# How Fair Value Is Calculated in Futures Markets

## What Is Fair Value

Fair value is the sale price agreed upon by a willing buyer and seller. The fair value of a stock is determined by the market where the stock is traded. Fair value also represents the value of a company’s assets and liabilities when a subsidiary company’s financial statements are consolidated with a parent company.

Specifically, the fair value is the theoretical calculation of how a futures stock index contract should be valued considering the current index value, dividends paid on stocks in the index, days to expiration of the futures contract, and current interest rates.

## Understanding Fair Value

Fair value can show the difference between the futures price and what it would cost to own all stocks in that index.

For example, the formula for the fair value on the S&P futures contract is:

﻿ \begin{aligned} &Fair~Value = Cash \times \{1+r(x/360)\} - Dividends\\ &\textbf{where:}\\ &Cash = \text{\small Current S\&P Cash Value}\\ &r = \text{\small Current interest rate paid to a broker to buy all }\\&\text{\small stocks in the S\&P 500 index}\\ &x = \text{\small Days to expiration of the futures contract}\\ &Dividends = \text{\small Amount of dividends until contract}\\&\text{\small expiration expressed in terms of points on the S\&P contract }\\ \end{aligned}﻿

## Fair Value Versus Futures Price

This value is often shown on financial news networks and displayed online before the equity markets open for trading. The fair value can provide a glimpse of overall market sentiment. The futures price may be different from the fair value due to the short-term influences of supply and demand for the futures contract. The fair value always refers to the front-month futures contract as opposed to a further out month contract.

This difference between the fair value result and the current S&P 500 futures price may represent an arbitrage opportunity for those assuming that the futures price will eventually revert back to the fair value price. Through arbitrage, a trader can profit from a price imbalance by simultaneously purchasing and selling an asset. The trade exploits the price differences among identical or similar financial instruments on different markets or in different forms.

The fair value and futures price will fluctuate during the course of the trading day. Futures contracts trade on the Chicago Mercantile Exchange while individual stocks as components of the S&P 500 are trading at dispersed stock exchanges around the country. Therefore, there are often discrepancies between the two.

Article Sources
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1. CME Group. "E-mini S&P 500 Futures Quotes."

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