A delta-one product gives approximately proportional, two-sided exposure to the price of an underlying asset or reference basket, without the changing payoff slope characteristic of a vanilla option. For a quant, the useful distinction is linear market exposure versus optionality: a position can have little spot curvature while still carrying substantial funding, dividend, liquidity and counterparty risk.
The name comes from delta, the sensitivity of value to the underlying price. Société Générale's market glossary includes forwards, futures and equity swaps in this family. “One” describes a normalised exposure convention; it does not mean that every contract, every position or every spot-delta calculation equals exactly one.
Start with the shares, then count the money
Consider a fictional long forward contract on 100 shares, with delivery price USD 100 per share. The initial stock price is also 100. Assume zero interest, zero dividends, no fees and full contractual performance. The forward starts with zero value. Its terminal economic payoff is
where is the number of shares and and are measured in USD per share.
| Terminal share price | Long-forward payoff |
|---|---|
| USD 95/share | −USD 500 |
| USD 100/share | USD 0 |
| USD 105/share | +USD 500 |
At 105, the payoff is . Cash settlement would exchange the net amount. Physical delivery would instead exchange USD 10,000 for shares worth USD 10,500; the USD 500 is the difference in economic value, rather than an additional payment alongside the shares.
With the same zero-carry assumptions, the value before expiry is , so
The position delta has units of shares, equivalently USD of value change per USD/share spot change. The per-share forward value has delta 1. A USD 1/share rise adds USD 100 to this position; a USD 1/share fall subtracts USD 100. Shorting the forward reverses those signs. Gamma is zero here because the slope does not change with spot. The payoff is an affine straight line, not a line that must pass through the origin.
Original fictional comparison with zero rates, dividends and costs. The stock P&L and forward payoff share the same slope, but their initial cash commitments differ. Collateral is separate from contract value.
Buying 100 fully paid shares at 100 would also produce USD 500 of price profit at 105, on an initial purchase cost of USD 10,000: a 5% price return. Dividing the forward's USD 500 by its zero initial contract value does not produce a meaningful return. A return on posted margin, allocated capital or notional uses a different denominator. Leverage depends on that financing and capital structure, not on the word “one”.
A family of exposures, several cash-flow arrangements
Matching the share exposure is only the first step when comparing ways to implement a trade.
| Instrument | What carries the exposure? | What must be specified separately? |
|---|---|---|
| Fully paid cash stock | Ownership of shares; price changes affect their market value | Upfront purchase cost, dividends, custody and any external financing |
| Forward | A future purchase or net price difference at an agreed delivery price | Maturity, delivery or cash settlement, embedded carry, collateral and bilateral credit terms |
| Exchange-traded future | Changes in a futures quote, scaled by the contract multiplier | Daily settlement, margin liquidity, expiry, rolling and the relationship between futures and spot prices |
| Equity swap or share CFD | Contractual cash flows referencing an equity's performance | Price versus total return, financing leg or charges, dividend adjustments, reset dates and counterparty terms |
A total-return equity swap can exchange share-price performance plus specified dividends against financing payments. A price-return arrangement need not include those dividends. As a concrete exchange example, ICE's FTSE 100 total-return futures FAQ describes index performance and gross distributions against SONIA-based funding plus a spread, with daily variation margin. Those particular terms are evidence of why the cash-flow definition matters; they are not a template for every equity swap or future.
For a share CFD, the contract captures the opening-to-closing price difference without conferring ownership of the underlying shares. Financing charges, fees and dividend adjustments affect the cash result. Singapore's MoneySense guide explains these mechanics and provider counterparty risk. The precise financing basis, adjustment rules and legal protections depend on the agreement and jurisdiction.
Why an actual spot delta can differ from one
For a clean forward on an investment asset with a constant continuous dividend yield , constant continuously compounded rate and remaining time in years, the frictionless carry model gives
Holding , , , and fixed when differentiating,
With a 2% annual continuous yield and half a year remaining, the per-share spot delta is , rather than exactly 1. It is still constant in spot in this model. The discounted dividend-yield term changes the slope; it does not introduce option-like curvature.
These are forward present-value sensitivities. A futures contract's daily cash settlement is calculated from changes in its own quote and its multiplier. That is a different object from differentiating a forward's present value with respect to spot. CME's carry explanation connects equity-index futures pricing to spot, financing and dividends, while recognising that market prices can depart from theoretical fair value. Discrete dividends, stochastic financing, contract resets and credit or funding adjustments require the corresponding valuation model; the formula above does not cover every member of the family.
Zero gamma leaves other risks in place
A linear equity position still loses value when the market moves against it. Margin calls can require cash before a favourable eventual outcome, and a forced closeout can prevent the position being held to its intended horizon. Bilateral payment promises depend on the counterparty; central clearing changes that structure and introduces its own margin and default-management arrangements. A hedge using a related index or a different expiry can retain basis risk.
Nor does an option become a delta-one product merely because its current delta is close to one: its slope can change as market conditions change. Conversely, optional instruments can be combined to create a linear payoff, as in put–call parity. Classify the exposure produced by the whole contract or portfolio, then inspect its cash flows and risks.
For a worked introduction to the commitment, carry relation and daily settlement distinction, read SelfMadeQuant's Forwards and Futures. The full lesson is available with a free signed-in account.
Sources
- Société Générale: Delta One, “What is a Delta One product?” and “Delta One trading desks”: market terminology, examples and linear replication. This article makes the normalisation and spot-delta qualifications explicit.
- John C. Hull, Options, Futures, and Other Derivatives, 9th Global Edition, §§5.6–5.8: continuous-yield forward pricing, existing-contract value and forward versus futures cash-flow timing. The calculations and figure here are original.
- CME Group: Calculating Fair Value: financing and dividends in index-futures carry. CME's displayed example uses its own simple-interest convention; the equation above uses continuous compounding.
- ICE: FTSE 100 Index Total Return Futures FAQ, 2026, questions 1–2 and 9: a specific total-return structure, financing, distributions, contract units and daily variation margin.
- MoneySense: Understanding contracts for difference, article updated 2 July 2026, “How CFDs work,” “Costs of trading CFDs” and “Your rights in corporate actions”: price differences, charges, ownership and contract adjustments. Its jurisdiction-specific rules are not asserted as universal rules here.