# Why futures prices converge upon spot prices

Mr. Mohan observed that future prices and spot prices are attracted to each other like opposite poles of magnets on expiry and it wasn't just once! Time and again he noticed that on expiry future prices and spot prices converge. But why is it so?

To understand this, one must remember that futures are derivative contracts that derive their value from underlying assets. Underlying price is a fundamental component for calculating the price of a future contract. Any changes in the underlying price will be reflected in that of the corresponding future contract.

Let's understand this with the help of an example.  If Tata Motors shares are currently trading at ₹450 and Tata Motors futures are trading at ₹460. There is a difference between the spot price and future price which attributes to the ‘Spot – Future Parity’ which states that this arises due to variables such as interest rates, dividends, time to expiry, etc.

This can also be expressed mathematically in the futures price formula which states that

Futures Price = Spot price * [1+ rf]– d

Where,

rf :Risk-free rate

d :Dividend

So here, in our example, there is no dividend. When calculated;

Futures price: ₹460

Spot price: ₹450

rf: 0.01111111

A risk-free rate is what you can earn throughout the year in an ideal environment.

Note: The mathematical value of futures prices calculated and market value by and large should be around the same value. However there could be slight variance mainly due to the associated costs.

In the F&O segment in the Indian stock markets at any given point, futures contracts for a particular underlying are available for 3 months. They are distinguished on the basis of expiry, namely;

• Near month: In the Near or (Current) month contract, there are 30 days or fewer left for Expiry.
• Next month: In the Next month contract, there are 60 days or fewer left for Expiry.
• Far month :In the Far month contract, there are 90 days or fewer left for Expiry.

Time to expiry is high in the far month contract, followed by the next month contract and the least in the near month contract.Thus the prices of these futures contracts are higher in line with the number of days left to expiry. This is also why upon expiry of the near month contract future prices and spot prices converge as time to expiry turns zero.

It can also be mathematically represented in the future price formula as rf = 0 & no dividend was announced. Effectively the formula evolves to be:

Futures Price = Spot price * [1+ 0] – 0 i.e. Futures Price = Spot price

Also, the convergence of future to spot happens because the market will not allow the same security to trade at two different prices at the same place at the same time.

## Arbitrage opportunities: Premium versus discount

As the Tata Motors futures are trading at ₹460 which is higher than the Tata Motors shares trading at ₹450, the Tata Motors futures are said to be trading at  “premium”. Here, futures price is higher than the spot price i.e. futures price > spot price.

Investors can take advantage of this opportunity by selling the futures and buying in cash with the intention of earning a risk-free profit. For instance, Mr. Jai sells Tata Motors futures at ₹460 in the F&O segment and buys Tata Motors shares at ₹450 in the cash segment. By doing this, he has effectively locked his profit of ₹10 per share.

However, if Tata Motors futures were trading at ₹440 which is lower than the Tata Motors shares price of ₹450, the Tata Motors futures is said to be trading at  “discount”. Here, futures price is less than spot price i.e. futures price < spot price.

Investors can try to take advantage of this opportunity by buying the futures and selling in the cash segment (only if they currently hold this position) with the intention of earning a risk-free profit. For instance, Mr. Dev buys Tata Motors futures at ₹440 in the F&O segment and sells his holdings of Tata Motors shares at ₹450 in the cash segment. By doing this, he has effectively locked his profit of ₹10 per share.

 Arbitrage opportunity Buy security Buying price Sell security Selling price Profit = Selling price - Buying price Premium Tata Motors shares ₹450 Tata Motors futures ₹460 ₹460 - ₹450 = ₹10 Discount Tata Motors futures ₹440 Tata Motors shares ₹450 ₹450 - ₹440 = ₹10

This is known as arbitrage. Traders may choose to take delivery or sell their shares as physical settlement to book their profits. These opportunities are not easily available to retail traders due to crowding out by institutional players and program trading.

×