; Net outflows = outflows minus the lesser of inflows and 75% of outflows.
NSFR: NSFR = Available stable funding ÷ Required stable funding ≥ 100%; One-year horizon. Secured funding from financial institutions under six months gets 0% ASF; six months to under one year gets 50%.
Repo outflow: Outflow = Maturing repo cash × run-off rate; Basel LCR rates by collateral: Level 1 = 0%, Level 2A = 15%, Level 2B RMBS = 25%, other Level 2B = 50%, non-HQLA = 100% (most counterparties).
Haircut value: Collateral value after haircut = Market value × (1 − haircut); Cash raised or HQLA credit is based on this value, not market value. LCR uses Basel-prescribed HQLA haircuts; central bank facilities set their own.
Repo cash from haircut: Cash lent = Collateral market value ÷ (1 + haircut), or Cash lent = Collateral market value × (1 − haircut); These are two different conventions and they give different cash amounts. For $120 million of collateral and a 4% haircut: 120 ÷ 1.04 = $115.38 million, but 120 × 0.96 = $115.2 million. The question specifies which convention to use, so follow it.

Quick revision

A repo is a sale plus a forward repurchase, economically a secured loan.
The cash borrower is the seller of the security; the cash lender receives the collateral.
A reverse repo is the same trade seen from the cash lender's side.
Repo interest = cash × repo rate × days ÷ day-count basis.
Cash lent = collateral value × (1 − haircut), so a higher haircut means less cash for the same collateral.
Haircuts protect the lender against a fall in collateral value during the term.
Tri-party repos use a third-party agent to hold collateral and handle settlement and substitution.
Central clearing reduces bilateral counterparty exposure and allows netting, but concentrates risk in the clearing house.
Most repos are short term, so borrowers face rollover risk.
Rising haircuts and falling collateral prices can force deleveraging and fire sales.
Repo runs resemble bank runs: lenders withdraw funding when confidence in collateral or the borrower drops.
Liquidity standards and buffers aim to reduce reliance on fragile short-term secured funding.

Common mistakes

Calling the cash lender the repo party Fix: Repo means selling collateral and borrowing cash. The cash lender is doing a reverse repo.
Applying the repo rate to collateral value Fix: Interest accrues on the cash actually lent, which is after the haircut.
Saying the tri-party agent guarantees the trade Fix: The agent is an administrator. Credit risk stays with the borrower. Only a CCP novates and guarantees.
Treating tri-party and centrally cleared repo as the same thing Fix: Tri-party is collateral management and settlement. Central clearing is novation, netting and margining by a CCP.
Treating the haircut as the amount of cash lent. Fix: Cash lent = value × (1 − haircut). The haircut is the borrower's equity share.
Confusing a repo with securities lending. Fix: Repo is a cash loan with securities as collateral. Securities lending is a loan of a security, usually against collateral, with a fee.
Treating the haircut as a percentage of cash lent. Fix: The base is collateral value. Cash lent = collateral × (1 − haircut).
Saying repo is safe because it is collateralised. Fix: Collateral protects only if it can be sold at or above the loan. Rollover and haircut risk remain.
Applying the same run-off rate to all repo funding. Fix: Rate depends on collateral. Level 1 collateral gives 0%. Only non-HQLA collateral from most counterparties gives 100%.
Mixing up the 30-day LCR horizon and one-year NSFR horizon. Fix: LCR is short-term stress survival. NSFR is structural, one-year funding stability.

Exam tips

Always state first which side the question asks about. Many wrong options are the right number for the wrong party.
Check whether the question gives a haircut or a margin ratio. They are different bases.
Expect a day-count trap. Use 360 unless the question says 365.
Link specials to short covering: a very low or negative repo rate means high demand for that bond.
For risk questions, remember haircuts protect the cash lender, and larger haircuts are applied to more volatile or less liquid collateral.
Questions often hinge on one word: guarantee, novation, netting or segregation. Match it to the structure.
Expect a case on repo run risk: haircuts rise, lenders pull back, dealers fire sell collateral.
Do the arithmetic with the right day count and haircut base before reading options.