Derivatives: exposure without capital

Derivatives let a fund change its market exposure without buying the underlying assets. That breaks an assumption hidden in everything so far: that the money invested equals the exposure. An equity futures contract can give 10 million of market exposure for a margin deposit of well under a million.

Futures: Exchange-traded agreements to buy or sell at a set price on a future date. Gains and losses are settled daily through variation margin. Exposure is the notional: contracts × price × multiplier.
Forwards: Like futures, but private (over the counter) and usually settled at the end. FX forwards are the standard tool for currency hedging.
Swaps: Exchanges of cash flows: fixed for floating interest (interest rate swaps), an index's total return for a funding rate (total return swaps), or credit protection (credit default swaps). They start with a value near zero but can carry large exposure.
Options: The right, but not the obligation, to buy (call) or sell (put) at a strike price. Their value moves non-linearly with the underlying, which is measured by delta (sensitivity) and gamma (how fast delta changes).

Three rules for measuring performance with derivatives

Return is on the fund's capital, not the margin. The denominator is NAV. Futures gains are part of the fund's return; margin is just collateral held in cash.
Weights follow exposure, not market value. A future with a market value near zero can carry a 15% exposure. Attribution uses notional (or delta-adjusted) exposure, offset by a matching negative cash position so weights still add to 100%.
Leverage is exposure divided by capital. Gross leverage adds long and short exposure; net leverage nets them. Both drive risk reporting and regulatory limits.

Futures overlay

A 100 million equity fund over one quarter. Cash earns 4% a year (1% for the quarter).

Physical equities

Equity futures notional

Market return this quarter

Capital (where the money is)100%

Market exposure

Effective equity exposure

Fund return on NAV

Of which futures

Return on margin (don't report this)

Futures P&L ÷ 8% initial margin

Options: why delta isn't enough

An option's value curves as the underlying moves. Delta gives the straight-line estimate; gamma adds the curvature, exactly as convexity does for bonds. For attribution, option positions are usually expressed as delta-adjusted exposure (delta × underlying value), and the part delta can't explain is reported as gamma, vega (volatility) and theta (time decay) effects.

Option value vs the underlying

A six-month option on a share priced at 100 (Black-Scholes, 3% interest rate).

Option

Strike

Volatility

Move in the share price

Option valueDelta estimateDelta + gamma

Option price now

Delta

Gamma

Actual change in value

Delta estimate

Delta + gamma estimate

For practitionersFutures are usually modelled in attribution as a long exposure in the underlying plus a short position in cash (synthetic cash), so cash equitization shows up as allocation rather than a residual. Interest rate futures and swaps are mapped to key-rate exposures; CDS to spread exposure; total return swaps to the reference asset with a financing leg. Margin and collateral cash, and the interest on them, belong in the portfolio's cash return. OTC valuations need an independent source, and daily valuation matters because a derivative's P&L can be large relative to its market value. UCITS funds measure global exposure either with the commitment approach (converting derivatives to equivalent underlying exposure, capped at 100% of NAV) or with value at risk.

All numbers are illustrative. The models are simplified for teaching: annual coupons, Black-Scholes options, simplified fee mechanics and no intra-period trading. Real systems add transaction-based returns, daily valuation, tax and corporate action processing, and reconciliation to the official TWR.