This presentation was used for training final MBA students in NMIMS, Mumbai who were pursuing major in Capital Markets in 2012. The topic of the training was pair trading and statistical arbitrage in securities markets. It was used to build an understanding about the statistical measures such as co-integration, correlation used for analysis and decision making for trading purposes. In these slides the steps to do pair training is explained in details, allowing you to write your very first pair trading strategy ready to be back-tested!! The Process for pair trading: • Create a list of pairs based on the same sector and similar market capitalization • Decide on the time horizon of trade ( hours, days, week or months etc) • Find pair correlation for the universe defined above, choose pair with correlation above 0.60 for the desired trading horizon • Check whether pair is co-integrated • Calculate Price Ratio, Moving Average of Price Ratio • To Normalize, calculate, standard deviation for Price Ratio and subsequently, calculate Z-score • Based on the Z-score, define the pair entry points. Generally, z-score above +2 and below -2 are considered to be good measure of probability of pair exhibiting mean reversion • Execute pair on rupee-neutral basis. • Define, Strict Stop-Loss and Profit mechanism before entering trade • Its good practice to allocate fund to different pair portfolio rather than one signal trade To access the restricted content, get in touch with us at contact@quantinsti.com

1. Statistical Arbitrage: Pair Trading
Shaurya Chandra
Quantinsti

2. Content Index
• Process of Quant- Trading Strategy
• Statistical Arbitrage
• Pair Trading Strategy
• Implementation Methodology
• Example of Prices of two Cement Stock
• Pair Ratio Behavior
• Why Pair Trading Work?
• Key Decision Points for Pair Trading & Risk Area
• Investor Decisions
• Stationary Process

3. Content Index
• What’s Co-integration?
• Correlation Vs. Co-integration
• Correlation Calculation
• Co-Integration
• Co-Integration- Mathematical Definition:
• Co-integration calculation
• Pair Ratio Movement for Above Example
• Z-score
• Process of Pair Selection
• Other key points to be kept in mind

4. Process of Quant- Trading Strategy
Hypothesis Formulation
Back-Testing & Hypothesis Verification
Parameter Optimization
Going Live with Strategy

5. Statistical Arbitrage
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6. Pair Trading Strategy
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7. Implementation Methodology
Select pair
of stocks that
move together
closely
1
Wait until
prices diverge
beyond a certain
threshold, then
short “winner”
and buy
“loser”
2
Reverse your
positions when
the two prices
converge --> Profit
from the reversal
in trend
3

8. 0.00
20.00
40.00
60.00
80.00
100.00
120.00
140.00
160.00
180.00
0
200
400
600
800
1000
1200
1400
3-Jan-05 3-Jan-06 3-Jan-07 3-Jan-08 3-Jan-09 3-Jan-10
ACC Ambuja
Example of Prices of two Cement Stock

9. 0.100
0.105
0.110
0.115
0.120
0.125
0.130
Price Ratio 30 Day MA
Pair Ratio Behavior

10. Why Pair Trading Work?
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11. Key Decision Points for Pair Trading & Risk Area
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12. Investor Decisions
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13. Stationary Process
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14. What’s Co-integration??
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15. Correlation vs Co-integration
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16. Correlation Calculation
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17. Co-Integration
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18. Co-Integration- Mathematical Definition:
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19. Co-Integration contd..
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20. Co-integration calculation
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21. 0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
Ratio Mean
Upper Line Lower line
Pair Ratio Movement for Above Example
Period:23-Oct-08
to 06-Nov-2009
30-Day Moving
Average
+/- 2.25 Deviation
Mean fairly Stable

22. -2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
Z-Score
Z-…
Z-score
Zscore = (Pair
Ratio –
mean)/
(Standard
Deviation)

23. Process of Pair Selection
• The Process:
• Create a list of pairs based on the same sector and similar market
capitalization
• Decide on the time horizon of trade ( hours, days, week or months etc)
• Find pair correlation for the universe defined above, choose pair with
correlation above 0.60 for the desired trading horizon
• Check whether pair is co-integrated
• Calculate Price Ratio, Moving Average of Price Ratio
• To Normalize, calculate, standard deviation for Price Ratio and subsequently,
calculate Z-score
• Based on the Z-score, define the pair entry points. Generally, z-score above
+2 and below -2 are considered to be good measure of probability of pair
exhibiting mean reversion
• Execute pair on rupee-neutral basis.
• Define, Strict Stop-Loss and Profit mechanism before entering trade
• Its good practice to allocate fund to different pair portfolio rather than one
signal trade

24. Other key points to be kept in mind
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25. Bibliography
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26. Thank You!
To Learn Automated Trading
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