Pairs Trading Analysis
Global Asset Allocation
Spring 2004
The Hemline Theorists
Pairs Trading Analysis

Introduction

Developing the Model

Results
Introduction


Long/short, market- and industryneutral strategy
Pair selection criteria:
• same industry
• mature companies
• long trading histories
• similar exposure to macro factors

Assume reversion to historical value
relationships
Developing the Model

Variable selection
• Stock price ratio
• Dividend yield ratio

Selecting in-sample period and data
frequency
• Daily data: 1987-2004
Pairs Trading Analysis:
Model Parameters



Variables Switched on or off
Deviation from mean historical ratio
required for trade signal
Translation of individual variable
trade signals into overall trade signal
Selecting Pairs – Ford and GM
GM/Ford Price Ratio
7.00
GM introduces its "GM10" family of
newly redesigned midsize cars.
Restores profitability through
streamlined operations.
6.00
5.00
4.00
3.00
Ford announces
highest earnings in
auto industry history
2.00
GM announces a restructuring of
its North American sales and
marketing operations, replacing
marketing division-specific
organizations with a single sales
1.00
2004
2003
2003
2002
2002
2001
2001
2000
2000
1999
1999
1998
1998
1997
1997
1996
1996
1995
1995
1994
1994
1993
1993
1992
1992
1991
1991
1990
1990
1989
1989
1988
1988
1987
1987
0.00
Model Demonstration
In-Sample Optimization

Find the model parameters that:
• Maximize average annual return on
trade days
• Trade on at least 10% of total days
• Limit maximum drawdown to 15%
• Sanity check to ensure model works
over time and is currently valid
Model Parameters
Sample Data
Average
Minimum
Maximum
Standard Dev
High Threshold
Low Threshold
GM/Ford
GM/Ford
Price Ratio
Div Yield Ratio
3.51
1.63
1.64
0.67
5.79
3.76
0.755
0.694
3.74
1.98
3.29
1.29
Model Inputs
Price Ratio
Dividend Yield Ratio
Overall Trade Signal Value
Variable On/Off (1/0)
1
1
2
Sensitivity
0.30
0.50
2
In-Sample Results
Model Results
Number of Total Days
Number of Days Traded
% of Days Traded
Cumulative Return
AACR - Total Days
AACR - Days Traded
Highest One-Day Return
Lowest One-Day Return
Number of Positive Days
Number of Negative Days
Largest Drawdown
3063
429
14.01%
138.36%
7.35%
65.90%
5.83%
-4.52%
237
192
-11.68%
Out-of-Sample Results
Model Results
Number of Total Days
Number of Days Traded
% of Days Traded
Cumulative Return
AACR - Total Days
AACR - Days Traded
Highest One-Day Return
Lowest One-Day Return
Number of Positive Days
Number of Negative Days
Largest Drawdown
1257
161
12.81%
39.09%
6.78%
66.92%
10.86%
-7.90%
79
82
-15.32%
Extending the Model to Other Pairs
Eli Lilly & Merck
Model Results
Number of Total Days
Number of Days Traded
% of Days Traded
Cumulative Return
AACR - Total Days
AACR - Days Traded
Highest One-Day Return
Lowest One-Day Return
Number of Positive Days
Number of Negative Days
Largest Drawdown
Coca-Cola & Pepsi
Model Results
1257
67
5.33%
42.32%
7.27%
273.18%
53.11%
-5.01%
29
38
-14.25%
Number of Total Days
Number of Days Traded
% of Days Traded
Cumulative Return
AACR - Total Days
AACR - Days Traded
Highest One-Day Return
Lowest One-Day Return
Number of Positive Days
Number of Negative Days
Largest Drawdown
1257
80
6.36%
26.66%
4.81%
109.27%
12.13%
-6.52%
38
42
-17.49%
Pairs Trading Analysis
Questions?
In Sample Optimization
GM/Ford Div. Yld. Ratio Sensitivity
Return on Days Traded
GM/Ford Price Ratio Sensitivity
0.3
0.4
0.5
0.6
0
0.1
0.2
0.7
0.8
0.9
1
0
5.7%
15.8%
18.6%
21.7%
19.5%
8.9%
9.7%
6.6%
1.1%
-0.8%
0.3%
0.1
10.2%
22.5%
27.4%
33.2%
32.7%
21.1%
23.7%
21.1%
14.4%
12.0%
12.0%
0.2
15.0%
30.1%
36.7%
46.4%
49.1%
36.2%
42.5%
41.4%
32.8%
29.1%
29.1%
0.3
13.3%
29.8%
38.0%
51.7%
57.0%
41.3%
51.7%
52.1%
39.5%
33.8%
33.8%
0.4
15.2%
34.3%
45.6%
65.5%
78.4%
62.7%
87.7%
103.0%
88.9%
77.4%
77.4%
0.5
13.8%
34.4%
44.4%
65.9%
81.0%
63.0%
96.2%
124.6%
108.8%
89.0%
89.0%
0.6
12.8%
31.9%
40.8%
63.7%
78.8%
58.0%
93.9%
129.5%
108.6%
78.7%
78.7%
0.7
18.0%
37.2%
40.8%
63.7%
78.8%
58.0%
93.9%
129.5%
108.6%
78.7%
78.7%
0.8
15.1%
30.7%
34.5%
56.9%
78.8%
58.0%
93.9%
129.5%
108.6%
78.7%
78.7%
0.9
21.9%
31.8%
37.1%
64.8%
76.8%
58.0%
93.9%
129.5%
108.6%
78.7%
78.7%
1
20.6%
31.8%
33.6%
58.1%
70.7%
55.5%
93.9%
129.5%
108.6%
78.7%
78.7%
In Sample Optimization
GM/Ford Div. Yld. Ratio Sensitivity
Percentage of Days Traded
GM/Ford Price Ratio Sensitivity
0.3
0.4
0.5
0.6
0
0.1
0.2
0.7
0.8
0.9
1
0
47.1%
40.9%
33.6%
28.5%
24.3%
21.3%
19.4%
17.8%
16.8%
16.7%
16.6%
0.1
43.9%
37.7%
30.4%
25.3%
21.1%
18.1%
16.2%
14.6%
13.6%
13.5%
13.5%
0.2
39.8%
33.7%
26.7%
21.6%
17.4%
14.3%
12.4%
10.8%
9.8%
9.7%
9.7%
0.3
36.1%
30.0%
23.0%
18.1%
13.9%
10.8%
9.0%
7.3%
6.4%
6.2%
6.2%
0.4
33.4%
27.4%
20.4%
15.4%
11.2%
8.2%
6.3%
4.7%
3.7%
3.6%
3.6%
0.5
31.7%
25.7%
18.9%
14.0%
9.8%
6.7%
4.9%
3.2%
2.3%
2.1%
2.1%
0.6
30.0%
24.4%
17.9%
13.3%
9.0%
6.0%
4.1%
2.5%
1.5%
1.4%
1.4%
0.7
27.5%
23.4%
17.9%
13.3%
9.0%
6.0%
4.1%
2.5%
1.5%
1.4%
1.4%
0.8
25.9%
22.2%
17.3%
13.2%
9.0%
6.0%
4.1%
2.5%
1.5%
1.4%
1.4%
0.9
21.7%
19.2%
16.0%
12.7%
8.9%
6.0%
4.1%
2.5%
1.5%
1.4%
1.4%
1
17.0%
15.0%
12.6%
10.7%
8.7%
5.9%
4.1%
2.5%
1.5%
1.4%
1.4%
In Sample Optimization
GM/Ford Div. Yld. Ratio Sensitivity
Maximum Drawdown
GM/Ford Price Ratio Sensitivity
0.3
0.4
0.5
0.6
0
0.1
0.2
0.7
0.8
0.9
1
0
-27.6%
-27.6%
-27.6%
-27.6%
-27.6%
-27.6%
-27.6%
-27.6%
-27.6%
-27.6%
-27.6%
0.1
-25.0%
-23.9%
-23.9%
-23.9%
-23.9%
-23.9%
-23.9%
-23.9%
-23.9%
-23.9%
-23.9%
0.2
-25.0%
-19.4%
-16.9%
-16.9%
-16.9%
-16.9%
-16.9%
-16.9%
-16.9%
-16.9%
-16.9%
0.3
-25.0%
-19.4%
-13.9%
-13.3%
-13.3%
-13.3%
-13.3%
-13.3%
-13.3%
-13.3%
-13.3%
0.4
-25.0%
-19.4%
-13.9%
-11.7%
-9.0%
-8.1%
-8.1%
-8.1%
-8.1%
-8.1%
-8.1%
0.5
-25.0%
-19.4%
-13.9%
-11.7%
-9.0%
-7.8%
-5.9%
-5.9%
-5.9%
-5.9%
-5.9%
0.6
-25.0%
-19.4%
-13.9%
-11.7%
-9.0%
-7.8%
-5.9%
-5.9%
-5.9%
-5.9%
-5.9%
0.7
-25.0%
-19.4%
-13.9%
-11.7%
-9.0%
-7.8%
-5.9%
-5.9%
-5.9%
-5.9%
-5.9%
0.8
-25.0%
-19.4%
-13.9%
-11.7%
-9.0%
-7.8%
-5.9%
-5.9%
-5.9%
-5.9%
-5.9%
0.9
-23.1%
-17.3%
-12.3%
-11.7%
-9.0%
-7.8%
-5.9%
-5.9%
-5.9%
-5.9%
-5.9%
1
-22.6%
-16.8%
-12.3%
-9.1%
-7.8%
-7.8%
-5.9%
-5.9%
-5.9%
-5.9%
-5.9%
In Sample Optimization
GM/Ford Div. Yld. Ratio Sensitivity
Ratio of Up Days to Down Days
GM/Ford Price Ratio Sensitivity
0.3
0.4
0.5
0.6
0
0.1
0.2
0.7
0.8
0.9
1
0
1.10
1.14
1.10
1.12
1.09
1.09
1.09
1.09
1.05
1.04
1.05
0.1
1.12
1.16
1.12
1.14
1.11
1.11
1.12
1.12
1.07
1.06
1.06
0.2
1.14
1.19
1.14
1.17
1.15
1.15
1.16
1.18
1.10
1.09
1.09
0.3
1.15
1.21
1.17
1.22
1.20
1.21
1.25
1.30
1.19
1.17
1.17
0.4
1.16
1.23
1.18
1.25
1.23
1.27
1.35
1.47
1.31
1.27
1.27
0.5
1.15
1.22
1.16
1.23
1.21
1.24
1.33
1.48
1.23
1.17
1.17
0.6
1.16
1.21
1.15
1.22
1.18
1.20
1.29
1.45
1.09
1.00
1.00
0.7
1.13
1.20
1.15
1.22
1.18
1.20
1.29
1.45
1.09
1.00
1.00
0.8
1.11
1.18
1.15
1.21
1.18
1.20
1.29
1.45
1.09
1.00
1.00
0.9
1.15
1.21
1.19
1.26
1.17
1.20
1.29
1.45
1.09
1.00
1.00
1
1.13
1.18
1.14
1.21
1.17
1.19
1.29
1.45
1.09
1.00
1.00