Futures Contracts

Overview

Futures are standardized contracts to buy or sell an underlying asset at a predetermined price on a specified future date. They are exchange-traded, centrally cleared, and marked-to-market daily.

Difficulty intermediate

Contract Specifications

Key Components

1. Underlying Asset: Commodity, index, currency, interest rate
2. Contract Size: Fixed quantity per contract
3. Delivery Month: When settlement occurs
4. Tick Size: Minimum price movement
5. Tick Value: Dollar value per tick
6. Last Trading Day: When trading stops
7. Delivery/Settlement: Physical or cash

Example: E-mini S&P 500 (ES)

Underlying: S&P 500 Index
Contract Multiplier: $50 per index point
Tick Size: 0.25 index points
Tick Value: $12.50
Trading Hours: Nearly 24 hours (CME Globex)
Settlement: Cash

Pricing

Fair Value

F = S × e^{(r - q)T}

Where:
F = Futures price
S = Spot price
r = Risk-free rate
q = Dividend yield (or convenience yield for commodities)
T = Time to maturity

For commodities with storage costs:
F = S × e^{(r + u - y)T}

Where:
u = Storage cost (as % of spot)
y = Convenience yield

where: F futures price · S spot · r risk-free rate · q dividend or convenience yield · T time to maturity (years) · u storage cost · y convenience yield. does: the no-arbitrage cost-of-carry price — finance the spot at r, lose the carry yield q (or pay storage u net of convenience y). If market F deviates from this, cash-and-carry / reverse-cash-and-carry arbitrage closes the gap. Foundation for contango (positive net carry) vs backwardation (negative net carry).

Cost of Carry Model

F = S + Cost of Carry

Cost of Carry = Financing + Storage - Income

Contango: F > S (upward-sloping forward curve)
Backwardation: F < S (downward-sloping forward curve)

where: F futures price · S spot · Financing cost to borrow capital to buy spot · Storage warehousing/insurance for physical commodities · Income dividends, coupons, or convenience yield from holding spot. does: linear (simple-interest) restatement of the cost-of-carry identity. Contango (positive net carry) is the normal state for financials and well-supplied commodities; backwardation signals scarcity, hedging demand, or high convenience yield (typical in oil shortages). Roll yield direction follows directly from the sign.

Margin and Leverage

Margin Types

Initial Margin: Deposit required to open position
Maintenance Margin: Minimum equity to keep position open
Variation Margin: Daily P&L settlement (mark-to-market)

Example:
ES Initial Margin: ~$12,000 (varies)
Contract Value: 5000 × $50 = $250,000
Effective Leverage: 250,000 / 12,000 ≈ 21x

Daily Settlement

Day 1: Buy ES at 5000
Day 2: ES settles at 5010
P&L = (5010 - 5000) × $50 = $500 credited to account

Day 3: ES settles at 4995
P&L = (4995 - 5010) × $50 = -$750 debited from account

Trading Strategies

1. Directional Trading

Long Futures: Bullish on underlying
Short Futures: Bearish on underlying

P&L = (Exit Price - Entry Price) × Multiplier

where: Exit Price and Entry Price quoted in index/contract units · Multiplier dollar value per point set by exchange (e.g. $50 for ES). does: linear directional payoff. Symmetric — gain and loss scale 1:1 with the underlying move times the multiplier. Used for clean directional bets, hedge ratios on index portfolios, and macro overlays.

2. Calendar Spread

Buy near-month futures
Sell far-month futures

Profit from changes in term structure (contango/backwardation)
Lower margin than outright position

3. Cash-and-Carry Arbitrage

When F > S × e^{(r-q)T}:
- Buy spot
- Sell futures
- Hold to delivery
- Earn riskless profit = F - S × e^{(r-q)T}

where: F market futures price · S × e^{(r-q)T} theoretical fair value from cost-of-carry · profit = the basis mispricing. does: classic textbook arb that enforces the fair-value formula. Funding desks and prop shops scan the calendar curve continuously; in liquid index futures the gap usually closes inside the bid-ask. Reverse arb (F < fair value) requires the ability to short spot, so it appears less often in markets with borrow constraints.

4. Hedging

Producer hedging (short hedge):
- Oil producer sells oil futures
- Locks in selling price

Consumer hedging (long hedge):
- Airline buys oil futures
- Locks in buying price

Major Futures Exchanges

Exchange	Key Products
CME Group	Equity index, interest rates, commodities
ICE	Energy, soft commodities, financials
Eurex	European equity indices, bonds
DCE/CZCE/SHFE	Chinese commodities, metals
MCX	Indian commodities
SGX	Asian equity indices, FX

Roll Yield

When rolling futures contracts:

Roll Yield = (New Contract Price - Old Contract Price) / Old Contract Price

In Contango (upward curve): Negative roll yield
In Backwardation (downward curve): Positive roll yield

This is a key consideration for long-term commodity exposure.

where: New Contract Price price of the deferred contract being rolled into · Old Contract Price price of the expiring contract being closed. does: measures the structural drag (or boost) a holder pays/earns just from rolling exposure forward. Dominant return driver for long-only commodity index funds (e.g. GSCI, BCOM) — explains why long-dated commodity exposure can underperform spot in persistent contango (the "negative carry" problem) and outperform in backwardation.

Risk Considerations

1. Leverage Risk: Small moves can wipe out margin
2. Mark-to-Market Risk: Daily settlement can trigger margin calls
3. Liquidity Risk: Far-month contracts may be illiquid
4. Delivery Risk: Physical delivery if not closed before last trading day
5. Gap Risk: Overnight moves can exceed margin

Checklist

• [ ] Understand contract specifications (size, tick, multiplier)
• [ ] Know margin requirements and maintenance levels
• [ ] Identify expiration/last trading date
• [ ] Understand settlement type (physical vs. cash)
• [ ] Check contract liquidity (open interest, volume)
• [ ] Monitor roll schedule if holding long-term
• [ ] Understand tax treatment (60/40 rule in US for Section 1256)

References

1. Hull, J.C. (2022). Options, Futures, and Other Derivatives (11th ed.). Pearson.
2. CME Group. (2023). "Futures Fundamentals." CME Group Education.
3. Erb, C. & Harvey, C.R. (2006). "The Tactical and Strategic Value of Commodity Futures." Financial Analysts Journal, 62(2), 69-97.