The Implied Repo Rate and Net Basis

A Treasury futures contract does not settle in cash — the short delivers an actual bond, chosen from a basket of eligible issues, and gets paid a price set by the futures price times that bond's conversion factor. Whichever bond is cheapest to buy and deliver against the shrinking futures obligation is the cheapest-to-deliver (CTD), and the trade of buying that bond, financing it in repo, and holding it to deliver into the future is a synthetic loan called the cash-and-carry. The return that loan earns, worked backwards from today's prices, is the implied repo rate — and comparing it to the real overnight repo rate is how a basis trader decides whether the future is rich or cheap.

The invoice price and the basis

At delivery, the short receives the invoice price: futures price times the CTD bond's conversion factor, plus accrued interest. The gap between the CTD bond's actual cash price and this invoice price is the gross basis:

$$\text{gross basis} = P_{\text{cash}} - (F \times CF)$$

Worked example: pricing the cash-and-carry

The CTD bond trades at a cash price of 99-16 (99.50 in decimal), with a conversion factor of 0.9200 against the contract. The futures price is 108-00 (108.00).

Invoice price. $F \times CF = 108.00 \times 0.9200 = 99.36$.

Gross basis. $99.50 - 99.36 = 0.14$, or 14 ticks (32nds) roughly — the cash bond is priced 0.14 points above what the futures market will pay for it at delivery.

Financing the position. Suppose the trade is held 30 days, the bond pays a semiannual coupon that accrues $0.38 over the period, and the trader funds the $99.50 purchase in repo at the going rate.

$$\text{implied repo rate} = \left(\frac{\text{invoice price} + \text{coupon income} - \text{cash price}}{\text{cash price}}\right) \times \frac{360}{30}$$ $$= \left(\frac{99.36 + 0.38 - 99.50}{99.50}\right) \times 12 = \left(\frac{0.24}{99.50}\right) \times 12 \approx 2.90\%$$

If the trader can actually borrow overnight repo at, say, 4.30% to fund the bond purchase, the cash-and-carry earns only 2.90% against a 4.30% funding cost — a losing trade, so nobody actually delivers this way; the basis stays "too rich" for cash-and-carry to arbitrage away, usually because the short optionality embedded in the contract (choice of CTD, timing of delivery) is worth something on its own.

Net basis: subtracting out the optionality

The gross basis mixes together a pure carry cost and the value of the delivery options the short holds (which bond to deliver, and roughly when). Subtracting the cost of carry (financing minus coupon income, converted to price terms) from the gross basis isolates the net basis, which approximates the market value of those delivery options:

$$\text{net basis} = \text{gross basis} - \text{cost of carry}$$

A net basis persistently above zero says the delivery options are being priced richly relative to a no-arbitrage benchmark; a basis trader sells the bond and buys the future (a "short the basis" trade) expecting that gap to narrow toward expiry, when the optionality value decays to nothing.

implied repo (2.90%) vs actual repo (4.30%) → carry trade unprofitable

Where it shows up

Basis trading desks live in the gap between implied repo and actual funding rates, and the CTD identity itself is a live risk: as yields rise, a different, longer-duration bond can become cheapest to deliver, changing a hedger's effective duration overnight. The same cash-and-carry logic — buy the asset, finance it, deliver into the future, compare the earned rate to funding cost — underlies basis trades in equity index futures, commodities, and crypto perpetuals alike.

Key terms

• Conversion factor — the price adjustment that equates a deliverable bond's yield to the contract's notional coupon.
• Cheapest-to-deliver (CTD) — the eligible bond that is cheapest to buy and deliver against a short futures position.
• Gross basis — cash price of the CTD minus the invoice price implied by the futures.
• Implied repo rate — the annualized return of the cash-and-carry trade, computed from today's cash and futures prices.
• Net basis — gross basis minus the cost of carry; approximates the value of the short's delivery options.