Introduction

This Chapter focuses on the practical aspect of hedging and how to determine the optimal number of futures contracts required to hedge a given exposure effectively. A proper understanding of this concept is crucial for risk management and protecting against adverse price movements. Additionally, we will explore the “tailing the hedge” adjustment, which allows for fine-tuning the hedge as market conditions change. Let’s dive into the details.

Optimal Number of Futures Contracts for Hedging

To determine the optimal number of futures contracts for hedging, we need to consider the size of the exposure we want to hedge and the contract size of the futures contracts. The hedge ratio, which represents the proportion of the exposure to be hedged with futures, is calculated using the formula:

$$ \text{Hedge Ratio = } \dfrac{\text{Exposure Size}}{\text{Contract Size} \times \text{Futures Price}}$$

The exposure size refers to the value of the asset or portfolio we want to protect from price fluctuations, while the contract size is the size of a single futures contract. The futures price is the prevailing market price of the futures contract.

Example: Suppose a corn farmer wants to hedge 10,000 bushels of corn with corn futures contracts, where each futures contract represents 5,000 bushels of corn. The current futures price is USD 4.50 per bushel. The hedge ratio can be calculated as follows:

$$ \text{Hedge Ratio = } \dfrac{\text{10,000 bushels}}{\text{5,000 bushels/contract} \times \text{USD 4.50/bushel}} \text{ = 0.4444}$$

The farmer would need to use 0.4444 (approximately 44.44%) of a futures contract to hedge 10,000 bushels of corn.

“Tailing the Hedge” Adjustment

Market conditions can change over time, and the initial hedge ratio may need adjustment to maintain an effective hedge. The “tailing the hedge” adjustment involves periodically rebalancing the hedge ratio to reflect the changing exposure or market dynamics.

Example: Let’s assume the corn farmer from the previous example observes that the price of corn has increased significantly since establishing the initial hedge. As a result, the farmer may decide to increase the hedge ratio to strengthen the hedge. Suppose the farmer adjusts the hedge ratio to 0.5, meaning 50% of a futures contract is used to hedge the exposure. This adjustment ensures that the hedge aligns with the current market conditions and provides better protection against price fluctuations.