How does stock futures arbitrage work in practice | Motilal Oswal

# How does stock futures arbitrage work in practice

The word arbitrage has different connotations. At a conceptual level, it refers to the differences in prices. When the NSE commenced operations in 1994, there used be huge difference in prices of the same stock between the BSE and the NSE. Brokers would buy the stock at a lower price on one exchange and sell at a higher price on the other exchange. This vanished over a period of time.
With the introduction of futures, a new kind of arbitrage came into being which is referred to as cash future arbitrage strategy. As we are aware, stock futures have a monthly expiry cycle and expire on the last Thursday of every month. At any time, there are 3 monthly contracts viz. the near month, mid-month and the far month. In stock-futures arbitrage you buy in the cash market and sell the same stock in the same quantity in the futures market. Since the futures price will expire at the same price as the spot price on the F&O expiry day, the difference becomes the risk-free spread for the arbitrageur. You can do arbitrage in futures and options.

Why is there a gap between cash price and futures price?
Since futures price pertain to a contract that is 1 month down the line there is a cost of carry; also, roughly known as the interest cost. So, if the annual risk-free rate of interest is 12% then the 1-month futures price must be at a 1% premium to the cash price. Of course, in reality the futures price is determined by a variety of other factors, but this is the key factor. Therefore, by buying in the cash market and selling in the futures you lock in that 1% returns per month. Consider the example.

Source: NSE
In the above live price chart of Reliance Industries, the cash price on 25th Jan is Rs.960.50 while the Feb 22nd Futures price is Rs.965.15. So, the arbitrage spread is {(965.15-960.50)/960.50} which works out to 0.48%. That is the return for a period f 28 days.
So, the annualized return in this case works out to (0.48% x (365/28) = 6.26%
Normally arbitrageurs prefer an annualized return of around 12-14% as they also need to cover their cost of funding and the transaction and statutory costs of doing the arbitrage, apart from the tax implications. So how does arbitrage work with futures.

How is the profit realized on an arbitrage transaction?
This is the most important part of the arbitrage transaction. You have locked in a riskless arbitrage profit but how do you actually realize the profits that you have locked. In the cash market you can actually realize profits by selling your shares. In the arbitrage market there are actually two ways of realizing the lock-in profit on the arbitrage transaction.

You can realize the profit on arbitrage by unwinding your trade; that means you reverse your long position in equity and your short position in futures simultaneously

You can hold on to your cash market position in your portfolio, but you can roll over your futures position to the next contract based on the spread

Let us understand both these methods in much greater detail.

As we are aware, in an arbitrage trade you buy in the cash market and sell in the futures market. That means you are long in cash market and short in the futures market on the same stock and in the same quantity. What is interesting to note is that you do not have to wait till the date of expiry to unwind your position. You can even unwind your arbitrage earlier if the spread has come down substantially. Let us understand this with an illustration.

Variable (in an arbitrage trade)Amount (in an arbitrage trade)Cash price of Reliance (purchased) on Feb 01Rs.920Feb Futures price of Reliance (sold) on Feb 01Rs.930Cash Futures spreadRs.10 (1.09%)Annualized spread on arbitrage 18.95% {1.09 x (365/21)}How will this arbitrage position get unwoundCash price of Reliance on Feb 11Rs.955Feb Futures price of Reliance on Feb 11Rs.958Cash Futures spreadRs.3Profit on Reliance Cash PositionRs.35 (955-920)Loss on Reliance Futures PositionRs.(-28) (930-958)Net profit / loss on arbitrageRs.7

The net profit of Rs.7 that he realizes by unwinding the arbitrage can be either seen as the profit on the transaction or the difference in the two spreads. It means one and the same thing. Remember, you are indifferent to the market price of cash and futures. What matters is only the spread? You will be profitable if the spread falls below Rs.10. In this case you are earning Rs.7 in just ten days.
The downside of this strategy is that each month you need to create fresh positions and keep unwinding them. This leads to higher transaction costs, higher statutory costs and also results in short term capital gains on your cash market profits. A better and more popular method of realizing profits on arbitrage is rolling over your futures.

Rolling your futures position each month..
You can avoid the hassles of unwinding and creating arbitrage positions each month by holding on to your cash positions and just rolling your futures position to the next month. Take the case below.

Source: NSE
The shaded portion captures the SBI futures price for the Jan contract and the Feb contract. Since your arbitrage position is long on cash market and short on Jan Futures, you can buy SBI Jan futures at Rs.320.80 and sell the Feb Futures at Rs.322.35. This results in an arbitrage spread of Rs.1.55 (0.48%). This is your spread earning for the month, and you have earned it without disturbing your cash market position. This is the practice most institutions follow in arbitrage.

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