Fair value is a crucial concept in financial markets, particularly in the context of stock index futures. In its broadest sense, fair value refers to the price at which an asset would change hands between a willing buyer and a willing seller, neither being under any compulsion to buy or sell, and both having reasonable knowledge of the relevant facts. Within the futures market, fair value specifically denotes the theoretically correct value of a stock index futures contract. This theoretical value is derived through a formula that considers several key factors such as the current index value, dividends of the stocks comprising the index, the expiration date of the futures contract, and the prevailing interest rates.
Formula for Calculating Fair Value
The fair value of a stock index futures contract is determined using a specific formula that takes into account the current price of the underlying index, the interest rate, the dividend yield of the index’s component stocks, and the time remaining until the contract’s expiration. The general formula for calculating the fair value of stock index futures, such as the S&P 500 futures, is as follows:
Fair Value=Cash×[1+𝑟×𝑥/360]−Dividends
Where:
Cash is the current cash value of the stock index.
r is the current interest rate, which is the cost of borrowing money to buy all the stocks in the index.
x is the number of days until the futures contract expires.
Dividends is the total amount of dividends expected to be paid by the stocks in the index until the contract expires, expressed in index points.
This formula encapsulates the cost-of-carry model, which incorporates the opportunity cost of holding the underlying stocks (reflected by the interest rate) and the income generated from these stocks (reflected by dividends).
To illustrate this with a concrete example, consider an S&P 500 futures contract. Suppose the current S&P 500 cash index is 3,500 points, the annual interest rate is 2%, the contract has 90 days until expiration, and the total expected dividends are 30 index points. The fair value would be calculated as follows:
Fair Value=3500×[1+0.02×90/360]−30
Fair Value=3500×[1+0.005]−30
Fair Value=3500×1.005−30
Fair Value=3517.5−30
Fair Value=3487.5
In this example, the fair value of the S&P 500 futures contract, given the provided parameters, is 3,487.5 points.
Relationship Between Fair Value and Futures Prices
The fair value of a stock index futures contract represents its theoretically correct price. However, the actual trading price of the futures contract can differ from this fair value due to various market dynamics. When the futures price is above the fair value, the market is said to be in “contango.” Conversely, when the futures price is below the fair value, the market is in “backwardation.”
This discrepancy between fair value and the actual futures price can indicate market sentiment. For example:
Contango: When futures prices are higher than the fair value, it often reflects bullish sentiment, as investors are willing to pay a premium for the expectation of future gains.
Backwardation: When futures prices are lower than the fair value, it usually indicates bearish sentiment, with investors anticipating a decline in the underlying index.
These differences are not just theoretical but have practical implications. They can create arbitrage opportunities, where traders exploit the price discrepancies to earn risk-free profits.
Arbitrage Trading
Arbitrage trading involves exploiting the price differences between related markets or instruments to earn a risk-free profit. In the context of stock index futures, if the futures price deviates significantly from the fair value, arbitrageurs can take advantage of this discrepancy. Here’s how it works:
Futures Price Above Fair Value (Contango):
1.The arbitrageur would sell the futures contract at the higher price.
2.Simultaneously, they would buy the underlying stocks of the index at the current market price.
3.On the expiration date, the futures contract and the value of the purchased stocks converge.
4.The arbitrageur earns a profit equal to the difference between the futures price and the fair value, minus transaction costs.
Futures Price Below Fair Value (Backwardation):
1.The arbitrageur would buy the futures contract at the lower price.
2.Simultaneously, they would short sell the underlying stocks of the index at the current market price.
3.On the expiration date, the futures contract and the short-sold stocks’ prices converge.
4.The arbitrageur earns a profit equal to the difference between the fair value and the futures price, minus transaction costs.
Arbitrage opportunities exist because, in efficient markets, prices eventually align with their fair values. However, these opportunities are usually short-lived as they are quickly identified and acted upon by traders, leading to the convergence of prices.
See also: 7 Things To Know Before Betting On A Stock Futures
Market Influencing Factors
Several factors influence the short-term supply and demand dynamics in the futures market, causing prices to fluctuate around the fair value. These factors include:
Interest Rates:
1.Changes in interest rates directly affect the cost of carrying the underlying assets, thereby impacting the fair value of futures contracts.
2.An increase in interest rates raises the cost of carry, leading to higher fair values for futures contracts, and vice versa.
Dividends:
1.Dividend announcements and payouts influence the expected dividends component in the fair value formula.
2.Higher-than-expected dividends reduce the fair value, while lower-than-expected dividends increase it.
Market Sentiment:
1.Investor sentiment, driven by economic data, geopolitical events, and market trends, affects futures prices.
2.Positive sentiment can push futures prices above fair value, while negative sentiment can drive them below fair value.
Supply and Demand Dynamics:
1.The number of buyers and sellers in the market influences futures prices.
2.High demand for futures contracts can push prices above fair value, while high supply can push them below fair value.
Liquidity:
1.The level of liquidity in the futures market affects how quickly prices can adjust to fair value.
2.High liquidity ensures that prices remain close to fair value, while low liquidity can lead to larger discrepancies.
Market Anomalies and External Shocks:
1.Unexpected events such as natural disasters, political upheaval, or financial crises can cause abrupt changes in market conditions, leading to significant deviations from fair value.
2.These anomalies often create temporary opportunities for arbitrage until the market stabilizes.
Understanding these factors and their interplay is crucial for traders and investors who seek to navigate the futures market effectively. By closely monitoring interest rates, dividends, market sentiment, and other influencing factors, they can better anticipate price movements and identify potential arbitrage opportunities.
Conclusion
Fair value in stock index futures is a fundamental concept that helps traders and investors determine the theoretically correct price of futures contracts. By considering the current index value, interest rates, dividends, and the time until expiration, the fair value formula provides a benchmark against which actual futures prices can be compared.
The relationship between fair value and actual futures prices offers insights into market sentiment and potential arbitrage opportunities. When futures prices deviate from fair value, arbitrage traders can exploit these discrepancies by simultaneously buying and selling related assets, thereby earning risk-free profits.
Several factors, including interest rates, dividends, market sentiment, supply and demand dynamics, liquidity, and external shocks, influence the short-term fluctuations of futures prices around fair value. By understanding these factors and their impact on the market, traders and investors can make informed decisions and optimize their trading strategies.
In essence, fair value serves as a compass in the complex and dynamic world of stock index futures, guiding market participants toward more rational and informed trading decisions. As the market evolves and new information emerges, staying attuned to the principles of fair value and its influencing factors remains a cornerstone of successful futures trading.
Related topics:
Do Stock Futures Predict The Market?
Stock Futures Soar As Markets Cheer Modi’s Likely Third Term