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Source: D. T. Max. “Jim Simons, the Numbers King.” The New Yorker, December 18 & 25, 2017 Issue

He hired another mathematician, whom he’d met at the I.D.A., and they began to create models that predicted the direction of currency prices. Simons told me that he staffed his “crazy hedge fund”—the company that became Renaissance Technologies—not with financiers but with physicists, astronomers, and mathematicians. He also invested heavily in computers and in the people who ran them. “If you’re going to analyze data, it really has to be clean,” he said. “Suppose it’s a series of stock prices. 31¼, 62½. Wait, stocks don’t double in a day—so there’s an error in the data! There’s all kinds of ways to get bugs out of data, and it’s important, because they can really screw you up.”

Please explain the bolded?

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    It's just a figure of speech, an example, simply meaning "Wow, look at that obviously broken data". There's nothing more to it than that. You're reading too much in to it. The writer's simply saying "Here's something that is almost certainly an error!" – Fattie Feb 21 '18 at 15:53
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Simons is highlighting the problems faced when trying to establish an accurate database of historical prices for analysis. Before his team of physicists and mathematicians can work their magic with their pointy stick, they need to be sure that they are working with an accurate database of historical data.

The problem arises because historical data published by the various data vendors is not always accurate. One of the most common errors one sees is historical stock prices not being adjusted for a stock split. Other types of errors may include missing dividend related data, errors in volumes traded, and other datum which may affect analysis.

So when Simons says “If you’re going to analyze data, it really has to be clean” he highlights the need to identify and correct errors in the database of historical data in order to facilitate analysis. "Wait, stocks don’t double in a day—so there’s an error in the data!". In other words, if you see some suspect data, it needs to be investigated and corrected if necessary.

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    +1. Stocks indeed can double in a day, but if you see an exact doubling from one day to the next, it is much more likely a stock split error in the data. – Ben Miller Feb 21 '18 at 4:54
  • Even better is to monitor the volume. If the price goes up 50%, 100% and there is no significant volume change, it's an error. – misantroop Feb 21 '18 at 9:32
  • It's the old axiom of Garbage In, Garbage Out. If you start with crappy data, your statistical model will learn patterns that are unconnected to reality. – Nuclear Wang Feb 21 '18 at 20:43
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It is somewhat amusing because there are instances of stocks doubling in a day; KBIO once increased 650% overnight.

But what he is saying is that you can have the best financial models in existence, but if they are fed dirty (ie, wrong or incorrect) information then they will give incorrect results. The quoted paragraph is describing occurrences from the late 1970s, when the data was very likely transcribed by hand and/or subject to transmission errors.

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    Not necessarily from 1970s. As indicated in another answer, it's possible that some third party data vendor did not properly account for splits / reverse splits in adjusting historical prices. This is probably more likely what the author was referring to. – ApplePie Feb 21 '18 at 11:32
  • The quote from the source article is literally about him setting up Renaissance in the late 1970s as one of the earliest algorithmic traders. – Magua Feb 21 '18 at 15:27
  • My bad, read the excerpt but not the source. – ApplePie Feb 21 '18 at 15:29
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To follow up on the @Magua answer, yes, stocks can double -- or more -- in a day. Note how the share price was only $2. In this case, "doubling" is only an extra $2/share. That's a reasonable increase (though obviously there's no mandate that it will ever happen).

But now it's $4/share, and then $8, then $16, $32, $64, $128, etc. And even though, for example, swings in GOOGL of $32/share are reasonable, you aren't going to see it double from $1100 to $2200 in one day.

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    There is absolutely no logic in what you're saying. The dollar value of a stock is essentially meaningless. In general smaller companies trade at lower prices but that's not a rule. Nokia is a $30bn company trading at $5. ATRI with less than $1bn cap is priced at $500. Market capitalization is the best rule to determine how much equities move. – misantroop Feb 21 '18 at 9:31
  • @misantroop nothing says that a one-day $2 move on a $5/share stock is mandatory. It's just less unlikely than a 40% change in a $500/share. – RonJohn Feb 21 '18 at 9:41
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    It's a poor measurement, still. Price is very much arbitrary because a stock can reverse split from $1 to $100 in a day. – misantroop Feb 21 '18 at 9:58
  • @misantroop sure, they can reverse split. But it's rare. When trying to validate/clean up data, you look for anomalies and then research them. Sometimes the anomaly is from bad data, and sometimes the anomaly is from something rare but legal (like a stock split or takeover bid). – RonJohn Feb 21 '18 at 10:10
  • Volume is by far the best indicator. Large moves are almost exclusively combined with large volume increases. – misantroop Feb 21 '18 at 10:22

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