# Understanding Futures Pricing Formula

17 July 2020

There is a reason why the futures pricing formula deserved a separate discussion. In futures trading spectrum, you will come across different sets of traders – some are intuitive traders who base their decisions on their hunches, and others are technical traders, who will go by the pricing formula. It is true that successful futures trading needs skills, knowledge, and experience, but before you begin, you’ll also need a fair understanding of the pricing formula to understand how to wade through the water.

So, what forms the base of futures price? A futures price is determined by the cost of its underlying asset and moves in sync with it. The cost of futures will rise if the cost of its underlying increases and will fall as it falls. But it is not always equal to the value of its underlying asset. They can be traded at different prices in the market. For example, the spot price of an asset can be different from its future price. This price difference is termed Spot-Future parity. So, what causes the prices to differ at different time frames? Interest rates, dividends, and time to expiry.  The futures price formula includes these factors. It is a mathematical representation of how futures price change if any of the market variable change.

Futures Price = Spot price *(1+ rf – d)

Where,

rf is the risk-free rate

d stands for dividend

A risk-free rate is what you can earn throughout the year in an ideal environment. A treasury bill is a good example of a risk-free rate. One can adjust it proportionately for a period of two months or three months till the futures expire. So, with that adjustment, the formula looks like,

Futures Price = Spot price * [1+ rf*(x/365) – d]

X represents the number of days to expiry

Let’s discuss it with an example. To help with calculation, we are assuming the following values.

The spot price of XYZ Corp. = Rs 2,380.5

Risk-free rate = 8.3528 percent

Days to expiry = 7 days

Futures Price = 2380.5 x [1+8.3528 ( 7/365)] – 0

We are assuming that the company isn’t paying a dividend on it; hence,  we have considered it as zero. But if any dividend is paid, it will also factor in the formula.

This futures price formula gives you what is called the ‘fair value.’ The difference between fair value and market price is caused by taxes, transaction charges, margin, and such. Using this formula, you can calculate a fair value for any expiration days.

Mid-month calculation

Number of days to expiry is 34 days

2380.5 x [1+8.3528 ( 34/365)] – 0

Far-month calculation

Number of days to expiry is 80 days

2380.5 x [1+8.3528 ( 80/365)] – 0

## Few More Things To Keep In Mind While Considering Futures Price

The price of a futures contract is the spot price of an underlying asset, adjusted for interest, time, and paid out dividends.

The variance between the spot price and futures price forms the ‘basis of spread.’ The spread is the maximum at the beginning of the series but converges towards the settlement date. The spot price and futures prices of an underlying are ideally equal at the expiration date.

## A Few Important Definitions

Buying vs. selling futures contracts: Futures are a standardised legal agreements. The buyer has a long position, and a seller has a short position in the futures.

Clearing house: Futures are traded in an active market through an exchange, also called a clearing house. In India, the National Stock Exchange of India Limited (NSE) partakes in futures trading through futures index.

Margin requirement: Margin is the amount deposited in the clearing house by the parties. It acts as an assurance that parties will honour the contract when the time comes. Both parties need to deposit a margin at the beginning of the trade. Due to marking to market process, if the initial margin falls below the maintenance amount, the party receives a margin call.

Marking to market:  It is a process to settle future prices daily. The futures price rise or fall daily because of active trading. Clearing houses have adopted a means to pay the price difference after each trading by debiting and crediting the differential amount from the margin amount deposited by the parties.

## Understanding Futures Price Quote

Speculators are traders who get involved in futures trading in the active market.  They aren’t looking to receive physical delivery of the commodity, but bet on market trends to secure profit from the deal. They base their biases on futures quotes, which is a technical tool to predict future price movements.

The chart is an example of a futures quote chart. This chart contains all information regarding the futures contract along with periodical price movement. At the very top, it mentions the name of the underlying commodity and expiration date. Apart from that, at the corner, you can check the current price and index of price movement. Open, and settlement prices are mentioned at the bottom of the graph.

## What Is Arbitrage In Futures?

Arbitrage involves simultaneously buying and selling futures contracts at different markets to earn profit from price differences. It is a trading strategy and used by many traders throughout the world because it involves no-risks for the arbitrager.

Consider a scenario of XYZ Corp.

Spot- 1280

Rf – 6.68%

Days to expiry (x) = 22
div = 0

Using futures pricing formula the value is

Futures price = 1280*(1+6.68 %( 22/365)) – 0

Futures price = 1285.15

According to the formula, the futures price will go up by Rs 5 only.

Now, if a significant price difference arises due to supply-demand imbalance, an opportunity to arbitrage gets created. Let’s consider the following table.

 Expiry Value Spot Trade P&L (Long) Futures Trade P&L (Short) Net P&L 1390 1290 – 1280 = 10 1310 – 1290 = 20 +10 + 20 = +30

But there can also be a situation where futures price drops below the spot price. A trader, however, can still indulge in arbitrage and gain. Here is how,

 Expiry Value Spot Trade P&L (Long) Futures Trade P&L (Short) Net P&L 1390 1280 – 1290 = -10 1290 – 1252 = 38 -10 + 38 = 28

Here Rs 1252 is the futures price in a long position.

## Conclusion

Futures trading needs some understanding and practice. Market variables involved which influence futures prices in the market. But learning the futures pricing formula is a great start. It will help you to understand futures quotes and plan your position is a better way.