I'm doing research on the Black Litterman Portfolio. I have 489 stock return data with zero, negative and positive values. How can I see the normality of the data? I have tried the Kolmogorov Smirnov and Shapiro Wilk test in RStudio but the p-value is very less than 0.05.
To assess the normality of your stock return data, you can use statistical tests such as the Shapiro-Wilk test, the Kolmogorov-Smirnov test, or the Anderson-Darling test. These tests can help you determine if your data is normally distributed or not.
However, it's important to note that stock returns are often not normally distributed and may have fat tails or skewness. In these cases, using normality assumptions may not be appropriate for certain statistical analyses.
One way to visualize the distribution of your data is to create a histogram or density plot. This can help you to see the shape of the distribution and any deviations from normality.
In addition to statistical tests and visualizations, you may also want to consider other methods for assessing normality, such as Q-Q plots or skewness/kurtosis tests. These methods can help you to determine if your data is normally distributed or not.
Overall, it's important to carefully assess the normality of your data before applying any statistical analyses that assume normality. If your data is not normally distributed, you may need to consider using non-parametric methods or other statistical techniques that do not rely on normality assumptions.
If you have already performed the Kolmogorov-Smirnov and Shapiro-Wilk tests and found that the p-values are less than 0.05, it suggests that the data may not be normally distributed. However, it is important to note that these tests can be sensitive to sample size, so even small deviations from normality can lead to the rejection of the null hypothesis.
One way to assess the normality of your data is to plot a histogram and a normal probability plot (also called a Q-Q plot) of your sample data. A histogram will give you a visual representation of the distribution of your data, while a normal probability plot will plot the ordered values of your data against the expected values under the assumption of normality. If the points in the normal probability plot follow a straight line, it suggests that the data may be normally distributed.
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