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7/15/2019 Mean Reversion Based on Autocorrelation: A Comparison Using the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs
http://slidepdf.com/reader/full/mean-reversion-based-on-autocorrelation-a-comparison-using-the-sp-100-constituent 1/18
Mean Reversion Based onAutocorrelation: A Comparison Using
the S&P 100 Constituent Stocks and
the 100 Most Liquid ETFs
May 2011
Authors:Christian L. Dunis
Jason Laws
Jozef Rudy
Corresponding author and presenter :
Jozef Rudy
Liverpool JMU, TATRA Asset Management
7/15/2019 Mean Reversion Based on Autocorrelation: A Comparison Using the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs
http://slidepdf.com/reader/full/mean-reversion-based-on-autocorrelation-a-comparison-using-the-sp-100-constituent 2/18
Outline•
Motivation
• Data used
– 2 types of data: daily and half-daily
– In- and out-of-sample periods
• Methodology
– 2 types of portfolios – from either pair of ETFs or shares
– Conditional parameters
– No optimization
• Results
– Comparison of results for ETF and share portfolios and daily, half-dailydata
• Conclusions
2
7/15/2019 Mean Reversion Based on Autocorrelation: A Comparison Using the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs
http://slidepdf.com/reader/full/mean-reversion-based-on-autocorrelation-a-comparison-using-the-sp-100-constituent 3/18
Motivation•
Contrarian profits explained by overreaction hypothesis (Lo andMacKinlay, 1990), where assumption of negative autocorrelation isvery common (Locke and Gupta, 2009)
• Recent decreasing performance of contrarian strategies (Khandaniand Lo, 2007)
• According to Kim (2009), after accounting for statistical biases,contrarian strategies are not profitable at all
• Majority of trading ideas well-known across Wall Street. A practical
implementation and parameters make every strategy “unique“(Chan, 2009)
• Unique idea: to increase sampling frequency from Close-Close toClose-Open-Close and compare performance for ETFs and shares
3
7/15/2019 Mean Reversion Based on Autocorrelation: A Comparison Using the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs
http://slidepdf.com/reader/full/mean-reversion-based-on-autocorrelation-a-comparison-using-the-sp-100-constituent 4/18
Data used
• S&P 100 Equities and 100 most liquid ETFs:
– Data : 2nd Jan 2002 – 26th Nov 2010
– Half-daily data : 2nd Jan 2002 – 26th Nov 2010
• Every day, pairs are formed from either 2 sharesor 2 ETFs that fulfill 3 criteria described inMethodology
• In- and Out-of-Sample Periods:
4
7/15/2019 Mean Reversion Based on Autocorrelation: A Comparison Using the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs
http://slidepdf.com/reader/full/mean-reversion-based-on-autocorrelation-a-comparison-using-the-sp-100-constituent 5/18
Methodology I
• In every sessions, 2 portfolios of pairs are formed
that contain either pairs of shares or ETFs with:
– Conditional correlation over 0.8
– Conditional autocorrelation in certain bounds
– Normalized return over previous period higher than 1
7/15/2019 Mean Reversion Based on Autocorrelation: A Comparison Using the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs
http://slidepdf.com/reader/full/mean-reversion-based-on-autocorrelation-a-comparison-using-the-sp-100-constituent 6/18
Methodology II
• Conditional correlation:
whereand , see JPMorgan (1996)
• Normalized return: , where
cov( , ) A B t t A B
t t
r r
1
cov( , ) cov( , ) (1 ) A B t A B t A B
r r r r r r
2 2
1 (1 )t t r
t t
t
Rr
1 1
ln( ) ln( )
A B
t t t A B
t t
P P R P P
7/15/2019 Mean Reversion Based on Autocorrelation: A Comparison Using the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs
http://slidepdf.com/reader/full/mean-reversion-based-on-autocorrelation-a-comparison-using-the-sp-100-constituent 7/18
Methodology III
• 2 Portfolios – from pairs of shares and ETFs,contain only 5 best pairs in any moment.
•
Best pairs are 5 pairs with the highest normalizedreturn, that fulfill before mentioned conditions
• None of the thresholds have been optimized,
thus possibility to obtain even better results.However, in-sample optimization would take verylong time
7/15/2019 Mean Reversion Based on Autocorrelation: A Comparison Using the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs
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Methodology IV
• Measure of profitability
For daily data :
For half-daily data:
. 252
R
Annualized Information Ratio
. 252*2 R
Annualized Information Ratio
7/15/2019 Mean Reversion Based on Autocorrelation: A Comparison Using the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs
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Costs of trading
• Trading costs one-way for both shares (longand short): 0.2%
– Transaction costs: 0.1% (0.05% * 2)
– Bid-ask spread: 0.1% (0.05% * 2)
• Net return calculation:
9
1 1ln( / ) ln( / )
t t t t t X X Y Y Ret P P P P TC
7/15/2019 Mean Reversion Based on Autocorrelation: A Comparison Using the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs
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Results – daily data
•
Portfolio consisting of 5 best pairs of shares
in-sample results
out-of-sample results
7/15/2019 Mean Reversion Based on Autocorrelation: A Comparison Using the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs
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Results – daily data
•
Portfolio consisting of 5 best pairs of ETFs
in-sample results
out-of-sample results
7/15/2019 Mean Reversion Based on Autocorrelation: A Comparison Using the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs
http://slidepdf.com/reader/full/mean-reversion-based-on-autocorrelation-a-comparison-using-the-sp-100-constituent 12/18
Results – half-daily data
•
Portfolio consisting of 5 best pairs of shares
in-sample results
out-of-sample results
7/15/2019 Mean Reversion Based on Autocorrelation: A Comparison Using the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs
http://slidepdf.com/reader/full/mean-reversion-based-on-autocorrelation-a-comparison-using-the-sp-100-constituent 13/18
Results – half-daily data
•
Portfolio consisting of 5 best pairs of ETFs
in-sample results
out-of-sample results
7/15/2019 Mean Reversion Based on Autocorrelation: A Comparison Using the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs
http://slidepdf.com/reader/full/mean-reversion-based-on-autocorrelation-a-comparison-using-the-sp-100-constituent 14/18
Results – half-daily data
Works with 10 … • Portfolio consisting of 10 best pairs of ETFs
out-of-sample results
7/15/2019 Mean Reversion Based on Autocorrelation: A Comparison Using the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs
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Results – half-daily data
and 20 as well… • Portfolio consisting of 20 best pairs of ETFs
out-of-sample results
7/15/2019 Mean Reversion Based on Autocorrelation: A Comparison Using the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs
http://slidepdf.com/reader/full/mean-reversion-based-on-autocorrelation-a-comparison-using-the-sp-100-constituent 16/18
Conclusions
• Information ratios for ETF pairs are higher thanfor pairs of shares
•
Half-daily sampling frequency provides betterresults than using a daily sampling frequency
• Spread returns of pairs with negative first-order
autocorrelation are easier to predict than thereturns of pairs with the same but positiveautocorrelation
7/15/2019 Mean Reversion Based on Autocorrelation: A Comparison Using the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs
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References•
Alexander, C. and Dimitriu, A. (2002) The Cointegration Alpha: Enhanced IndexTracking and Long-Short Equity Market Neutral Strategies. SSRN eLibrary,
http://ssrn.com/paper=315619
• Burgess, A. N. (2003) Using Cointegration to Hedge and Trade International
Equities. In Dunis, C., Laws, J. And Naïm, P. [eds.] Applied Quantitative Methods for
Trading and Investment. John Wiley & Sons, Chichester, 41-69.
• Chan, E. (2009) Quantitative Trading: How to Build Your Own Algorithmic TradingBusiness, John Wiley & Sons, Inc., New Jersey.
• Jpmorgan (1996) Riskmetrics, New York.
• Khandani, A. E. and Lo, A. W. (2007) What Happened to the Quants in August
2007? Journal of Investment Management, 5, 4, 5-54.
• Kim, H. (2009) On the Usefulness of the Contrarian Strategy across National StockMarkets: A Grid Bootstrap Analysis. Journal of Empirical Finance, 16, 5, 734-744.
• Lo, A. W. and Mackinlay, A. C. (1990) When Are Contrarian Profits Due to Stock
Market Overreaction? The Review of Financial Studies, 3, 2, 175-205.
• Locke, S. and Gupta, K. (2009) Applicability of Contrarian Strategy in the Bombay
Stock Exchange. Journal of Emerging Market Finance, 8, 2, 165-189.17
7/15/2019 Mean Reversion Based on Autocorrelation: A Comparison Using the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs
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Thank you for your attention
Q & A
18