intercept -0.0001 0.0006 -0.12 0.9043 -0.0013
0.0011
–––––––––––End of Summary––––––––
–––
Obviously, there is indeed a highly negative correlation. We can access the results as
follows:
In [ 82 ]: model.beta
Out[82]: x -2.752894
intercept -0.000074
dtype: float64
This input, in combination with the raw log return data, is used to generate the plot in
Figure 6-9, which provides strong support for the leverage effect:
In [ 83 ]: plt.plot(xdat, ydat, ‘r.’)
ax = plt.axis() # grab axis values
x = np.linspace(ax[ 0 ], ax[ 1 ] + 0.01)
plt.plot(x, model.beta[ 1 ] + model.beta[ 0 ] * x, ‘b’, lw= 2 )
plt.grid(True)
plt.axis(‘tight’)
plt.xlabel(‘EURO STOXX 50 returns’)
plt.ylabel(‘VSTOXX returns’)
Figure 6-9. Scatter plot of log returns and regression line
As a final cross-check, we can calculate the correlation between the two financial time
series directly:
In [ 84 ]: rets.corr()
Out[84]: EUROSTOXX VSTOXX
EUROSTOXX 1.000000 -0.729538
VSTOXX -0.729538 1.000000
Although the correlation is strongly negative on the whole data set, it varies considerably
over time, as shown in Figure 6-10. The figure uses correlation on a yearly basis, i.e., for
252 trading days:
In [ 85 ]: pd.rolling_corr(rets[‘EUROSTOXX’], rets[‘VSTOXX’],
window= 252 ).plot(grid=True, style=‘b’)
