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Index futures: A case for arbitrage-II

Kshama Fernandes

Generally, arbitrage requires identifying two distinct market places where something is traded, and then waiting for opportunities to buy in one market at one price and sell in the other market at a higher price. This same process is at work for stock/futures arbitrage. One could think of an arbitrage opportunity between the spot index and index futures as an arbitrage across time, ie the spot index and the index futures contract which have basically the same underlying basket of stocks, trading at two different prices across time (after accounting for time value of money).

The arbitrage logic remains the same for the stock futures arbitrage as for arbitrage across any other markets. The market participants in stock futures will enter an arbitrage trade whenever (a) buying stock and selling futures generates a return that exceeds financing costs, or (b) selling stock and buying futures results in an effective yield (cost of borrowing), that falls below marginal lending rates. Completed arbitrages will require a reversal of the starting positions, and the costs of both buying and selling stocks and futures must be included in the calculations.

Thus, the total costs of an arbitrage trade reflects the bid-ask spreads on all of the stocks involved in the arbitrage, the bid-ask spreads for all futures positions, and all commission charges on both stocks and futures. Based on the costs involved, the arbitrageur would evaluate two independent arbitrage bounds, the upper bound and the lower bound.

During those times when futures prices exceed the upper arbitrage boundary, profit could be made by financing the purchase of stocks and selling futures (the trading strategy referred to in the previous article as lending funds to the market). And when the futures prices are below the lower bound, profits could be made by selling stocks, buying futures, and investing at the marginal lending rates (the trading strategy referred to as lending securities to the market). In both cases, the completed arbitrages would require an unwinding of all the original trades.

Now given that it is possible to exploit arbitrage opportunities in the stock/futures markets, who would be ideally placed to exploit the same? Well, actually anybody willing to put in the money required to buy the minimum quantity of spot Nifty portfolio can enter into arbitrage. And what does spot Nifty portfolio mean? It is the 50 stocks in the index, bought in the proportion in which they exist in the index. But what if you were managing a mutual fund and already owned a well diversified index-like portfolio? Well, then exploiting arbitrage opportunities would be the most logical thing to do. Here's a nice way one could use a portfolio of shares earning nothing to help juice up returns by earning revenues from stocklending via the futures markets.

The index futures market offers a riskless mechanism for (effectively) loaning out securities and earning a positive return for them. You would sell off your securities and contract to buy them back in the future at a fixed price. Since you are perfectly hedged, there is no price risk and since your counterparty on both legs of the transaction is the National Securities Clearing Corporation there is no credit risk.

The basic idea is quite simple. You would sell all 50 stocks in S&P CNX Nifty and buy them back at a future date using the index futures. You would soon receive money for the shares you have sold. You can deploy this money as you like until futures expiration. On this date, you would buy back your shares, and pay for them.

How would we go about doing this? Let us have a step-by-step look at the process.

Suppose you have Rs 5 million of the S&P CNX Nifty portfolio (in their correct proportion, with each share being present in the portfolio with a weight that is proportional to its market capitalisation). What you would need to do is:

Sell off all the shares of the 50 companies on the cash market (this can be done using a single keystroke using the offline order entry capability of the NEAT software) and buy index futures of an equal value. A few days later, you will receive money and have to make delivery of the 50 shares. You then deploy this money at the riskless interest rate. On the date that the futures expire, at 3:15 PM, you put in 50 orders (using NEAT again) to buy the entire S&P CNX Nifty portfolio. A few days later, you will need to pay in the money and get back your shares.

Sounds very simple, doesn't it? But when is this worthwhile? When the spot-futures basis (the difference between spot S&P CNX Nifty and the futures S&P CNX Nifty) is smaller than the riskless interest rate that you can find in the economy. If the spot-futures basis is 2.5% per month and you are loaning out the money at 1.5% per month, it is not profitable. Conversely, if the spot-futures basis is 1% per month and you are loaning out money at 1.2% per month, this stocklending could be profitable.

Hence it is possible to make a riskless or arbitrage profit both by lending securities in the stock market and by lending funds (refer to last weeks article). But when should one lend securities and when should one lend funds? As mentioned earlier, when the spot-futures basis is "too wide", lending money to the market is attractive. When the spot-futures basis is "too low", borrowing money from the market (ie stocklending) is attractive. If one is highly attractive, the other will be highly unattractive. Obviously, both cannot be attractive at the same time. The market will bounce around; sometimes the basis will be too thin and sometimes it will be too wide. Alert traders will spot these opportunities and connect them up with either stocklending or fund-lending, depending upon the situation.

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

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