Futures Basis and Cost of Carry Models

Understanding futures basis

The futures basis is defined as the difference between the futures price and the spot price of an underlying asset:

$\text{Basis} = F(t,T) - S(t)$

Where:

• $F(t,T)$ is the futures price at time $t$ for delivery at time $T$
• $S(t)$ is the spot price at time $t$

The basis can be positive (contango) or negative (backwardation), reflecting market expectations and carrying costs.

Cost of carry model fundamentals

The cost of carry model establishes the theoretical relationship between spot and futures prices based on arbitrage principles. The basic formula is:

$F(t,T) = S(t) \cdot e^{(r+c-y)(T-t)}$

Where:

• $r$ is the risk-free interest rate
• $c$ is the storage/carrying cost rate
• $y$ is the convenience yield or income rate
• $(T-t)$ is the time to maturity

This model is fundamental for arbitrage-free pricing and forms the basis for futures trading strategies.

Components of carrying costs

Storage costs

Physical commodities incur storage costs including:

• Warehouse fees
• Insurance
• Transportation
• Quality degradation

Financing costs

The cost of funding the spot position:

• Interest on borrowed funds
• Opportunity cost of capital
• Margin requirements

Income/convenience yield

Benefits from holding the physical asset:

• Dividend payments for stocks
• Interest payments for bonds
• Convenience yield for commodities

Applications in trading

Arbitrage opportunities

When futures prices deviate from cost of carry relationships, arbitrage opportunities may exist:

Hedging considerations

The basis affects hedging decisions through:

• Hedge ratio calculations
• Roll yield management
• Basis risk assessment

Market implications

Price discovery

The basis provides information about:

• Market expectations
• Supply and demand conditions
• Storage capacity constraints

Market conditions

Different basis states indicate:

• Contango and Backwardation
• Storage availability
• Market stress

Time series considerations

The basis exhibits important temporal properties:

• Mean reversion tendencies
• Seasonal patterns
• Convergence to zero at expiration

These patterns are crucial for:

• Statistical arbitrage strategies
• Risk management models
• Trading system design

Risk factors

Key risks in basis trading include:

• Basis risk
• Storage cost uncertainty
• Interest rate fluctuations
• Market liquidity risk
• Operational risks

Understanding these risks is essential for:

• Position sizing
• Risk limits
• Performance attribution

Real-world applications

Energy markets

• Natural gas storage trades
• Oil contango plays
• Power generation spreads

Agricultural markets

• Grain storage strategies
• Seasonal basis patterns
• Quality premiums/discounts

Financial futures

• Index arbitrage
• Fixed income basis trading
• Currency basis strategies