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Rounding Errors to Knock Your Stocks Off

2000· article· en· W1980779426 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

aboutThe title or abstract carries a Canadian signal from the geographic lexicon.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueMathematics Magazine · 2000
Typearticle
Languageen
FieldDecision Sciences
TopicStock Market Forecasting Methods
Canadian institutionsnot available
Fundersnot available
KeywordsDecimalRoundingMathematicsIndex (typography)ComputationArithmeticRound-off errorStatisticsValue (mathematics)Stock (firearms)AlgorithmComputer scienceHistory

Abstract

fetched live from OpenAlex

Introduction As the total value of all daily stock transactions on the Vancouver Stock Exchange kept rising in 1982 and 1983, the exchange's index kept falling. How could this be happening? The cause of the divergence between the mathematical and computed averages consisted in an erroneous algorithm to round the last digits during the computation of the index. Public documents, e.g., Quinn's article [2] include the following pieces of information. The index is the arithmetic average of the selling prices of the nearly 1400 stocks listed on the Vancouver Stock Exchange. The computation of the index started in January of 1982, with the index then pegged to 1000. In about November of 1983, exchange officials estimated that the index should have been at least at 900 and perhaps above 1000, but the computed value of the index was down near 520. The index was computed every time the price of a stock changed, which occurred about 2800 times per day. The computer carried a total of eight decimal digits during the computation, but it truncated the last two digits to display and record the index with only three decimal digits past the decimal point. Thus, if it computed the value 540.32567, then it would record 540.325 for the index. The magnitude of the discrepancy-about 520 instead of 1000 or so-indicated that the cause involved more than only an erroneous rounding of an otherwise correct computation. Indeed, with a computer carrying eight decimal digits, the relative rounding error caused by each addition cannot exceed one half of one unit in tlhe last digit, which is (1/2) X 101-8. In the worst case, if all 1399 additions of all 1400 stock prices suffered from the maximum relative error, errors would compound to at most

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.007
metaresearch head score (Gemma)0.009
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMetaresearch, Insufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Other design · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.900
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0070.009
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.002
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0130.015

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.157
GPT teacher head0.423
Teacher spread0.266 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it