Repo and Reverse Repo

A bond dealer buys $500 million of Treasuries this morning and must pay for them tonight, without having $500 million. Elsewhere, a corporate treasurer is sitting on idle cash for one night, but will not lend it unsecured to a dealer she has never met. One trade solves both problems, thousands of times a day: the repurchase agreement, or repo.

Think of a pawn shop. You need cash today and you own something valuable, so you leave the watch behind the counter and walk out with money. Next week you pay a little more than you took and collect the watch. Nobody thinks you sold it. Repo is a pawn shop for high-quality bonds, at institutional scale and mostly overnight.

Same trade, two names

One transaction, two sides, and the name depends on where you are standing.

• Repo (repo out): you start with securities and end up with cash. You are the borrower of cash.
• Reverse repo (reverse in): you start with cash and end up holding securities. You are the lender of cash.

Every repo is somebody else's reverse repo. If a hedge fund repos bonds to a money-market fund, the fund has done a reverse repo. Nothing else about the trade differs.

The two legs

Every repo has a start leg today and an end leg at maturity. Interest is never paid separately; it is buried in the gap between the two prices.

START LEG — today bonds worth 10.20m cash 10.00m

END LEG — next morning cash 10.00m + interest same bonds come back

The cash returned on the end leg is the repurchase price:

$$\text{repurchase price} = C \times \left(1 + r \times \frac{d}{360}\right)$$

In words: give back the cash $C$ you borrowed, plus simple interest at the repo rate $r$ for the $d$ days you had it. US repo uses an actual-over-360 year, so one night earns one three-hundred-sixtieth of the annual rate.

Worked example: one night of funding

A dealer needs cash against $10 million face of Treasury notes trading at 102, so worth $10.20 million.

1. Apply the haircut. A 2 percent haircut means the collateral must exceed the cash by 2 percent: $10{,}200{,}000 / 1.02 = 10{,}000{,}000$, so the dealer receives $10.00 million.
2. Compute the interest. At an overnight rate of 4.32 percent, $10{,}000{,}000 \times 0.0432 \times \tfrac{1}{360} = 1{,}200$, or $1,200.
3. Settle the end leg. Next morning the dealer pays $10,001,200 and the bonds come back.

The haircut is the lender's cushion. If the dealer fails overnight, the lender holds $10.20 million of bonds against $10.00 million of exposure and can sell them immediately rather than queue in a bankruptcy court, because repo has a legal safe harbour. That is why repo trades below unsecured overnight lending.

Worked example: repo as a leverage machine

Repo is also the leverage tool of fixed income. Suppose the dealer buys $100 million of a five-year note yielding 4.60 percent and funds it in overnight repo at 4.35 percent, with a 2 percent haircut.

• Equity required: just the haircut, so $2 million supports a $100 million position. That is 50 to 1.
• Daily income: $100{,}000{,}000 \times 0.046 / 360$, about $12,778 of coupon accrual.
• Daily funding cost: $98{,}000{,}000 \times 0.0435 / 360$, about $11,842.
• Net carry: roughly $936 a day on $2 million of equity, near 17 percent annualised.

Now the other side. A five-year note has a DV01 near $45,000 per $100 million, so a 10 basis point rise in yields costs $450,000 in a day, more than a fifth of her equity, and the lender will call for that margin the same afternoon. High leverage and a thin cushion are one fact viewed twice.

General collateral versus special

If the lender wants some safe bond, the trade is general collateral (GC) and the rate sits near the policy rate. If the lender wants one particular bond, usually because they sold it short and must deliver it, that bond goes special and the cash lender accepts a far lower rate to get hold of it. A bond repoing at 1.50 percent when GC is 4.32 percent is telling you there is a scramble to borrow it.

Where it shows up

Repo funds dealer inventory, finances relative-value trades, sources bonds for short sales, and gives cash investors a safe overnight home. It is also where the price of money gets set: SOFR is computed directly from overnight Treasury repo transactions. When repo rates spike, as in September 2019, the system has run short of collateral or reserves — and stress in this quiet corner reaches everywhere else within days.

Key terms

• Repo — sell securities now, buy them back later; economically, borrowing cash against collateral.
• Reverse repo — the mirror side: lending cash, taking collateral.
• Start leg / end leg — the opening exchange and the closing reversal.
• Repo rate — the interest implied by the gap between the two prices.
• Haircut — collateral value in excess of cash advanced.
• General collateral / special — any acceptable bond, versus one specific bond in heavy demand that repos far below GC.