What is Index Arbitrage?

Cash futures is quite simple. Reliance is trading at Rs.2100 in the cash market and Rs.2118 in the 1-month futures. You buy Reliance in cash equivalent to the lot size and sell one lot of Reliance futures. The profit of Rs.18 in one month is locked in. Now let us take another example. The Nifty spot is at 15,800 and the Nifty futures is at 15,960. That is a 160 points clear arbitrage profit or close to 100 bps in a month. But there is a problem. How do you capture this arbitrage?

You cannot technically buy the Nifty. The answer is index arbitrage where you buy the Nifty as a single basket on one side and simultaneously sell Nifty futures to lock in the index arbitrage spread. Effectively, the index arbitrage is a stock index arbitrage where you buy the components of the Nifty in the same proportion. Since that is not practical manually, it is done through algorithms and program trades. Let us look at what is index arbitrage and how to index arbitrage trading works. The detailed explanation below will help to understand what is index arbitrage is a concept and how index arbitrage trading happens in practice.

What is Index Arbitrage?

Broadly index arbitrage is an all-encompassing term. It broadly includes 3 types of index arbitrage opportunities. Let us look at these stock index arbitrage ideas.

• Index arbitrage can be arbitrage between the same index traded on two different exchanges; like the Nifty on the NSE and the Nifty on the SGX, although the currency denominations are different the underlying is the same.

• Index arbitrage can also be between two indexes that have a standard relative value with a high correlation but have diverged recently. For example, one can look at arbitrage between the Nifty and the Sensex as a case in point of index arbitrage.

• Finally, it can be the kind of arbitrage we have already explained in the introductory part of the chapter wherein you buy a basket of stocks and sell index futures against that. This has to be algorithm-driven and it has to be done with high capital commitment.

Getting the hang of index arbitrage 101

Index arbitrage is a trading strategy to profit from differences between one or more versions of an index or between an index and its components. The latter is the more common form of index arbitrage but remember it is very capital intensive and also technology-intensive as such strategies need complex algorithms to capture opportunities and also need low latency execution to get the best price. Most often, such arbitrage opportunities exist only for a few milliseconds.

Understanding the concept of index fair value

If you want to understand index arbitrage, you need to grasp the concept of index fair value. In the futures market, fair value is the equilibrium price for a futures contract. You can define the futures price as the spot price plus the cost of carrying. What does the cost of carrying consist of? In index arbitrage, the cost of carrying includes compounded interest that could have been earned as an opportunity cost and dividends lost because the investor owns the futures contract instead of stocks.

Typically, the index arbitrage comes into play when the futures contract trades substantially off its fair value. Note the use of the word substantially. You cannot trade small divergences from the fair value because it requires capital, you incur brokerage costs, you incur statutory costs and it entails tax implications. Let us now turn to some mathematics for understanding the concept of fair value.

Fair value of Futures = cash * {1+r(x/360)} – dividends)

In the above formula:

Cash refers to the spot value of the Nifty, for example, | “r” is the current interest rate that would be paid to a broker or the risk-free rate of interest | Dividends are the total dividends paid until futures contract expiration which again nets your fair value.

How does index arbitrage work on Nifty?

Trading terminals have the facility of executing an index basket, especially for institutional clients. When the basket is executed, all the Nifty stocks are bought in the same proportion of the Nifty, and equivalent Nifty futures are sold. The system can set triggers when the index arbitrage basket is to be executed to make the best of the opportunity.

Index arbitrage takes significant capital, high-speed trading, and low commissions to be profitable. This makes more sense for large institutions that can move around huge capital for small returns and trade on sheer volumes. The more components in any index, the greater the chances of some being mispriced, and the greater the index arbitrage opportunities. Hence a larger index like Nifty with 50 stocks is more likely to throw up index arbitrage opportunities.

What is Cash-and-Carry Arbitrage?

Cash-and-carry-arbitrage is another name for cash-futures arbitrage. It is a market-neutral strategy. On the one side, you purchase a long position in the stock or the commodity. On the other side, you take an offsetting position by selling futures in the stock or the commodity. This is considered to be a relatively risk-free strategy although the cost of carrying differs widely between equities and commodities.

What is Spatial Arbitrage?

Spatial arbitrage does look esoteric and it is a rather complex and opportunistic form of arbitrage. To that extent, it is not arbitrage in the traditional sense. One of the most common forms of spatial arbitrage is what is called Geographical arbitrage. How exactly does this geographical arbitrage work in practice?

The first such case was after the Japanese Tsunami in 2011.This led to a spike in Asian demand for Crude and LNG, which increased exponentially in the months after the Tsunami. Simultaneously, there was an over-supply of WTI crude due to a spurt in shale production and the US just did not have storage. The Spatial Arbitrage trade here would have been to buy Brent futures and sell WTI Futures hoping for mean reversion. That eventually did happen but remember, this is not a risk-free arbitrage.

The other example was the huge dichotomy between Brent Crude and WTI Crude in late April 2020 after WTI dipped into negative on expiry day being contracts for mandatory delivery compared to Brent which is cash-settled futures. A strategy of buying WTI Futures and selling Brent would have been an example of spatial arbitrage. Once again, this is not risk-free because markets can be irrational much longer than traders can remain solvent.