Author: shyam

A pairs trading strategy involves answering these questions:

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

We saw how to answer the first two questions: understanding, defining, finding, and investigating pairs.

Trading strategy

We can start with a simple trading strategy: we buy the spread if it is one standard deviation below the average and sell the spread if its is one standard deviation above the average.

To keep things simple, we’ll ignore execution details like lot-size, actual $ p&l, etc… and focus on the viability of the strategy. We calculate p&l in terms of unit-spread, i.e., how many ‘spreads’ of p&l did the strategy create?

For BANKNIFTY vs. ICICIBANK, we simulated the strategy outlined above based on the daily close of the nearest to expiry futures from Jan-2010:

The top chart is the the spread.
The 2nd is the trade: green implies the strategy went long the spread, red implies short.
The 3rd chart indicates the p&l of that specific trade (in spreads).
The last chart indicates the cumulative p&l (in spreads).
 
The p&l for this strategy over the entire time-period is +69.3189 spreads.

Asymmetric strategy

The idea behind the above strategy is to bet on mean-reversion on both sides. However, if you see closely, the shorts were not nearly as profitable as the longs. You could be better off just going long the spread whenever it hit one standard deviation and staying out of the market when the spread hit the upper band.

BANKNIFTY vs. ICICIBANK, long-only p&l +454.3036:

BANKNIFTY vs. HDFCBANK, long-only p&l +231.5225:

Conclusion

Some caveats:

1. The signals are intermittent, but you need to keep running the algorithms everyday to capture the alpha. This requires an investment in systems on your part.
2. The backtest ignores execution risk. For example, the hedge ratio is around 0.09830581 and there’s no way you can trade 1/10th of a contract. So your actual executable spread = 10 ICICIBANK – BANKNIFTY. That’s 11 contacts and it still doesn’t give you precision.

On the plus side:

1. The backtest doesn’t do any risk management. This would’ve stop-loss’ed most of the bad trades.
2. There is money to be made on the right pairs.

Related articles

• Bank Nifty vs. HDFC Bank and ICICI Bank (stockviz.biz)
• The Bank Nifty – ICICI Bank Pair (stockviz.biz)
• Charting Theme Performance (stockviz.biz)

We defined the spread between a pair to be:

spread = A – βB

where A and B are prices and β is the first regression coefficient.

The β is also known as the hedge ratio.

Neither β, nor the relationship is “guaranteed” to be stable. Here are the p-values and β of Bank Nifty vs. ICICI Bank nearest to expiry futures, with a 50-day look-back:

As you can see, the spread has periods of stability and adjustment. And sometimes, the stability is the anomaly.

To be continued…

Related articles

• Finding Pairs to Trade (stockviz.biz)
• Bank Nifty vs. HDFC Bank and ICICI Bank (stockviz.biz)

Correlation

When we discussed banks and introduced pair trading, we pointed out that a pairs trading strategy involves answering these questions:

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

Traders new to pair trading often mistake the correlation of prices to be indicative of “similarity”. For example, consider the Bank Nifty, HDFC Bank and ICICI bank. Here’s the chart of the closing price of the nearest to expiration futures contract:

And there are some really tight correlations:

However, this is only part of the story. What we need are pairs who’s price movements are mean reverting. Looking at price correlation alone is not enough.

Spreads

We need the spread between pairs to be “stable”, i.e., mean reverting.

spread = A – βB

where A and B are prices and β is the first regression coefficient.

200-day spreads

Here are the spreads between these pairs using 200-day data for regression:

50-day spreads

Here are the spreads between these pairs using 50-day data for regression:

Testing for cointegration

You don’t have to visually inspect spreads to see if they are mean-reverting. The most straightforward way of checking if a time-series is co-integrated is to perform a Dickey-Fuller test on it. If the p-value is less than 0.10, then this could be a good pair for trading.

If you are trading futures, then a 200-day fit may not make much sense. The latest 30-day test between BANKNIFTY and HDFCBANK has a surprisingly low p-value of 0.057, indicating that there is a potential trade there.

To be continued…

Related articles

• Bank Nifty vs. HDFC Bank and ICICI Bank (stockviz.biz)