The contract size can matter more than the formula
At an illustrative S&P 500 level of 7,500, one ES contract represents $375,000 of index exposure. MES represents $37,500, and NES represents $3,750. Those are 100-to-10-to-1 steps in hedge granularity.
The consequence is easy to miss. A mathematically correct target hedge can still be materially wrong after it is rounded to a whole contract. The smaller the portfolio or the smaller the intended hedge, the larger that implementation error can become.
1% worst-case error on a full hedge
ES needs about $18,750,000 of portfolio value before half a contract is only 1% of target notional.
Micro changes the scale by 10×
MES lowers the same 1% threshold to $1,875,000.
Nano changes it by another 10×
NES lowers the threshold again to $187,500.
Partial hedges are harder
A 50% hedge has half the target notional, so the same contract creates twice the relative rounding error. A 25% hedge creates four times the relative error.
The exact worst-case rounding formula
If contract notional is N and the intended hedge notional is H, rounding to the nearest whole contract can miss by at most half a contract. The worst-case relative sizing error is therefore 0.5 × N ÷ H.
This is a bound, not a prediction. Actual rounding error can be smaller or even zero when the target hedge happens to land on an exact contract multiple. The bound answers a different question: how bad can whole-contract granularity be before any beta error, basis risk, slippage, commissions, margin, taxes, or roll costs are considered?
Minimum portfolio size for a 1% worst-case sizing error
| Contract | 100% hedge | 50% hedge | 25% hedge |
|---|---|---|---|
| ES | $18,750,000 | $37,500,000 | $75,000,000 |
| MES | $1,875,000 | $3,750,000 | $7,500,000 |
| NES | $187,500 | $375,000 | $750,000 |
The partial-hedge columns are the important result. Contract granularity is not just a small-account issue. At this index level, even MES needs about $3,750,000 before the worst-case whole-contract error on a 50% hedge falls to 1% of the intended hedge notional.
What the rounding looks like in actual portfolios
These examples target a full beta-one hedge and round to the nearest whole contract. Positive error means the rounded hedge is larger than the target; negative error means it is smaller.
| Portfolio | ES error | MES error | NES error |
|---|---|---|---|
| $100,000 | 0 contracts · -100.0% | 3 contracts · 12.5% | 27 contracts · 1.3% |
| $250,000 | 1 contract · 50.0% | 7 contracts · 5.0% | 67 contracts · 0.5% |
| $500,000 | 1 contract · -25.0% | 13 contracts · -2.5% | 133 contracts · -0.3% |
| $1,000,000 | 3 contracts · 12.5% | 27 contracts · 1.3% | 267 contracts · 0.1% |
At $100,000, ES rounds to zero contracts and therefore provides no hedge under a nearest-contract rule. MES rounds to three contracts and overshoots the target by 12.5%. NES rounds to 27 contracts and overshoots by 1.25%. The hedge equation is identical; the implementable result is not.
What this analysis does not say
Smaller contracts are not automatically better trades. More contracts can mean more tickets, more bid/ask exposure, and different liquidity. This analysis isolates only whole-contract sizing granularity. It does not estimate whether a hedge should be entered, whether portfolio beta is measured correctly, or whether S&P 500 futures are the right benchmark.
The 7,500 index level is deliberately illustrative. CME uses the same level in its published ES/MES/NES comparison. As the index level changes, contract notionals and dollar thresholds change proportionally, while the 100:10:1 granularity relationship remains the same.
Methodology, data, and reuse
Analysis date: 2026-09-15. Contract multipliers come from CME Group: ES $50 per S&P 500 point, MES $5, and NES $0.50. We multiply each by an illustrative 7,500 index level, then solve the half-contract rounding bound for 1%, 2%, and 5% maximum error at 100%, 50%, and 25% hedge targets.
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