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. The first value...