# Copyright 2016-present CERN – European Organization for Nuclear Research
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from typing import Tuple
import matplotlib as mpl
import numpy as np
import pandas as pd
from pandas import Index
from qf_lib.common.utils.dateutils.get_values_common_dates import get_values_for_common_dates
from qf_lib.common.utils.returns.beta_and_alpha import beta_and_alpha_full_stats
from qf_lib.containers.series.qf_series import QFSeries
from qf_lib.plotting.charts.chart import Chart
from qf_lib.plotting.decorators.axes_formatter_decorator import PercentageFormatter
[docs]class RegressionChart(Chart):
"""
Creates a regression chart.
Parameters
-----------
benchmark_tms: QFSeries
timeseries of the benchmark
strategy_tms: QFSeries
timeseries of the strategy
tail_plot: bool
plot tail data
custom_title: bool
add custom title to the plot
"""
def __init__(self, benchmark_tms: QFSeries, strategy_tms: QFSeries, tail_plot=False, custom_title=False):
super().__init__()
self.assert_is_qfseries(benchmark_tms)
self.assert_is_qfseries(strategy_tms)
self.benchmark_tms = benchmark_tms.to_simple_returns()
self.strategy_tms = strategy_tms.to_simple_returns()
self.tail_plot = tail_plot
self.custom_title = custom_title
[docs] def plot(self, figsize: Tuple[float, float] = None):
self._setup_axes_if_necessary(figsize)
self._apply_decorators()
datapoints_tms, regression_line, beta, alpha, r_squared, max_ret = self._prepare_data_to_plot()
self._plot_data(datapoints_tms, regression_line, beta, alpha, r_squared, max_ret)
if self.tail_plot:
_, regression_line, beta, alpha, r_squared, max_ret = self._prepare_data_to_plot(tail=True)
self._plot_tail_data(regression_line, beta, alpha, r_squared, max_ret)
self.axes.set_xlabel(self.benchmark_tms.name)
self.axes.set_ylabel(self.strategy_tms.name)
if self.custom_title is not False and isinstance(self.custom_title, str):
self.axes.set_title(self.custom_title)
else:
self.axes.set_title('Linear Regression')
def _prepare_data_to_plot(self, tail=False):
strategy_rets = self.strategy_tms.to_simple_returns()
benchmark_rets = self.benchmark_tms.to_simple_returns()
strategy_rets, benchmark_rets = get_values_for_common_dates(strategy_rets, benchmark_rets)
datapoints_tms = pd.concat((benchmark_rets, strategy_rets), axis=1)
if tail:
def get_tail_indices():
avg_rets = strategy_rets.mean()
std_rets = strategy_rets.std()
# Tail events are < the avg portfolio returns minus one std
return strategy_rets < avg_rets - std_rets
tail_indices = get_tail_indices()
strategy_tail_returns = strategy_rets.loc[tail_indices]
beta, alpha, r_value, p_value, std_err = beta_and_alpha_full_stats(
strategy_tms=strategy_tail_returns, benchmark_tms=benchmark_rets)
else:
beta, alpha, r_value, p_value, std_err = beta_and_alpha_full_stats(
strategy_tms=strategy_rets, benchmark_tms=benchmark_rets)
max_ret = datapoints_tms.abs().max().max() # take max element from the whole data-frame
x = np.linspace(-max_ret, max_ret, 20)
y = beta * x + alpha
regression_line = QFSeries(data=y, index=Index(x))
return datapoints_tms, regression_line, beta, alpha, r_value ** 2, max_ret
def _plot_data(self, datapoints_tms, regression_line, beta, alpha, r_squared, max_ret):
colors = Chart.get_axes_colors()
self.axes.scatter(x=datapoints_tms.iloc[:, 0], y=datapoints_tms.iloc[:, 1],
c=colors[0], alpha=0.6, edgecolors='black', linewidths=0.5)
self.axes.axhline(0, color='black', axes=self.axes, linewidth=1)
self.axes.axvline(0, color='black', axes=self.axes, linewidth=1)
self.axes.plot(regression_line.index.values, regression_line.values, axes=self.axes, color=colors[1])
self.axes.set_xlim([-max_ret, max_ret])
self.axes.set_ylim([-max_ret, max_ret])
props = dict(boxstyle='square', facecolor='white', alpha=0.5)
textstr = '$\\beta={0:.2f}$\n$\\alpha={1:.2%}$$\%$\n$R^2={2:.2}$'.format(beta, alpha, r_squared)
font_size = mpl.rcParams['legend.fontsize']
self.axes.text(
0.05, 0.95, textstr, transform=self.axes.transAxes, bbox=props, verticalalignment='top', fontsize=font_size)
self.axes.xaxis.set_major_formatter(PercentageFormatter())
self.axes.yaxis.set_major_formatter(PercentageFormatter())
def _plot_tail_data(self, regression_line, beta, alpha, r_squared, max_ret):
colors = Chart.get_axes_colors()
self.axes.plot(regression_line.index.values, regression_line.values, axes=self.axes, color=colors[2])
self.axes.set_xlim([-max_ret, max_ret])
self.axes.set_ylim([-max_ret, max_ret])
props = dict(boxstyle='square', facecolor=colors[2], alpha=0.5)
textstr = 'tail $\\beta={0:.2f}$\ntail $\\alpha={1:.2%}$$\%$\ntail $R^2={2:.2}$'.format(beta, alpha, r_squared)
font_size = mpl.rcParams['legend.fontsize']
self.axes.text(
0.80, 0.35, textstr, transform=self.axes.transAxes, bbox=props, verticalalignment='top', fontsize=font_size)