The DOI matches its Crossref record; 495 of the 495 references it cites were found in a registry or an index; 3 of the 26 sources its claims cite were checked for support.
… and the Cross-Section of Expected Returns
Abstract
Hundreds of papers and factors attempt to explain the cross-section of expected returns. Given this extensive data mining, it does not make sense to use the usual criteria for establishing significance. Which hurdle should be used for current research? Our paper introduces a new multiple testing framework and provides historical cutoffs from the first empirical tests in 1967 to today. A new factor needs to clear a much higher hurdle, with a t-statistic greater than 3.0. We argue that most claimed research findings in financial economics are likely false. (JEL C12, C52, G12)
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
The paper argues that conventional significance thresholds are too lenient for cross-sectional return factors because hundreds of factors have been tested, and it proposes multiple-testing adjustments that imply a much higher hurdle. It concludes that a newly proposed factor should generally have a t-statistic above 3.0, and that many published factors would not survive this standard.
Key findings
- The authors catalogue 313 articles and 316 factors, including 250 published articles and 63 working papers covering 68 factors; they note that this likely understates the true number of tested factors.
- Under multiple-testing adjustments, benchmark t-statistics rise well above 1.96: Bonferroni reaches 3.78 by 2012 and 4.00 by 2032; Holm is close to Bonferroni; BHY stabilizes around 3.39 after 2010 at 1% FDR.
- When allowing for unobserved tests, they estimate about 71% of tried factors are missing; benchmark t-statistics become 4.01 for Bonferroni, 3.96 for Holm, 3.68 for BHY at 1%, and 3.18 for BHY at 5%, leading them to recommend a minimum threshold near 3.0.
- Of 296 published significant factors, they classify 158 as false discoveries under Bonferroni, 142 under Holm, 132 under BHY at 1%, and 80 under BHY at 5%.
Methods
- The authors assemble a hand-collected sample of factor-proposing papers from leading finance, economics, and accounting journals, plus selected SSRN working papers, and record reported t-statistics for 316 factors.
- They classify factors into “common” risk factors and firm “characteristics,” then apply three multiple-testing procedures: Bonferroni and Holm for family-wise error rate control, and Benjamini-Hochberg-Yekutieli for false discovery rate control.
- To address unpublished or hidden tests, they use a truncated exponential simulation framework to estimate the total number of trials and adjusted benchmarks, and they also estimate a model with correlation among factor returns to derive threshold t-statistics.
Limitations
- The paper states that not all factor discoveries should be treated equally: theory-motivated factors may deserve a lower hurdle than purely empirical ones, though a t-statistic of 2.0 is still too low.
- The paper states that its tests are unconditional, so a factor that appears marginal unconditionally could matter in some economic environments and not others.
- The paper acknowledges that its factor list underrepresents the population because it focuses mainly on top journals, selects only some working papers, often includes only representative variants of similar characteristics, and cannot observe failed tests; it also takes published t-statistics as given and notes weak identification of the correlation parameter.
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Claims the paper makes
59 Own interpretation · 46 No basis given · 42 Own result · 9 No full text of the sources · 5 Not checked yet · 5 Own method · 4 Sources not found · 1 Supported · 1 Not supported · 1 Couldn’t confirm · accuracy not yet measured
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“However, the bulk of the papers we consider have substantial overlapping sample periods.”
§ … and the Cross-Section of Expected Returns > 3.1 Why multiple testing?
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: unclear — It is unclear why the paper says it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We catalogue 316 different factors.”
§ … and the Cross-Section of Expected Returns > 1. The Search Process
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Across the various specifications of ρ in Table 5, we find that the optimized objective function reaches its lowest point when ρ = 0.2.”
§ … and the Cross-Section of Expected Returns > 4.3 How large is ρ?
plaincorrelational- Asserted: passes — The authors put it forward as true.
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- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In particular, the threshold t-statistics are little changed for alternative values of N .”
§ … and the Cross-Section of Expected Returns > 4.2 Results
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Turning to the estimates of threshold t-statistics and focusing on FWER, we see that they are not monotonic in the level of correlation.”
§ … and the Cross-Section of Expected Returns > 4.2 Results
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Not surprisingly, these statistics are smaller than the corresponding thresholds based on the full sample.”
§ … and the Cross-Section of Expected Returns > 3.6 p-value adjustment when all tests are published (M = R)
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Based on our estimates, 71% of all tried factors are missing.”
§ … and the Cross-Section of Expected Returns > 3.7.2
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Focusing on the baseline case in panel A and at ρ = 0, we estimate that researchers have tried M = 1,297 factors and 60.4% (= 1-0.396) are true discoveries.”
§ … and the Cross-Section of Expected Returns > 4.2 Results
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Compared to Bonferroni, one more factor (test 9) is discovered; that is, four factors rather than three are significant.”
§ … and the Cross-Section of Expected Returns > Example 4.4.1
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We estimate the average pairwise correlation among these factors to be 0.15 for the 1985-2014 period.”
§ … and the Cross-Section of Expected Returns > 4.3 How large is ρ?
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Probably not a substantial claim. 77
- It may state two separate claims as one. 64
At least one cited source doesn’t support this claim or points to a different paper, and none confirmed it — see the verdicts below.
In the paper
“Barras, Scaillet, and Wermers (2010) argue for a correlation of zero among fund returns (i.e., excess returns against benchmark factors)”
§ … and the Cross-Section of Expected Returns > 4.3 How large is ρ?
What the sources say
- Disputedcites Barras, Scaillet, and Wermers (2010) sourceExperimental — accuracy not yet measured
Section I.C, “Cross-Sectional Dependence among Funds,” reports an average pairwise correlation of 0.08 between four-factor model residuals, not zero. The authors describe the dependencies as sufficiently low for their estimators and explicitly incorporate the observed correlations in simulations; they do not argue that fund residuals are uncorrelated. (LLM, conf=0.88)
Checked by a reasoning model — may be wrong.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Disputed
Every source the paper cites for this claim was checked and supports it.
In the paper
“Instead of FDR, recent research by Lehmann and Romano (2005) develops methods to directly control the realized FDP.In particular, they propose a step-down method to control for the probability of FDP exceeding a threshold value.”
§ … and the Cross-Section of Expected Returns > 3.7.4 Methods controlling the FDP.
What the sources say
- Supportedcites Lehmann and Romano (2005) source
The section on the false discovery proportion defines control as P{FDP > γ} ≤ α and develops a step-down procedure to meet that bound. The Conclusions state that the paper considers two step-down methods that control the FDP in this sense. Thus, “directly control the realized FDP” is supported as probabilistic control, not a guarantee for every realization; page numbers are not supplied in our copy. (LLM, conf=0.94)
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
- Supported
The cited sources that could be checked couldn’t confirm or dispute this claim.
In the paper
“For example, it is well known that two of the most popular factors, the Fama and French (1992) HML and SMB, are correlated.”
§ … and the Cross-Section of Expected Returns > Additional information
What the sources say
- Could not verifycites Fama and French (1992) sourceExperimental — accuracy not yet measured
The discussion in “A. Rational Asset-Pricing Stories” reports a −0.26 correlation between firm size and book-to-market equity, not between returns on the HML and SMB factors. Searches for “HML SMB factors correlated” and “high minus low small minus big factor returns correlation” found no passage in our copy reporting the claimed factor correlation. (LLM, conf=0.77)
boostedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Could not verify
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We end with 63 working papers.”
§ … and the Cross-Section of Expected Returns > 1. The Search Process
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Hundreds of papers and factors attempt to explain the cross-section of expected returns.”
§ … and the Cross-Section of Expected Returns > Abstract
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In total, we focus on 313 articles, among which are 250 published articles.”
§ … and the Cross-Section of Expected Returns > 1. The Search Process
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In summary, for single tests, using the usual 5% cutoff, 10 out of 10 are discovered.Allowing for multiple tests, the cutoffs are far smaller, with BHY at 0.85%, Holm at 0.60%, and Bonferroni at 0.5%.”
§ … and the Cross-Section of Expected Returns > 3.4.3 Benjamini, Hochberg, and Yekutieli's adjustment.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Using this information, the new benchmark t-statistics for Bonferroni and Holm are estimated to be 4.01 and 3.96, respectively, both slightly higher than when M = R.”
§ … and the Cross-Section of Expected Returns > 3.7.2
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: M factors are tried, but only factors that exceed a certain t-statistic threshold are published; the threshold is set at 1.96.
- The authors state this as an assumption: The sample covers a fraction r of t-statistics between 1.96 and 2.57, and all t-statistics above 2.57 are covered.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Based on our sample of observed t-statistics of published factors, 30 we obtain three benchmark t-statistics.”
§ … and the Cross-Section of Expected Returns > 3.6 p-value adjustment when all tests are published (M = R)
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Other specifications of N change the estimate of λ but leave the other parameters almost intact.”
§ … and the Cross-Section of Expected Returns > 4.2 Results
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The BHY implied t-statistic increases from 3.39 to 3.68 at 1% significance and from 2.78 to 3.18 at 5% significance.”
§ … and the Cross-Section of Expected Returns > 3.7.2
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: M factors are tried, but only factors that exceed a certain t-statistic threshold are published; the threshold is set at 1.96.
- The authors state this as an assumption: The sample covers a fraction r of t-statistics between 1.96 and 2.57, and all t-statistics above 2.57 are covered.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“While all ten factors would be discovered under single hypothesis testing, only three to six factors would be discovered under a multiple hypothesis test.”
§ … and the Cross-Section of Expected Returns > 3.4.3 Benjamini, Hochberg, and Yekutieli's adjustment.
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Both Bonferroni and Holm adjusted benchmark t-statistics are monotonically increasing in the number of discoveries.”
§ … and the Cross-Section of Expected Returns > 3.6 p-value adjustment when all tests are published (M = R)
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Notice that these numbers are not far away from our previous estimates of 3.78 (Holm adjustment that controls FWER at 5%) and 3.38 (BHY adjustment that controls FDR at 1%).”
§ … and the Cross-Section of Expected Returns > 4.2 Results
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Indeed, these numbers are smaller than the numbers under our default specification of c(M) (i.e., c(M)= M j =1 1 j ).However, they are above 3.0 and therefore are consistent with our overall message.”
§ … and the Cross-Section of Expected Returns > 3.7.2
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“At least 316 factors have been tested to explain the cross-section of expected returns.”
§ … and the Cross-Section of Expected Returns > 5. Conclusion
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In particular, the quantities we choose to match and their values for the baseline sample (i.e., r = 1/2) are given by: ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ T = Total number of discoveries = 353, Q 1 = The 20th percentile of the sample of t-statistics = 2.39, Q 2 = The 50th percentile of the sample of t-statistics = 3.16, Q 3 = The 90th percentile of the sample of t-statistics = 6.34.”
§ … and the Cross-Section of Expected Returns > 4.1 A model with correlations
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may state two separate claims as one.
- The authors state this as an assumption: The sample covers a fraction r of t-statistics between 1.96 and 2.57, and all t-statistics above 2.57 are covered.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For the other parameter estimates, both p 0 and M are increasing in ρ.”
§ … and the Cross-Section of Expected Returns > 4.2 Results
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“BHY implied benchmarks, on the other hand, are not monotonic.They fluctuate before year 2000 and stabilize at 3.39 (pvalue = 0.07%) after 2010.”
§ … and the Cross-Section of Expected Returns > 3.6 p-value adjustment when all tests are published (M = R)
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“For instance, when γ = 0.10 and α = 0.05, the benchmark t-statistic is 2.70 (p-value = 0.69%), which is much higher than the conventional cutoff of 1.96.”
§ … and the Cross-Section of Expected Returns > 3.7.4 Methods controlling the FDP.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Figure 3 shows that our main conclusions do not materially change.For example, the Holm at 113 factors is 3.29 (p-value = 0.10%), while Holm at 316 factors is 3.64 (p-value = 0.03%).”
§ … and the Cross-Section of Expected Returns > 3.7 Robustness 3.7.1 Test statistics dependence.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“If we change α d to 5%, the corresponding BHY implied benchmark t-statistic is 2.78 (p-value = 0.54%) in 2012 and 2.81 (p-value = 0.50%) in 2032, still much higher than the starting value of 1.96.”
§ … and the Cross-Section of Expected Returns > 3.6 p-value adjustment when all tests are published (M = R)
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In the end, BHY leads to six significant factors (tests 8, 7, 4, 9, 6, and 2), three more than Bonferroni and two more than Holm.”
§ … and the Cross-Section of Expected Returns > 3.4.3 Benjamini, Hochberg, and Yekutieli's adjustment.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“M×c(M) α d is 6, and we reject the null hypothesis for the first six ordered tests and fail to reject for the remaining four tests.”
§ … and the Cross-Section of Expected Returns > 3.4.3 Benjamini, Hochberg, and Yekutieli's adjustment.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Based on this factor group, the Bonferroni and Holm implied threshold t-statistics are 3.54 and 3.20 (5% significance), respectively, and the BHY implied thresholds are 3.23 (1% significance) and 2.67 (5% significance) by 2012.”
§ … and the Cross-Section of Expected Returns > 3.6 p-value adjustment when all tests are published (M = R)
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“When ρ is increased to 0.60, we estimate that a total of M = 1,775 factors have been tried and around 39.9% (= 1-0.601) are true factors.”
§ … and the Cross-Section of Expected Returns > 4.2 Results
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Based on our estimate that 71% of tried factors are missing and by simulating the missing tests as in Appendix A, we find that the BHY implied threshold equals 3.05 at 5% significance and 3.17 at 1% significance.”
§ … and the Cross-Section of Expected Returns > 3.7.2
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: M factors are tried, but only factors that exceed a certain t-statistic threshold are published; the threshold is set at 1.96.
- The authors state this as an assumption: The sample covers a fraction r of t-statistics between 1.96 and 2.57, and all t-statistics above 2.57 are covered.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Starting from the smallest p-value and going up, we see that p (b) is below α w M+1-b until b = 5, at which point p (5) is above α w 10+1-5 .Therefore, the smallest b that satisfies p (b) > α w M+1-b is 5 and we reject the null hypothesis for the first four ordered tests (we discover four factors) and fail to reject the null for the remaining six tests.”
§ … and the Cross-Section of Expected Returns > Example 4.4.1
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Most of these factors have been proposed over the last ten years.”
§ … and the Cross-Section of Expected Returns > 5. Conclusion
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Among these factors, HML, MOM, DCG, SRV, and MRT are significant across all types of t-statistic adjustments, EP, LIQ, and CVOL are sometimes significant, and the rest are never significant.”
§ … and the Cross-Section of Expected Returns > 3.6 p-value adjustment when all tests are published (M = R)
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For Bonferroni, the benchmark t-statistic starts at 1.96 and increases to 3.78 by 2012.It reaches 4.00 in 2032.”
§ … and the Cross-Section of Expected Returns > 3.6 p-value adjustment when all tests are published (M = R)
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Holm implied t-statistics always fall below Bonferroni t-statistics, consistent with the fact that Bonferroni always results in fewer discoveries than Holm.However, Holm tracks Bonferroni closely and their differences are small.”
§ … and the Cross-Section of Expected Returns > 3.6 p-value adjustment when all tests are published (M = R)
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In total, 164 factors were discovered in the past nine years, roughly doubling the 84 factors discovered in all previous years.”
§ … and the Cross-Section of Expected Returns > 3.5 Summary statistics
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Across various correlation specifications, our estimates show that in general a t-statistic of 3.9 and 3.0 is needed to control FWER at 5% and FDR at 1%, respectively.”
§ … and the Cross-Section of Expected Returns > 4.2 Results
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The Holm implied t-statistic (3.96), while not necessarily increasing in the number of trials, is also higher than before (3.64).”
§ … and the Cross-Section of Expected Returns > Step IV Repeat Steps I-III 10,000 times to generate a distribution of benchmark t-statistics.
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“When r = 1, the median estimate for the total number of trials is 817, 54 almost the same as our previous estimate of 820 based on the original sample.”
§ … and the Cross-Section of Expected Returns > Step IV Repeat Steps I-III 10,000 times to generate a distribution of benchmark t-statistics.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“While these frameworks differ in their assumptions, they are consistent in their conclusions.”
§ … and the Cross-Section of Expected Returns > 5. Conclusion
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Unsurprisingly, the Bonferroni implied benchmark t-statistic (4.01) is larger than 3.78, which is what we obtain when ignoring unpublished works.”
§ … and the Cross-Section of Expected Returns > Step IV Repeat Steps I-III 10,000 times to generate a distribution of benchmark t-statistics.
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The fitted density closely tracks the histogram and has a population mean of 2.07.”
§ … and the Cross-Section of Expected Returns > Additional information
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The BHY implied t-statistic increases from 3.39 to 3.68 at 1% significance and from 2.78 to 3.18 at 5% significance.”
§ … and the Cross-Section of Expected Returns > Step IV Repeat Steps I-III 10,000 times to generate a distribution of benchmark t-statistics.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The population mean estimate is 2.22 in panel”
§ … and the Cross-Section of Expected Returns > Additional information
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- The authors state this as an assumption: Our sample covers only half of all factors with t-statistics between 1.96 and 2.57.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“To be clear, we only count those that have t-statistics or equivalent statistics reported.Roughly twenty new factors fail to satisfy this requirement.”
§ … and the Cross-Section of Expected Returns > H3.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“As already mentioned, some of these factors are highly correlated.For example, we include four versions of idiosyncratic volatility, that is,Fama and MacBeth (1973),Ali, Hwang, and Trombley (2003),Ang et al. (2006), andFu (2009).”
§ … and the Cross-Section of Expected Returns > H3.
What the sources say
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“There are a few very large t-statistics in our sample.We fit the truncated exponential model without dropping any large t-statistics.”
§ … and the Cross-Section of Expected Returns > H3.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“When r doubles, the estimate of M also approximately doubles and the Bonferroni and Holm implied t-statistics increase by about 0.2, whereas the BHY implied t-statistics increase by around 0.03 (under both significance levels).”
§ … and the Cross-Section of Expected Returns > Contribution
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Our previous estimate of 820 is a one-shot estimate based on the truncated sample.The results in Table A.1 are based on repeated estimates based on resampled data: we resample many times, and 817 is the median of all these estimates.”
§ … and the Cross-Section of Expected Returns > H3.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Under these assumptions about the joint distribution of the test statistics, we find via simulations that FWER is 100% and FDR is 26%, both exceeding 5%.”
§ … and the Cross-Section of Expected Returns > H3.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: For the simulation example, the t-statistics for the 700 hypotheses are independent; a false factor's t-statistic follows N(0,1), and a true factor's t-statistic follows N(2,1).
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We want to emphasize that there are many forces that make our guidance lenient; that is, a credible case can be made for an even higher threshold for discovery.”
§ … and the Cross-Section of Expected Returns > 3.1 Why multiple testing?
plain- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Nevertheless, whether suggested by theory or empirical work, a t-statistic of 2.0 is too low.”
§ … and the Cross-Section of Expected Returns > Abstract
plain- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We pursue the multiple testing framework because it yields immediate guidance on whether a discovered factor is real.”
§ … and the Cross-Section of Expected Returns > 3.1 Why multiple testing?
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“While our focus is on the cross-section of equity returns, our message applies to many different areas of finance.”
§ … and the Cross-Section of Expected Returns > Abstract
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Given this extensive data mining, it does not make sense to use the usual criteria for establishing significance.”
§ … and the Cross-Section of Expected Returns > Abstract
plain- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In finance and economics, it is very difficult to publish replication studies.”
§ … and the Cross-Section of Expected Returns > 3.1 Why multiple testing?
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“A factor derived from a theory should have a lower hurdle than a factor discovered from a purely empirical exercise.”
§ … and the Cross-Section of Expected Returns > Abstract
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Intuitively, in the extreme case in which all tests are the same (i.e., correlation = 1.0), we do not need to adjust at all: FWER is the same as the type I error rate for single tests.”
§ … and the Cross-Section of Expected Returns > 3.7 Robustness 3.7.1 Test statistics dependence.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“However, this evidence is only suggestive given the weak identification of ρ in our model.”
§ … and the Cross-Section of Expected Returns > 4.3 How large is ρ?
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Such information, when appropriately incorporated, can be helpful in making the method more accurate (i.e., less stringent).”
§ … and the Cross-Section of Expected Returns > 4. Correlation among Test Statistics
plainconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“First, the benchmark t-statistic based on our incomplete sample provides a lower bound of the true t-statistic benchmark.In other words, if M (total number of tests) > R (total number of discoveries), then we would expect fewer factors than when M = R,foot_22 so future t-statistics need to at least surpass our benchmark to claim significance.”
§ … and the Cross-Section of Expected Returns > 3.6 p-value adjustment when all tests are published (M = R)
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“as in single hypothesis testing, a decrease in the type I error rate often leads to an increase in the type II error rate and vice versa.”
§ … and the Cross-Section of Expected Returns > 3.3.2 False discovery rate.
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Despite the rapid development of multiple testing methods, they have not attracted much attention in the finance literature.”
§ … and the Cross-Section of Expected Returns > 3.2 A multiple testing framework
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“As a result, they often lead to a very limited number of discoveries, if any.”
§ … and the Cross-Section of Expected Returns > 3.3.2 False discovery rate.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Although there are around 300 published ones, hundreds or even thousands of factors could have been constructed and tested.”
§ … and the Cross-Section of Expected Returns > 3.3.2 False discovery rate.
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The nonsignificant ones typically belong to papers that propose a number of factors.These likely represent only a small subsample of nonsignificant t-statistics for all tried factors.”
§ … and the Cross-Section of Expected Returns > 3.5 Summary statistics
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
In the paper
“while Ferson and Chen (2013) calibrate this number to be between 0.04 and 0.09.”
§ … and the Cross-Section of Expected Returns > 4.3 How large is ρ?
What the sources say
- Not matchedcites Ferson and Chen (2013)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“It is less stringent (i.e., leads to more discoveries) than FWER and usually much less so when many tests are performed.”
§ … and the Cross-Section of Expected Returns > 3.3.2 False discovery rate.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It can also be shown that Holm is uniformly more powerful than Bonferroni in that tests rejected (factors discovered) under Bonferroni are always rejected under Holm, but not vice versa.”
- Also stated in: § Example 4.4.1 · plain
“In general, Holm's approach leads to more discoveries and all discoveries under Bonferroni are also discoveries under Holm's criteria.”
§ … and the Cross-Section of Expected Returns > Example 4.4.1
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Also stated in: § Example 4.4.1 · plain
In the paper
“Green, Hand, and Zhang (2013a) focus on accountingbased factors and find the average correlation to be between 0.06 and 0.20.”
§ … and the Cross-Section of Expected Returns > 4.3 How large is ρ?
What the sources say
- Not matchedcites Green, Hand, and Zhang (2013a)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Although the BHY method is robust to arbitrary dependence among test statistics, it does not use any information about the dependence structure.”
§ … and the Cross-Section of Expected Returns > 4. Correlation among Test Statistics
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may state two separate claims as one.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“Our sample has limitations in making a direct inference on the level of correlation.”
§ … and the Cross-Section of Expected Returns > 4.3 How large is ρ?
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“As a result, our results are best interpreted as the estimated t-statistic thresholds for a hypothetical level of correlation.”
§ … and the Cross-Section of Expected Returns > 4.1 A model with correlations
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“These two forces work against each other and result in the nonmonotonic pattern for the threshold t-statistics under FWER.”
§ … and the Cross-Section of Expected Returns > 4.2 Results
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Similarly, BHY may generate too few discoveries when tests are independent or positively correlated.”
§ … and the Cross-Section of Expected Returns > 3.7 Robustness 3.7.1 Test statistics dependence.
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Multiple testing adjustments will usually generate different results.”
§ … and the Cross-Section of Expected Returns > 3.4 p-value adjustment: Three approaches
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“We want to stress that the three types of adjustments in our paper are robust to the heterogeneity in the time of discovery and testing methods among individual studies.That is, despite the varying degrees of sample overlap and the differences in the testing methods, our adjustment procedures guarantee that the type I errors (however they are defined) are controlled under their prespecified levels”
§ … and the Cross-Section of Expected Returns > 3.6 p-value adjustment when all tests are published (M = R)
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Unfortunately, we do not always observe the time series of factor returns (when a t-statistic is based on long-short strategy returns) or the time series of slopes in cross-sectional regressions (when a t-statistic is based on the slope coefficients in cross-sectional regressions).Because few researchers post their original data, often all we have is the single t-statistic that summarizes the sign”
§ … and the Cross-Section of Expected Returns > 4. Correlation among Test Statistics
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Like Bonferroni, Holm also restricts FWER at α w without any requirement on the dependence structure of p-values.”
§ … and the Cross-Section of Expected Returns > Example 4.4.1
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In sum, across various scenarios, we think the minimum threshold t-statistic is 3.18, corresponding to BHY's adjustment for M >R at 5% significance.Alternative cases all result in even higher benchmark t-statistics.”
§ … and the Cross-Section of Expected Returns > 3.7.2
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: M factors are tried, but only factors that exceed a certain t-statistic threshold are published; the threshold is set at 1.96.
- The authors state this as an assumption: The sample covers a fraction r of t-statistics between 1.96 and 2.57, and all t-statistics above 2.57 are covered.
In the paper
“McLean and Pontiff (2015) estimate the correlation among anomaly returns to be around 0.05.”
§ … and the Cross-Section of Expected Returns > 4.3 How large is ρ?
What the sources say
- Not checked — no full text of the sourcecites McLean and Pontiff (2015) source
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Intuitively, at any fixed significance level α, the law of large numbers forces the false discovery rate (FDR) to converge to a constant.”
§ … and the Cross-Section of Expected Returns > 3.6 p-value adjustment when all tests are published (M = R)
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In the context of multiple testing, any type of adjustment procedure can become too stringent when there is a certain dependence structure in the data.This is because these procedures are primarily designed to guard against type I errors.Under a certain correlation structure, they may penalize type I errors too harshly and lead to a high type II error rate.”
§ … and the Cross-Section of Expected Returns > 3.7 Robustness 3.7.1 Test statistics dependence.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“However, when we have multiple tests, the exact type II error rate typically depends on a set of unknown parameters and is therefore difficult to assess.”
§ … and the Cross-Section of Expected Returns > 3.3.2 False discovery rate.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“If this type of positive dependence exists among test statistics, all three methods would likely generate fewer significant factors than desired.”
§ … and the Cross-Section of Expected Returns > 3.7 Robustness 3.7.1 Test statistics dependence.
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In theory, under independence, Bonferroni and Holm approximately achieve the prespecified significance level α when the number of tests is large.”
§ … and the Cross-Section of Expected Returns > 3.7 Robustness 3.7.1 Test statistics dependence.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Bonferroni operates as a single-step procedure that can be shown to restrict FWER at levels less than or equal to (M 0 ×α w )/M, without any assumption on the dependence structure of the p-values.”
§ … and the Cross-Section of Expected Returns > Example 4.4.1
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In the context of our paper, we are sure that many tests have been tried in the finance literature.”
§ … and the Cross-Section of Expected Returns > 3.3.2 False discovery rate.
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Since less stringent hurdles are applied to the second to the (k -1)th p-values, more discoveries are generated under Holm's than Bonferroni's adjustment.”
§ … and the Cross-Section of Expected Returns > Example 4.4.1
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Moreover, most of the research that does involve multiple testing focuses on the Bonferroni adjustment,foot_8 which is known to be too stringent.”
§ … and the Cross-Section of Expected Returns > 3.2 A multiple testing framework
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“First, sample quantiles are less susceptible to outliers compared to means and other moment-related sample statistics.Our t-statistic sample does have a few influential observations, and we expect quantiles to be more useful descriptive statistics than the mean and the standard deviation.Second, simulation studies show that quantiles in our model are more sensitive to changes in parameters than”
§ … and the Cross-Section of Expected Returns > 4.1 A model with correlations
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In sum, after taking testing multiplicity into account, we believe the minimum threshold t-statistic for 5% significance is about 2.8, which corresponds to a p-value (if a single test) of 0.5%.”
§ … and the Cross-Section of Expected Returns > 3.6 p-value adjustment when all tests are published (M = R)
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: The test results of all tried factors are available (M = R).
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Since M 0 ≤ M, Bonferroni also controls FWER at level α w .”
§ … and the Cross-Section of Expected Returns > Example 4.4.1
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“An overparameterized distribution for the continuous distribution in the mixture model, albeit flexible, may result in imprecise estimates.We therefore use the simple one-parameter exponential distribution family.”
§ … and the Cross-Section of Expected Returns > H3.
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The Bonferroni adjusted t-statistic is monotonically increasing in the number of trials, so the t-statistic benchmark”
§ … and the Cross-Section of Expected Returns > H3.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The normality assumption for the μ i 's requires the reported X i 's to randomly represent either long/short or short/long strategy returns.”
§ … and the Cross-Section of Expected Returns > Additional information
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
- The authors state this as an assumption: The first-step population parameters μ_i's are independently generated from a normal distribution.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In the quantitative asset management industry, significant results are not published-they are considered”
§ … and the Cross-Section of Expected Returns > Additional information
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We attempt to navigate the zoo and establish new benchmarks to guide empirical asset pricing tests.”
§ … and the Cross-Section of Expected Returns > Acknowledgements
plain- Asserted: fails — The authors may not put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The authors may not put it forward as true. It may be too vague to check against evidence. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We can easily think of scenarios in which average returns of different strategies are correlated, even when population means are known.”
§ … and the Cross-Section of Expected Returns > Additional information
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Simulation studies in Scott and Berger (2006) show how the discovery probabilities for a few initial signals increase when more noise is added to the original sample.”
§ … and the Cross-Section of Expected Returns > H3.
What the sources say
- Not checked — no full text of the sourcecites Scott and Berger (2006) source
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Independence, as we previously discussed, is likely to be violated in our context.”
§ … and the Cross-Section of Expected Returns > H3.
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. The paper may give no reason why it holds.
None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“In astronomy and physics, even higher threshold t-statistics are often used to control for testing multiplicity.For instance, the high profile discovery of Higgs Boson has a t-statistic of more than 5 (p-value less than 0.0001%).”
§ … and the Cross-Section of Expected Returns > H3.
What the sources say
- Not matchedcites ATLAS Collaboration (2012)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites CMS Collaboration (2012)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites Harvey and Liu (2014b)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“For the academic literature, factors with”
§ … and the Cross-Section of Expected Returns > Additional information
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We think the baseline model is the best among all three models as it not only overcomes the missing data problem for the original sample, but also avoids guessing the fraction of missing observations in the 1.96-2.57range.”
§ … and the Cross-Section of Expected Returns > 5. Conclusion
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“Truncated distributions have been used to study hidden tests (i.e., publication bias) in medical research.”
§ … and the Cross-Section of Expected Returns > Additional information
What the sources say
- Not checked — no full text of the sourcecites Begg and Berlin (1988) source
- Not matchedcites Thornton and Lee (2000)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“A certain form of conditional independence is unavoidable for Bayesian hierarchical modeling 57”
§ … and the Cross-Section of Expected Returns > Additional information
What the sources say
- Not checked — no full text of the sourcecites [57] source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The number of true nulls M 0 is unknown, so we usually cannot make Bonferroni more powerful by increasing α w to α = Mα w /M 0 (note that M 0 α/M = α w ).”
§ … and the Cross-Section of Expected Returns > H3.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In addition, extreme values are pivotal statistics for heavy-tailed distributions and are key for model estimation.”
§ … and the Cross-Section of Expected Returns > H3.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The multiple testing framework is robust to outliers.The procedures are based on either the total number of tests (Bonferroni) or the order statistics of t-statistics(Holm and BHY).”
§ … and the Cross-Section of Expected Returns > H3.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The normality assumptions in both H1 and H2 are important as they are necessary to guarantee the properness of the posterior distributions.”
§ … and the Cross-Section of Expected Returns > Step IV Repeat Steps I-III 10,000 times to generate a distribution of benchmark t-statistics.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Importantly, the optimal amount of data mining is not zero since some data mining produces knowledge.”
§ … and the Cross-Section of Expected Returns > 5. Conclusion
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“First, our t-statistic sample may underrepresent all factors with t-statistics exceeding 2.57.foot_33Hence, our estimates of the total trials are biased (too low), which affects our calculation of the benchmarks.”
§ … and the Cross-Section of Expected Returns > A.2 Simulated Benchmark t-statistics under Independence
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Intuitively, t-statistics that are based on similar sample periods are more correlated than t-statistics that are based on distinct sample periods.Therefore, the degree of overlap in sample period helps identify the correlation coefficient.”
§ … and the Cross-Section of Expected Returns > H3.
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“However, in medical research, insignificant results are still viewed as an indispensable part of the overall statistical evidence and are given much more prominence than in the financial economics research.”
§ … and the Cross-Section of Expected Returns > Additional information
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
None of the sources cited for this claim have been checked yet.
In the paper
“Our research quantifies the warnings of both Fama (1991) and Schwert (2003).”
§ … and the Cross-Section of Expected Returns > Acknowledgements
What the sources say
- Not checked yetcites Fama (1991) source
Checked before — its earlier verdict is held back until a new check runs.
- Not matchedcites Schwert (2003)
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not checked yet
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In this sense, the truncated distributional framework suits our study better-1.96is the obvious hurdle that research needs to overcome to be published.”
§ … and the Cross-Section of Expected Returns > Additional information
plain- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We do not pursue a likelihood-based estimation.Given that we have more than a thousand factors and each of them is associated with an indicator variable that is missing, the likelihood function involves high-dimensional integrals and is difficult to optimize.This leads us to a GMM-based approach.”
§ … and the Cross-Section of Expected Returns > H3.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may state two separate claims as one.
In the paper
“More sophisticated generalizations modify the basic model but are unlikely to change the fundamental hierarchical testing structure.”
§ … and the Cross-Section of Expected Returns > Additional information
What the sources say
- Not checked — no full text of the sourcecites [56] Benjamini, 1995, Controlling the false discovery rate: A practical and powerful approach to multiple testing, Journal of the Royal Statistical Society Series B source
hedged- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The common variance assumption may look restrictive, but we can always scale factor returns by changing the dollar investment in the long-short strategy.”
§ … and the Cross-Section of Expected Returns > Additional information
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In contrast to the usual normal density, exponential distribution is better at modeling extreme observations.”
§ … and the Cross-Section of Expected Returns > H3.
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
The authors state this as an assumption.
Published t-statistics are econometrically sound with respect to data errors, coding errors, misalignment, heteroscedasticity, autocorrelation, clustering, outliers, and similar issues.
“Importantly, we take published t-statistics as given.That is, we assume they are econometrically sound with respect to the usual suspects (data errors, coding errors, misalignment, heteroscedasticity, autocorrelation, clustering, outliers, etc.).”
The authors state this as an assumption.
The test results of all tried factors are available (M = R).
“We now apply the three adjustment methods previously introduced to the observed factor tests, under the assumption that the test results of all tried factors are available.”
The authors state this as an assumption.
For each factor, the corresponding long-short strategy return standard deviation is normalized to σ = 15% per year.
“For each factor, suppose researchers construct a corresponding long-short trading strategy and normalize the return standard deviation to be σ = 15% per year, which is close to the annual volatility of the market index.”
The authors state this as an assumption.
Strategy returns are jointly normal and have zero serial correlation.
“Assuming joint normality and zero serial correlation for strategy returns, this t-statistic has a normal distribution”
The authors state this as an assumption.
Each μ_i is an independent draw from a mixture distribution with a point mass at zero and an exponential distribution with mean parameter λ.
“We assume that each μ i is an independent draw from the following mixture distribution:”
The authors state this as an assumption.
The contemporaneous correlation between two strategies' returns is ρ, and noncontemporaneous correlations are zero.
“As a starting point, we assume that the contemporaneous correlation between two strategies' returns is ρ.The noncontemporaneous correlations are assumed to be zero.”
The authors state this as an assumption.
M factors are tried, but only factors that exceed a certain t-statistic threshold are published; the threshold is set at 1.96.
“Finally, to incorporate the impact of hidden tests, we assume that M factors are tried, but only factors that exceed a certain t-statistic threshold are published.We set the threshold t-statistic at 1.96 and focus on the subsample of factors that have a t-statistic larger than 1.96.”
The authors state this as an assumption.
The sample covers a fraction r of t-statistics between 1.96 and 2.57, and all t-statistics above 2.57 are covered.
“To overcome this missing data problem, we assume that our sample covers a fraction r of t-statistics in between 1.96 and 2.57 and that all t-statistics above 2.57 are covered.”
The authors state this as an assumption.
The estimation framework assumes a balanced panel with M factors and N periods of returns.
“Our estimation framework assumes a balanced panel with M factors and N periods of returns.”
The paper relies on this without support.
Many factors were tried by empiricists, failed, and never made it to publication or even a working paper.
“there are surely many factors that were tried by empiricists, failed, and never made it to publication or even a working paper.”
The authors state this as an assumption.
The t-statistics are independent.
“Assuming independence, we model observed t-statistics as draws from an exponential distribution with mean parameter λ and a known cutoff point of 2.57.”
“The underlying assumption for the model in Appendix A is the independence among t-statistics, which may not be plausible given our previous discussions on test dependence.”
The authors state this as an assumption.
Observed t-statistics follow an exponential distribution with mean parameter λ and a known cutoff point of 2.57.
“Assuming independence, we model observed t-statistics as draws from an exponential distribution with mean parameter λ and a known cutoff point of 2.57.”
The authors state this as an assumption.
For the baseline result, all tried factors with t-statistics above 2.57 are observed and those with t-statistics in the range (1.96, 2.57) are ignored.
“for our baseline result, we assume all tried factors with t-statistics above 2.57 are observed and ignore those with t-statistics in the range of (1.96, 2.57).”
The authors state this as an assumption.
The density curve of the t-statistic distribution is monotonic, so it is easier to find factors with small t-statistics than with large ones.
“One restriction that we think any of these distributions should satisfy is the monotonicity of the density curve.Intuitively, it should be easier to find factors with small t-statistics than with large ones.”
The authors state this as an assumption.
For the simulation example, the t-statistics for the 700 hypotheses are independent; a false factor's t-statistic follows N(0,1), and a true factor's t-statistic follows N(2,1).
“we assume that the t-statistics for the 700 hypotheses are independent.Moreover, we assume the t-statistic for a false factor follows a normal distribution with mean of zero and variance of 1.0, that is, N (0,1); for a true factor, we assume its t-statistic follows a normal distribution with mean of 2.0 and variance of 1.0, that is, N (2,1).”
The authors state this as an assumption.
Neglected significant t-statistics follow the empirical distribution of the t-statistic sample.
“under the assumption that neglected significant t-statistics follow the empirical distribution of our t-statistic sample, by varying r, we can assess how this underrepresentation of our t-statistic sample affects results.”
The authors state this as an assumption.
Our sample covers only half of all factors with t-statistics between 1.96 and 2.57.
“with the ad hoc assumption that our sample covers only half of all factors with t-statistics between 1.96 and 2.57.”
The authors state this as an assumption.
Factor returns are independent conditional on mean γ_i μ_i and common variance σ^2.
“factor returns are independent conditional on mean γ i μ i and common variance σ 2”
The authors state this as an assumption.
The first-step population parameters μ_i's are independently generated from a normal distribution.
“μ i 's are independently generated from a normal distribution”
The authors state this as an assumption.
The first-step population parameters γ_i's are generated from a Bernoulli distribution, with γ_i = 0 with probability p_0.
“γ i 's are simply generated from a Bernoulli distribution, that is, γ i = 0 with probability p 0”
The paper relies on this without support.
The reported X_i's randomly represent either long/short or short/long strategy returns.
“The normality assumption for the μ i 's requires the reported X i 's to randomly represent either long/short or short/long strategy returns.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“We use twenty-two firm-level predictors that are commonly used in the asset pricing literature (Chordia et al. 2017;Harvey et al. 2016;Lewellen 2015;McLean and Pontiff 2016).These variables have been shown to explain most of the cross-sectional variation in expected returns.”
From Empirical asset pricing via machine learning: evidence from the European stock market (2021) · cites this paper as Harvey et al. 2016
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“In both stock and aggregate return predictions, there presumably exists a much larger set of predictors that were tested but failed to predict returns and were thus never reported.”
From Empirical Asset Pricing via Machine Learning (2020) · cites this paper as Harvey, Liu, and Zhu (2016)
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“Another solution to address the data-snooping issue is to employ an out-of-sample analysis to examine if the best technical trading rules from the in-sample estimation performs well out of sample (Sullivan et al. 1999; Harvey et al. 2016).”
From Technical trading and cryptocurrencies (2021) · cites this paper as Harvey et al. 2016
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ … and the Cross-Section of Expected Returns > 3.4.3 Benjamini, Hochberg, and Yekutieli's adjustment.
“p BH Y (i) = ⎧ ⎨ ⎩ p (M) if i = M, min[p BH Y (i+1) , M×c(M) i p (i) ] if i ≤ M -1,”
§ … and the Cross-Section of Expected Returns > 3.4.3 Benjamini, Hochberg, and Yekutieli's adjustment.
“In the end, BHY leads to six significant factors (tests 8, 7, 4, 9, 6, and 2), three more than Bonferroni and two more than Holm.”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ … and the Cross-Section of Expected Returns > 4.1 A model with correlations
“we assume that our sample covers a fraction r of t-statistics in between 1.96 and 2.57”
§ … and the Cross-Section of Expected Returns > 4.2 Results
“r is the assumed proportion of missing factors with a t-statistic between 1.96 and 2.57.”
Citations
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Metadata
- Authors
- Harvey, C. R., Liu, Y., & Zhu, H.
- Affiliations
- National Bureau of Economic Research (US)
- Texas A&M University (US)
- Venue
- Review of Financial Studies
- Publisher
- Oxford University Press (OUP)
- Published
- 2015-10-09
- Volume
- 29
- Issue
- 1
- Pages
- 5-68
- ISSN
- 0893-9454 (ISSN-L)
- 1465-7368
- OpenAlex
- W4211170237
- Cited by
- 2,119
- References
- 446
- Citations by year
- 2026: 293 · 2025: 204 · 2024: 199 · 2023: 202 · 2022: 192 · 2021: 213 · 2020: 218 · 2019: 183 · 2018: 172 · 2017: 138 · 2016: 64 · 2015: 25
- FWCI
- 254.19
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Review of Financial Studies (publishedVersion)
- Topics
- Social Sciences › Economics, Econometrics and Finance › Finance › Financial Markets and Investment Strategies
- Social Sciences › Economics, Econometrics and Finance › Finance › Financial Risk and Volatility Modeling
- Social Sciences › Business, Management and Accounting › Accounting › Financial Analysis and Corporate Governance
- Keywords
- cross-section of expected returns, multiple comparisons, false positives, significance threshold, data mining
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-11, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-11 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Cited sources are checked with a language model’s help (gpt-6-sol).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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