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Why Correlation Alone Cannot Determine a Stock’s Chance of Rising

Article Quant Q&A · Author: Contango
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Summary

The document poses a probability question: whether the chance that one stock rises can be inferred from another stock’s rise probability and the correlation between their movements. It also asks whether probabilities and correlations across several stocks could be used to infer the chance that another stock rises.

The accepted response gives a concise statistical limitation: correlation alone is insufficient; the joint probability distribution is also needed. The post offers no derivation, dataset, or worked example, so it establishes the point without showing how to estimate the missing joint information. Its practical lesson is to avoid treating correlation as a direct conversion between event probabilities, especially when modeling co-movement or portfolio risk.

Key ideas

  • A single asset’s rise probability and pairwise correlation do not determine another asset’s rise probability.
  • The joint probability distribution contains information that correlation does not capture.
  • Extending the question to multiple assets requires more than their rise probabilities and correlations.

Tags

StatisticsEquitiesPortfolio construction
Full text
# If stock A has a 60% chance of rising, and stocks A and B have 80% correlation, what is the chance of stock B rising?


# If stock A has a 60% chance of rising, and stocks A and B have 80% correlation, what is the chance of stock B rising?












As in the subject, I'm interested in a math puzzle of sorts:

If stock A has a 60% chance of rising, and stocks A and B have an 80% correlation, what is the chance of stock B rising?

Would it be possible to extend this concept so that if we know the probabilities of stocks A,B,C,D rising, we can work out the probability of stock E rising, given tha stock E has some correlation to stocks A,B,C,D?

Update:

For an indepth tutorial video on the basics of probability, see the Khan Academy Tutorial Videos on Probability.

## Answer by Joshua Ulrich (score 9, accepted)

https://quant.stackexchange.com/a/1269

You can't determine this with just the correlation; you need to know the joint probability.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.