Using index futures: A case for arbitrage

In the past few weeks we have been looking at how index futures can be used for hedging and speculation by different market participants. One reason why index futures are particularly appealing is because they present an interesting opportunity for everybody. In the coming weeks, we shall look at how these derivative contracts can be used for arbitrage.

Well, there are many ways in which one could define "arbitrage". The strictest concept of arbitrage is what is called "academic arbitrage". In academic arbitrage, it is possible to trade to generate a riskless profit without investment. For example, assume that futures contracts on the S&P CNX Nifty start trading at the Singapore Exchange (SGX) and that there are no barriers to trading across exchanges or countries. If one month Nifty futures trade at 1560 on NSE and at 1570 on the Singapore Exchange, a trader could enter into the following two transactions simultaneously:
Buy 200 Nifties on the NSE for Rs 1560
Sell 200 Nifties on the SGX for Rs 1570

These two transactions would generate a riskless profit of Rs 2000. Since both trades are assumed to occur simultaneously, there is no investment. Such an opportunity qualifies as an academic arbitrage opportunity - that is, it affords riskless profits without investment.

Obviously, in well-functioning markets, such opportunities rarely exist. If they did, it would mean that we would all become rich using this continuous money-generating device. It's like money being left on the street without being claimed. And we all know that this does not happen. Arbitrage opportunities however do exist for very brief periods, and get instantly wiped out as investors buy/sell in the hope of making arbitrage profits.

The example we discussed above spoke of arbitrage across two markets, where the same product sells at two different prices at the same time. Arbitrage opportunities also exist when the same product sells at two different prices across time (after accounting for time value of money). For example, assume that the cost of carrying (financing costs) is 12 per cent a year, the spot Nifty is at 1540 and the one-month Nifty futures contracts trade for 1560.

Clearly, the futures seem overpriced giving rise to an opportunity for arbitrage. The fair value of the one-month futures contract is about 1555 (1540 plus cost of carry at 1 per cent a month). Now an investor could generate arbitrage profits by selling one-month Nifty futures contracts and buying a spot Nifty portfolio of the same value as the futures contracts sold and make a riskless profit of Rs 5 per Nifty. This is an example of arbitrage across time. We shall now look in detail at strategies for exploiting such opportunities when the futures contracts trade at prices higher than their fair value.

In such cases we can profit by selling futures, buying the asset spot and carrying it. Since completed arbitrages require the unwinding of all the original trades entered into, profits come in after the unwinding. Hence in a sense the short futures and long spot trades amount to lending money to the market, albeit at no risk. Here is how it works.

Traditional methods of loaning money into the stock market suffer from two risks -price risk of shares and credit risk of possible default by the counterparty. Index futures market supplies a technique by which one can lend money into the market without suffering any exposure to market movements and without bearing any credit risk.

It's a simple idea. What the lender does is to buy all 50 stocks of S&P CNX Nifty on the cash market, and simultaneously sell them at a future date on the futures market. It's like a repo. There is no price risk since the position is completely hedged. Since he enters into these trades with the clearing corporation as the counterparty on both legs, there is no credit risk. He would obviously get into these trades if he thought the futures contract he is using were overpriced. The fact that the transactions are riskless makes this strategy an ideal lending mechanism for risk-averse entities like banks and corporate treasuries.

Let's look at a few numerical examples. Assume that on August 3, S&P CNX Nifty is at 1550. A futures contract trading for August expiration is for 1590. Rajesh feels that the futures are overpriced and would like to earn this return (40/1550 for 27 days). How can he do so? We know that he must buy spot index and sell futures. Here is what he would do:

1. Buying the Nifty spot means buying all the 50 index stocks in the proportion in which they exist in the index. Assume he buys Rs one million of S&P CNX Nifty. For doing this, he places 50 market orders and ends up paying slightly more due to impact cost. Assume he obtains the spot Nifty portfolio for Rs 1554.

2. Next he sells Rs one million of the futures at Rs 1590. The futures market being extremely liquid, the market order goes through at zero impact cost.

3. A few days later he takes the delivery of the shares and waits. (While waiting he could get a few dividends in hand which would add to his returns). This is the point at which he is "lending money to the market".

4. On the expiration day of the futures contract, Rajesh puts in market orders to sell off his Nifty portfolio, in effect placing 50 market orders to sell off all the shares.

5. A few days later he makes delivery of the shares and receives the money for them. This is the point at which "his money is repaid to him".

And what is the interest he receives for the same? On the day he unwinds his position the index happens to have closed at 1565 and his sell orders go through at 1560 (due to impact cost). The value of the futures on the last day is always equal to the value of the spot, hence the futures position simultaneously expires at 1565. What Rajesh has gained is Rs 6 (ie 1560-1554, about 0.38 per cent) on the spot S&P CNX Nifty and Rs 25 ( 1590-1565 about 1.6 per cent) on the futures giving him a return of 1.98 per cent for 27 days.

This is a case of how index futures can be used for arbitrage. This can also be thought of as a technique for riskless lending of funds to the market. In the next article we shall look at how futures markets enable riskless lending of securities to the market.

The author is a faculty member at the Department of Management Studies, Goa University. She handles capital markets and derivatives.

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