Understanding the Futures Pricing Formula

In futures trading, there are distinct categories of traders, some referred to as intuitive traders who base their decisions on gut instincts. Achieving success in trading demands a combination of skills, expertise, and experience to transform your trading activities into profitable ventures. Nonetheless, gaining a solid grasp of the futures pricing formula is crucial when entering the realm of futures trading.

What Is the Futures Pricing Formula?

The synchronised fluctuations in the cost of the underlying asset determine the future price. When the cost of the underlying asset rises, the future price also increases, and conversely, if the cost of the underlying asset decreases, the future price drops as well.

It's important to note that the future price is not necessarily equal to the current value of the underlying asset. These two entities can be traded at distinct prices in the market, reflecting various factors and market dynamics.

The formula for computing futures prices can be expressed as:

Futures Prices = Spot Price * [1 + (RF * (X/365) - D)], where:

The risk-free return rate, RF, signifies the rate you can earn throughout the year in a perfect market. A risk-free rate typically relies on the interest rate for a Treasury Bill, which is usually quoted per annum.

Therefore, it necessitates proportional adjustment for the number of days until expiry. The rationale for adjusting risk-free interest returns is to assess the minimum return that would have been earned if the investment had been made on the futures date. In this way, it represents the opportunity cost of investing in security in the present instead of the future. The futures price, in turn, accounts for the time value of money.

The number of days until expiry refers to X. As the formula suggests, the futures price directly correlates with X. If the number of days to expiry increases, the futures price also increases.

The company pays dividends (D) until expiry. The company does not pay the dividend to the holder of a futures contract; it only pays it to the shareholders on the record date. Even though the holder does not receive the dividend, the declaration of a dividend affects the price of the securities and, consequently, the futures price. After the company pays the dividend, the spot price usually goes down by the amount of the dividend paid. This shows that new shareholders do not qualify for the dividend payment. Therefore, it is crucial to make dividend adjustments to the futures price.

Futures Pricing Illustration

Let’s assume the spot price of a stock is ₹1,000, the risk-free rate is 6% per annum, the contract expires in 60 days (X = 60), and there are no dividends (D = 0).

Using the formula:

Futures Price = 1,000 × [1 + (0.06 × 60/365)]

= 1,000 × [1 + 0.00986]

= ₹1,009.86

This means the futures contract should ideally trade at ₹1,009.86. The slight premium over the spot price reflects the cost of carry—essentially, the opportunity cost of capital for holding the asset until expiry.

Important Things to Keep in Mind While Analysing Future Prices

Some important things to keep in mind when conducting such analysis are:

• Underlying Asset: Understand the underlying asset that the futures contract represents. Different assets, such as commodities, financial instruments, or stock market indices, have unique drivers and price behaviours.
  

• Spot Price: The current spot price of the underlying asset is a critical reference point. Changes often influence futures prices in the spot price, so monitor it closely.
  

• Expiration Date: Be aware of the contract's expiration date. Futures prices can vary depending on how close or far the contract is from expiration. Understanding this relationship is essential for timely trading decisions.
  

• Costs and Carry: Consider the cost of carry, which includes expenses like storage, insurance, and financing costs. These costs can impact the futures price, especially for physical commodities.
  

• Interest Rates: Keep an eye on prevailing interest rates. Changes in interest rates can affect futures prices, particularly for financial futures contracts.
  

• Supply and Demand: Factor in the supply and demand dynamics for the underlying asset. Factors like production, consumption, geopolitical events, and weather conditions can influence prices.
  

• Market Sentiment: Sentiment plays a significant role in futures markets. Stay informed about news that can affect market sentiment, as it can lead to rapid price movements.
  

• Volatility: Futures markets can be volatile. Understand the asset's historical and implied volatility levels to gauge potential price swings.
  

Importance of Understanding Futures Pricing Formula

Comprehending the futures pricing formula is crucial for several reasons:

• Risk Management: Traders and investors use futures contracts to guard against price fluctuations in the underlying asset. Understanding how futures prices are determined helps in managing and mitigating risk effectively.
  

• Speculation: Speculators aim to profit from price movements in futures contracts. By understanding the pricing formula, they can make informed trading decisions and potentially capitalize on market opportunities.
  

• Arbitrage: Knowledge of futures pricing allows arbitrageurs to identify and exploit price discrepancies between the futures market and the underlying asset, thereby earning risk-free profits.
  

Some Essential Definitions Related to Pricing Futures Contract

Some crucial definitions related to pricing futures contract are as follows:

• Clearing House
  

In an active market, an exchange called a clearinghouse facilitates futures trading. In India, the National Stock Exchange Limited (NSE) engages in futures trading through the future index.

• Buying vs Selling Futures Contract
  

Futures contracts represent legal and standardized agreements. Typically, the buyer holds a long position while the seller takes a short position.

• Margin Requirement
  

Margin refers to the total amount deposited by the parties in the clearinghouse. It serves as a guarantee that all parties will fulfil their contractual obligations. At the outset of a trade, both parties must deposit a margin. If the initial margin significantly drops below the maintenance amount due to market fluctuations, the party in question will receive a margin call.

• Marking to Market
  

Marking to market is a daily settlement process for future prices. The fluctuations in future prices result from active trading. Following each trading session, clearinghouses credit or debit the margin amount from the differential amount deposited by the parties to account for price differences.

Different Futures Pricing Models

1. Cost of Carry Model

This is the most widely used model. It assumes the futures price equals the spot price plus the cost of carrying the asset until the contract's expiration. The cost of carry includes interest (opportunity cost), storage, insurance, and other related expenses.

2. Expectations Model

This model assumes that the futures price reflects the expected future spot price. If investors believe that the price of the underlying asset will rise, futures will trade at a premium. This model works well in perfectly efficient markets without arbitrage opportunities.

3. Normal Backwardation and Contango

These are concepts within futures pricing. In contango, futures prices are higher than the expected future spot price, usually due to high carry costs. In normal backwardation, futures prices are lower, often due to hedgers transferring risk to speculators.

4. Arbitrage Pricing Theory

This approach assumes that any difference between futures and theoretical prices will be eliminated by arbitrage. Traders exploit mispricing until the futures price realigns with its fair value.

Each model provides unique insights based on assumptions and market conditions.

Summing Up

Based on the cost-of-carry model, the futures pricing formula is a fundamental concept for anyone involved in futures trading or investing. It considers factors like the spot price, interest rates, time to expiration, and the cost of carrying the asset. By grasping this formula, traders and investors can make informed decisions, manage risk, and seize opportunities in the dynamic world of futures markets.