Cash-and-Carry and the Implied Repo Rate: Carry Arbitrage in Index, Gold and Treasury Futures

A cash-and-carry trade buys an asset today, finances it, and sells a futures contract against it, locking in the difference between the futures price and the cost of holding the asset to expiry. The implied repo rate is the financing rate that makes that trade break even: it converts a futures price into an interest rate, so a desk can compare it directly with what money actually costs in the repo or SOFR market.

In short: every futures price on a storable or financial asset contains an implied interest rate. Solve the cost-of-carry formula backwards and you get it. If the implied repo rate is above your real financing rate, buying the asset and selling the future earns the difference; if it is below, the reverse trade (sell the asset, buy the future) is the cheap way to hold it. In practice the spread rarely closes to zero, because the arbitrage needs balance sheet, the dividend or coupon inputs are uncertain, short selling is costly, and futures are marked to market daily. Professionals do not ask “is the future at fair value?” They ask “what rate is the future lending at, and can I beat it?”

This article assumes you know the basic carry formula from how futures prices are set. Here we work through the professional version for three asset classes, with real exchange conventions and dated rates.

The misconception: “fair value is a single number”

Media coverage treats fair value as a line the futures price should sit on. CME Group’s own definition is more careful. Its “Calculating Fair Value” page calls fair value “the theoretical assumption of where a futures contract should be priced given such things as the current index level, index dividends, days to expiration and interest rates,” and adds that “the actual futures price will not necessarily trade at the theoretical price.” Each input is an assumption. Change the interest rate you plug in, and fair value moves. That is the key insight: the futures price is observed, the financing rate is not, so the useful question runs the other way. Given the price, which rate is implied?

One idea, three asset classes

Strip the formula to its skeleton. Holding an asset from today to expiry costs financing and (for commodities) storage, and earns any income the asset pays. So:

Futures price = spot price + financing cost + storage cost minus income

Rearrange to isolate financing and divide by time, and you have the implied repo rate:

Implied repo rate = [(futures price + income minus storage) / spot price minus 1] x (360 / days)

The 360-day year is the money-market convention used for SOFR and in CME’s fair value formula. The table shows what “income” and “storage” mean in each market.

Market	Income while you hold the asset	Storage and holding costs	Where the arbitrage lives
Stock index	Dividends	Execution and custody of hundreds of stocks	Bank and dealer index-arbitrage desks
Gold	Lease income if you lend the metal out	Vault, insurance, assay	Bullion banks
Treasury bonds	Coupons	Repo haircut, balance sheet	Relative-value funds and dealers
Grains, energy	Convenience of holding inventory	Warehouse or tank fees, insurance	Physical merchants with storage

For the last row, the “income” is the convenience yield, the value of having physical inventory on hand. Because only firms that already own the inventory can capture it, the reverse arbitrage breaks down and commodity curves can sit in backwardation for long periods. That theory of storage gets its own deep dive in this section. This article sticks to the three markets where the carry arithmetic is close to binding.

Stock index futures: fair value and the implied rate

CME’s formula, checked

CME Group gives the stock index fair value formula as:

Fair value = Cash x [1 + r x (x / 360)] minus Dividends

where r is the interest rate, x is days to expiration, and dividends are expressed in index points to expiry. CME’s own worked example uses an S&P 500 of 1146.00, a 5.7% rate, 78 days, and 3.47 points of dividends, giving 1146 x (1 + 0.057 x 78/360) minus 3.47 = 1156.68. We reran that in Python and got the same figure. With the future at 1157.00, CME calls it 0.32 points over fair value.

Worked example: the December 2026 E-mini

The E-mini S&P 500 (ES) is $50 times the index and settles in cash to a Special Opening Quotation on the third Friday of the contract month (contract details in stock index futures explained). The December 2026 contract settles on Friday, December 18, 2026, which is 38 days after November 10, 2026.

Inputs. The index level and dividends are illustrative. The rate is real: the New York Fed published SOFR at 3.88% for November 9, 2026, with the federal funds target range at 3.75% to 4.00%.

Index: 6,800.00
Financing rate: 3.88% (SOFR, as of November 9, 2026)
Days to expiry: 38
Expected dividends to expiry: 8.50 index points

Fair value:

Financing: 6,800 x 0.0388 x 38 / 360 = 27.85 points
Fair value: 6,800 + 27.85 minus 8.50 = 6,819.35

Now suppose ES trades at 6,825.00. It is 5.65 points above fair value, worth 5.65 x $50 = $282.51 per contract. But a desk does not think of that as “5.65 points rich.” It solves for the rate:

Implied repo: [(6,825.00 + 8.50) / 6,800.00 minus 1] x 360 / 38 = 4.67%
Spread over SOFR: 4.67% minus 3.88% = 79 basis points

Two useful rules fall out of the arithmetic:

One index point is worth about 14 basis points of implied rate at this tenor (1 / 6,800 x 360 / 38 = 13.9 bp). Short-dated futures convert small price gaps into large rate gaps, which is why near-expiry pricing looks noisy in rate terms.
Day count matters at the margin. Using a 365-day year, the fair value is 6,818.97, about 0.4 points lower. That is roughly 5 basis points of rate, which is about the size of the edge desks fight over. Know which convention your counterparty and your fair value vendor use.

Is 79 basis points an arbitrage?

On paper, a desk could buy the roughly 500 index stocks in the right weights ($340,000 of stock per ES contract at 6,800), borrow at SOFR, and sell the future at 6,825. At expiry it delivers nothing (the contract cash-settles) but its stock is worth the settlement value, so it captures the 5.65-point gap plus or minus how well its basket tracked the index.

Costs, using illustrative but realistic institutional numbers: 2 basis points each way to trade the basket ($136 on $340,000) and $2 round trip on the future. Total $138, or about 2.8 index points. That leaves $144.51 of profit per contract, about 4 basis points of the $340,000 notional for five weeks’ use of balance sheet. Small, but positive.

The catch is that almost nobody can actually borrow at SOFR against a stock basket on an unlimited basis. What the future really offers is an alternative to financing equities on a bank balance sheet, and balance sheet has a price. CME’s own research makes that concrete. In “Quantifying and Hedging Equity Financing Risk” (2025), CME compared the financing rate implied by quarterly E-mini rolls with three-month Term SOFR across ten rolls from December 2022 to March 2025:

Roll	ES roll implied rate	3-month Term SOFR	Premium
Dec 2022	4.95%	4.507%	0.45%
Dec 2023	5.99%	5.377%	0.62%
Dec 2024	5.77%	4.353%	1.42%
Mar 2025	4.94%	4.299%	0.64%
Average of 10 rolls	5.59%	4.97%	0.62%

Source: CME Group, “Quantifying and Hedging Equity Financing Risk,” Table 2. (The same paper’s Table 1 shows a slightly different December 2024 roll rate, 5.96%, which would put that quarter’s premium nearer 1.6%.) CME notes that “December 2024 funding pressures drove the convenience yield to levels not seen since the 2008 financial crisis.”

So a 79 basis point implied spread is not unusual. It is within the normal range of what CME measured, and it reflects a real cost. The spread widens at year-end, when banks shrink balance sheets for regulatory snapshots, and in stress.

CME also found that changes in the E-mini roll rate tracked changes in the box rate (the risk-free rate implied by S&P 500 option box spreads) with an 89% correlation, against 57% for Term SOFR. The box rate concept comes from Jules van Binsbergen and William Diamond of the Wharton School and Peter Van Tassel of the New York Fed (“Options for Calculating Risk-Free Rates,” Liberty Street Economics, October 2, 2023), who estimated that from January 1996 to April 2023 the box rate averaged 35 basis points above Treasury yields, peaking at roughly 130 basis points in October 2008. The lesson for an index desk: the right benchmark for the futures-implied rate is not the Treasury yield, but the rate at which equity investors can actually borrow, which is higher and moves with funding stress.

The financing spread as its own product

CME now lists a contract that trades this spread directly. Adjusted Interest Rate (AIR) S&P 500 Total Return futures are priced as the S&P 500 Total Return Index minus accrued financing (at SOFR or at EFFR, depending on the version) plus a “financing spread adjustment,” and they are quoted in basis points of that spread. A desk long the stocks and short AIR futures is effectively running a total return swap through a clearing house, and the price of the trade is the financing spread. CME’s 2025 paper shows AIR calendar spreads being used to hedge the roll premium on E-minis.

Long-run evidence

Academic work agrees that the implied rate is persistently different from market rates. Nicholas Gunther, Robert Anderson, Lisa Goldberg and Alex Papanicolaou (“The Implied Futures Financing Rate,” UC Berkeley CDAR working paper, February 2021) estimated the rate implied by S&P 500 futures from January 1996 to June 2019. They found it “often attractive relative to market rates on explicit financings,” but that “the relationship between the implicit and explicit financing rates was volatile and varied considerably based on legal and economic regimes,” with the Commodity Futures Modernization Act of 2000, the 2008 crisis and the recovery each shifting the spread.

Gold: the implied rate and the lease rate

Gold pays no dividend, but it can be lent. A holder who lends metal to a bank earns a lease rate, and that lease income plays the role dividends play for equities. COMEX gold futures (GC) cover 100 troy ounces (details in gold futures explained).

Worked example, illustrative prices:

Spot gold: $4,000.00 per ounce
Gold future 91 days out: $4,036.40
SOFR: 3.88%

Implied repo: (4,036.40 / 4,000.00 minus 1) x 360 / 91 = 3.60%.

That is 28 basis points below SOFR. In carry terms, the futures price is roughly:

F = S x [1 + (financing + storage minus lease rate) x t / 360]

so the 28 basis points measure the lease rate net of storage and insurance. If gold could not be lent at all, the future “should” sit at 4,000 x (1 + 0.0388 x 91/360) = $4,039.23, which is $283 per 100-ounce contract above the actual price.

Who can arbitrage that? Only someone who owns gold, can store it in a COMEX-approved vault in deliverable form, and can lend it. A bullion bank holding metal compares two ways to earn a return on it: sell spot and buy futures (earning cash at SOFR, giving up 3.60% implied), or lease the metal out. The futures price settles where those choices balance for the marginal holder. In stress, when physical metal is scarce in one location, the implied rate can move sharply, because the trade requires moving metal between vaults that are not interchangeable.

Treasury futures: gross basis, net basis and the implied repo rate

Treasury futures add one layer: the short can deliver any bond from a basket, adjusted by a conversion factor (CF). The mechanics of conversion factors and delivery are covered in Treasury futures and the cheapest to deliver. The arithmetic of carry is the same idea in bond clothing.

The definitions

Invoice price at delivery = futures price x CF + accrued interest at delivery.
Gross basis = bond clean price minus futures price x CF.
Carry = coupon income over the holding period minus the repo cost of financing the bond.
Net basis = gross basis minus carry. It is the price of the short’s delivery options (which bond, and when in the month).
Implied repo rate (IRR) = the financing rate at which buying the bond, selling the future and delivering exactly breaks even.

With a coupon paid during the holding period, the standard IRR formula is:

IRR = (invoice price + coupon minus purchase cost) / (purchase cost x d / 360 minus coupon x d2 / 360)

where purchase cost is the clean price plus accrued interest today, d is days to delivery, and d2 is days from the coupon to delivery.

Worked example

All bond and futures prices here are illustrative, and the conversion factor is assumed rather than taken from CME’s tables, so treat the numbers as a template.

Bond: 4.25% coupon, paying February 15 and August 15, clean price 99.50
Settlement November 12, 2026; delivery assumed March 31, 2027 (139 days)
Accrued interest today: 1.0279 (89 of 184 days in the period)
Coupon of 2.125 received February 15, 2027, 44 days before delivery
Accrued at delivery: 0.5166
Conversion factor: 0.8800 (assumed)
Futures price: 112.85
Repo rate: 3.88%

Step by step (computed in Python):

Invoice: 112.85 x 0.88 + 0.5166 = 99.8246
Purchase cost: 99.50 + 1.0279 = 100.5279
IRR: (99.8246 + 2.125 minus 100.5279) / (100.5279 x 139/360 minus 2.125 x 44/360) = 3.69%
Gross basis: 99.50 minus 112.85 x 0.88 = 0.192 points, or 6.14/32nds
Carry: coupon income of 1.6137 points minus financing of 1.5060 points = 0.1077 points, or 3.45/32nds
Net basis: 6.14 minus 3.45 = 2.70/32nds, about $84 per $100,000 face

The IRR of 3.69% is below the 3.88% repo rate. A trader who buys this bond in repo and sells futures would, if forced to deliver on the last day, earn less than the cost of financing. That is normal: the 2.70/32nds of net basis is what the market charges for the delivery options the short receives. When the IRR rises above repo (net basis turns negative), the futures are rich and cash-and-carry becomes a genuine arbitrage, which is the core of the hedge fund basis trade discussed in the Treasury basis trade.

To hedge $10 million face of this bond, a desk sells about 10,000,000 x 0.88 / 100,000 = 88 contracts, the conversion factor hedge ratio.

Why carry arbitrage is imperfect

Every version of the trade hits the same frictions, in different proportions.

Balance sheet is not free. Buying the asset puts it on a bank or fund balance sheet, where capital and leverage rules charge for it. The CME roll data shows that charge spiking into year-end 2024. Arbitrage capital is finite, and the spread is its price.
Inputs are forecasts. Index dividends to expiry are estimates; a surprise special dividend or a cut moves fair value. For gold, the lease rate is a private, dealer-quoted market. For bonds, the cheapest-to-deliver can switch as yields move.
The reverse trade is harder. If futures are cheap, the arbitrage requires selling or borrowing the asset. Stock borrow costs, bond “specialness” in repo, and the scarcity of lendable gold all make the reverse leg more expensive than the forward one. So the no-arbitrage band is asymmetric.
Futures are not forwards. Futures are marked to market every day (how futures margin works). A short future loses cash when the asset rallies, while the matching gain on the asset is unrealised and usually sits with a different lender. Gunther and co-authors note the dynamic hedging this forces, and the related convexity adjustment, as a reason the simple static formula does not hold exactly.
Settlement and tracking risk. Index futures settle to a Special Opening Quotation built from opening prints of each stock, not to a price a desk can be sure of trading at. A basket that does not exactly replicate the index adds tracking error.
Funding can vanish. Repo haircuts and prime brokerage terms can change overnight. A trade with a few basis points of edge cannot absorb a sudden rise in funding costs.

These frictions explain the patterns in the data. For index futures, the implied rate sits above funding benchmarks on average (62 basis points over Term SOFR in CME’s sample), because the future saves the buyer balance sheet. For Treasury futures, the implied repo rate usually sits below actual repo, by the value of the delivery options. In both markets the gap moves at quarter-ends and year-ends and blows out in crises (2008, March 2020). It is less an arbitrage than a market price for balance sheet and optionality.

What can go wrong for the arbitrageur

Margin calls before convergence. The trade is hedged on paper but not in cash. A sharp rally creates variation margin calls on the short future that must be paid the same day.
Spread widening. A desk that sold a future at a 79 basis point implied spread shows a loss if the spread widens to 150 basis points before expiry. It only gets the original spread if it can hold to the end.
Forced unwinds. When many funds run the same carry trade with borrowed money, a funding shock makes them all exit at once, which pushes the spread further against them. The Treasury market in March 2020 is the standard case.
Model and data errors. A wrong dividend estimate or the wrong conversion factor turns an apparent edge into a loss. At a 38-day tenor, a 1-point dividend error is worth 14 basis points of implied rate.

The short version

The cost-of-carry formula can be run in reverse: given the futures price, solve for the financing rate it implies. For our December 2026 E-mini example, the future at 6,825 implied 4.67% against SOFR at 3.88%, a 79 basis point spread that matches what CME has measured as the normal premium for equity financing. Gold futures imply a rate net of the lease rate, and Treasury futures imply a repo rate whose shortfall to actual repo is the price of the short’s delivery options. In each market, the gap between implied and actual rates is not a free lunch: it is the price of balance sheet, of uncertain inputs, of costly short selling, and of daily margin. This article explains the mechanism; it is not a recommendation to run the trade.