# Are my stock returns non-normally distributed?

Hello stats community,

I have a Q-Q plot for my stock returns with a sample of n=262. I drew the plot with qqnorm and qqline(qtype=8). Most of the returns, except for 3 outliers, tend to follow the normal line.

However, when I perform the Shapiro Wilk test, I get a p-value of 0.003197, telling me that I can reject the null-hypothesis that my returns are drawn from a normal distribution.

Test Results:
STATISTIC:
W: 0.983
P VALUE:
0.003197


Am I missing something? Should I follow my observations or trust the SW test?

• Trust the test, first and foremost. QQ-plots are just informal tools for building your intuition... These stock returns are not normally distributed, exhibiting a well-documented issue of fat tails. Try t-distribution (t location-scale distribution) instead. – stans - Reinstate Monica Aug 19 '18 at 20:44
• I don't see the contradiction. The outliers on the left and the one on the right are extreme enough to think that data is not from a normal distribution. The kurtosis is much less than 3. – Michael R. Chernick Aug 19 '18 at 20:48
• I do not understand the question: the QQ plot and the test concord with one another – user603 Aug 19 '18 at 20:49
• @Michael That's got to be an excess kurtosis, which is positive due to the long tails. – whuber Aug 19 '18 at 22:42
• @MichaelLew's answer is good. If you told us more about why you care about Normality you might get a more precise answer: What is the particular question you're trying to answer? What analytical procedure do you plan to follow after this, and how would it change if you did or didn't accept the assumption of Normality? (The trivial/sarcastic answer to your question is "Yes".) – Ben Bolker Aug 19 '18 at 23:53