Tests of normality

In finance, knowledge about normal distribution is very important for two reasons. First, stock returns are assumed to follow a normal distribution. Second, the error terms from a good econometric model should follow a normal distribution with a zero mean. However, in the real world, this might not be true for stocks. On the other hand, whether stocks or portfolios follow a normal distribution could be tested by various so-called normality tests. The Shapiro-Wilk test is one of them. For the first example, random numbers are drawn from a normal distribution. As a consequence, the test should confirm that those observations follow a normal distribution:

from scipy import stats 
import scipy as sp
sp.random.seed(12345)
mean=0.1
std=0.2
n=5000
ret=sp.random.normal(loc=0,scale=std,size=n)
print 'W-test, and P-value' 
print(stats.shapiro(ret))
W-test, and P-value
(0.9995986223220825, 0.4129064679145813)

Assume that our confidence level is 95%, that is, alpha=0.05....