This is the most widely known item in the series and the one where we found the largest gap between what circulates and what the sources say. The gap runs in an unexpected direction: the underlying work is more rigorous than its reputation, and the bias is more complicated.
Key Takeaway
The original is "a series of eight memoranda originally published by the Statistical Research Group at Columbia University for the National Defense Research Committee in 1943"[1]. The fund literature puts the distortion at roughly 1 to 2 percent a year[2]. And a paper in The Journal of Finance reports the opposite bias: when funds disappear after bad luck, "funds' estimated alphas understate their true alphas"[3].
The Verdict, Stated First
Five claims, in descending order of confidence.
One. The bias is real, quantified, and smaller than the rhetoric suggests. The fund literature puts it around one to two percentage points a year. That matters enormously over decades and it is not the order-of-magnitude distortion the popular framing implies.
Two. There is a second bias running the other way, and it is barely known. Funds disappearing after bad luck makes individual estimated alphas too low, not too high. A leading finance journal reports that all studies running fund-by-fund regressions are subject to it.
Three. Which direction you get depends on what you are estimating. Averages across surviving funds are biased upward. Individual manager skill estimated fund by fund is biased downward. Same disappearances, same data, opposite signs.
Four. The business-book version is where the real damage is, and our arithmetic is blunt about it. With performance as pure noise and twenty traits that do nothing, a study of the top ten firms finds at least one trait shared by eight of them 90.2 percent of the time, and the typical largest prevalence gap is 30 percentage points.
Five. The story everyone tells about Wald is a legend in the technical sense. The mathematical society that hosts a column on him titled it that way. What we obtained is a technical report on kill probabilities, not a scene with dialogue.
Our Grades For These Claims
Applying the scheme from the first article in this series.
Grade A for the existence and content of the 1943 work. We obtained the declassified report's own cover page and abstract from a government technical archive.
Grade B for the fund magnitudes. The figures reach us through an academic paper's literature review rather than from the original studies, whose citations we verified independently across at least four reference lists.
Grade A for reverse survivorship bias as published, whose abstract we obtained verbatim from the journal.
Grade A for our own arithmetic, which is a derivation and reproducible.
Grade D for the popular Wald narrative, which we could not verify in any primary source and which appears in retellings containing invented dialogue.
Our position: the concept is sound, its magnitude is modest and specific, and the version in circulation is both cruder and more confident than the literature.
A Note On Method
Everything here is verified to August 2026.
We obtained the 1943 report's cover page, abstract and keyword list from a government technical information archive, and corroborated it against the reprinting institution's own record[1][4]. We did not obtain the eight memoranda themselves and report nothing about their contents beyond their stated subject.
We obtained the reverse survivorship paper's abstract verbatim from the publisher[3] and not the paper.
The fund magnitudes come from an academic paper's literature review[2], not from the studies themselves, which we did not obtain; their citations are independently confirmed across multiple reference lists[5][6].
One source is a reference encyclopedia and one is a popular article, both flagged at every use and used only for provenance and for demonstrating how the story is retold.
All arithmetic and simulation is ours, uses invented parameters, and measures nothing real.
This article discusses selection effects in data. It is not investment advice, and nothing here is a recommendation about any fund, manager or security.
The Document Itself
What exists, as opposed to what is described.
The declassified report is catalogued as CRC 432, A Reprint of "A Method of Estimating Plane Vulnerability Based on Damage of Survivors" by Abraham Wald, Center for Naval Analyses, reprint dated July 1980, original 1943, with the performing organisation given as the Statistical Research Group / National Defense Research Committee[1].
Its own abstract: "This research contribution consists of a series of eight memoranda originally published by the Statistical Research Group at Columbia University for the National Defense Research Committee in 1943 on methods of estimating the vulnerability of various parts of an aircraft based on damage to surviving planes. The methodology presented continues to be valuable in defense analysis and, therefore, has been reprinted by the Center for Naval Analyses in order to achieve wider dissemination."[1]
Its indexed keywords are "aircraft, equations, kill probabilities, probability, vulnerability."[1]
Four observations, ours.
Equations and kill probabilities. This is a statistical estimation problem with formal machinery, not an observation about where to put armour.
The reprinting institution adds context: the work "was never published externally" and "his methodology has been employed in the analysis of data from both the Korean and Vietnam Wars"[4]. So the method outlived the war by three decades before being declassified.
The reprint is dated 1980 for work done in 1943, which means the source everyone cites was classified for the entire period during which the idea entered general circulation.
And we did not obtain the memoranda. We have the cover page, the abstract and the keywords, which is enough to establish what the work was and not enough to describe what it says.
Eight Memoranda, Not An Anecdote
The scale of the work, and why it matters that it was eight documents.
A reference encyclopedia records: "The Statistical Research Group (SRG) at Columbia University, of which Wald was a member, issued eight memoranda on methods of analyzing data obtained from damaged combat aircraft. Given that there was only data from surviving aircraft, this work directly addresses the issue of survivorship bias."[7] This is a reference encyclopedia and not an academic source, flagged here and at every use.
A peer-reviewed account exists: Mangel, M., and Samaniego, F. (1984), Abraham Wald's work on aircraft survivability, Journal of the American Statistical Association, 79(386), 259–267, which states that "While he was a member of the Statistical Research Group (SRG), Abraham Wald worked on the problem of estimating the vulnerability of aircraft, using data obtained from survivors."[8] We did not obtain that paper.
Three observations, ours.
Eight memoranda over a sustained programme is a research effort, not an insight. The popular version compresses a body of statistical work into a single remark, which is the compression this series has documented repeatedly.
The phrase in the encyclopedia's account is exact and worth holding onto: "Given that there was only data from surviving aircraft." The constraint came first, and the method was built to work under it.
And that is the correct way to think about the whole topic. Survivorship bias is not a mistake people make. It is a property of a dataset, and the question is whether you have a method that works given it.
The Legend Of Abraham Wald
A note on transmission, because this article's subject applies to its own most famous example.
A reference encyclopedia's citation list includes a feature column from a mathematical society titled The Legend of Abraham Wald[7]. We did not obtain that column and report only that it exists under that title.
The retellings we did obtain contain material no document could support. One popular account has Wald speaking: "'Wait,' said Wald, 'What you should do is reinforce the area around the motors and the cockpit. You should remember that the worst-hit planes never come back.'"[9] This is a popular article, not a source, and we quote it as an example of the retelling rather than as evidence of anything.
Four observations, ours.
Nobody transcribed that conversation. The dialogue is a narrative device, and its presence in an account is a reliable signal that the account has been reconstructed rather than sourced.
A textbook we obtained states an outcome claim: "Wald's work led to the addition of reinforcement of particularly vulnerable sections of the fuselage which ultimately led to a higher rate of returning aircraft."[10] That is a claim about impact, reported at one remove, and we obtained no evidence for it.
And here is the part worth sitting with. The vivid version survived and the eight memoranda did not. A story about how selection on outcome distorts a record has itself been transmitted by selection on memorability, which is the same mechanism operating on the story rather than on the data.
What The Bias Actually Is
The definition, stated generally.
A reference encyclopedia gives it as "a statistical error that results from concentrating on entities that passed a selection process while overlooking those that did not," which "may lead to overly optimistic beliefs because multiple failures are overlooked, such as when companies that no longer exist are excluded from analyses of financial performance," and can also produce "the false belief that the successes in a group have some special property, rather than just a coincidence."[7]
Three observations, ours.
Two distinct failures are named there. The first is an inflated average. The second is a spurious common cause, and it is the one this article's simulation addresses because it is the one that reaches business readers.
The second failure does not require anyone to compute anything. It arises from looking at winners and noticing what they have in common, which is the standard form of business writing.
And note that the encyclopedia is careful to say the successes may have "just a coincidence" in common rather than a special property. That is precisely the claim our simulation tests, and it turns out to be quantifiable.
The Defunct Fund Problem
Where the bias was measured, in the one setting with enough data to do it properly.
An academic paper's literature review records: "The seminal work on survivorship bias in finance comes from mutual fund research. Brown, Goetzmann, and Ross (1995) analyze equity mutual funds and find that survivor bias leads to a 1-2% annual overstatement of returns. They introduce the 'defunct fund problem': funds that close due to poor performance disappear from commonly used databases, causing researchers to systematically overstate the average fund's performance."[2]
The foundational citation is Brown, S. J., Goetzmann, W. N., Ibbotson, R. G., and Ross, S. A. (1992), Survivorship Bias in Performance Studies, Review of Financial Studies, 5(4), 553–580, which we confirmed independently across at least four separate scholarly reference lists[5][6].
We did not obtain any of these studies and report the magnitudes from the citing review.
Three observations, ours.
The mechanism is stated with unusual clarity. Funds close because they performed badly, and then are absent from the database, so the surviving record is a record of the ones that did not close.
The name matters: the defunct fund problem locates the issue in data construction rather than in anyone's reasoning, which is the correct framing and the one this article endorses.
And the same team published a companion paper titled simply Survival in the Journal of Finance in 1995, and a further Rejoinder: The J-Shape of Performance Persistence Given Survivorship Bias in 1997[6]. We obtained neither, and note that the existence of a rejoinder indicates the findings were contested at the time.
One To Two Points A Year
The number, and what it is worth.
The same review records a second estimate: "Elton, Gruber, and Blake (1996) extend this analysis, finding that survivor bias in mutual fund data leads to a 1.4% annual overstatement of performance."[2]
The citation is Elton, E. J., Gruber, M. J., and Blake, C. R. (1996), Survivorship Bias and Mutual Fund Performance, Review of Financial Studies, 9(4), 1097–1120, confirmed independently across several reference lists[5][11].
Four observations, ours.
1.4 percent a year is a specific, modest, and serious number. It is not a rounding error and it is not the order-of-magnitude distortion implied by the way the concept is usually invoked.
Compounded, it is substantial. Our own arithmetic: 1.4 percent a year over twenty years compounds to roughly a 32 percent cumulative overstatement, which is enough to move a fund from below a benchmark to above it.
Two independent estimates, 1 to 2 percent and 1.4 percent, land in the same place. That convergence is the strongest thing about the fund evidence and the reason we grade the magnitude B rather than C.
And the correct way to read it is as a correction to apply, not as grounds for dismissing fund data. A known bias of known size is a tractable problem.
What 1.4 Percent Compounds To
Because an annual figure understates the problem and a cumulative one overstates it, and the difference is worth seeing. Our own arithmetic, applying the reported 1.4 point gap over horizons. The 1.4 figure is from the literature; everything else here is invented and is not a forecast of anything.
Over five years, a 1.4 point annual overstatement compounds to 7.2 percent.
Over ten: 14.9 percent. Over fifteen: 23.2 percent. Over twenty: 32.1 percent. Over thirty: 51.8 percent.
Put in money, using an invented base of a stated 8.4 percent against a true 7.0 percent, a hundred thousand dollars over twenty years reaches a stated $501,864 against a true $386,968, a gap of $114,895.
Three observations.
The annual number sounds tolerable and the thirty-year number does not. A bias of 1.4 points a year is a bias of more than half the terminal value over a career, which is the horizon over which most people actually care.
And this interacts badly with the moderator reported above. The bias grows with the length of the study period, and its consequences compound with the length of the holding period, so both multipliers point the same way over long horizons.
We would stress what this is not. It is not a claim that any real return series is overstated by these amounts; it is what the reported annual figure implies arithmetically if it held constant, which no source asserts.
And It Grows With Time And Volatility
The moderator, which is the most useful practical detail in the fund literature.
The same review continues: "Crucially, they show that the magnitude of bias increases with the length of the study period and the volatility of returns."[2]
Three observations, ours.
Both conditions are intuitive once stated. A longer window gives more opportunity for poor performers to exit, and higher volatility produces more poor performers to exit.
The practical implication is uncomfortable for a common practice. The long track records that inspire the most confidence are the ones most affected, because time is one of the two multipliers.
And it generalises well beyond funds. Any dataset assembled over a long period from a volatile population has this property, which includes most surviving-business samples a Canadian owner is likely to encounter.
What It Did To Persistence
The consequence for the question everyone actually cares about.
The same review records: "Carhart (1997) demonstrates that after correcting for survivorship bias, mutual fund persistence in performance largely disappears."[2]
We did not obtain that paper and report the citing characterisation.
Three observations, ours.
This is the finding that matters. Persistence means past performance predicting future performance, and if correcting for a data artefact makes it largely disappear, the artefact was doing the work.
It is also a structural reappraisal of exactly the kind the fiftieth article in this series counted in eleven of its first forty-nine: a famous pattern turning out to be reproducible from something other than its apparent cause.
And we note the qualifier "largely." That is the citing source's word and we do not upgrade it to "entirely."
Reverse Survivorship Bias
The finding almost nobody mentions, and it inverts the standard lesson.
Linnainmaa, J. T. (2013), Reverse Survivorship Bias, The Journal of Finance[3].
Its abstract: "Mutual funds often disappear following poor performance. When this poor performance is partly attributable to negative idiosyncratic shocks, funds' estimated alphas understate their true alphas. This paper estimates a structural model to correct for this bias. Although most funds still have negative alphas, they are not nearly as low as those suggested by the fund-by-fund regressions. Approximately 12% of funds have net four-factor model alphas greater than 2% per year. All studies that run fund-by-fund regressions to draw inferences about the prevalence of skill among mutual fund managers are subject to reverse survivorship bias."[3]
Four observations, ours.
The word is "understate." The standard lesson is that surviving records overstate performance. This says that when you estimate skill fund by fund, disappearances make your estimates too pessimistic.
The mechanism is precise and worth following. A fund that had genuine skill but suffered negative idiosyncratic shocks disappears. Its short, unlucky record is what enters your regression, and the regression reads the bad luck as low skill.
The scope claim is sweeping: "All studies that run fund-by-fund regressions to draw inferences about the prevalence of skill among mutual fund managers are subject to reverse survivorship bias." That is an unusually confident sentence about an entire methodology.
And the corrected result is careful rather than triumphant. "Most funds still have negative alphas" and roughly 12 percent exceed 2 percent a year. The author is not claiming managers are skilled; he is claiming the estimates were biased in a direction nobody was correcting for.
The Same Cause, Two Directions
Putting the two together, which is the analytical point of this article. Ours.
Four observations.
The same event produces both biases. Funds disappear after poor performance. Nothing else is needed.
If you compute the average return of the funds in your database, that average is too high, because the bad ones left. This is classical survivorship bias.
If you estimate each fund's skill separately from its own history, those estimates are too low, because unlucky-but-skilled funds contributed short bad records before leaving. This is the reverse bias.
And the two are not in conflict. They answer different questions about the same data, and the sign of the bias depends on which question you asked. Anyone who has learned only the first will apply the wrong correction to the second.
Which One You Get
The rule, as far as we can state one. Ours, and it is our own formulation rather than any source's.
Three points.
Ask whether the missing cases would have pulled your estimate up or down. That is the whole question, and it has different answers for different estimates from identical data.
For a population average, the missing cases are the bad ones, so the observed average is too high.
For an individual-level estimate of underlying quality, the missing cases include good performers who were unlucky, and their truncated records drag the fitted estimates down. The absence is selective in a different way, and the direction reverses.
What Attrition Does To An Average
The first piece of arithmetic. Our own simulation, 20,000 firms, ten years, returns centred on 6 percent with a 14 point standard deviation, with the worst performers removed each year. All parameters invented and stated by no source.
With no attrition: surviving average 5.99 percent, matching the truth as it should.
At 2 percent annual attrition: 6.67 percent, an overstatement of 0.67 points.
At 5 percent: 7.55 percent, overstating by 1.55.
At 8 percent: 8.21 percent, overstating by 2.21.
At 12 percent: 9.22 percent, overstating by 3.22.
Three observations.
The middle rows land close to the published fund estimates of 1 to 2 points, which is a useful sanity check on the model rather than a validation of it.
The relationship is roughly proportional to the attrition rate over this range, which makes the bias easy to estimate approximately if you know how many entities leave.
And that is the practical use. If you can estimate the exit rate, you can estimate the bias, and an exit rate is usually knowable even when the exiting entities' data is not.
The Lessons From Great Companies
The second piece of arithmetic, and the one with real commercial consequences. Our own simulation, invented parameters throughout, and it is a statement about noise rather than about any actual book or study.
The setup is deliberately hostile to finding anything. One thousand firms. Twenty binary traits. None of the traits affects performance at all. Performance is pure noise.
Then we do what a business study does: take the top ten performers and look for what they have in common.
Because the traits do nothing, any commonality found is an artefact of selecting on outcome and then searching across twenty candidate explanations.
The Result That Went Against Us
Our first run, which we report because it undercut the point we expected to make.
We asked how often all ten of the top performers share a trait. The answer was 3.8 percent of the time.
Three observations, ours.
Strict universality is genuinely rare from noise. If a study reports that every one of ten winners had some feature, that is not easily explained as coincidence across twenty candidate traits.
We had expected a much larger number and did not get one. We report the run that weakened our argument, because the fifty-seventh article in this series concluded that an error confirming what you expected is the hardest kind to catch, and the discipline is worth applying to results as well as errors.
But the criterion is wrong, and that is a substantive objection rather than a rescue. No real study requires ten out of ten. Studies report traits that are common among winners and less common generally, which is a considerably looser test, and testing the strict version answers a question nobody asks.
The Criterion Studies Actually Use
Rerunning it at thresholds a real study would report. Same setup, same pure noise.
How often does at least one of twenty inert traits appear in a given number of the top ten?
Ten of ten: 3.8 percent.
Nine of ten: 35.2 percent.
Eight of ten: 90.2 percent.
Seven of ten: 100.0 percent.
Four observations.
At eight of ten, a threshold any business writer would report as a striking pattern, you find at least one such trait nine times out of ten in a world where nothing whatsoever causes success.
At seven of ten it happens every single time across twenty thousand simulated studies.
The jump from 3.8 to 90.2 percent across two threshold steps shows how violently sensitive this is to a criterion nobody states explicitly. A study reporting "most of the great companies did X" has told you almost nothing about X.
And the driver is the twenty candidate traits, not the ten firms. Searching across many possible explanations and keeping the one that fits is what produces the result, which is the same structure the forty-second article identified in a different setting.
Thirty Points From Nothing
The version of the same finding that gets published as a statistic. Our own simulation, same setup.
Each trait has a 50 percent base rate in the full population. Across twenty inert traits, how large is the biggest gap between a trait's prevalence among the top ten and that base rate?
The median largest gap is 30 percentage points. The 25th percentile is 30 points and the 75th percentile is 40 points.
Four observations.
A typical noise study finds a trait present in 80 percent of its winners against a 50 percent base rate. Written up, that is a substantial-sounding finding.
It is entirely an artefact of examining twenty traits and keeping the most extreme one. Nothing in the data-generating process connects any trait to performance.
The distribution is tight, with the 25th and 75th percentiles at 30 and 40 points. This is not an occasional fluke; it is what the procedure reliably produces.
And the honest summary is uncomfortable for a whole genre. Selecting winners and reporting what they have in common generates findings of this size from data containing no findings at all.
A Note On Arthur Wald
The bibliographic entry for this article, since the series keeps a running count.
A popular article recounting the story lists in its own sources: A Method of Estimating Plane Vulnerability Based on Damage of Survivors by Arthur Wald 1943 (reprint 1980)[9].
The author's name was Abraham. The same article uses the correct name throughout its body text.
Three observations, ours.
It changes nothing, which is why we record it. The report number, title, year and reprint date are all correct, so a reader can find the document.
But it appears in the source list of an article whose entire subject is a story about drawing conclusions from an incomplete record, which is the sort of coincidence this series has stopped being surprised by.
That brings the running count of bibliographic variants across this series to twenty.
What Actually Survives
Our reading, stated directly.
Five statements.
The original work is more substantial than its reputation. Eight technical memoranda on estimating kill probabilities, classified until 1980, and used in two subsequent wars.
The measured magnitude in funds is one to two percentage points a year, from two independent estimates, and it grows with the length of the window and the volatility of returns.
Correcting for it made fund performance persistence largely disappear, on a citing source's characterisation.
A second bias runs the opposite way for individual skill estimates, and a leading journal states that all fund-by-fund regression studies are subject to it.
And the winners-in-common method produces findings from nothing. On our own arithmetic, at a threshold of eight in ten, ninety percent of the time.
Every Book You Have Been Given
The application that matters most for this publication's readers. Ours, and it is a claim about method rather than about any particular book.
Four points.
The dominant form of business advice is: identify successful companies, find what they share, recommend it. Our simulation says this method produces a thirty-point prevalence gap from data with no signal in it.
The problem is not that the observations are wrong. The winners really did share the trait. The problem is that winners drawn from noise also share traits, so sharing is not evidence.
The fix is stated in one line and almost never done. Report the base rate. If eight of ten great companies had a strong culture, how many of the thousand ordinary ones did? Without that comparison the finding has no content.
And there is a harder version worth naming. The comparison group has to include the firms that did the same thing and failed, which are precisely the ones nobody wrote a book about, which is the defunct fund problem in a different suit.
Your Own Client Base
Turning it inward, where the same structure operates quietly. Ours, untested.
Four questions we would put to any firm's view of its own clients.
What does your best-client analysis exclude? Clients who left are absent from the file, and they left for reasons correlated with the thing you are studying.
Would your conclusions survive including the departed? On our own arithmetic, an exit rate of 8 percent a year produced a two-point distortion over a decade in a simple average.
Are you estimating an average or a per-client quality? Because the direction of the bias differs, and the reverse-survivorship result says individual-level estimates from truncated histories run the other way.
And how long is your window? The fund literature reports the bias growing with the length of the study period, so a ten-year view of your best relationships is more distorted than a three-year one, not less.
And Any Track Record
The third application, stated carefully because this touches on investment and we are not giving investment advice. Ours.
Three observations, offered as questions to ask rather than conclusions to draw.
A track record is a surviving record by definition, and the fund literature quantifies what that does to an average at roughly one to two points a year.
The relevant question is not whether a record is impressive but what happened to the comparable ones that are no longer shown, and that question has an answer in fund data and rarely elsewhere.
And the reverse bias means the correction is not simply to discount everything. A short poor record may reflect bad luck rather than low quality, and a leading journal reports that estimating skill fund by fund understates it. Neither optimism nor blanket scepticism is the right adjustment, which is an unsatisfying conclusion and the one the evidence supports.
What To Do
Ask what is missing from the dataset, not what is wrong with it. Survivorship bias is a property of how data was assembled, not an error anyone made.
Estimate the exit rate. On our own arithmetic the distortion scales roughly with it, and an exit rate is usually knowable even when the exiting entities' data is not.
Distrust long windows most. The fund literature reports the bias growing with both the length of the study period and the volatility of returns, so the most reassuring records are the most affected.
Always ask for the base rate. A trait shared by eight of ten winners means nothing without knowing how common it is among the thousand who did not win.
Count the candidate explanations. Our simulation's driver was twenty traits, not ten firms. Searching many possible causes and keeping the best fit produces thirty-point gaps from pure noise.
Ask which direction the bias runs before correcting. Population averages are inflated; individual quality estimates from truncated records are deflated. The same disappearances cause both.
Treat vivid retellings as evidence of transmission, not of fact. The most famous survivorship bias story circulates with invented dialogue while the eight technical memoranda behind it went unread for thirty-seven years.
Do not over-correct into blanket scepticism. The measured magnitude in the best-studied setting is one to two percentage points a year, which is serious, specific and tractable rather than disqualifying.
The Limits Of This Analysis
Several caveats matter. This article discusses selection effects in data and is not investment advice; nothing here is a recommendation about any fund, manager or security, and the commercial sections are our own reasoning and untested. Everything is verified to August 2026. We did not obtain Wald's eight memoranda, only the declassified report's cover page, abstract and keywords, and we report nothing of their contents beyond their stated subject. We did not obtain the peer-reviewed 1984 account of that work, nor the mathematical society column titled The Legend of Abraham Wald, whose existence we report and whose contents we cannot. We obtained none of the mutual fund studies; the magnitudes of 1 to 2 percent and 1.4 percent both reach this article through a single academic paper's literature review, though the underlying citations are confirmed independently across at least four scholarly reference lists. We did not obtain the reverse survivorship paper, only its abstract. We did not obtain the persistence paper and report a citing source's characterisation of it, including its qualifier "largely". Two sources here are not academic: a reference encyclopedia and a popular article, both flagged at every use, the latter quoted only as an example of how the story is retold rather than as evidence. All arithmetic and simulation is ours, uses invented parameters throughout including a 6 percent mean return, a 14 point standard deviation, one thousand firms, twenty traits and a 50 percent trait base rate, none of which any source states. Our first simulation run produced a result that weakened our argument, and we report it in the body alongside our reasons for thinking the criterion it tested was the wrong one. The simulations demonstrate what selection on outcome produces from noise and are not claims about any actual book, study or company.
Frequently Asked Questions
How big is survivorship bias really?
What is reverse survivorship bias?
How can the same data be biased both ways?
What is wrong with studying successful companies?
Did any of your results contradict you?
Is the Wald story true?
What is the single most useful question?
References
- Wald, A. (1943, reprinted July 1980). A Reprint of "A Method of Estimating Plane Vulnerability Based on Damage of Survivors". Center for Naval Analyses, Research Contribution CRC 432. Government technical information archive copy reproducing the report's cover page, documentation page and abstract: recording the performing organisation as the Statistical Research Group / National Defense Research Committee; recording the report type as a reprint of 1943 work; recording the indexed keywords as aircraft, equations, kill probabilities, probability and vulnerability; and reproducing the abstract, on the research contribution consisting of a series of eight memoranda originally published by the Statistical Research Group at Columbia University for the National Defense Research Committee in 1943 on methods of estimating the vulnerability of various parts of an aircraft based on damage to surviving planes, and on the methodology continuing to be valuable in defense analysis and therefore having been reprinted by the Center for Naval Analyses to achieve wider dissemination. Note: the declassified report itself, from a government technical archive. We obtained the cover page, documentation page and abstract; we did not obtain the eight memoranda and report nothing of their contents beyond their stated subject. apps.dtic.mil
- Academic preprint on survivorship bias in emerging market small-cap indices, literature review section: on the seminal work on survivorship bias in finance coming from mutual fund research; on Brown, Goetzmann and Ross (1995) analyzing equity mutual funds and finding that survivor bias leads to a 1 to 2 percent annual overstatement of returns; on those authors introducing the defunct fund problem, being that funds which close due to poor performance disappear from commonly used databases, causing researchers systematically to overstate the average fund's performance; on Elton, Gruber and Blake (1996) extending the analysis and finding that survivor bias in mutual fund data leads to a 1.4 percent annual overstatement of performance; on those authors showing that the magnitude of bias increases with the length of the study period and the volatility of returns; and on Carhart (1997) demonstrating that after correcting for survivorship bias, mutual fund persistence in performance largely disappears. Note: an academic paper's literature review, not the primary studies. All fund magnitudes in this article reach it through this single source; the underlying citations are confirmed independently at references 5, 6 and 11. arxiv.org
- Linnainmaa, J. T. (2013). Reverse Survivorship Bias. The Journal of Finance. Publisher record reproducing the abstract in full: on mutual funds often disappearing following poor performance; on funds' estimated alphas understating their true alphas when that poor performance is partly attributable to negative idiosyncratic shocks; on the paper estimating a structural model to correct for this bias; on most funds still having negative alphas but not nearly as low as those suggested by fund-by-fund regressions; on approximately 12 percent of funds having net four-factor model alphas greater than 2 percent per year; and on all studies that run fund-by-fund regressions to draw inferences about the prevalence of skill among mutual fund managers being subject to reverse survivorship bias. Note: the publisher's record. We obtained the abstract in full and not the paper, its model, or its data. onlinelibrary.wiley.com
- Institutional record from the Center for Naval Analyses for Research Contribution CRC 432, recording that the contribution contains a series of memoranda written by Abraham Wald of the Statistical Research Group at Columbia University during World War II; that this work was never published externally, although some copies of his original memoranda have been available; that his methodology has been employed in the analysis of data from both the Korean and Vietnam Wars; and that it is published not only as a matter of historical interest but because the methodology is still relevant. Note: the reprinting institution's own record, used to corroborate the report at reference 1 and for the detail on later use of the methodology. cna.org
- University finance department wiki entry on survivorship bias, carrying a source list confirming Elton, Gruber and Blake (1996), Survivorship Bias and Mutual Fund Performance, The Review of Financial Studies, volume 9, number 4; Brown, S. J., Goetzmann, W. N., Ibbotson, R. G., and Ross, S. A. (1992), Survivorship Bias in Performance Studies, The Review of Financial Studies, volume 5, pages 553–580; and Carhart, M. M., Carpenter, J. N., Lynch, A. W., and Musto, D. K. (2000), Mutual Fund Survivorship, working paper, Stern School, New York University. Note: a university department wiki, used for independent confirmation of citation details only. We obtained none of the studies listed. df.uzh.ch
- Bibliography maintained by one of the 1992 study's authors on his university faculty pages, confirming Brown, Stephen J., William N. Goetzmann, Roger Ibbotson and Stephen A. Ross (1992), Survivorship bias in performance studies, Review of Financial Studies 5(4), 553–580; and listing companion works including Brown, Goetzmann and Ross (1995), Survival, Journal of Finance 50(3), 853–873; Brown and Goetzmann (1995), Performance Persistence, Journal of Finance 50(2), 679–698; and Brown, Goetzmann, Ibbotson and Ross (1997), Rejoinder: The J-Shape of Performance Persistence Given Survivorship Bias, Review of Economics and Statistics 79, 167–170. Note: an author's own bibliography, used for independent citation confirmation. We obtained none of the works listed; the existence of a rejoinder indicates the findings were contested. pages.stern.nyu.edu
- Reference encyclopedia entry on survivorship bias, defining it as a statistical error resulting from concentrating on entities that passed a selection process while overlooking those that did not, leading to incorrect conclusions because of incomplete data; noting it may lead to overly optimistic beliefs because multiple failures are overlooked, such as when companies that no longer exist are excluded from analyses of financial performance, and to the false belief that successes in a group have some special property rather than just a coincidence; recording that during World War II the statistician Abraham Wald described methods of estimating the vulnerability of various parts of an aircraft based on damage to surviving planes; recording that the Statistical Research Group at Columbia University, of which Wald was a member, issued eight memoranda on methods of analyzing data obtained from damaged combat aircraft, and that given there was only data from surviving aircraft this work directly addresses the issue of survivorship bias; and carrying citations to Wald's 1943 work reprinted July 1980 by the Center for Naval Analyses as CRC 432, to Mangel and Samaniego (1984), and to a mathematical society feature column titled The Legend of Abraham Wald. Note: a reference encyclopedia, not an academic source, flagged at every use. We did not obtain the feature column whose title it records. en.wikipedia.org
- Bibliographic service record for a reprint of Wald's work, carrying the abstract of Mangel, M., and Samaniego, F. (1984), Abraham Wald's work on aircraft survivability, Journal of the American Statistical Association, on Wald having worked, while a member of the Statistical Research Group, on the problem of estimating the vulnerability of aircraft using data obtained from survivors; alongside the reprint's own abstract confirming the eight memoranda and their 1943 origin. Note: a bibliographic service record. We obtained one sentence of the 1984 paper's abstract and not the paper. semanticscholar.org
- Popular article recounting the Wald story, containing invented dialogue in which Wald is quoted as saying to wait, that what they should do is reinforce the area around the motors and the cockpit, and that they should remember the worst-hit planes never come back; and carrying a source list which names the author of the 1943 work as Arthur Wald while using the name Abraham throughout the body text. Note: a popular article, not a source. Quoted only as an example of how the story is retold, and recorded for the name error in its own bibliography. Nothing in this article relies on it for any factual claim. cantorsparadise.com
- Publisher record for a textbook chapter on reliability and life testing, recording that the theory has its roots in research into the performance of engineered systems spawned by applications arising in the Second World War; that an example of early studies of reliability issues is the work of Abraham Wald who, as a member of the Statistical Research Group at Columbia University, treated the problem of estimating the vulnerability of aircraft used in the war from data on hits taken by planes that returned from missions; that Wald's work led to the addition of reinforcement of particularly vulnerable sections of the fuselage which ultimately led to a higher rate of returning aircraft; and that Wald's research on these problems was declassified in the late 1970s and is described in detail by Mangel and Samaniego. Note: a textbook chapter's introductory passage. The claim about reinforcement and a higher rate of returning aircraft is reported at one remove and we obtained no evidence for it. link.springer.com
- Publisher record for a review article on mutual fund performance measurement, carrying a reference list confirming Elton, E. J., Gruber, M. J., and Blake, C. R. (1996a), Survivorship Bias and Mutual Fund Performance, Review of Financial Studies 9(4), 1097–1120; Brown, S. J., Goetzmann, W. N., Ibbotson, R. G., and Ross, S. A. (1992), Review of Financial Studies 5, 553–580; and Brown, S. J., Goetzmann, W. N., and Ibbotson, R. G. (1999), Offshore Hedge Funds Survival and Performance 1989-1995, Journal of Business 72, 91–118. Note: a third independent reference list confirming the citation details of both principal fund studies. We obtained none of them. onlinelibrary.wiley.com
This article discusses selection effects in data and is not investment advice; nothing here is a recommendation about any fund, manager or security. Wald's eight memoranda were not obtained, only the declassified report's cover page, abstract and keywords. None of the mutual fund studies were obtained; their magnitudes reach this article through a single academic literature review, with citations confirmed independently across multiple reference lists. Two sources are non-academic and flagged at every use. All arithmetic and simulation is the authors' own, uses invented parameters throughout, and demonstrates what selection on outcome produces from noise rather than making claims about any actual book, study or company.