Co-integration based trading strategy to capture index futures arbitrage in the Indian stock market

Abstract

An arbitrage opportunity refers to a situation where riskless gains can be made by taking offsetting positions. On the other hand, statistical arbitrage requires taking offsetting position in instruments which have behaved similarly in the past. An arbitrage opportunity here will result in a profit situation only if the instruments behave the way they did in past, thus carrying risk to some extent. Index-futures arbitrage is a classic example of statistical opportunity. Index futures basically track the index itself and thus it is reasonable to believe that there should be a similarity in the returns of the two. Any difference in the returns over a reasonable period of time should result only from over buying or over selling of one compared to the other. Even in efficient market condition, the prices must correct to counter the change and come back to the previous level so equilibrium. To comply with, the cumulative sum of the difference of daily returns of the index and futures must be mean reverting. It is this phenomenon that we intend to capture through our co-integration model. The Ornstein - Ulhenbeck process (also called as OU process), through which we apply the co-integration model, is a mean reverting process with well-defined parameters. To enter into an arbitrage trade, we need to be confident of the mean reverting behaviour of the cumulative sum of the difference of the returns of nifty index and nifty futures. The cumulative sum of the difference of the returns over the last 60 days is calibrated to determine the parameters of the OU process. Once the parameters suggest mean reversion, we can enter into the trade depending upon the distance from the long term mean. We set up the trade signals under the assumption that the process approaches towards the mean. However, it is not practical to take a position in Nifty index itself. Two approaches were used to tackle this problem. First, we used each of the major stocks underlying nifty index as the substitute of nifty index. Secondly, we chose that stock as an alternative to the nifty index which exhibited the highest correlation with the nifty. Further analysis was done on the point of entry and exit from the trade. It was realised that the farther from the mean we entered into the trade, higher returns per trade was realised. However, it was accompanied with less number of trade opportunities and less stable returns. Also, it is found that farther off the entry and exit points, worse is the performance of the trade. The above strategy leads to good returns when compared to investments in nifty in the same period. However, the high transaction associated with buying/selling a stock make the strategy to be a less attractive one unless one can ensure low transaction costs by virtue of being an institutional investor. Another insight from this was to use pairs of stocks from the same sector, expected to behave similarly, as the derivatives trading on them can be traded with very transaction costs. A complete analysis involving the major stocks was done for all the sectors leading us to find the profitable pairs.