6. Futures

Algo-wide warnings.

1. Continuous contracts are stitched from expiring contracts — the adjustment method (back/ratio/none) changes your P&L and can make prices negative. Know your vendor's method; for return calcs prefer ratio-adjusted or compute per-contract.
2. Daily mark-to-market: futures settle P&L every day to margin — not buy-and-hold like stocks. Model cash flows and margin, not just entry/exit.
3. Notional ≠ margin. A contract controls large notional on small margin → high leverage. Size on notional, not margin.
4. Roll dates create gaps; trade volume migrates to the next contract before expiry.

Contract Mechanics

Contract Specs

Def. Standardized terms: underlying, size/multiplier, tick, expiry, delivery. Formula. $\text{Notional}=\text{Price}\times \text{Multiplier}$. E.g. ES (E-mini S&P) multiplier = $50/point; CL (crude) = 1,000 bbl. Signal. Determines $ per tick and capital at risk. Algo. Hard-code multiplier & tick value per symbol; a wrong multiplier silently scales all P&L. $\text{Tick value}=\text{tick size}\times \text{multiplier}$.

Initial vs Maintenance Margin

Def. Initial = to open; maintenance = floor before a margin call. Formula. Set by exchange (SPAN/portfolio margining). $\text{Leverage}=\frac{\text{Notional}}{\text{Margin}}$. Signal. Low margin → high leverage → amplified P&L and ruin risk. Algo. Model margin calls: if equity < maintenance, forced liquidation. Backtests that ignore this overstate survivability.

Mark-to-Market / Daily Settlement

Def. Gains/losses credited/debited to margin daily at the settlement price. Formula. $\text{Daily P\&L}=({\text{Settle}}_t-{\text{Settle}}_{t-1})\times \text{Multiplier}\times \text{Contracts}$. Signal. No unrealized-until-close; cash moves daily. Algo. Compute returns from daily settle changes; reinvestment/compounding differs from buy-and-hold equities.

Expiry & Settlement (cash vs physical)

Def. Cash-settled (index, e.g. ES) pays the difference; physically-settled (crude, grains) delivers the commodity. Signal. Physical delivery risk if you hold into delivery (the WTI-negative-2020 trap). Algo. Always roll or close before First Notice Day / Last Trade Day for physically-settled contracts in a live system.

Pricing & Basis

Fair Value / Cost of Carry

Def. No-arbitrage futures price from spot + carry. Formula. $F=S\times e^{(r+\text{storage}-\text{yield})\cdot T}$. For index futures: $F=S\cdot e^{(r-q)\cdot T}$ (q = dividend yield). Signal. Futures rich/cheap vs fair value → index-arb / basis trade signal. Algo. Equity-index fair value drives program trading; needs accurate dividend & rate inputs.

Basis

Def. Difference between futures and spot. Formula. $\text{Basis}=F-S$ (sometimes $S-F$ in ag markets — check convention). Signal. Converges to 0 at expiry. Basis trades exploit deviations from carry. Algo. Sign convention varies by market — verify before coding a basis strategy.

Implied Repo Rate

Def. Return implied by buying spot & selling the future (cash-and-carry). Formula. Back out $r$ from $F=S\cdot e^{rT}$. Signal. Compare to actual financing rate → cash-and-carry arb signal. Algo. Key in bond futures (cheapest-to-deliver dynamics).

Convergence

Def. Futures price converges to spot as expiry approaches. Formula. $F(T,T)=S(T)$, basis → 0. Signal. The mechanism guaranteeing basis trades resolve. Algo. Drives roll yield; the curve's slope determines whether rolling helps or hurts (see commodities §3).

Curve & Spreads

Calendar / Inter-month Spread

Def. Long one expiry, short another of the same future. Formula. $\text{Spread}=F(T_1)-F(T_2)$. Signal. Trades curve shape (contango/backwardation), lower outright directional risk. Algo. Margin offset makes spreads capital-efficient; build a clean spread series carefully across rolls.

Inter-commodity / Inter-market Spread

Def. Spread between related futures (e.g. crack, crush, ES vs NQ, bond curve trades). Formula. Ratio-weighted leg combination. Signal. Relative-value plays; lower vol than outrights. Algo. Normalize by multiplier/notional so legs are balanced (dollar-neutral, not contract-neutral).

Roll & Roll Yield

Def. Closing the expiring contract and opening the next; roll yield = return from curve shape. Formula. $\text{Roll Yield}\approx \frac{F_{\text{near}}-F_{\text{far}}}{F_{\text{far}}}$. Negative in contango, positive in backwardation. Signal. Dominates long-term futures returns (see §3 commodities). Algo. Choose a roll rule (e.g. N days before expiry, or volume/OI crossover) and apply it consistently; the rule materially affects backtest results.

Key Futures Markets (quick reference)

Algo: micros (MES/MNQ) let strategies size finely and cut leverage — prefer them for small-account or fractional sizing.

Stock Index vs VIX Futures

Equity Index Futures

Def. Cash-settled futures on an index (ES, NQ). Signal. Trade 23h/day → react to overnight news before cash open; basis to cash = sentiment/funding. Algo. Use for overnight gap modeling and as the hedge instrument for equity portfolios.

VIX Futures

Def. Futures on the forward 30-day implied vol of SPX. Signal. Curve usually in contango (term structure of vol) → long VIX ETPs (VXX) bleed via roll. Algo. Short-vol / roll-harvest strategies are profitable in calm regimes but have catastrophic left tails (Feb 2018 "Volmageddon") — size for the tail, not the average.