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Why is the Pearson correlation coefficient used to derive correlations between stock returns if the stock returns are not normally distributed? I was under the assumption that the data should be normally distributed or close to that but in case of stock returns, especially short time series of daily returns, they are not.

Carl
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T. Acco
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    Before fitting time series models to return series, Johnson transformation should be utilized to transform distributions of returns to standard normal distribution. This transformation enables us to fit time series models with Gaussian innovations to the data series. Hence, we can work with standard normal distributions, rather than original, usually leptokurtic, distributions of returns. The normality of innovations has the important advantage that it allows us to take advantages of Pearson correlation to well characterize the dependence structure of innovations.Physica A 405 (2014)35–51 – Nick Mar 12 '17 at 12:27
  • You would have to ask the people who do this. However, regarding Pearson correlations & normality you might be interested in reading this: [Pearson's or Spearman's correlation with non-normal data](http://stats.stackexchange.com/q/3730/7290). – gung - Reinstate Monica Mar 12 '17 at 12:33
  • @gung I think that link almost makes this a duplicate question. – Peter Flom Mar 12 '17 at 14:35
  • @PeterFlom, yeah, I was on the fence about that. It's up to you. – gung - Reinstate Monica Mar 12 '17 at 15:13
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    Possible duplicate of [Pearson's or Spearman's correlation with non-normal data](http://stats.stackexchange.com/questions/3730/pearsons-or-spearmans-correlation-with-non-normal-data) – Kodiologist Mar 12 '17 at 15:28
  • @Nick This question is specific to stock returns. Many similar questions that are more general have been broached here, for [example](http://stats.stackexchange.com/questions/38273/how-robust-is-pearsons-correlation-coefficient-to-violations-of-normality). However, I would really like to see your comment expanded into an answer because I want the specific OP question addressed. – Carl Mar 13 '17 at 00:49

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