Transcript Optimal Trading of a Mean-Reverting Process MS&E 444, Spring 2008 Shih-Arng (Tony) Pan, Wei Wang, Chen Tze Wee, Ren Fung Yu.

Optimal Trading of a
Mean-Reverting Process
MS&E 444, Spring 2008
Shih-Arng (Tony) Pan, Wei Wang, Chen Tze Wee, Ren Fung Yu
Introduction
• Xt is the spread between two correlated
stocks:
• To maximize power utility of wealth at T,
the optimal position of Xt to hold is:
Choosing correlated stocks
• Stocks were chosen from the S&P 100
index
• Chose stock pairs with the highest
correlation of daily returns (>0.75).
• Examples:
– International Paper/Weyerhauser
– Merrill Lynch/Morgan Stanley
– Chevron/Exxon Mobil
– Baker Hughes/Schlumberger
1
25
49
73
97
121
145
169
193
217
241
265
289
313
337
361
385
409
433
457
481
505
529
553
577
601
625
1
25
49
73
97
121
145
169
193
217
241
265
289
313
337
361
385
409
433
457
481
505
529
553
577
601
625
Merrill Lynch/Morgan Stanley
January 2003 – December 2004
35
30
25
20
Unadjusted
15
10
5
0
15
10
Adjusted
5
0
-5
-10
Parameters
• Parameters k and σ were estimated using
MLE using January 2003 to December
2004 data.
• The strategy was implemented after
January 2005, out of sample.
• Power Utility parameter: γ= -0.1
• Transaction cost: 0.15% of initial wealth
(constant)
Maximize Immediate Utility w/ Scaled Margins
Chevron-Exxon (k=5.51, σ=6.47)
5
Price
0
-5
-10
0
100
200
300
400
500
600
700
Jan 2005 to Apr 2007
original strategy
original strategy with scaled margin
maximize immediate utility strategy with scaled margin
Position
0.6
0.4
0.2
0
Wealth (TC always deducted)
-0.2
0
100
200
300
400
500
600
700
500
600
700
Jan 2005 to Apr 2007
2
1
0
-1
0
100
200
300
400
Jan 2005 to Apr 2007
Moving Window (of 1.5 years)
Baker Hughes - Schlumberger
20
Price
10
0
-10
-20
0
100
200
300
400
500
600
Jan 2005 to Dec 2006
original strategy
original strategy with scaled margin
maximize immediate utility strategy with scaled margin
Position
0.4
0.2
0
-0.2
Wealth (TC always deducted)
-0.4
0
100
200
300
400
500
600
400
500
600
Jan 2005 to Dec 2006
4
2
0
-2
0
100
200
300
Jan 2005 to Dec 2006
Moving Window (of 1.5 years)
Citigroup – Lehman Brothers
0
Price
-10
-20
-30
-40
0
100
200
300
400
500
600
Jan 2005 to Dec 2006
original strategy
original strategy with scaled margin
maximize immediate utility strategy with scaled margin
Position
0.3
0.2
0.1
0
Wealth (TC always deducted)
-0.1
0
100
200
300
400
500
600
400
500
600
Jan 2005 to Dec 2006
1.5
1
0.5
0
-0.5
0
100
200
300
Jan 2005 to Dec 2006
Annual Return Histogram (18 pairs)
Moving Window:
Return = 1.0764
Volatility = 0.3428
No Moving Window:
Return = 1.0418
Volatility = 0.5511
Conclusion
• Theoretical strategy too risky for market
conditions.
• Maximizing immediate utility w/ scaled
margin strategy shows promise.
• Moving Window parameter estimation
improves returns, but not enough to beat
market.
• Better stock pairs, or a process with even
more memory is required.