Repurchase agreements (repos)

How does a repo work?

A repurchase agreement (repo) is the sale of a security with a simultaneous agreement by the seller to buy the same (or a similar) security back from the buyer on a future repurchase date , at an agreed repurchase price . The security seller is the cash borrower. The security buyer is the cash lender. Seen from the lender’s side, the same trade is a reverse repurchase agreement (reverse repo).

The difference between what the borrower gets now and what it pays back is interest, quoted as the repo rate . The security is collateral. The seller keeps the economic ownership: coupons and income on the security still belong to it, and the buyer earns the repo rate.

$$\text{Repurchase price} = P_0 \times \left(1 + r \times \frac{\text{days}}{360}\right)$$

Here $P_0$ is the purchase price (the cash lent) and $r$ is the annual repo rate. Money market interest uses a 360-day year.

Why is the loan smaller than the bond?

To protect the lender against a fall in the collateral’s value, the borrower hands over more than it receives. The initial margin is the ratio of the security’s price to the cash lent. At 100% the loan is fully collateralized; above 100% it is over-collateralized. The same idea seen from the collateral side is the haircut : the share of the collateral’s value that is not lent.

$$\text{Initial margin} = \frac{S_0}{P_0}$$

$$\text{Haircut} = \frac{S_0 - P_0}{S_0}$$

What happens when the collateral moves?

Repos keep the collateral cushion in place through margin calls. Either side may ask for more collateral, or the release of some, so that the cushion stays equal to the original initial margin. This payment is the variation margin .

$$\text{VM}_t = (\text{Initial margin} \times P_t) - S_t$$

Here $P_t$ is the loan plus the interest accrued to date $t$, and $S_t$ is the security’s current price. A positive result means the collateral is too small and the borrower must post more. A negative result means it is over-collateralized, and the borrower may ask for some back.

Terms and documents

Repos run from overnight to a term repo , any maturity longer than one day. A repo can name a specific security, or a group of eligible securities, such as government bonds of a given maturity. The second kind is a general collateral repo , done at the general collateral repo rate . A master repurchase agreement or similar document governs all trades between two parties: margining, substitution of collateral and events of default.

Repurchase agreementsale of a security with an agreement to buy it back

• By term Use it overnight to a longer period
  • Overnight repo Use it one day
  • Term repo Use it any maturity longer than one day
• By collateral Use it what is delivered
  • Specific security Use it special collateral rate applies
  • General collateral Use it any security from an agreed basket
• By who handles it Use it administration of collateral and cash
  • Bilateral repo Use it directly between the two parties
  • Triparty repo Use it third-party agent values and holds collateral

Most repos are very short and use the safest, most liquid collateral, usually sovereign bonds, because cash lenders want safety and liquidity first.

Why do market participants use repos?

Repo usesthree market uses, plus central banks

• Finance a security position Memorize own cash needed falls to the haircut
• Earn secured short-term income Memorize lender (reverse repo) holds collateral
• Borrow a security to short it Memorize reverse repo, sell, buy back later
• Central bank policy Use it short-term, temporary changes in reserves

1. Finance a security. A dealer that buys a bond must pay at once, even if it plans to sell later. It repos the bond and borrows most of the price from another bank or an asset manager. Its own funding need shrinks to the haircut.
2. Earn secured short-term income. Banks, mutual funds and pension funds lend cash against collateral with minimal liquidity or default risk. Overnight repos with high-quality collateral pay the least. Longer terms or weaker collateral pay more. On a bank’s balance sheet these appear as securities purchased under agreements to resell.
3. Borrow a security to sell it short. A hedge fund that expects a bond to fall does a reverse repo to borrow it, sells it, and later buys it back to return it.

$$\text{Profit} = P_0 \times \left(1 + r \times \frac{\text{days}}{360}\right) - \text{buyback price}$$

Central banks also use repos to make short-term, temporary changes to the reserves in the banking system, for example by lending cash and taking securities to raise reserves for a while.

What sets the repo rate?

Factor	Repo rate goes…
Short-term money market rates rise	Up (repo rates track them)
Weaker collateral (equities, emerging-market bonds)	Up
Longer repo term	Up (normally)
Collateral in high demand (on-the-run, “special”)	Down, possibly below zero
Loan undercollateralized or no collateral delivered	Up

A repo that requires delivery of one particular security, as a short sale does, is a special trade, done at the special collateral rate . When that security is in very high demand, the rate can fall below the general collateral rate, or even below zero. A negative repo rate means the security buyer pays interest on the cash it lends, to get the scarce bond.

Exam tip Riskier, longer or less covered collateral pays more. Scarce collateral is the one thing that pays less.

What can go wrong?

Memorize

Repo riskscollateral reduces risk but does not remove it

• Default risk Memorize primary exposure, collateral may be hard to sell
• Collateral risk Memorize illiquid collateral, or correlated with the counterparty
• Margining risk Memorize late or wrong valuations, margin calls feed forced selling
• Legal risk Memorize ability to enforce rights under the agreement
• Netting and settlement risk Memorize offsetting obligations and taking possession
• Rollover and liquidity risk Use it mostly overnight, lenders can stop rolling

Collateral lowers risk but does not remove it. Default risk remains the main exposure: collateral from a weak counterparty is more likely to be tested, and it may be illiquid, fall in price or be hard to take over legally. Collateral risk means the collateral should be liquid and should not move with the counterparty’s own credit, so it still has value if the counterparty fails. Margining risk is late or wrong collateral valuation. In a market fall, big margin calls can force further selling. Legal risk is whether the rights under the contract can be enforced. Netting and settlement risk is whether obligations can be offset and collateral or cash taken in settlement.

Because most repos are overnight and uncommitted, the lender can simply stop rolling them when confidence drops. Heavy reliance on repo funding has pushed firms into distress when this happened.

Participants often use a third party to manage these risks. In a bilateral repo , the two parties deal directly. In a triparty repo , a custodian or clearinghouse values and holds the collateral and administers cash and securities. The agent brings cost efficiency, access to a larger collateral pool and many counterparties, and specialist valuation and safekeeping. It does not change the credit risk between the parties if one defaults.

Go deeper Why the seller keeps the coupon

The repo is economically a loan, not a sale. The seller still bears the price risk of the bond and still receives its coupons, and pays the repo rate for the cash. The buyer’s return is that repo rate, not the bond’s coupon.

Go deeper Negative special repo rates

When many investors need the same bond, for example to deliver against a short sale, the owner can lend it out very cheaply. Cash lenders accept a repo rate below zero: they pay interest on the cash they lend, in return for getting the scarce bond. The rate moves by security, not by credit quality.

Go deeper Repo and cost of carry

Financing a bond through a repo is the cost-of-carry part of pricing a forward on that bond. The forward price reflects the repo rate paid on the borrowed cash less the coupon income. This returns in the derivatives topic.