We recently discussed linear regression by using it to inspect the relationship between two banking stocks. Lets try and extend that treatment to an index and its predominant constituents.

### Bank Nifty

The Bank Nifty is composed of 12 bank stocks with ICICIBANK and HDFCBANK making up 29.27% and 28.26% of the index, respectively. Lets start with the scatterplot of daily log returns of the nearest to expiration futures.

Notice the strong relationship between the index and the banks?

### Q-Q Plots

Index vs. Banks have a predominantly Gaussian distribution. HDFC vs. ICICI – not so much.

### Pairs trading

With this knowledge in hand, can we trade pairs made out of these three? The rules for pairs trading is fairly straightforward:

- find stocks that move together
- take a longâ€“short position when they diverge and unwind on convergence

The execution of a pairs trading strategy involves answering these questions:

- How do you identify “stocks that move together?”
- Should they be in the same industry?
- How far should they have to diverge before you enter the trade?
- When is a position unwound?

Bank Nifty, HDFC Bank and ICICI Bank certainly fit the criteria.

### Co-integrated prices

If the long and short components fluctuate due to common factors, then the prices of the component portfolios would be co-integrated and the pairs trading strategy should work.

If we have two non-stationary time series X and Y that become stationary when differenced (these are called integrated of order one series, or I(1) series) such that some linear combination of X and Y is stationary (aka, I(0)), then we say that X and Y are cointegrated. In other words, while neither X nor Y alone hovers around a constant value, some combination of them does, so we can think of cointegration as describing a particular kind of long-run equilibrium relationship.

For a light introduction to co-integration, read this post on Quora.

*To be continued…*

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