High-dimensional test for alpha in linear factor pricing models with sparse alternatives
We consider the problem of testing for the presence of alpha in Linear Factor Pricing Models. We propose a novel test of the max-of-squares type, which is designed to deal with the high dimensionality of the securities and the sparse alternatives. We rigorously show that the proposed test has attrac...
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Veröffentlicht in: | Journal of econometrics 2022-07, Vol.229 (1), p.152-175 |
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creator | Feng, Long Lan, Wei Liu, Binghui Ma, Yanyuan |
description | We consider the problem of testing for the presence of alpha in Linear Factor Pricing Models. We propose a novel test of the max-of-squares type, which is designed to deal with the high dimensionality of the securities and the sparse alternatives. We rigorously show that the proposed test has attractive theoretical properties and demonstrate its superior performance via Monte Carlo experiments. These results are established when the number of securities is larger than the time dimension of the return series, and the alternative hypothesis is sparse, i.e. the alpha vector is sparse. As a general alternative, we suggest to combine the max-of-squares type test and a sum-of-squares type test, to benefit from the power advantages of both tests. We apply the two proposed tests to the monthly returns on securities in the Chinese and the U.S. stock markets, respectively under the Fama–French three-factor model, and confirm the usefulness of the proposed tests in detecting the presence of alpha. |
doi_str_mv | 10.1016/j.jeconom.2021.07.011 |
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We propose a novel test of the max-of-squares type, which is designed to deal with the high dimensionality of the securities and the sparse alternatives. We rigorously show that the proposed test has attractive theoretical properties and demonstrate its superior performance via Monte Carlo experiments. These results are established when the number of securities is larger than the time dimension of the return series, and the alternative hypothesis is sparse, i.e. the alpha vector is sparse. As a general alternative, we suggest to combine the max-of-squares type test and a sum-of-squares type test, to benefit from the power advantages of both tests. We apply the two proposed tests to the monthly returns on securities in the Chinese and the U.S. stock markets, respectively under the Fama–French three-factor model, and confirm the usefulness of the proposed tests in detecting the presence of alpha.</description><identifier>ISSN: 0304-4076</identifier><identifier>EISSN: 1872-6895</identifier><identifier>DOI: 10.1016/j.jeconom.2021.07.011</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Alternatives ; Discriminant analysis ; High dimensionality ; Linear factor pricing model ; Monte Carlo simulation ; Return on assets ; Securities in stock markets ; Securities markets ; Sparse alternatives ; Tests for alpha ; Usefulness</subject><ispartof>Journal of econometrics, 2022-07, Vol.229 (1), p.152-175</ispartof><rights>2021 Elsevier B.V.</rights><rights>Copyright Elsevier Sequoia S.A. 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We propose a novel test of the max-of-squares type, which is designed to deal with the high dimensionality of the securities and the sparse alternatives. We rigorously show that the proposed test has attractive theoretical properties and demonstrate its superior performance via Monte Carlo experiments. These results are established when the number of securities is larger than the time dimension of the return series, and the alternative hypothesis is sparse, i.e. the alpha vector is sparse. As a general alternative, we suggest to combine the max-of-squares type test and a sum-of-squares type test, to benefit from the power advantages of both tests. We apply the two proposed tests to the monthly returns on securities in the Chinese and the U.S. stock markets, respectively under the Fama–French three-factor model, and confirm the usefulness of the proposed tests in detecting the presence of alpha.</description><subject>Alternatives</subject><subject>Discriminant analysis</subject><subject>High dimensionality</subject><subject>Linear factor pricing model</subject><subject>Monte Carlo simulation</subject><subject>Return on assets</subject><subject>Securities in stock markets</subject><subject>Securities markets</subject><subject>Sparse alternatives</subject><subject>Tests for alpha</subject><subject>Usefulness</subject><issn>0304-4076</issn><issn>1872-6895</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNqFkFFLwzAUhYMoOKc_QQj43HrTpE37JDLUCQNfFHwLWXqzpbTNTLqJ_96M-e7Thcs5h3M-Qm4Z5AxYdd_lHRo_-iEvoGA5yBwYOyMzVssiq-qmPCcz4CAyAbK6JFcxdgBQiprPyOfSbbZZ6wYco_Oj7umEcaLWB6r73VZTN9LejagDtdpM6b0LzrhxQwffYh_pt5u2NO50iJgcE4ZRT-6A8ZpcWN1HvPm7c_Lx_PS-WGart5fXxeMqM1zClAlRr6UxtuWNEM3aQsulKHmBZVOyCmtji6IprUANKATwqrVGGiFsKzTYNedzcnfK3QX_tU_dVef3qUQfVSGZkKLidZlU5Ullgo8xoFVpxqDDj2KgjhBVp_4gqiNEBVIliMn3cPKlqXhwGFQ0DkeDrQtoJtV690_CL8W-fnc</recordid><startdate>202207</startdate><enddate>202207</enddate><creator>Feng, Long</creator><creator>Lan, Wei</creator><creator>Liu, Binghui</creator><creator>Ma, Yanyuan</creator><general>Elsevier B.V</general><general>Elsevier Sequoia S.A</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8BJ</scope><scope>FQK</scope><scope>JBE</scope></search><sort><creationdate>202207</creationdate><title>High-dimensional test for alpha in linear factor pricing models with sparse alternatives</title><author>Feng, Long ; Lan, Wei ; Liu, Binghui ; Ma, Yanyuan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c370t-448b7ccfd39449bf0d374532e59516e8cf2295f4ea0e44036dfc7c44fd4a0fb33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Alternatives</topic><topic>Discriminant analysis</topic><topic>High dimensionality</topic><topic>Linear factor pricing model</topic><topic>Monte Carlo simulation</topic><topic>Return on assets</topic><topic>Securities in stock markets</topic><topic>Securities markets</topic><topic>Sparse alternatives</topic><topic>Tests for alpha</topic><topic>Usefulness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Feng, Long</creatorcontrib><creatorcontrib>Lan, Wei</creatorcontrib><creatorcontrib>Liu, Binghui</creatorcontrib><creatorcontrib>Ma, Yanyuan</creatorcontrib><collection>CrossRef</collection><collection>International Bibliography of the Social Sciences (IBSS)</collection><collection>International Bibliography of the Social Sciences</collection><collection>International Bibliography of the Social Sciences</collection><jtitle>Journal of econometrics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Feng, Long</au><au>Lan, Wei</au><au>Liu, Binghui</au><au>Ma, Yanyuan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>High-dimensional test for alpha in linear factor pricing models with sparse alternatives</atitle><jtitle>Journal of econometrics</jtitle><date>2022-07</date><risdate>2022</risdate><volume>229</volume><issue>1</issue><spage>152</spage><epage>175</epage><pages>152-175</pages><issn>0304-4076</issn><eissn>1872-6895</eissn><abstract>We consider the problem of testing for the presence of alpha in Linear Factor Pricing Models. We propose a novel test of the max-of-squares type, which is designed to deal with the high dimensionality of the securities and the sparse alternatives. We rigorously show that the proposed test has attractive theoretical properties and demonstrate its superior performance via Monte Carlo experiments. These results are established when the number of securities is larger than the time dimension of the return series, and the alternative hypothesis is sparse, i.e. the alpha vector is sparse. As a general alternative, we suggest to combine the max-of-squares type test and a sum-of-squares type test, to benefit from the power advantages of both tests. 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subjects | Alternatives Discriminant analysis High dimensionality Linear factor pricing model Monte Carlo simulation Return on assets Securities in stock markets Securities markets Sparse alternatives Tests for alpha Usefulness |
title | High-dimensional test for alpha in linear factor pricing models with sparse alternatives |
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