In derivatives markets, the term basis is frequently used. Let's clarify what basis means in the context of equity index futures. In the context of equity index futures, the basis refers to the difference between the futures price and the spot price of the underlying assets. This difference reflects the net cost of carry for the futures contract. Essentially, the costs associated with holding the position like interest expenses against which the benefits of holding such as anticipated dividends are offset. To calculate the basis, the formula is futures price minus the spot price of the underlying asset. For example, if the E-mini futures contract is trading at 4,570 index points, while the S&P 500 index is at 4,558.82 points, the basis is simply the difference between these two values. Here 11.18 index points.

A positive basis, where the futures price is higher than the spot price, typically means that interest rates exceed dividend yields, creating a positive cost of carry. Conversely, a negative basis where the future's price trades at a discount to spots suggests that dividend yields are higher than interest rates, creating a negative cost of carry.

The theoretical fair value of the basis is driven by the cost of carry, influenced by the relationship between interest rates and expected dividends. However, different investors may calculate slightly different fair values for the basis depending on their funding costs and their assumptions about future dividends. As a result, the basis may oscillate within a certain range during the trading day, reflecting these differences.

Let's take a closer look at how the S&P 500 E-mini futures basis behaved on a typical market day, specifically November 22nd, 2023. In this chart, we see the basis fluctuating throughout the trading day with the timeline shown in central European time, CET. Note that 3:30 PM CET marks the start of the standard trading hours for US stocks, which corresponds to 9:30 AM Eastern time. As the chart shows, the basis was around 12 points at market open and remained within a relatively narrow range of 11.5 to 9.5 points for the the rest of the day. This range is indeed quite limited, and there's a reason for that. When the basis moves too far from its fair value, it opens up arbitrage opportunities. If the basis is cheap, meaning that futures are trading below their fair value market, participants can profit by buying futures and shorting the index's underlying components.

Conversely, if the basis is rich, meaning futures are trading above fair value, participants could short the futures and buy the index components.

These arbitrage activities help keep the basis within a narrow range, keeping the futures price close to the theoretical fair value over time. The narrow range represents the trading costs of the arbitrage trade. While the basis may not be the primary focus for investors hedging market risk with futures, it's still advantageous to execute a futures trade when the basis is favorable. For example, it's generally better to sell futures when the basis is rich rather than cheap and vice versa. So it is an important factor for hedges to bear in mind when entering into a new position.