Hedging Strategies with Futures Contracts

Fundamental concepts of futures hedging

Futures hedging is based on the principle that losses in one market can be offset by gains in another. The effectiveness of a futures hedge depends on the correlation between spot and futures prices and the hedge ratio chosen.

The basic hedging equation can be expressed as:

$\text{Hedge Ratio} = \frac{\text{Futures Position Size}}{\text{Spot Position Size}} = \rho \frac{\sigma_s}{\sigma_f}$

Where:

• $\rho$ is the correlation coefficient between spot and futures prices
• $\sigma_s$ is the volatility of spot prices
• $\sigma_f$ is the volatility of futures prices

Long hedging vs short hedging

Long hedging

Long hedging involves buying futures contracts to protect against potential price increases. This strategy is typically used by:

• Manufacturers needing raw materials
• Food processors requiring agricultural commodities
• Portfolio managers planning future security purchases

Short hedging

Short hedging involves selling futures contracts to protect against potential price decreases. Common applications include:

• Commodity producers protecting future production
• Portfolio managers hedging existing positions
• Exporters managing foreign exchange risk

Cross-hedging considerations

Cross-hedging occurs when the asset being hedged differs from the underlying asset of the futures contract. The effectiveness depends on:

1. Correlation between the two assets
2. Relative price volatilities
3. Market liquidity of the futures contract

The optimal cross-hedge ratio can be calculated using:

$h^* = \frac{\text{Cov}(S,F)}{\text{Var}(F)}$

Where:

• $h^*$ is the optimal hedge ratio
• $S$ represents spot price changes
• $F$ represents futures price changes

Basis risk management

Basis risk refers to the potential for the spot-futures price relationship to change unexpectedly. The basis is defined as:

$\text{Basis} = \text{Spot Price} - \text{Futures Price}$

Key factors affecting basis risk include:

• Storage costs
• Interest rates
• Transportation costs
• Local supply and demand conditions

Rolling futures hedges

Rolling hedges involve replacing expiring futures contracts with new positions in longer-dated contracts. This strategy is crucial for:

1. Long-term hedging programs
2. Maintaining continuous protection
3. Managing contango and backwardation effects

The rolling cost can be calculated as:

$\text{Rolling Cost} = (F_2 - F_1) \times \text{Number of Contracts}$

Where:

• $F_1$ is the price of the expiring contract
• $F_2$ is the price of the new contract

Measuring hedge effectiveness

Hedge effectiveness can be evaluated using several metrics:

1. R-squared from regression analysis
2. Reduction in portfolio variance
3. Value at Risk (VaR) improvement

The variance reduction can be calculated as:

$\text{Variance Reduction} = 1 - \frac{\text{Var}(\text{Hedged Portfolio})}{\text{Var}(\text{Unhedged Portfolio})}$

Applications in portfolio management

Portfolio managers use futures hedging for:

1. Tactical asset allocation
2. Risk management
3. Portfolio rebalancing
4. Transition management

The strategy often involves implementing algorithmic portfolio rebalancing techniques to maintain optimal hedge ratios.

Dynamic hedging considerations

Dynamic hedging with futures requires:

1. Regular monitoring of hedge ratios
2. Adjustment for changes in correlation
3. Management of transaction costs
4. Consideration of market liquidity

The hedge ratio adjustment frequency depends on:

• Market volatility
• Transaction costs
• Risk tolerance
• Operational capabilities