“Pairs Strategy” is a short-term speculation Strategy. “Pair Trading” is in essence a Contrarian Investment Strategy. “Pairs Trading” is a medium term Trading Strategy.

A. The Strategy
1. Find 2 Stocks whose prices have moved together for a long period of time.
2. When the spread between them widens, short the Winner and long the Loser.

A.1. How to identify the Stocks that move together?
1. Observe the Stocks Prices over a period of 12 months. This period of observation is called the FORMATION PERIOD.
(THE BELOW IS MY METHOD. THIS SHOULD GIVE THE SAME RESULT AS TRIED BY THE AUTHORS)
2. Take all the Stock Prices during the observation period and determine the Correlation between the Stock Prices.
3. If the Correlation of 2 Stock Prices during the Observation Period is close to 1, then we can say that these 2 Stocks are ready to form a pair.
4. Determine whether the Stocks with correlation close to 1 are from the same industry. If they are from the same industry, them form them into a pair. (Stocks from the same industry can be found if the SIC code of the 2 Stocks are the same).
5. Determine whether the Stocks with correlation close to 1 are from different industry, however the 2 different industries are related to each other. If this condition is satisfied, then form these 2 Stocks into a pair.

(THE METHOD PROPOSED BY THE AUTHORS)
1. Construct a Cumulative Returns Index for each Stock over the Formation Period.
2. Choose a Matching Partner for each Stock by finding a Stock which minimises the sum of squared deviations between the 2 Normalised Prices. (Normalised Prices can be found by using a method like taking each Stock Price and subtracting the Mean of the Stock Prices over the observation period and then diving this difference with the Standard Deviation of the Stock Prices over the observation period).

A.2 How far do the Stocks in the Pair have to Diverge before we can apply this Strategy?
When the Stock Prices of the Stocks in the Pair diverge by more than 2 Standard Deviations, then we start the TRADING PERIOD(The Trading Period has to be considered to be 6 month as per the paper).
The Standard Deviation of the Stock Prices was determined from the observations of the Stock Prices made during the Formation Period.

A.3 When should we unwind the position?
We should unwind the position at the point where the Stock Prices of the Pair crosses each other.
If the Stock Prices of Pair do not cross during the Trading Period, then we unwind on the last day of the Trading Period.
If one of the Stocks in the Pair is delisted, then we close position in the Pair.

B. Why this Strategy should earn returns?
By shorting the Winner and buying the Loser, if history repeats itself, the prices will converge and the arbitrageur will profit.

C. How to reduce Risk on the Portfolio through this Strategy?
The risk, after using the strategy, can be reduced by increasing the number of pairs selected for trading. As the number of Pairs in the Portfolio increases, the portfolio Standard Deviation falls. Also it is noticed that as the number of Pairs in the Portfolio increases, the minimum realised returns increases; while the maximum realised excess returns remains relatively stable.

D. What is the observed returns from this Strategy?
For formulating this strategy, the researchers have studied data from the US Market between 1962 and 2002. They have found that adopting this strategy can yield 11% excess returns.

# ILLUSTRATION

The main industry I want to study for picking a Stock for a Pair is the Power Generating Industry.

Some of the Key Players in the Industry in India are as follows:

1. Gujarat Industries Power Company Ltd.
2. Jaiprakash Power Ventures Ltd.
3. JSW Energy Ltd.
4. NHPC Ltd.
5. NTPC Ltd.
6. Power Grid Corporation India Ltd.
7. Reliance Industries Ltd.
8. SJVN Ltd.

The related industry to the Power Industry is the Coal Industry.

Some of the Key Players in this Industry are as follows:

1. Coal India Ltd
2. Gujarat Mineral Development Corporation Ltd
3. Gujarat Natural Resources Ltd
4. Auroma Coke Ltd
5. Austral Coke & Projects Ltd

37% of the fuel requirements of the Power Generating Companies is met through Coal. Coal is the biggest single source of energy for electricity production and its share is growing. The efficiency of converting coal into electricity matters: more efficient power plants use less fuel and emit less climate-damaging carbon dioxide.

In the BSE and NSE, there is an index for the Power Sector and also for the Energy Sector.

However, BSE and NSE does not maintain any index for Coal Industry separately. There is however, an index for Mining & Metal Industry. Coal Industry is considered under this industry.

## Selecting Stocks to form pair from the Power Industry.

The Stocks being studied are as follows:

1. Gujarat Industries Power Company Ltd. (GIPCL)
2. Jaiprakash Power Ventures Ltd. (JPVL)
3. JSW Energy Ltd. (JSW)
4. NHPC Ltd. (NHPC)
5. NTPC Ltd. (NTPC)
6. Power Grid Corporation India Ltd. (PGRID)
7. Reliance Industries Ltd. (RIL)
8. SJVN Ltd. (SJVN)

The following steps were followed:

1. The Historical Prices from 1-Jun-2017 to 31-May-2018 were collected for each of the Stocks.
2. From the Historical Prices gathered in Step 1, the normalised prices of each day for each Stocks was calculated as (Stock Price – Mean(Stock Prices)) / Standard Deviation(Stock Prices).
3. From the normalised prices determined in Step 2, the distance was calculated for each day for each pair by squaring the difference between the normalised prices for the day of each pair.
4. Lastly, the square of the distances determined in Step 3 were summed to find the distance between each pair. This figure is provided in the table below.
 GIPCL JPVL JSW NHPC NTPC PGRID RIL SJVN GIPCL JPVL 73.93 JSW 373.48 252.88 NHPC 379.05 450.83 607.67 NTPC 270.75 230.36 199.22 620.60 PGRID 367.39 495.96 780.77 402.08 474.66 RIL 484.97 599.09 861.60 210.93 686.01 193.01 SJVN 356.87 253.64 145.23 493.60 338.50 746.79 722.27

The least distance is found between GIPCL and JPVL.

So, we form a pair between Gujarat Industries Power Company Ltd and Jaiprakash Power Ventures Ltd.

## Selecting Stocks to form pair from the Coal Industry.

The Stocks being studied are as follows:

1. Coal India Ltd (CIL)
2. Gujarat Mineral Development Corporation Ltd (GMDC)
3. Gujarat Natural Resources Ltd (GNRL)
4. Auroma Coke Ltd (ACL)
5. Austral Coke & Projects Ltd (ACPL)

The following steps were followed:

1. The Historical Prices from 1-Jun-2017 to 31-May-2018 were collected for each of the Stocks.
2. From the Historical Prices gathered in Step 1, the normalised prices of each day for each Stocks was calculated as (Stock Price – Mean(Stock Prices)) / Standard Deviation(Stock Prices).
3. From the normalised prices determined in Step 2, the distance was calculated for each day for each pair by squaring the difference between the normalised prices for the day of each pair.
4. Lastly, the square of the distances determined in Step 3 were summed to find the distance between each pair. This figure is provided in the table below.
 CIL GMDC GNRL ACL ACPL CIL GMDC 453.70 GNRL 775.53 331.07 ACL 274.49 267.53 656.18 ACPL 632.37 168.82 209.24 430.89

The minimum distance is between GMDC and ACPL. However, ACPL is not a solvent company. Thus, we will not form any pair in this sector.

## Selecting Stocks to form pair from the Power and Coal Industry.

The Stocks from Power Industry being studied are as follows:

1. Gujarat Industries Power Company Ltd. (GIPCL)
2. Jaiprakash Power Ventures Ltd. (JPVL)
3. JSW Energy Ltd. (JSW)
4. NHPC Ltd. (NHPC)
5. NTPC Ltd. (NTPC)
6. Power Grid Corporation India Ltd. (PGRID)
7. Reliance Industries Ltd. (RIL)
8. SJVN Ltd. (SJVN)

The Stocks from Coal Industry being studied are as follows:

1. Coal India Ltd (CIL)
2. Gujarat Mineral Development Corporation Ltd (GMDC)
3. Gujarat Natural Resources Ltd (GNRL)
4. Auroma Coke Ltd (ACL)
5. Austral Coke & Projects Ltd (ACPL)

The following steps were followed:

1. The Historical Prices from 1-Jun-2017 to 31-May-2018 were collected for each of the Stocks.
2. From the Historical Prices gathered in Step 1, the normalised prices of each day for each Stocks was calculated as (Stock Price – Mean(Stock Prices)) / Standard Deviation(Stock Prices).
3. From the normalised prices determined in Step 2, the distance was calculated for each day for each pair by squaring the difference between the normalised prices for the day of each pair.
4. Lastly, the square of the distances determined in Step 3 were summed to find the distance between each pair. This figure is provided in the table below.
 CIL GMDC GNRL ACL ACPL GIPCL 552.48 123.18 345.02 288.26 100.93 JPVL 435.14 145.78 425.48 181.98 150.66 JSW 142.16 270.44 680.09 118.87 516.34 NHPC 686.09 328.67 180.44 712.26 242.99 NTPC 412.42 208.79 545.87 148.91 438.62 PGRID 841.18 477.22 278.55 656.26 399.97 RIL 830.04 559.33 201.94 866.16 347.25 SJVN 150.68 248.28 557.56 261.02 408.01

The minimum distance is between GIPCL and ACPL. However, ACPL is not a solvent company. Thus, we will not form this pair.

The second minimum distance is between JSW and ACL. However, ACL is not a solvent company. Thus, we will not form this pair.

The third minimum distance is between GIPCL and GMDC. However, GIPCL already appears in our pair from Power Industry. Thus, we will not form this pair.

The fourth minimum distance is between JSW Energy and Coal India Ltd. We will form this pair.

## List of Rules for Trading with the Pairs formed

1. Trading begins from the next day at the end of the Observation Period.
2. Trading Window is 6 months.
3. I will enter trade when the Standard Deviation of the Stock Price in the pair is more than 2 Standard Deviations.
4. I will short the Stock in the Pair whose price is 2 Standard Deviations above the Mean Price and long the Stock in the Pair whose price is 2 Standard Deviations is below the Mean Price. (The Price mentioned here is the normalised price. The normalised price is determined as follows: (Stock Price on a Given Date – Mean(Stock Price for the Past 1 Year) / Standard Deviation(Stock Price for the Past 1 Year).
5. I will trade on the day when the Standard Deviation of the Stock to Long is 2 Standard Deviations below the Mean Price.
6. I will exit trading in the pair when the Prices of the Stocks in the Pair crosses.
7. If the Prices do not cross at the end of 6 months, I will exit trading in this Pair at the market price as of that day.
8. If any of the companies in the pair closes down during the Trading Period, I will exit trading in the pair at the market price as of that day.
9. I will trade multiple number of times during the Trading Window of 6 months in the Pair following the rules 4 to 8.