Mean Reversion Based on Autocorrelation: A Comparison Using the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs

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

[email protected]

Liverpool JMU, TATRA Asset Management

mailto:[email protected]

mailto:[email protected]



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



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



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



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



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



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



Methodology IV

• Measure of profitability

For daily data :

For half-daily data:

. 252

R

Annualized Information Ratio

. 252*2 R

Annualized Information Ratio



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



Results – daily data

•

Portfolio consisting of 5 best pairs of shares

in-sample results

out-of-sample results



Results – daily data

•

Portfolio consisting of 5 best pairs of ETFs

in-sample results




Results – half-daily data

•

Portfolio consisting of 5 best pairs of shares

in-sample results





•

Portfolio consisting of 5 best pairs of ETFs

in-sample results





Works with 10 … • Portfolio consisting of 10 best pairs of ETFs





and 20 as well… • Portfolio consisting of 20 best pairs of ETFs




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



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










Thank you for your attention

Q & A

18

Documents

Mean Reversion Based on Autocorrelation: A Comparison Using the S&P 100 Constituent Stocks and the 100 Most Liquid ETFs