Python for Finance Cookbook

Non-Gaussian distribution of returns

Run the following steps to investigate the existence of this first fact by plotting the histogram of returns and a Q-Q plot.

1. Calculate the normal Probability Density Function (PDF) using the mean and standard deviation of the observed returns:

r_range = np.linspace(min(df.log_rtn), max(df.log_rtn), num=1000)mu = df.log_rtn.mean()sigma = df.log_rtn.std()norm_pdf = scs.norm.pdf(r_range, loc=mu, scale=sigma) 

2. Plot the histogram and the Q-Q plot:

fig, ax = plt.subplots(1, 2, figsize=(16, 8))# histogramsns.distplot(df.log_rtn, kde=False, norm_hist=True, ax=ax[0]) ax[0].set_title('Distribution of MSFT returns', fontsize=16) ax[0].plot(r_range, norm_pdf, 'g', lw=2,            label=f'N({mu:.2f}, {sigma**2:.4f})')