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Lay out how repurchase agreements (repos) operate and work out the settlement amount of a repo.

FRM® Part II · Liquidity and Treasury Risk Measurement and Management · Repurchase Agreements and Financing · FRM2.LTR.13.a

The idea

A repurchase agreement (repo) is the sale of securities combined with a binding promise to buy them back on a set date at a set price, so economically it is a collateralised loan. The seller of the securities is the cash borrower and the buyer is the cash lender. The same trade viewed from the lender's side is a reverse repo. The repurchase price is the cash lent plus interest, and some markets count 365 days in a year where US dollar trades use 360. Write Cash, Rate and Days for the cash lent, the repo rate and the days to repurchase. Interest = Cash × Rate × Days ÷ 360. Cash lent is the collateral's market value, written Value, reduced by a haircut. Cash = Value × (1 − Haircut). The lender is therefore over-collateralised. Typical slips are charging interest on market value instead of cash lent, using the wrong day count, and mixing up the repo and reverse repo labels.

Formulas

Interest on a US dollar repo

Interest = Cash × Rate × Days ÷ 360

Cash
the cash lent, after the haircut
Rate
the repo rate, annualised
Days
calendar days to repurchase

The repurchase price is cash plus this interest. Charge interest on cash lent, not on market value, and count calendar days; some markets use 365 rather than 360.

Cash lent against repo collateral

Cash = Value × (1 − Haircut)

Value
the market value of the collateral
Haircut
the haircut, as a fraction of market value

The lender is over-collateralised by the haircut. If collateral must instead equal a stated percentage of cash, divide value by that percentage.

A practice question

From the question bank, with the reason each wrong option is wrong.

In a standard repurchase agreement (repo), which description of the transaction is correct?

  1. The cash borrower buys securities from the cash lender and commits to resell them later at a higher price.Why not: Reverses the direction of cash and securities: the party that sells the securities and receives the cash is the borrower.
  2. The securities are sold outright, with no obligation to repurchase, and the price difference is the seller's capital gain.Why not: Describes an outright sale; a repo has a binding repurchase commitment and the price difference is interest on the cash.
  3. The cash borrower sells securities to the cash lender and commits to buy them back at a later date at a higher price. - correct
  4. The cash lender lends securities of equal value to the borrower for a fee, and no cash changes hands.Why not: Describes a securities-for-securities loan; in a repo cash is exchanged for securities.

A repo is a sale with a forward repurchase at a higher price. The seller of the securities is the cash borrower and the price difference is interest, so economically it is a collateralised loan.

A harder one

A repo desk delivers securities with a market value of USD 105,000,000 and the lender requires collateral equal to 105% of the cash advanced (a 5% margin). The term is 60 days at a repo rate of 2.5% (actual/360). The repurchase price is closest to:

  1. USD 100,416,667 - correct
  2. USD 105,437,500Why not: Treats the whole market value as the cash lent, so interest is charged on the collateral rather than on the cash advanced.
  3. USD 100,165,625Why not: Treats the margin as a haircut, cash = MV x 0.95; here collateral is 105% of cash so cash = MV / 1.05.
  4. USD 110,709,375Why not: Applies the margin in the wrong direction, so cash exceeds the collateral value.

Cash = 105,000,000 / 1.05 = 100,000,000. Interest = 100,000,000 x 0.025 x 60/360 = USD 416,667, so the repurchase price is USD 100,416,667.

The hardest tier

A repo borrower received cash of USD 114 million against collateral with a market value of USD 120 million (a 5% haircut, cash = MV x 0.95). The haircut is maintained for the life of the trade. After some days the collateral's market value falls to USD 112 million. Ignoring accrued interest, the additional collateral market value the borrower must deliver is closest to:

  1. USD 8.0 million - correct
  2. USD 7.6 millionWhy not: Computes the cash that would have to be returned (112 x 0.95 = 106.4, so 7.6), not the extra collateral needed to keep the loan.
  3. USD 5.7 millionWhy not: Applies the 5% haircut to the cash lent (0.05 x 114) rather than restoring the required collateral value.
  4. USD 6.0 millionWhy not: Re-applies the 5% haircut to the original market value (0.05 x 120), which is not the collateral shortfall.

Required collateral = cash / (1 - haircut) = 114 / 0.95 = 120. Current collateral is 112, so the variation margin call is 120 - 112 = 8.0 million. The cash lent does not change.

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