Empirical Asset Pricing via Machine Learning

Shihao Gu, Bryan Kelly, Dacheng Xiu · Review of Financial Studies / arXiv · 2020 · quantitative-finance · 10.1093/rfs/hhaa009 · record gu2020-ml-asset-pricing
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Where this record's text came from. 2026-08-14, 2026-08-15 and 2026-08-16 schema-0.3 passes: every quote verified as an exact substring of the staged text and anchored at merge time; concept terms verified present; every edge endpoint an existing node. 2026-08-14 RE-SOURCED. The stored fulltext_url was https://arxiv.org/abs/1904.00745, which is a DIFFERENT PAPER: Chen, Pelger & Zhu, "Deep Learning in Asset Pricing" (verified - that page names Luyang Chen/Markus Pelger as authors, and "Bryan Kelly" appears there only in the acknowledgements as a discussant). That wrong URL is the origin of the earlier untaggable flag "interleaved-sources". Re-sourced from NBER w25398; the staged file contains all three GKX authors and ZERO occurrences of Pelger / Luyang Chen / "Deep Learning in Asset Pricing". NOTE the staged text is the WORKING PAPER, not the published RFS article that DOI 10.1093/rfs/hhaa009 points to.

The quality of the text these quotes were cut from. interleaved-sources: stored full text mixes Gu-Kelly-Xiu (Empirical Asset Pricing via ML) with Chen-Pelger-Zhu (Deep Learning in Asset Pricing) text; clean per-claim attribution not possible. Skipped for facet-enrichment until re-sourced.

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Other fields define these differently the same word, defined another way in another discipline
machine learning 14 fields · neural networks 3 fields

Tags on this paper

Every tag the record carries, each linking to every other paper in the corpus that carries it. A tag appears here whether or not its words occur in the article — the spans below are only the ones a sentence in this paper licenses. Of the 14 concept tags on this paper, 12 are grounded in a quoted sentence.

asset pricing machine learning risk premium return prediction expected return neural networks regression trees elastic net support vector machines variable importance out-of-sample R2 predictive performance traditional econometric prediction techniques Diebold-Mariano test the sample is cut into three disjoint periods that keep the data's time ordering: the model is estimated on the training period alone, while the hyperparameters are chosen by scoring forecasts on the second period and re-estimating from the training data at every step the third period is used for neither estimation nor tuning, which is what makes it the only one of the three that is truly out of sample - the validation fits are not, because they are an input to the estimation the out-of-sample R-squared is computed against a forecast of zero rather than against the historical mean return, because the historical mean of an individual stock is so noisy that benchmarking against it would lower the bar - and the paper states the size of the choice: every method's monthly R-squared rises by roughly three percentage points under the conventional denominator the Diebold-Mariano comparison is applied to the cross-sectional AVERAGE of each month's prediction errors rather than to individual stock errors, because the test's weak-dependence condition is unlikely to hold across a cross-section of stocks with potentially strong dependence the network architectures are fixed in advance instead of searched over, because searching uncountably many is called unrealistic and unnecessary - and what the authors say they hope to obtain is a reasonable LOWER BOUND on machine-learning performance, not the best network the squared-error objective is replaced by a hybrid of squared loss for relatively small errors and absolute loss for relatively large ones, with the crossover controlled by a tuning parameter optimised adaptively from the data trees in the forest are de-correlated by offering each branch only a randomly drawn subset of the predictors, so that a single dominant predictor cannot force the same early split in every bootstrap sample and collapse the variance reduction that averaging is supposed to provide the network is estimated from several different random initialisations and the forecasts are averaged, because the optimiser is stochastic and a single seed's forecast carries variance that has nothing to do with the data the interpretation of which methods win is checked against two simulated data sets whose generating processes are known - one linear and additive, one nonlinear with pairwise interactions - so that the ranking can be shown to track the property it is being credited to comparative

Method, as described: comparative empirical analysis

Legend

relation to other work	`claim_relations`	how this paper stands to another: agrees, contradicts, extends, qualifies
claim type	`claim_type`	the shape of the claim: existence, mechanism, method, critique, prediction, null
concept edge	`concept_edges`	an asserted relation between two concepts, with the sentence asserting it
concept	`concepts`	an idea the paper works with, quoted where the paper uses it
contribution	`contribution`	what the paper claims to add
control	`controls`	an experiment run to eliminate a rival explanation
limitation	`limitations`	what the paper says its evidence cannot support
mechanism	`mechanisms`	how the reported effect is said to come about
method	`method`	how the paper produced its evidence
object of study	`object_of_study`	what the paper is about — the thing it investigates
phenomenon	`phenomenon`	the effect or regularity under study
research question	`research_question`	the question the paper sets itself
sense	`senses`	a distinct use of a term, quoted where the paper fixes it
transfer	`transfers`	a method or concept carried in from another field

The paper

The full text is not reproduced here. This article is not cleared for redistribution, so the page carries the tag layer only. Its evidence sentences are withheld; the grounding status remains with each tag, and the article itself is at https://doi.org/10.1093/rfs/hhaa009. The reading view exists for the papers whose licence permits it.

Every tag on this page

claim_relations 3 · claim_type 1 · concept_edges 3 · concepts 12 · contribution 1 · controls 1 · limitations 9 · mechanisms 9 · method 1 · object_of_study 1 · phenomenon 1 · research_question 1 · senses 5 · transfers 1

Relations on this page carry a quotation for the claim. Where a relation was separately evidenced — and so tested against the vocabulary for its type — the row says so; none of 3 relations here carry that mark. The rest are the tagger’s reading of the sentence quoted beside them.

facet	tag	field	conf.	whose words
object_of_study	Measurement of equity risk premia, treated as a prediction problem, across the machine learning method repertoire. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`object_of_study`		the paper's words
research_question	How do machine learning methods compare for the canonical problem of empirical asset pricing, measuring asset risk premia? Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`research_question`		the paper's words
contribution	Provides benchmarks for the predictive accuracy of machine learning methods in measuring risk premia, robust across specifications. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`contribution`		the paper's words
claim_type	method Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`claim_type`		the paper's words
phenomenon	trees and neural networks improve return prediction over linear and generalized linear models, traced to their allowance of interactions among predictors Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`phenomenon`		the paper's words
method	comparative Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: comparative	`method`		the paper's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: the sample is cut into three disjoint periods that keep the data's time ordering: the model is estimated on the training period alone, while the hyperparameters are chosen by scoring forecasts on the second period and re-estimating from the training data at every step	`mechanisms[0]`	0.85	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: the third period is used for neither estimation nor tuning, which is what makes it the only one of the three that is truly out of sample - the validation fits are not, because they are an input to the estimation	`mechanisms[1]`	0.95	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: the out-of-sample R-squared is computed against a forecast of zero rather than against the historical mean return, because the historical mean of an individual stock is so noisy that benchmarking against it would lower the bar - and the paper states the size of the choice: every method's monthly R-squared rises by roughly three percentage points under the conventional denominator	`mechanisms[2]`	0.95	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: the Diebold-Mariano comparison is applied to the cross-sectional AVERAGE of each month's prediction errors rather than to individual stock errors, because the test's weak-dependence condition is unlikely to hold across a cross-section of stocks with potentially strong dependence	`mechanisms[3]`	0.85	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: the network architectures are fixed in advance instead of searched over, because searching uncountably many is called unrealistic and unnecessary - and what the authors say they hope to obtain is a reasonable LOWER BOUND on machine-learning performance, not the best network	`mechanisms[4]`	0.85	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. about this quote: 2026-08-16: THE EXTRACTION HAS STRIPPED THE MATH SYMBOLS INSIDE THIS QUOTE. It reads "The Huber loss, H(?), is a hybrid ... controlled by a tuning parameter, , that can be optimized adaptively" - the argument of H and the NAME OF THE TUNING PARAMETER are both absent from the staged file, leaving a bare comma where the symbol was. The quote is an exact substring and the file is incomplete here. The tag deliberately describes the parameter by its role rather than naming it, because naming it would mean supplying a character the staged text does not contain. also in: the squared-error objective is replaced by a hybrid of squared loss for relatively small errors and absolute loss for relatively large ones, with the crossover controlled by a tuning parameter optimised adaptively from the data	`mechanisms[5]`	0.85	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: trees in the forest are de-correlated by offering each branch only a randomly drawn subset of the predictors, so that a single dominant predictor cannot force the same early split in every bootstrap sample and collapse the variance reduction that averaging is supposed to provide	`mechanisms[6]`	0.95	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: the network is estimated from several different random initialisations and the forecasts are averaged, because the optimiser is stochastic and a single seed's forecast carries variance that has nothing to do with the data	`mechanisms[7]`	0.95	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: the interpretation of which methods win is checked against two simulated data sets whose generating processes are known - one linear and additive, one nonlinear with pairwise interactions - so that the ranking can be shown to track the property it is being credited to	`mechanisms[8]`	0.95	the tagger's words
limitations	The headline R2 uses a denominator without demeaning; the paper states the common alternative convention raises every method's R2 by roughly three percentage points. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: comparing this paper's R2 against an R2 computed the usual way, against historical mean returns: the paper says that convention raises all its numbers by roughly three percentage points	`limitations[0]`	1.0	the tagger's words
limitations	The paper states its improved predictions are measurements only, and do not identify economic mechanisms or equilibria. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: reading the results as evidence about economic mechanisms: the paper says the measurements do not tell us about mechanisms or equilibria	`limitations[1]`	1.0	the tagger's words
limitations	The set of methods compared is explicitly not exhaustive, and support vector machines are excluded with a stated reason. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: reading the comparison as covering the machine learning toolkit: the paper says it is not exhaustive and names an exclusion	`limitations[2]`	1.0	the tagger's words
limitations	The paper describes its own interpretive goal as modest. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: reading the variable-importance results as an account of why a predictor works: the stated goal is only to identify influential covariates	`limitations[3]`	1.0	the tagger's words
limitations	The conditions underlying the Diebold-Mariano test are stated to be unlikely to hold for the stock-level analysis; the paper modifies the test rather than proceeding. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the reported model-comparison p-values as standard Diebold-Mariano results: the test was adapted because its conditions were judged unlikely to hold	`limitations[4]`	1.0	the tagger's words
limitations	The predictor literature the study draws on is stated to exclude an unknown larger set of predictors that were tested, failed and never reported. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the 900+ signal set as the space of tested predictors: the paper says an unknown larger set failed and was never reported	`limitations[5]`	1.0	the tagger's words
limitations	The finding that shallow networks beat deeper ones is attributed, with hedging, to the data available rather than established as a property of the problem. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: generalising shallow-beats-deep beyond this setting: the paper attributes it, hedged, to the small data and low signal-to-noise ratio here	`limitations[6]`	0.9	the tagger's words
limitations	The estimation target is defined in terms of an information set the paper calls true and unobservable. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: treating the target as an observable quantity: the conditioning information set is stated to be unobservable	`limitations[7]`	1.0	the tagger's words
limitations	The paper's central term is stated to have no settled definition, and the definition used is stipulated by the authors. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: reading "machine learning" here as a standard term: the paper says the definition is inchoate and stipulates its own three-part one	`limitations[8]`	1.0	the tagger's words
transfers	the architecture and vocabulary of the biological nervous system - neurons, synapses, axons, signals passed between layers - carried into empirical asset pricing as the description of a feed-forward network Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`transfers[1]`	0.85	the tagger's words
controls	parameter penalisation and deliberately conservative model-selection criteria applied across the whole method comparison Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: overfitting and false discovery as the source of apparent predictive power - the flexible functional forms being compared can fit noise, and without the penalty the comparison would reward whichever method fits it best · outcome (stated by the tagger, no quotation): held	`controls[0]`	0.95	the tagger's words
concepts	machine learning Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: machine learning	`concepts[1]`		the paper's words
concepts	risk premium Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: risk premium	`concepts[2]`		the paper's words
concepts	expected return Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: expected return	`concepts[4]`		the paper's words
concepts	neural networks Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: neural networks	`concepts[5]`		the paper's words
concepts	regression trees Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: regression trees	`concepts[6]`		the paper's words
concepts	elastic net Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: elastic net	`concepts[7]`		the paper's words
concepts	support vector machines Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: support vector machines	`concepts[8]`		the paper's words
concepts	variable importance Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: variable importance	`concepts[9]`		the paper's words
concepts	out-of-sample R2 Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: out-of-sample R2	`concepts[10]`		the paper's words
concepts	predictive performance Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. about this quote: This quote ends on 'as' because what it introduces is a displayed formula that the staged extraction does not carry as readable text (the text continues: "Roos 2 = 1 - (i,t)T3 (ri,t+1 - ri,t+1)2 (i,t)T3 "). The quote is verbatim and the formula is in the paper; the quote was not extended, because extending it would put extraction debris inside a quotation. also in: predictive performance	`concepts[11]`		the paper's words
concepts	traditional econometric prediction techniques Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: traditional econometric prediction techniques	`concepts[12]`		the paper's words
concepts	Diebold-Mariano test Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Diebold-Mariano test	`concepts[13]`		the paper's words
senses	out-of-sample R2 - denominator is the sum of squared excess returns, NOT demeaned, so the benchmark forecast is zero Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[0]`	1.0	the tagger's words
senses	out-of-sample R2 - the conventional sense, benchmarked against historical mean returns, which the paper says would raise all its numbers by about three percentage points Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[1]`	1.0	the tagger's words
senses	machine learning - the authors' stipulated three-part sense: high-dimensional prediction models, regularization, and search algorithms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[2]`	1.0	the tagger's words
senses	risk premium - used interchangeably with expected return, while the paper notes components one may wish to distinguish Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[3]`	1.0	the tagger's words
senses	variable importance - a ranking used to identify influential covariates, explicitly not an account of mechanism Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[4]`	1.0	the tagger's words
claim_relations	qualifies → Green et al. (2013), Harvey et al. (2016), Welch and Goyal (2008) — the predictor-counting literature Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. differs in: WHETHER THE COUNT IS OF PREDICTORS OR OF REPORTED PREDICTORS. Three surveys are cited with their totals - 330 stock-level signals, 316 factors, nearly 20 aggregate-market predictors - and then: 'Quotation withheld.' The denominator of the search is unobservable, so the counts bound the published literature and not the work done	`claim_relations[0]`	0.95	the tagger's words
claim_relations	builds-on → Welch and Goyal (2008) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. differs in: WHAT THE BENCHMARK IS. The comparison point is not a rival method's success but a documented FAILURE: 'nearly all of the macroeconomic return predictor variables in the survey of Welch and Goyal (2008) Quotation withheld.' A negative result is doing the work of a baseline, which is only legible if the reader knows the sign convention of this R2 - and the record already carries two senses of it	`claim_relations[1]`	0.95	the tagger's words
claim_relations	distinguishes-from → principal components regression (PCA) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. differs in: WHETHER THE DIMENSION REDUCTION KNOWS WHAT IT IS PREDICTING. 'Quotation withheld' Two reductions of the same data differing only in whether the target is in scope when the axes are chosen	`claim_relations[2]`	0.95	the tagger's words
concept_edges	risk premium —same-as→ expected return Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. strength of the relation: 1 also in: risk premium · expected return	`concept_edges[0]`		the tagger's words
concept_edges	predictive performance —operationalised-as→ out-of-sample R2 Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. strength of the relation: 1 · about this quote: This quote ends on 'as' because what it introduces is a displayed formula that the staged extraction does not carry as readable text (the text continues: "Roos 2 = 1 - (i,t)T3 (ri,t+1 - ri,t+1)2 (i,t)T3 "). The quote is verbatim and the formula is in the paper; the quote was not extended, because extending it would put extraction debris inside a quotation. also in: predictive performance · out-of-sample R2	`concept_edges[1]`		the tagger's words
concept_edges	machine learning —contrasted-with→ traditional econometric prediction techniques Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. strength of the relation: 1 also in: machine learning · traditional econometric prediction techniques	`concept_edges[4]`		the tagger's words

Interpretive choices

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