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Statistical Arbitrage for Multiple Co-integrated Stocks.

ABSTRACT: In this article, we analyse optimal statistical arbitrage strategies from stochastic control and optimisation problems for multiple co-integrated stocks with eigenportfolios being factors. Optimal portfolio weights are found by solving a Hamilton-Jacobi-Bellman (HJB) partial differential equation, which we solve for both an unconstrained portfolio and a portfolio constrained to be market neutral. Our analyses demonstrate sufficient conditions on the model parameters to ensure long-term stability of the HJB solutions and stable growth rates for the optimal portfolios. To gauge how these optimal portfolios behave in practice, we perform backtests on historical stock prices of the S&P 500 constituents from year 2000 through year 2021. These backtests suggest three key conclusions: that the proposed co-integrated model with eigenportfolios being factors can generate a large number of co-integrated stocks over a long time horizon, that the optimal portfolios are sensitive to parameter estimation, and that the statistical arbitrage strategies are more profitable in periods when overall market volatilities are high.

Supplementary information

The online version contains supplementary material available at 10.1007/s00245-022-09838-3.

SUBMITTER: Li TN

PROVIDER: S-EPMC9171503 | biostudies-literature | 2022 Jun

REPOSITORIES: biostudies-literature

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Statistical Arbitrage for Multiple Co-integrated Stocks.

Li Thomas Nanfeng TN Papanicolaou Andrew A

Applied mathematics and optimization 20220607 1

In this article, we analyse optimal statistical arbitrage strategies from stochastic control and optimisation problems for multiple co-integrated stocks with eigenportfolios being factors. Optimal portfolio weights are found by solving a Hamilton-Jacobi-Bellman (HJB) partial differential equation, which we solve for both an unconstrained portfolio and a portfolio constrained to be market neutral. Our analyses demonstrate sufficient conditions on the model parameters to ensure long-term stability ...[more]

PMID: 35694046

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Project description:Background Many microarray experiments search for genes with differential expression between a common “reference” group and multiple test groups, like in the case of time-course designs or of various treatments versus a control condition. In such cases, currently employed statistical approaches based on t-test or close derivatives have limited efficacy, mostly because estimation of noise is done on only two groups at time. Alternative approaches based on ANOVA correctly capture noise from all the groups, but then do not confront single test groups with the reference. We therefore conceived a statistical test for pairwise comparisons between the reference group and each test group that uses within-group variance calculated from all the groups. Results We implemented an R-Bioconductor package named Mulcom, with a statistical test derived from the Dunnett’s test, designed to compare multiple experimental groups against a common reference. In addition to the basic Dunnett’s t value, the package includes an optional minimal fold-change threshold, m. Thanks to automated, permutation-based estimation of False Discovery Rate (FDR), the package also permits fast optimization of the test, to obtain the maximum number of significant genes at a given FDR value. When applied on a time-course experiment profiled in parallel on two microarray platforms, and compared with currently used tests, Mulcom displayed higher concordance of significant genes in the two array platforms, and higher enrichment in functional annotation to categories related to the biology of the experiment. Conclusions The Mulcom package provides a fast and powerful tool for the identification of differentially expressed genes when several experimental conditions are compared with a common reference. We found that Mulcom leads to lists of differentially expressed genes that are particularly consistent across microarray platforms and enriched in significant classes of genes. In our opinion, the main reasons for these good performances are three: (i) within-group variability is estimated from all experimental groups even if only two of them are compared each time; (ii) the optional fold-change threshold m avoids false positives due to aberrantly low within-group variability; (iii) automated test optimization allows maximizing sensitivity without compromising specificity.

Dataset Information

Statistical Arbitrage for Multiple Co-integrated Stocks.

Supplementary information

Publications

Statistical Arbitrage for Multiple Co-integrated Stocks.

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