{"id":"https://openalex.org/W2052762859","doi":"https://doi.org/10.1111/j.1540-6261.1985.tb02388.x","title":"Approximate Factor Structures: Interpretations and Implications for Empirical Tests","display_name":"Approximate Factor Structures: Interpretations and Implications for Empirical Tests","publication_year":1985,"publication_date":"1985-12-01","ids":{"openalex":"https://openalex.org/W2052762859","doi":"https://doi.org/10.1111/j.1540-6261.1985.tb02388.x","mag":"2052762859"},"language":"en","primary_location":{"id":"doi:10.1111/j.1540-6261.1985.tb02388.x","doi":"https://doi.org/10.1111/j.1540-6261.1985.tb02388.x","is_oa":false,"landing_page_url":"https://doi.org/10.1111/j.1540-6261.1985.tb02388.x","pdf_url":null,"source":{"id":"https://openalex.org/S5353659","display_name":"The Journal of Finance","issn_l":"0022-1082","issn":["0022-1082","1540-6261"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","erih-plus","fnege-1-star","ft50","jufo-3","norway-2","poland-200","russia-white-list-1","utd24","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Finance","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081330903","display_name":"Mark S. Grinblatt","orcid":"https://orcid.org/0000-0001-9857-6769","observed_orcids":["https://orcid.org/0000-0001-9857-6769"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"MARK GRINBLATT","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5011644728","display_name":"Sheridan D. Titman","orcid":"https://orcid.org/0000-0002-0935-7394","observed_orcids":["https://orcid.org/0000-0002-0935-7394"]},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"SHERIDAN TITMAN","raw_affiliation_strings":["Both authors are from the Graduate School of Management, University of California at Los Angeles. We wish to thank Philip Dybvig, Jonathan Ingersoll, Richard Roll, Bruce Rothschild, and Michael Rothschild for comments on an earlier draft of this paper"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Both authors are from the Graduate School of Management, University of California at Los Angeles. We wish to thank Philip Dybvig, Jonathan Ingersoll, Richard Roll, Bruce Rothschild, and Michael Rothschild for comments on an earlier draft of this paper","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":3.4089,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.92180969,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"40","issue":"5","first_page":"1367","last_page":"1367"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10047","display_name":"Financial Markets and Investment Strategies","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10047","display_name":"Financial Markets and Investment Strategies","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.002099999925121665,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.000699999975040555,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/arbitrage-pricing-theory","display_name":"arbitrage pricing theory","score":0.8579999804496765},{"id":"https://openalex.org/keywords/factor-models","display_name":"factor models","score":0.47999998927116394},{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"principal component analysis","score":0.7360000014305115},{"id":"https://openalex.org/keywords/idiosyncratic-risk","display_name":"idiosyncratic risk","score":0.9739999771118164},{"id":"https://openalex.org/keywords/factor-loadings","display_name":"factor loadings","score":0.8119999766349792},{"id":"https://openalex.org/keywords/large-economies","display_name":"large economies","score":0.38100001215934753}],"concepts":[{"id":"https://openalex.org/C2781350838","wikidata":"https://www.wikidata.org/wiki/Q2200026","display_name":"Rothschild","level":2,"score":0.8549518585205078},{"id":"https://openalex.org/C10879293","wikidata":"https://www.wikidata.org/wiki/Q726474","display_name":"Factor analysis","level":2,"score":0.6465404033660889},{"id":"https://openalex.org/C2781039887","wikidata":"https://www.wikidata.org/wiki/Q1391724","display_name":"Factor (programming language)","level":2,"score":0.5942762494087219},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.5909620523452759},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.5593088269233704},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.5026228427886963},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.49976396560668945},{"id":"https://openalex.org/C51234621","wikidata":"https://www.wikidata.org/wiki/Q2149495","display_name":"Testability","level":2,"score":0.4862312376499176},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46673309803009033},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4367374777793884},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.41922783851623535},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.4166105091571808},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25990211963653564},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23827263712882996},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.07858827710151672},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07844316959381104},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1111/j.1540-6261.1985.tb02388.x","doi":"https://doi.org/10.1111/j.1540-6261.1985.tb02388.x","is_oa":false,"landing_page_url":"https://doi.org/10.1111/j.1540-6261.1985.tb02388.x","pdf_url":null,"source":{"id":"https://openalex.org/S5353659","display_name":"The Journal of Finance","issn_l":"0022-1082","issn":["0022-1082","1540-6261"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","erih-plus","fnege-1-star","ft50","jufo-3","norway-2","poland-200","russia-white-list-1","utd24","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Finance","raw_type":"journal-article"},{"id":"doi:10.2307/2328118","doi":"https://doi.org/10.2307/2328118","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2328118","pdf_url":null,"source":{"id":"https://openalex.org/S5353659","display_name":"The Journal of Finance","issn_l":"0022-1082","issn":["0022-1082","1540-6261"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","erih-plus","fnege-1-star","ft50","jufo-3","norway-2","poland-200","russia-white-list-1","utd24","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Journal of Finance","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:bla:jfinan:v:40:y:1985:i:5:p:1367-73","doi":null,"is_oa":false,"landing_page_url":"http://links.jstor.org/sici?sici=0022-1082%28198512%2940%3A5%3C1367%3AAFSIAI%3E2.0.CO%3B2-3&origin=repec","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"display_name":"Partnerships for the goals","score":0.41999998688697815,"id":"https://metadata.un.org/sdg/17"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1496663595","https://openalex.org/W1973784058","https://openalex.org/W1978409019","https://openalex.org/W2010681793","https://openalex.org/W2016940815","https://openalex.org/W2019923367","https://openalex.org/W2028115657","https://openalex.org/W2145035301","https://openalex.org/W2147194602","https://openalex.org/W2162328283","https://openalex.org/W3022468529"],"related_works":["https://openalex.org/W2083182804","https://openalex.org/W1580850395","https://openalex.org/W1983851681","https://openalex.org/W1984835395","https://openalex.org/W1524974811","https://openalex.org/W2115229614","https://openalex.org/W7098646889","https://openalex.org/W7095969381","https://openalex.org/W2036201180","https://openalex.org/W1966774138"],"abstract_inverted_index":{"ABSTRACT":[0],"This":[1],"paper":[2],"provides":[3],"some":[4,148],"new":[5],"insights":[6,118],"about":[7],"approximate":[8,33],"factor":[9,34,58,92],"structures,":[10],"as":[11,60],"defined":[12,61],"by":[13,62,97,141],"Chamberlain":[14,111],"and":[15,18,112],"Rothschild":[16,113],"[2],":[17],"their":[19],"implications":[20],"for":[21],"empirical":[22],"tests.":[23],"First,":[24],"we":[25,66],"show":[26,67,128],"that":[27,30,42,54,68,129],"any":[28,102],"economy":[29,53],"satisfies":[31,55],"an":[32,52,56],"structure":[35],"can":[36],"be":[37,95,132],"transformed,":[38],"in":[39,88,137,155],"a":[40],"manner":[41,139],"does":[43],"not":[44],"alter":[45],"the":[46,110,120,123,138,145,150],"characteristics":[47],"of":[48,75,78,81,104,109,122,147,149],"investor":[49],"portfolios,":[50],"into":[51,119],"exact":[57],"structure,":[59],"Ross":[63],"[9].":[64],"Second,":[65],"principal":[69],"components":[70],"analysis":[71],"represents":[72],"just":[73],"one":[74],"many":[76],"methods":[77],"forming":[79],"groups":[80],"well\u2010diversified":[82],"portfolios":[83],"with":[84],"no":[85],"idiosyncratic":[86],"risk":[87],"large":[89,156],"samples.":[90],"Correct":[91],"loadings":[93],"will":[94],"obtained":[96],"regressing":[98],"security":[99],"returns":[100],"on":[101],"group":[103],"these":[105],"portfolios.":[106],"Our":[107],"interpretations":[108],"results":[114],"also":[115],"provide":[116],"additional":[117],"testability":[121],"Arbitrage":[124],"Pricing":[125],"Theory.":[126],"We":[127],"securities":[130,152],"cannot":[131],"repackaged":[133,151],"to":[134],"hide":[135],"factors":[136],"suggested":[140],"Shanken":[142],"[10]":[143],"without":[144],"variance":[146],"approaching":[153],"infinity":[154],"economies.":[157]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2016-06-24T00:00:00"}