Explain repurchase agreements, what they are used for and the risks they carry
The idea
A repurchase agreement, or repo, is a sale of a security combined with an agreement to buy it back at a higher price on a later date. Economically it is a collateralised loan: the seller borrows cash, the buyer lends it, and the price difference is the interest, at the repo rate, conventionally calculated on an actual/360 basis. The same trade seen from the lender's side is a reverse repo. The lender advances less than the collateral's value, and that haircut protects it against a fall in the collateral price. Repo rates and haircuts are higher for lower-quality or less liquid collateral and longer terms, and lower when the collateral is in special demand. Dealers use repo to finance inventory and reverse repo to borrow securities for short sales, and central banks use it to conduct monetary policy. The main risks are counterparty default combined with a decline in collateral value, and liquidity risk when lenders withdraw funding.
A practice question
In a repurchase agreement, the party that sells the security and agrees to buy it back is:
- lending cashWhy not: That is the counterparty, whose side of the trade is a reverse repo.
- borrowing cash — correct
- buying protectionWhy not: Describes a credit default swap, not a repo.
The seller in a repo receives cash now and repays more later, so it is borrowing against the security as collateral.
A harder one
A dealer repos bonds with a market value of 10.2 million at a 2% haircut for 30 days at a repo rate of 4.5% (actual/360). The repurchase price is closest to:
- 10,033,485 — correct
- 10,238,250Why not: Ignores the haircut and lends the full 10.2 million.
- 10,032,972Why not: Uses a 365-day year instead of the actual/360 basis given.
Loan = 10.2m x 0.98 = 9,996,000. Interest = 9,996,000 x 0.045 x 30/360 = 37,485. Repurchase price = 10,033,485.
The hardest tier
A lender advances cash against collateral worth 50 million with a 4% haircut. The collateral's value falls to 46 million and the borrower then defaults. Ignoring interest, the lender's loss is:
- 0Why not: Assumes the haircut covers any fall. It covers only 2 million, and the price fell 4 million.
- 4 millionWhy not: Measures the fall in collateral value without crediting the haircut.
- 2 million — correct
Loan = 50m x 0.96 = 48m. The lender keeps collateral worth 46m, so its loss is 48 - 46 = 2 million.
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