Stephane Cheung Yukinobu Hamuro Katsuhiko Okada
Detecting stock market seasonalityA period mining approach
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Detecting stock market seasonalityA period mining approach
Stephane Cheung* /Yukinobu Hamuro* / Katsuhiko Okada * ***Kwansei Gakuin University Business School**Magne-Max Capital Management, Japan FSA registered Investment Advisor
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Market seasonality
Fact finding• Agrawal and Tandon (1994) JIMF
18 countries Seasonality, daily, weekend effect, last trading day of the month, large pre-and inter holiday return. Jan, return.
• Bouman and Jacobsen (2002) AER36 global markets out of 37 examined have “sell in May effect”, or “Halloween effect”, including Japan
• Kamstra, Kramer and Levi (2003) AERMarkets in northern hemisphere demonstrate “sell in May” but not in southern hemisphere. SAD effect
• Sakakibara, Yamasaki and Okada (2013) IRFJapan is unique as Jun. is a good month while most other financial markets demonstrate lower June return -> “Dekansho-bushi” effect
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Market Seasonality
• Mark Twain famously observed that October is the most dangerous month to invest in stock market. …The tragedy of pudd’nhead Wilson. 1894.
• The Stock Exchange world is in a sort of twilight state at the moment. The potential buyers seem to have “sold in May and gone away”….. Financial Times May,30 1964
• ‘Sell in May and Go away’, famous Wall Street adage is once again in focus. Would the market behave as the old saying goes? Many investors in the market have anxiety in a corner of their minds……Nihon Keizai Shimbun, April 30, 2013
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4
316 yearsJacobsen Global Fin.
Data index
82 yearsDow Jones index
50 yearsDow Jones index
1693-2009 1929-2011 1961-2011Jan 0.69 1.0 1.2Feb 0.09 0.0 0.0Mar -0.03 0.4 1.1April 0.49 1.4 2.0May 0.02 -0.2 -0.1June -0.12 0.5 -0.6July -0.31 1.5 0.9Aug 0.44 0.8 0.2Sep -0.49 -1.3 -0.8Oct -0.5 0.0 0.5Nov 0.35 0.8 1.2Dec 0.81 1.5 1.5
Nov-April 2.42 5.2 7.2May-Oct -0.96 1.28 0.09
Diff 3.38 3.92 7.11
Nikkei 225
TOPIX
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
First-half YearLast-half Year
Mea
n M
onth
ly R
etur
n (%)
Mean monthly return of Nikkei 225 and TOPIXJan 1971-Dec 2014
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If fund managers had followed the “words of wisdom”…
0
500
1000
1500
2000
2500
3000
3500
1989
/12
1990
/09
1991
/06
1992
/03
1992
/12
1993
/09
1994
/06
1995
/03
1995
/12
1996
/09
1997
/06
1998
/03
1998
/12
1999
/09
2000
/06
2001
/03
2001
/12
2002
/09
2003
/06
2004
/03
2004
/12
2005
/09
2006
/06
2007
/03
2007
/12
2008
/09
TOPIX
-80%
-70%
-60%
-50%
-40%
-30%
-20%
-10%
0%
10%
Dekansho-bushi Investment Full Year Investment
Japan’s Lost 2 decades
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Research question and expectations
Seasonality found in an index level implies that seasonality does exist in individual stock level, or industry level.
The best season for holding stock i may be different from stock j. Finding seasonality in individual stock level enable us to create a
portfolio durable for trading throughout the year.
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Data centric approach
• Traditional financial economist approacha. Researchers come up with some insightsb. Create a model (Hypothesis building)c. Collect datad. Conduct an empirical test to prove or disprove the model (accept or reject the hypothesis)e. Conclusion and conjecture
• Data centric approacha. There is no model. We don’t even have the hypothesisb. Large scale datac. Methodologies to detect correlation, potential predictability, to handle sparse data structure. d. Pattern implies hypothesis
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The Period Mining Model
• Look for stocks that has high propensity to perform well at a given date. (Period Mining)
• Use previous -4 to -1 years for training data• Rolling window up to present• Mining universe is TOPIX 500. Minimum market value of its
composite is 130bil yen ($1.2bil)
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10
Methodology (Image)
2001-2004
2005
Model Building Period
2002-2005
2006
Portfolio formation based on the model created in 2001-4
Rolling window up to present
Portfolio simulation up to 2015.
Model Building Period
Period Mining: 4 steps in model building
Historical data of Stock Price for a stock (eg. Toyota)
1. Enumeration PhaseEnumerating statistics (eg. abnormal return) of all periods defined by combination of starting date and holding period for each term.(We call this period as "item")
3. Filtering PhaseFiltering items by aggregated statistics which match the given conditions (eg. lower bound of duration days).
4. Organizing PhaseSelect items so that there is no overlap and maximize the total abnormal return.
starting date: 1,2,...,125 holding period: 1,2,...,125 125 × 125 = 15,625 items per stock per term
2. Aggregation PhaseAggregating the statistics on each item for last n years (n = 4 in this exp.)
Selected Items (Periods)to hold
term: 125days starting from Jan 1st or July 1st
28 terms from 2001 to 2014
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Enumeration Phase
1 2 3 4 5 6 7 8 .... 124 125 126 127 250
date
……
…
…
term 1
term 2…
starting date: 1,2,...,125 holding period: 1,2,...,125
125 × 125 × 500 equities ≒ 7.8M items per term
Enumerate stock price statistics on period ps,e
s=1, e=2s=1, e=3s=1, e=4
:s=1, e=125s=2, e=3s=2, e=4
:s=2, e=125s=3, e=4s=3, e=5
s=3, e=127
s=125, e=126s=125, e=127
s=125, e=250
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Aggregation Phase
a) Holding periodb) Average of abnormal returnc) SD of abnormal returnd) Average of zigzag rate
:
:
:
:
:
Aggregate all the items based on the following four
criteria
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Filtering Phase
notation min max Rationale
lh lower bound for holding period 0 20 Lower bound: Too short holding period is not favorable due to transactions cost. Upperbound :Index level seasonality is 6 monthuh upper bound for holding period 10 125
lr lower bound for average of abnormal return 0.01 0.1 Abnormal return is higher the better. but
extremely high abnormal return may be due to other reasons than seasonality.ur upper bound for average of abnormal
return 0.11 2.1
us upper bound for SD of abnormalreturn 0.01 1.0 Prefer items that generate stable abnormal
return in the four year training period
lz lower bound for zigzag rate 0 1It is preferable if average trend of stock price movement is monotonously increase in the holding period.
Select periods matching the given 6 conditions. The optimal parameters will be estimated using machine learning technique (Bayesian
Global Optimization).declare
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Organizing Phase
1 2 3 4 5 6 7 8 .... 125 126 127 128 ..... 256 date
1 2 3 4 5 6 7 8 .... 125 126 127 128 ..... 256 date
Objective : maximize the sum of all abnormal returnSubject to : selected periods are not overlapped each other
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Item set for Toyota
Item set for Hitachi
Item set for Sony
Time line
Creating calendar time portfolio
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Jan 4
*Toyota*Hitachi
*Toyota*Hitachi*Sony
*Hitachi*Sony *Sony
Feb 4 Feb 9 Mar 19 Mar 25
Results
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Performance summary
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PeriodMining Model
EW
PeriodMining Model
VWTOPIX TOPIX Mid
400Annualized daily return 14.32% 9.25% 4.67% 5.65%
Annualized daily risk 22.80% 23.47% 22.95% 21.99%
Maximum daily gain 12.60% 12.39% 13.73% 12.87%
Maximum daily drawdown -10.51% -9.20% -9.52% -10.62%
Sharpe ratio 0.628 0.394 0.204 0.257
2005年1月ー2014年12月
Calendar time portfolio performance since inception. Benchmark index: TOPIX , Initial NAV:100, 2005-2014
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Performance difference (right scale)
Period Mining Model
TOPIX
-10
90
190
290
390
490
0
50
100
150
200
250
300
350
2005
0105
2005
0303
2005
0428
2005
0628
2005
0823
2005
1020
2005
1216
2006
0215
2006
0412
2006
0609
2006
0804
2006
0929
2006
1128
2007
0126
2007
0326
2007
0523
2007
0718
2007
0911
2007
1108
2008
0110
2008
0307
2008
0507
2008
0701
2008
0826
2008
1023
2008
1219
2009
0220
2009
0417
2009
0617
2009
0812
2009
1009
2009
1208
2010
0205
2010
0405
2010
0603
2010
0729
2010
0924
2010
1122
2011
0121
2011
0318
2011
0519
2011
0713
2011
0907
2011
1107
2012
0105
2012
0301
2012
0426
2012
0625
2012
0820
2012
1016
2012
1211
2013
0213
2013
0410
2013
0607
2013
0802
2013
0930
2013
1126
2014
0128
2014
0326
2014
0523
2014
0717
2014
0911
2014
1111
Calendar time portfolio performance since inception. Benchmark index: TOPIX Mid 400, Initial NAV:100, 2005-2014
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Performance difference (right scale)
Period Mining Model
TOPIX Mid 400
-10
90
190
290
390
490
0
50
100
150
200
250
300
350
2005
0105
2005
0304
2005
0506
2005
0701
2005
0829
2005
1027
2005
1227
2006
0224
2006
0424
2006
0622
2006
0818
2006
1017
2006
1214
2007
0215
2007
0413
2007
0613
2007
0809
2007
1009
2007
1205
2008
0207
2008
0407
2008
0605
2008
0801
2008
0930
2008
1128
2009
0130
2009
0331
2009
0601
2009
0728
2009
0925
2009
1125
2010
0126
2010
0325
2010
0526
2010
0722
2010
0916
2010
1117
2011
0119
2011
0317
2011
0519
2011
0714
2011
0909
2011
1110
2012
0112
2012
0308
2012
0509
2012
0704
2012
0830
2012
1029
2012
1226
2013
0228
2013
0426
2013
0626
2013
0822
2013
1022
2013
1218
2014
0221
2014
0421
2014
0619
2014
0815
2014
1015
2014
1212
Controlling for “size” and “book-to-market ratio”Three factor model
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Rp,t Rf ,t i i (Rm,t Rf ,t ) siSMBt hiHML i,t
Coefficient Standard error
t-value p-value
Intercept 0.00026 5.675E-05 4.63 0.00000
Rm-Rf 0.01061 4.674E-05 226.92 0.00000
SMB 0.00131 1.009E-04 12.998 0.00000
HML 0.00169 1.492E-04 7.834 0.00000
Annualized alpha 6.50%
The daily performance against the benchmark
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-2.00%
-1.50%
-1.00%
-0.50%
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
2005
0105
2005
0307
2005
0510
2005
0706
2005
0902
2005
1104
2006
0106
2006
0307
2006
0509
2006
0705
2006
0901
2006
1101
2007
0104
2007
0306
2007
0508
2007
0704
2007
0831
2007
1101
2008
0107
2008
0306
2008
0508
2008
0704
2008
0902
2008
1104
2009
0107
2009
0309
2009
0512
2009
0708
2009
0904
2009
1109
2010
0112
2010
0311
2010
0514
2010
0712
2010
0908
2010
1110
2011
0113
2011
0314
2011
0517
2011
0713
2011
0909
2011
1111
2012
0116
2012
0313
2012
0515
2012
0711
2012
0907
2012
1107
2013
0111
2013
0313
2013
0515
2013
0711
2013
0909
2013
1111
2014
0115
2014
0314
2014
0516
2014
0714
2014
0910
2014
1112
Period Mining Portfolio, Composite of stocks and holding period
Number of shares in the portfolio and average holding period
Approximately 400 stocks in the portfolio. There is a little
difference between in the first half and the second half
Average holding period is
about a week
Returns are not so concentrated in the first half.
Abnormal return
Raw return
Are we holding more stocks in the earlier month? Maybe...
Where does the profit (abnormal return) come from?
When and where does the profit come from?
Longer the holding period, better the return? Not really.
Abnormal return Raw return
How long will the strategy work?
Pairs trading (Relative value arbitrage strategy) demonstrate “profitability” beyond various risk measures, short-sale constraints and transaction costs. Gatev et.al. RFS, 2004
However, the profitability has been waned as more and more hedge funds employ similar “pairs trading” strategies.
Seasonality trading is an unexplored approach; chances of enjoying hefty profit could potentially be high.
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Conclusion
• Seasonal anomaly in the stock market has been documented in the literature for quite a while, and yet, the anomaly hasn’t been arbitraged away by professionals even today.
• The difficulty lies in the potential arbitrage profit is only guaranteed in the years, not in the months.
• We endeavored to look for patterns of seasonal investor behavior in large 500 firms listed in TSE 1st.
• To detect the pattern, we used period mining technique and other related techniques commonly used in the computational science.
• Portfolio of stocks in their best season of the year outperform the benchmark index by a substantial margin.
• This “seasonal arbitrage” will remain to be profitable as few participants are playing in this market.
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