Statistical analysis CAC40(^FCHI)

What is CAC40?

CAC40(^FCHI) is the French stock market. It measures of the 40 most significant stocks.

How to get historical data cac40 in python?

Some code has been written below to collect data from yahoo finance.
df = yf.download('^FCHI',
start='1985-01-01',
end='2021-07-28',
progress=False)
df = df.loc[:, ['Adj Close']]
df.rename(columns={'Adj Close':'adj_close'}, inplace=True)
df['simple_rtn'] = df.adj_close.pct_change()
df['log_rtn'] = np.log(df.adj_close/df.adj_close.shift(1))
df[['simple_rtn','log_rtn']].tail(20)

How to see Cac40 log and simple data in python?

Define Realise volatility
def realized_volatility(x):
 return np.sqrt(np.sum(x**2))
df_rv = df.groupby(pd.Grouper(freq='M')).apply(realized_volatility)
df_rv.rename(columns={'log_rtn''rv'}, inplace=True)
df_rv.rv = df_rv.rv * np.sqrt(12)
fig, ax = plt.subplots(21, sharex=True)
ax[0].plot(df)
ax[1].plot(df_rv)
[<matplotlib.lines.Line2D at 0x7f703738a710>,
 <matplotlib.lines.Line2D at 0x7f7037333a50>,
 <matplotlib.lines.Line2D at 0x7f7037333c10>]
fig, ax = plt.subplots(31, figsize=(2420), sharex=True)
df.adj_close.plot(ax=ax[0])
ax[0].set(title = 'CAC40 time series',
ylabel = 'Stock price ($)')
df.simple_rtn.plot(ax=ax[1])
ax[1].set(ylabel = 'Simple returns (%)')
df.log_rtn.plot(ax=ax[2])
ax[2].set(xlabel = 'Date',
ylabel = 'Log returns (%)')
[Text(0, 0.5, 'Log returns (%)'), Text(0.5, 0, 'Date')]

Plot price cac40, simple and log price


import cufflinks as cf
from plotly.offline import iplot, init_notebook_mode
init_notebook_mode()
df_rolling = df[['simple_rtn']].rolling(window=21) \
.agg(['mean''std'])
df_rolling.columns = df_rolling.columns.droplevel()
df_outliers = df.join(df_rolling)
def indentify_outliers(rown_sigmas=3):
   x = row['simple_rtn']
   mu = row['mean']
   sigma = row['std']
   if (x > mu + 3 * sigma) | (x < mu - 3 * sigma):
    return 1
   else:
    return 0
df_outliers['outlier'] = df_outliers.apply(indentify_outliers,
axis=1)
outliers = df_outliers.loc[df_outliers['outlier'] == 1,
['simple_rtn']]
fig, ax = plt.subplots()
ax.plot(df_outliers.index, df_outliers.simple_rtn,
color='blue', label='Normal')
ax.scatter(outliers.index, outliers.simple_rtn,
color='red', label='Anomaly')
ax.set_title("CAC40 returns")
ax.legend(loc='lower right')
<matplotlib.legend.Legend at 0x7f70323a8910>
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)
fig, ax = plt.subplots(12, figsize=(168))
# histogram
sns.distplot(df.log_rtn, kde=False, norm_hist=True, ax=ax[0])
ax[0].set_title('Distribution of CAC40 returns', fontsize=16)
ax[0].plot(r_range, norm_pdf, 'g', lw=2,
label=f'N({mu:.2f}{sigma**2:.4f})')
ax[0].legend(loc='upper left');
/usr/local/lib/python3.7/dist-packages/seaborn/distributions.py:2557: FutureWarning:

`distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).

df.log_rtn.plot(title='Daily CAC40 returns')
<matplotlib.axes._subplots.AxesSubplot at 0x7f7032068b50>
df = yf.download(['^FCHI''^VIX'],
start='1985-01-01',
end='2021-07-28',
progress=False)
df = df[['Adj Close']]
df.columns = df.columns.droplevel(0)
df = df.rename(columns={'^FCHI''Cac40''^VIX''vix'})
df['log_rtn'] = np.log(df.Cac40 / df.Cac40.shift(1))
df['vol_rtn'] = np.log(df.vix / df.vix.shift(1))
df.dropna(how='any', axis=0, inplace=True)
corr_coeff = df.log_rtn.corr(df.vol_rtn)
ax = sns.regplot(x='log_rtn', y='vol_rtn', data=df,
line_kws={'color''red'})
ax.set(title=f'FCHI vs. VIX ($\\rho$ = {corr_coeff:.2f})',
ylabel='VIX log returns',
xlabel='FTSE100 log returns')
[Text(0, 0.5, 'VIX log returns'),
 Text(0.5, 0, 'FTSE100 log returns'),
 Text(0.5, 1.0, 'FCHI vs. VIX ($\\rho$ = -0.42)')]
We can see that both the negative slope of the regression line and a strong negative correlation between the two series confirm the existence of the leverage effect in the return series
more updates to follow CAC40

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