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Article: Basket trading under co-integration with the logistic mixture autoregressive model

TitleBasket trading under co-integration with the logistic mixture autoregressive model
Authors
KeywordsBasket trading
Co-integration
Em algorithm
Logistic mixture
Relative value trading
Issue Date2011
PublisherRoutledge. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/14697688.asp
Citation
Quantitative Finance, 2011, v. 11 n. 9, p. 1407-1419 How to Cite?
AbstractIn this paper, we propose a co-integration model with a logistic mixture auto-regressive equilibrium error (co-integrated LMAR), in which the equilibrium relationship among cumulative returns of different financial assets is modelled by a logistic mixture autoregressive time series model. The traditional autoregression (AR) based unit root test (ADF test), used in testing co-integration, cannot give a sound explanation when a time series passes the ADF test. However, its largest root in the AR polynomial is extremely close to, but less than, one, which is most likely the result of a mixture of random-walk and mean-reverting processes in the time series data. With this background, we put an LMAR model into the co-integration framework to identify baskets that have a large spread but are still well co-integrated. A sufficient condition for the stationarity of the LMAR model is given and proved using a Markovian approach. A two-step estimating procedure, combining least-squares estimation and the Expectation-Maximization (EM) algorithm, is given. The Bayesian information criterion (BIC) is used in model selection. The co-integrated LMAR model is applied to basket trading, which is a widely used tool for arbitrage. We use simulation to assess the model in basket trading strategies with the statistical arbitrage feature in equity markets. Data from several sectors of the Hong Kong Hang Seng Index are used in a simulation study on basket trading. Empirical results show that a portfolio using the co-integrated LMAR model has a higher return than portfolios selected by traditional methods. Although the volatility in the return increases, the Sharpe ratio also increases in most cases. This risk-return profile can be explained by the shorter converging period in the co-integrated LMAR model and the larger volatility in the 'mean-reverting' regime. © 2011 Taylor & Francis.
Persistent Identifierhttp://hdl.handle.net/10722/143391
ISSN
2015 Impact Factor: 0.794
2015 SCImago Journal Rankings: 0.565
ISI Accession Number ID
Funding AgencyGrant Number
HKU200707176133
HK GRFHKU7036/06P
Funding Information:

The research of Philip L. H. Yu and W. K. Li is supported by the HKU Small Project Funding (200707176133). We thank the three referees and the Editor for suggestions that led to improvement of the paper. We thank also Ms Vicki Geall and Dr Andrew Carverhill for their help in polishing the paper. W. K. Li also acknowledges HK GRF grant HKU7036/06P for partial support.

References

 

DC FieldValueLanguage
dc.contributor.authorCheng, Xen_HK
dc.contributor.authorYu, PLHen_HK
dc.contributor.authorLi, WKen_HK
dc.date.accessioned2011-11-24T10:04:58Z-
dc.date.available2011-11-24T10:04:58Z-
dc.date.issued2011en_HK
dc.identifier.citationQuantitative Finance, 2011, v. 11 n. 9, p. 1407-1419en_HK
dc.identifier.issn1469-7688en_HK
dc.identifier.urihttp://hdl.handle.net/10722/143391-
dc.description.abstractIn this paper, we propose a co-integration model with a logistic mixture auto-regressive equilibrium error (co-integrated LMAR), in which the equilibrium relationship among cumulative returns of different financial assets is modelled by a logistic mixture autoregressive time series model. The traditional autoregression (AR) based unit root test (ADF test), used in testing co-integration, cannot give a sound explanation when a time series passes the ADF test. However, its largest root in the AR polynomial is extremely close to, but less than, one, which is most likely the result of a mixture of random-walk and mean-reverting processes in the time series data. With this background, we put an LMAR model into the co-integration framework to identify baskets that have a large spread but are still well co-integrated. A sufficient condition for the stationarity of the LMAR model is given and proved using a Markovian approach. A two-step estimating procedure, combining least-squares estimation and the Expectation-Maximization (EM) algorithm, is given. The Bayesian information criterion (BIC) is used in model selection. The co-integrated LMAR model is applied to basket trading, which is a widely used tool for arbitrage. We use simulation to assess the model in basket trading strategies with the statistical arbitrage feature in equity markets. Data from several sectors of the Hong Kong Hang Seng Index are used in a simulation study on basket trading. Empirical results show that a portfolio using the co-integrated LMAR model has a higher return than portfolios selected by traditional methods. Although the volatility in the return increases, the Sharpe ratio also increases in most cases. This risk-return profile can be explained by the shorter converging period in the co-integrated LMAR model and the larger volatility in the 'mean-reverting' regime. © 2011 Taylor & Francis.en_HK
dc.languageengen_US
dc.publisherRoutledge. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/14697688.aspen_HK
dc.relation.ispartofQuantitative Financeen_HK
dc.rightsThis is an electronic version of an article published in [include the complete citation information for the final version of the article as published in the print edition of the journal]. [JOURNAL TITLE] is available online at: http://www.informaworld.com/smpp/ with the open URL of your articleen_US
dc.subjectBasket tradingen_HK
dc.subjectCo-integrationen_HK
dc.subjectEm algorithmen_HK
dc.subjectLogistic mixtureen_HK
dc.subjectRelative value tradingen_HK
dc.titleBasket trading under co-integration with the logistic mixture autoregressive modelen_HK
dc.typeArticleen_HK
dc.identifier.emailYu, PLH: plhyu@hkucc.hku.hken_HK
dc.identifier.emailLi, WK: hrntlwk@hku.hken_HK
dc.identifier.authorityYu, PLH=rp00835en_HK
dc.identifier.authorityLi, WK=rp00741en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1080/14697688.2010.506445en_HK
dc.identifier.scopuseid_2-s2.0-80052298848en_HK
dc.identifier.hkuros197789en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-80052298848&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume11en_HK
dc.identifier.issue9en_HK
dc.identifier.spage1407en_HK
dc.identifier.epage1419en_HK
dc.identifier.isiWOS:000299886100011-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridCheng, X=26429080500en_HK
dc.identifier.scopusauthoridYu, PLH=7403599794en_HK
dc.identifier.scopusauthoridLi, WK=14015971200en_HK

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