How are Futures Prices Determined?

For traders who rely on technical analysis for devising trading strategies, price movements and past trends aid in decision making. Some traders use intuition while undertaking trading decisions. However, is imperative to set the foundation stone by understanding how futures price is determined.

The futures price of an asset is directly dependent upon the price of the underlying asset which is the current cash cost of purchase whereas the futures price fixes the price of the asset at a future date. The price of the underlying asset forms the base for the futures price. There is a high correlation between the spot and futures price for any asset which tends to be in the same direction. Therefore, if the spot price of a security increases, the futures price of the security also increases and vice-versa.

While the spot and futures prices move in the same direction, the spot price and futures price are not always the same. The difference between the spot and futures price is referred to as Spot-Futures parity. The reason for such difference can be attributed to multiple factors such as interest rates, dividends and time to expiry. Cumulatively, these factors aid in calculating the fair value of the futures price. The gap between the fair value and market value mainly occurs due to other costs such as transaction charges, taxes, margin, etc.

The formula to calculate futures price is as follows –

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

where –

1. RF refers to the rate of risk-free return. A risk-free rate is the rate that can be earned throughout the year in a perfect market. The interest rate for a Treasury Bill can be the basis for a risk-free rate which is generally quoted on a per annum basis. Hence, it has to be adjusted proportionately for the number of days till expiry. The rationale behind adjustment for risk-free interest returns is to evaluate the minimum return earned if the investment was made on the futures date. Thus, it is the opportunity cost of investing in security in the present versus the future. The futures price adjusts for the time value of money.
2. X refers to the number of days till expiry. As suggested by the formula, X is directly proportional to the futures price. If the number of days to the expiry increase so does the futures price.
3. D refers to dividends paid by the company till expiry. The dividend is not paid to the holder of a futures contract; it is only paid to the shareholders on the record date. Although the dividend is not received, the declaration of a dividend has an impact on the price of the securities and consequently the futures price. After the dividend is paid, the spot price typically reduces to the extent of the dividend paid. This depicts that new shareholders are not eligible for the dividend payment. As a result, it is imperative for dividend adjustments to be made to the futures price.

Let’s consider an example for the calculation of futures price. The spot price for Stock A is Rs. 1280, the risk-free rate of interest is 6.68% per annum and the number of days to expiry is 22. The company has declared a dividend of Re. 1 to be paid before the expiry of the contract.

In this case, the futures price is calculated as Rs. 1280 * [1 + 6.68% * (22/365)] – 1 = Rs. 1284.15. According to this formula, the futures price will increase by Rs. 4.

The difference between the spot and futures price leads to the origination of the concept of premium and discount. If the futures price is trading at a price higher than the spot, futures are said to be traded at a premium. Scientifically, the futures price will be more than the spot price. However, in practice, this may not be the case. If the spot price is higher than the futures price, the future is said to be trading at a discount. The concept of premium and discount are applied to various trades and strategies.

To analyze the implications of premium and discount, let’s discuss the price movements of the spot and futures price –

1. At the start of the series, the difference between the spot and futures price is high. As the number of days to expiry reduces, the difference between the prices also reduces.
2. More often than not, the futures price is higher than the spot price. The reason for the futures prices being higher is discussed above.
3. At times, the futures price could be lower than the spot price. Generally, due to short term imbalances in the demand and supply, futures trade at a discount to the spot.
4. Irrespective of the future trading at a premium or discount, the spot and futures price converge on expiry. At the end of the series, the difference between the spot and the futures price is zero i.e., the time value of money becomes zero on expiry. If you do not square off your position on the day of expiry, the exchange will automatically square it off. The price for settlement will be the spot price since the spot and futures price is the same on expiry.

Having understood the pricing of futures contracts, the price movement of spot and futures prices, the next step is understanding the strategies which can be applied to maximize returns from futures trading. The thumb rule while trading in futures is to purchase the cheaper asset and sell the expensive one.

Consider the following example –

The spot price of Wipro Limited is Rs. 653. The risk-free rate of return is 8.35% per annum. The number of days to expiry is 30 days. The expected dividend up to expiry is zero.

On applying the futures pricing formula discussed above,

Futures Price = 653 * [1 + 8.35% * (30/365)] – 0 = Rs. 658

Adjusting for charges and other costs, the theoretical futures price must be around Rs. 658. Let’s suppose the futures contract is trading at Rs. 700. Here, there is a drastic difference between the theoretical futures price and the market price of the futures contract. A trading opportunity is presented, the trader must purchase the cheaper asset and sell the expensive one.

In this case, the trader will sell the futures contract of Wipro and purchase in the spot market i.e., Buy Wipro in Spot at Rs. 653 and Sell Wipro Futures at Rs. 700.

Let’s analyze the profits or losses for the trade at different price levels –

1. The price on expiry is Rs. 675 –
   In the spot trade, the profit earned is the difference between Rs. 675 and Rs. 653 = Rs. 22.
   In the future trade, the profit earned is the difference between Rs. 700 and Rs. 675 = Rs. 25.
   The net profit earned is Rs. 47.
2. The price on expiry is Rs. 645 –
   In the spot trade, the loss is the difference between Rs. 645 and Rs. 653 = Rs. 8
   In the future trade, the profit earned is the difference between Rs. 700 and Rs. 645 = Rs. 55.
   The net profit earned is Rs. 47.
3. The price on expiry is Rs. 715 –
   In the spot trade, the profit earned is the difference between Rs. 715 and Rs. 653 = Rs. 62.
   In the future trade, the loss is the difference between Rs. 700 and Rs. 715 = Rs. 15.
   The net profit earned is Rs. 47.

In conclusion, irrespective of the price movements, the profit earned from the transaction remains constant. The spread is essentially limited to the range mentioned above. Such transactions are called ‘Cash and Carry’ Arbitrage since the risk involved is mitigated but executing contrasting positions.

Additionally, there are various other strategies that can be formulated by analyzing the values of the spot and futures price. These include bull calendar spreads, bear calendar spreads, pull back strategy, etc. You may note that most futures strategies are technical in nature. Prices of securities tend to be highly volatile and are influenced by fundamental changes in the underlying asset. Support and resistance levels are mainly tested by fundamental changes in security. Hence, it is essential to analyze the security fundamentally as well before investing.