# Futures Pricing – Concept, Price Calculation, Examples, Calendar Spread & more

Last Updated Date: Aug 30, 2023Futures Pricing is a vital concept but many investors do not really get to know about it.

This happens because most of the trade in futures happen through technical analysis, which does not require studying about the pricing of futures.

However, there are yet other type of traders in the futures market who make use of quantitative trading strategies.

These type of strategies include calendar spread, index arbitrage and more. In that case, it would be helpful to know something about its pricing mechanism.

## About Futures Pricing

The importance of futures pricing emerges from the fact that there is always a slight difference between the spot price and future price of a security.

But it is no big reveal that the value of a future is derived from the value of its underlying spot price.

This is why there is a direct relationship between the spot price of a security and its future price. But the fact remains that there is a difference between both the prices.

For example, the spot price of Nifty index could be INR 8677 at present. And at the same time, the future value of the Nifty index could be INR 8690.

This gap between the spot and future vlaue of the security is the ‘basis’ or the ‘spread’ between the spot and future price of Nifty index and in this case, the spread is 13 points.

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## Understanding of Futures Pricing & Spot Price

This difference in the price between the spot and future price of the Nifty index is attributable to a concept called ‘Spot – future parity’.

As is already clear, spot future parity arises due to a difference between the spot and futures price of the underlying security.

The reason behind this parity is due to various factors such as the following:

- The difference in interest rates (r
_{f)} - Dividend aspects (d)
- Time left to expiry

Thus, it will be right to say that future pricing formula is nothing but the mathematical expression of the difference between the spot price of the underlying security and its future price at the same time.

Expressed in the form of an equation, it will translate to:

Futures price = Spot price * (1 + r_{f}) – d

Here,

R_{f}= Risk free rate (This is the rate which you can earn annually)

D = Dividend

### Let us assume a risk free rate of RBI’s treasury bills

Let us assume that at present, the current rate is 8.6%. Keeping this rate in mind, let us take an example to illustrate how future pricing works.

Let us say that the spot price of Reliance is INR 1180 at present. For a 7 day expiry period, here is how the futures contract will be valued for Reliance.

Futures price = 1180 * ( 1 + 8.6% * 7 / 365) – 0

(Assuming that Reliance will not be paying out any dividend in the days to come)

After calculation, we will get the price as INR 1182. Thus, we can say that the fair value of a future of reliance is INR 1182.

Though, it is possible that the actual future price of Reliance may be INR 1183 or INR 1184. This typical actual price is known as the ‘market price’ of reliance future.

Now, this difference in the future pricing and market price can erupt due to certain costs and this includes various taxes, transaction charges, margin money etc.

But we can say that the future rate is by large, the fairest price at which the valuation of a future of reliance should be made.

Using this data, we can also calculate the future rates for mid month and far month contracts.

### Futures Price Calculation for Mid Month:

Let us say that the number of days to expiry of the contract is 34.

Thus, the future pricing will be equal to:

1180 * ( 1 + 8.6% * 34 / 365) – 0

= INR 1189

### Pricing of Futures Calculation for Far Month:

Let us say that the number of days to expiry of the contract is 80.

Thus, the future pricing will be equal to:

1180 * (1 + 8.6% * 80 / 365) – 0

= INR 1202

If at the same time, we were to look at the actual rate of the futures contracts for these trades, there is a good chance that we may discover different prices.

As discussed above, the difference mainly occurs due to the addition of various market costs.

It is also possible that the market intermediaries may be factoring the weight of dividend on this calculation as well.

It is worthy to note that as the term to expiry rises, the difference between the future pricing and market pricing also widens.

If the futures rate of a security is indeed trading at a higher one than its alternative in the spot market, we can say that it is trading at a premium.

A closer look at the facts of futures trading will reveal the following facts:

- During the beginning of a contract, the number of days to expiry is quite high. Hence, the future rate and the market rate will show a wider difference between each other.
- Usually, throughout the life cycle of a futures contract, the market pricing of a security will remain higher than its futures pricing.
- On the day of expiry of the contract, the future pricing and market pricing will always be the same.

There are times when the future price may be lower than the spot pricing as well. This will mainly happen when the demand and supply for futures are not balanced.

This is when we can say that the future is trading at a discount to its spot price.

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## Practical Example of Futures Pricing Formula

A practical example of future pricing formula will be able to highlight how it works.

Even though most traders may not need it, the use of a futures pricing formula is a requisite if you have to understand about the trading techniques which employ quantitative data.

Let us take an example to understand the concept.

Suppose that the spot price of Infosys is INR 853.

The risk free return at present is 8.35%

Days to expiry is 30 days

Dividend = 0

Ideally, the trading price of the futures contract should be = 853 * (1 + 8.35% * 30 / 365) – 0 = INR 858.9

So, ideally as per the calculation, the trading price of the Infosys future should be INR 858.9.

However, there can be an instance where the current trading price of the future may be in contrast to the one we have just calculated.

So, let us say that the current futures value of the stock is actually INR 900. Market imbalances can often give rise to a situation such as this one.

However, this price difference also opens up the scope for a trade. In this situation, we can say that the future market price is an expensive relative to the fair value.

Also, this implies that the spot price of a security is trading at a far cheaper price with respect to its futures.

### The design of the trade will take place in the following manner:

- Purchase Infosys in the spot market for INR 853
- Sell Infosys Futures for INR 900

From our current discussion we know that on the date of expiry, the prices of spot and future will converge with each other.

So let us take a few random examples to understand how the change in price will impact the situation and profit and loss.

VALUE OF EXPIRY |
P&L IN SPOT MARKET |
P&L IN FUTURE MARKET |
NET P&L |

875 | 875 – 853 = + 22 | 900 – 875 = + 25 | + 22 + 25 = + 47 |

845 | 845 – 853 = – 8 | 900 – 845 = + 55 | – 8 + 55 = + 47 |

915 | 915 – 853 = + 62 | 900 – 915 = – 15 | + 62 – 15 = + 47 |

As evident from the above example, the quantum of profits is guaranteed once you enter into a trade such as this one. The concept which is illustrated here is ‘Cash and carry arbitrage’.

## What are Calendar Spreads?

An extension of the concept of cash and carry arbitrage is calendar spread.

The idea here is to extract a profit from the spread which will result from two future contracts which are based on the same underlying security but have different dates of expiry.

So, continuing the above example, let us say that Infosys is trading in the spot market at INR 853. For an expiry of 30 days, the current value of futures is INR 858.

The actual market value of the 30 day future contract is INR 900. Mid month future contract for 65 days expiry is INR 863. But the actual market value of the mid month future contract is INR 865.

As evident, the current month future price is far above its fair value. But the same is not the case for the mid month future contract.

If a comparison takes place between the current month futures contract and the mid month futures contract, we will see that the latter is cheaper.

Thus, to design a calendar spread, you will have to buy a mid month future contract for INR 865 and sell a current future contract for INR 700. It is easily discernible that the spread between the two trades is 35 points.

It is notable that due to the hedged position of the trade, there will be a significant reduction in the value of the margins involved in this trade.

Now, first, the current month futures will expire. At this point, the spot price and future price of the underlying security will converge.

### Here is how the whole trade will work out:

VALUE AT EXPIRY |
P&L FOR CURRENT MONTH |
P&L FOR MID MONTH |
NET P&L |

860 | 900 – 860 = + 40 | 860 – 865 = – 5 | + 40 – 5 = + 35 |

890 | 900 – 890 = + 10 | 890 – 865 = + 25 | + 10 + 25 = + 35 |

925 | 900 – 925 = – 25 | 925 – 865 = + 60 | – 25 + 60 = + 35 |

Even though the above trade runs on the assumption that the mid month rate of the futures contract will remain close to its fair value, we can see that there is a good way to find out what the profits will be like.

## To Conclude Futures Pricing

So, in this article, we took a look at the futures pricing formula and carried out practical computation as well.

However, this discussion is vital to understand the concepts which we have discussed here, including calendar spread, cash and carry spread and premium and discount of futures price.

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