Basis & fair value: why ES ≠ SPX

Tuesday 15 September 2026, 10:00 ET (21:00 ICT), ticker NQ. Two data feeds on our lab’s desk both said “NQ”: the futures feed showed 29,135.75 on the expiring September contract (NQU6, three days from expiry), while an options-level projection already mapped to the December contract (NQZ6) showed 29,366.04—same symbol label, same second, 230.29 points apart. Those 230 points were three months of net financing cost.

The same arithmetic is why ES never equals the S&P 500 index. This lesson shows how to compute the gap, why it shrinks to zero, and why it says nothing about direction.

Key terms

Spot (giá giao ngay): the price of the underlying now Definition. For ES that is the S&P 500 index (SPX); for NQ the Nasdaq-100 (NDX). An index is computed from stock prices; you cannot buy it directly.

Futures contract (hợp đồng tương lai): an agreement that settles in cash against the index on a fixed date, the expiry Definition. ES and NQ contracts expire on the third Friday of March (H), June (M), September (U) and December (Z).

Basis (chênh lệch cơ sở): futures minus spot, in points Definition.

Cost of carry (chi phí nắm giữ): the annual financing rate (lãi suất vốn, the interest rate on cash tied up in holding the stocks until expiry) minus the dividend yield (tỷ suất cổ tức năm, the annual dividends those stocks pay along the way) Definition.

Fair value (giá hợp lý): spot plus the cost of carry: the futures price at which nobody can lock in a riskless profit by buying one side and selling the other Definition.

Convergence (hội tụ): the basis shrinking to zero by expiry, when the contract settles to the index Definition.

Terms you need: Traders roll (chuyển kỳ hạn) to the next quarterly contract before the front one expires (MKT1.02); the new contract carries a full quarter of carry, so the basis jumps back up. A limit order (lệnh giới hạn) waits at a chosen price, rounded to the nearest tick (bước giá, 0.25 points on ES and NQ), and RTH (phiên chính) is the regular day session (M0.04).

Chart first: the gap has a timer

How it works

The formula in one line

Fair value ≈ spot × (1 + (r − d) × days ÷ 365) Definition

r is the yearly financing rate, d the yearly dividend yield (both as decimals), days the calendar days to expiry. The basis is spot × (r − d) × days ÷ 365. Desks use exact day counts and the dividend calendar; the simple form is within a point.

Financing pushes fair value up; dividends, which the futures holder never collects, push it down. With rates above the dividend yield, as now, fair value sits above spot: contango (bù hoãn mua).

Why ES stays near fair value

If ES traded far above fair value, an institutional desk could sell ES, buy the underlying stock basket and lock in the difference at expiry; far below, the reverse. This index arbitrage (kinh doanh chênh lệch chỉ số) is a textbook no-arbitrage mechanism Definition (Natenberg, Option Volatility and Pricing, forward and futures pricing chapter); how tightly ES and NQ track theoretical fair value intraday is not yet measured by our lab.

Convergence, then the jump

Each day the basis shrinks by about spot × (r − d) ÷ 365: about 0.52 points a day on SPX 6,800 with 2.8% net carry Definition. On expiry morning the contract settles to the index, so the basis is zero. The roll then hands you a contract with a full quarter of carry again.

NQ uses the same formula, but NDX companies pay much smaller dividends than the S&P 500, so the NQ basis is almost all interest and larger as a share of price Definition.

Proxies: QQQ and SPY are not NQ and ES

Many studies, including several of our lab’s, use QQQ or SPY (exchange-traded funds on NDX and SPX) because their history is free. Three things change on futures:

1. Close time. The stock market and the ETFs close at 16:00 ET (04:00 ICT next morning in winter). NQ keeps trading, and many futures charts, including our lab’s NQ studies, end the day session at 16:15 ET. The two “prior closes” are 15 minutes apart, so their gaps differ.
2. Two conversions. QQQ is a fund share whose ratio to NDX drifts with fees and dividends; NDX to NQ adds the carry.
3. The roll. An ETF never expires; a continuous futures chart switches contracts each quarter and can jump without a market move.

A QQQ result therefore carries the scope chip “Nasdaq index” (IDX), with NQ extrapolated. Our lab’s finding that small opening gaps fill more often than large ones on QQQ (2013–2026 in-sample: 0–0.25% gaps filled about 85% vs about 19% above 2%; out-of-sample 2025–2026 the >2% bucket filled 26.7% on n = 15, so the monotone size pattern held in sample; NQ by extrapolation) is one example MeasuredNasdaq index.

Myth / hypothesis: “ES is 47 points over SPX, so the market expects a rally” (or, below, “a drop”). Lore The premium is carry arithmetic that decays to zero by expiry whatever price does. Whether the small residual between futures and fair value predicts anything is not yet measured.

What the data says

Worked example: translate a level before you buy

Illustrative numbers: SPX 6,800.00, financing 4.0%, dividends 1.2%, 90 days to the ES expiry.

• Financing: 6,800 × 0.040 × 90 ÷ 365 = +67.07
• Dividends: 6,800 × 0.012 × 90 ÷ 365 = −20.12
• Basis: 46.95 points, so fair value = 6,846.95

ES trades at 6,849.25: 2.30 points rich to fair value, 0.03% of price. Noise, not a signal.

Now the use that matters. An options source publishes a level at SPX 6,780; your chart is ES. In ES points: 6,780 + 6,780 × 0.028 × 90 ÷ 365 = 6,826.81, so 6,826.75 to the nearest tick. A long limit at 6,780 on ES would sit 47 points below the level you meant: a different trade.

With SPX unchanged, the basis is 15.65 with 30 days left, 2.61 with five, zero at expiry. Redo the conversion every day, and again at the roll.

The mirror and the failure

The mirror. When dividends exceed financing, fair value sits below spot: backwardation (bù hoãn bán). When short-term interest rates sit below the S&P 500 dividend yield (as when US rates were near zero in 2020–2021), the formula puts ES fair value below SPX Definition. ES under SPX then reflects low interest rates relative to dividends, not bearish traders. The short side converts the same way: a short at SPX 6,850 is ES 6,850 + 47.29 = 6,897.25.

The failure. In September 2026 roll week, a level converted with December’s ratio and drawn on a September chart landed about 230 points from where it belonged. The same trap waits if your ATAS X chart and your TopstepX order ticket sit on different contract months. Check both before you trade (MKT1.02, PLAT2.02).

Do it on the platform

Prop-firm note. Evaluation accounts require you to roll to the new front-month contract on the firm’s schedule and never hold into expiry; the Prop Firm course (PROP2.05) covers contract-roll rules on dated rule cards.

Common mistakes

Common mistake: Reading the premium as a forecast. “ES is 40 over SPX, so buyers are in control” mistakes financing for opinion. Compute fair value first.

Common mistake: Treating a QQQ result as an NQ result. A QQQ gap-fill rate uses a 16:00 ET close, a fund share and no roll: evidence about the Nasdaq index, applied to NQ by extrapolation.

Drill: convert before you draw

Use SPX 6,800.00, financing 4.0%, dividends 1.2% (illustrative).

1. ES fair value with 90, 30 and 0 days to expiry?
2. SPX 6,750 in ES points with 90 days left, to the nearest 0.25?
3. In roll week, which three places do you check the contract month before trading that level?

What we don’t know yet

• How tightly ES and NQ track theoretical fair value second by second during RTH and ETH, and whether small residuals around fair value carry any short-horizon information: not yet measured by our lab.

Recap

• Fair value = spot + financing − dividends to expiry. ES sits above SPX by arithmetic, not by forecast.
• The basis shrinks every day, is zero at expiry and resets to a full quarter of carry at the roll.
• Convert index levels with your own contract’s basis on the same date, and make chart, order platform and data source show the same contract month.

Further reading

• Sheldon Natenberg, Option Volatility and Pricing, forward and futures pricing chapters: cost of carry, fair value and index arbitrage.
• CME Group contract specifications: E-mini S&P 500, E-mini Nasdaq-100. Check them on the day you rely on them.
• Our lab: the December 2026 NQ contract traded about 230 points above September, about 3.2% a year of net carry.
• Our lab: opening-gap fill rates on QQQ, 2013–2026, applied to NQ only by extrapolation.

Prerequisites and next

Read M0.02, M0.04 and M0.05 first. Next: M1.01 starts reading the auction: once you know which numbers are only arithmetic, the rest are about buyers and sellers. MKT1.02 goes deeper into the roll.

Educational content only. Not financial advice. Futures trading involves substantial risk of loss. Not affiliated with Topstep; firm rules change; check the Topstep help center.