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# Copyright 2014 Quantopian, Inc. |
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# |
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# Licensed under the Apache License, Version 2.0 (the "License"); |
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# you may not use this file except in compliance with the License. |
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# You may obtain a copy of the License at |
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# |
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# http://www.apache.org/licenses/LICENSE-2.0 |
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# |
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# Unless required by applicable law or agreed to in writing, software |
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# distributed under the License is distributed on an "AS IS" BASIS, |
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
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# See the License for the specific language governing permissions and |
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# limitations under the License. |
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import functools |
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import logbook |
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import math |
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import numpy as np |
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import zipline.utils.math_utils as zp_math |
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import pandas as pd |
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from pandas.tseries.tools import normalize_date |
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from six import iteritems |
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from . risk import ( |
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alpha, |
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check_entry, |
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choose_treasury, |
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downside_risk, |
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sharpe_ratio, |
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sortino_ratio, |
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) |
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from zipline.utils.serialization_utils import ( |
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VERSION_LABEL |
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) |
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log = logbook.Logger('Risk Cumulative') |
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choose_treasury = functools.partial(choose_treasury, lambda *args: '10year', |
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compound=False) |
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def information_ratio(algo_volatility, algorithm_return, benchmark_return): |
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""" |
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http://en.wikipedia.org/wiki/Information_ratio |
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Args: |
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algorithm_returns (np.array-like): |
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All returns during algorithm lifetime. |
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benchmark_returns (np.array-like): |
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All benchmark returns during algo lifetime. |
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Returns: |
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float. Information ratio. |
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""" |
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if zp_math.tolerant_equals(algo_volatility, 0): |
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return np.nan |
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# The square of the annualization factor is in the volatility, |
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# because the volatility is also annualized, |
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# i.e. the sqrt(annual factor) is in the volatility's numerator. |
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# So to have the the correct annualization factor for the |
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# Sharpe value's numerator, which should be the sqrt(annual factor). |
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# The square of the sqrt of the annual factor, i.e. the annual factor |
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# itself, is needed in the numerator to factor out the division by |
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# its square root. |
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return (algorithm_return - benchmark_return) / algo_volatility |
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class RiskMetricsCumulative(object): |
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""" |
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:Usage: |
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Instantiate RiskMetricsCumulative once. |
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Call update() method on each dt to update the metrics. |
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""" |
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METRIC_NAMES = ( |
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'alpha', |
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'beta', |
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'sharpe', |
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'algorithm_volatility', |
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'benchmark_volatility', |
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'downside_risk', |
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'sortino', |
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'information', |
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) |
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def __init__(self, sim_params, env, |
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create_first_day_stats=False): |
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self.treasury_curves = env.treasury_curves |
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self.start_date = sim_params.period_start.replace( |
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hour=0, minute=0, second=0, microsecond=0 |
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) |
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self.end_date = sim_params.period_end.replace( |
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hour=0, minute=0, second=0, microsecond=0 |
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) |
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self.trading_days = env.days_in_range(self.start_date, self.end_date) |
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# Hold on to the trading day before the start, |
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# used for index of the zero return value when forcing returns |
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# on the first day. |
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self.day_before_start = self.start_date - env.trading_days.freq |
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last_day = normalize_date(sim_params.period_end) |
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if last_day not in self.trading_days: |
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last_day = pd.tseries.index.DatetimeIndex( |
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[last_day] |
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) |
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self.trading_days = self.trading_days.append(last_day) |
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self.sim_params = sim_params |
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self.env = env |
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self.create_first_day_stats = create_first_day_stats |
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cont_index = self.trading_days |
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self.cont_index = cont_index |
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self.cont_len = len(self.cont_index) |
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empty_cont = np.full(self.cont_len, np.nan) |
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self.algorithm_returns_cont = empty_cont.copy() |
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self.benchmark_returns_cont = empty_cont.copy() |
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self.algorithm_cumulative_leverages_cont = empty_cont.copy() |
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self.mean_returns_cont = empty_cont.copy() |
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self.annualized_mean_returns_cont = empty_cont.copy() |
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self.mean_benchmark_returns_cont = empty_cont.copy() |
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self.annualized_mean_benchmark_returns_cont = empty_cont.copy() |
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# The returns at a given time are read and reset from the respective |
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# returns container. |
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self.algorithm_returns = None |
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self.benchmark_returns = None |
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self.mean_returns = None |
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self.annualized_mean_returns = None |
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self.mean_benchmark_returns = None |
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self.annualized_mean_benchmark_returns = None |
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self.algorithm_cumulative_returns = empty_cont.copy() |
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self.benchmark_cumulative_returns = empty_cont.copy() |
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self.algorithm_cumulative_leverages = empty_cont.copy() |
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self.excess_returns = empty_cont.copy() |
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self.latest_dt_loc = 0 |
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self.latest_dt = cont_index[0] |
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self.benchmark_volatility = empty_cont.copy() |
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self.algorithm_volatility = empty_cont.copy() |
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self.beta = empty_cont.copy() |
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self.alpha = empty_cont.copy() |
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self.sharpe = empty_cont.copy() |
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self.downside_risk = empty_cont.copy() |
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self.sortino = empty_cont.copy() |
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self.information = empty_cont.copy() |
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self.drawdowns = empty_cont.copy() |
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self.max_drawdowns = empty_cont.copy() |
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self.max_drawdown = 0 |
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self.max_leverages = empty_cont.copy() |
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self.max_leverage = 0 |
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self.current_max = -np.inf |
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self.daily_treasury = pd.Series(index=self.trading_days) |
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self.treasury_period_return = np.nan |
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self.num_trading_days = 0 |
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def update(self, dt, algorithm_returns, benchmark_returns, leverage): |
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# Keep track of latest dt for use in to_dict and other methods |
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# that report current state. |
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self.latest_dt = dt |
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dt_loc = self.cont_index.get_loc(dt) |
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self.latest_dt_loc = dt_loc |
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self.algorithm_returns_cont[dt_loc] = algorithm_returns |
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self.algorithm_returns = self.algorithm_returns_cont[:dt_loc + 1] |
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self.num_trading_days = len(self.algorithm_returns) |
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if self.create_first_day_stats: |
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if len(self.algorithm_returns) == 1: |
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self.algorithm_returns = np.append(0.0, self.algorithm_returns) |
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self.algorithm_cumulative_returns[dt_loc] = \ |
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self.calculate_cumulative_returns(self.algorithm_returns) |
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algo_cumulative_returns_to_date = \ |
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self.algorithm_cumulative_returns[:dt_loc + 1] |
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self.mean_returns_cont[dt_loc] = \ |
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algo_cumulative_returns_to_date[dt_loc] / self.num_trading_days |
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self.mean_returns = self.mean_returns_cont[:dt_loc + 1] |
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self.annualized_mean_returns_cont[dt_loc] = \ |
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self.mean_returns_cont[dt_loc] * 252 |
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self.annualized_mean_returns = \ |
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self.annualized_mean_returns_cont[:dt_loc + 1] |
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if self.create_first_day_stats: |
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if len(self.mean_returns) == 1: |
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self.mean_returns = np.append(0.0, self.mean_returns) |
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self.annualized_mean_returns = np.append( |
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0.0, self.annualized_mean_returns) |
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self.benchmark_returns_cont[dt_loc] = benchmark_returns |
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self.benchmark_returns = self.benchmark_returns_cont[:dt_loc + 1] |
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if self.create_first_day_stats: |
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if len(self.benchmark_returns) == 1: |
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self.benchmark_returns = np.append(0.0, self.benchmark_returns) |
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self.benchmark_cumulative_returns[dt_loc] = \ |
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self.calculate_cumulative_returns(self.benchmark_returns) |
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benchmark_cumulative_returns_to_date = \ |
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self.benchmark_cumulative_returns[:dt_loc + 1] |
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self.mean_benchmark_returns_cont[dt_loc] = \ |
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benchmark_cumulative_returns_to_date[dt_loc] / \ |
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self.num_trading_days |
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self.mean_benchmark_returns = self.mean_benchmark_returns_cont[:dt_loc] |
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self.annualized_mean_benchmark_returns_cont[dt_loc] = \ |
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self.mean_benchmark_returns_cont[dt_loc] * 252 |
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self.annualized_mean_benchmark_returns = \ |
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self.annualized_mean_benchmark_returns_cont[:dt_loc + 1] |
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self.algorithm_cumulative_leverages_cont[dt_loc] = leverage |
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self.algorithm_cumulative_leverages = \ |
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self.algorithm_cumulative_leverages_cont[:dt_loc + 1] |
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if self.create_first_day_stats: |
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if len(self.algorithm_cumulative_leverages) == 1: |
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self.algorithm_cumulative_leverages = np.append( |
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0.0, |
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self.algorithm_cumulative_leverages) |
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if not len(self.algorithm_returns) and len(self.benchmark_returns): |
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message = "Mismatch between benchmark_returns ({bm_count}) and \ |
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algorithm_returns ({algo_count}) in range {start} : {end} on {dt}" |
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message = message.format( |
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bm_count=len(self.benchmark_returns), |
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algo_count=len(self.algorithm_returns), |
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start=self.start_date, |
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end=self.end_date, |
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dt=dt |
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) |
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raise Exception(message) |
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self.update_current_max() |
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self.benchmark_volatility[dt_loc] = \ |
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self.calculate_volatility(self.benchmark_returns) |
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self.algorithm_volatility[dt_loc] = \ |
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self.calculate_volatility(self.algorithm_returns) |
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# caching the treasury rates for the minutely case is a |
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# big speedup, because it avoids searching the treasury |
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# curves on every minute. |
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# In both minutely and daily, the daily curve is always used. |
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treasury_end = dt.replace(hour=0, minute=0) |
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if np.isnan(self.daily_treasury[treasury_end]): |
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treasury_period_return = choose_treasury( |
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self.treasury_curves, |
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self.start_date, |
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treasury_end, |
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self.env, |
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) |
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self.daily_treasury[treasury_end] = treasury_period_return |
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self.treasury_period_return = self.daily_treasury[treasury_end] |
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self.excess_returns[dt_loc] = ( |
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self.algorithm_cumulative_returns[dt_loc] - |
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self.treasury_period_return) |
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self.beta[dt_loc] = self.calculate_beta() |
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self.alpha[dt_loc] = self.calculate_alpha() |
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self.sharpe[dt_loc] = self.calculate_sharpe() |
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self.downside_risk[dt_loc] = \ |
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self.calculate_downside_risk() |
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self.sortino[dt_loc] = self.calculate_sortino() |
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self.information[dt_loc] = self.calculate_information() |
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self.max_drawdown = self.calculate_max_drawdown() |
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self.max_drawdowns[dt_loc] = self.max_drawdown |
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self.max_leverage = self.calculate_max_leverage() |
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self.max_leverages[dt_loc] = self.max_leverage |
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def to_dict(self): |
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""" |
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Creates a dictionary representing the state of the risk report. |
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Returns a dict object of the form: |
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""" |
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dt = self.latest_dt |
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dt_loc = self.latest_dt_loc |
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period_label = dt.strftime("%Y-%m") |
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rval = { |
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'trading_days': self.num_trading_days, |
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'benchmark_volatility': |
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self.benchmark_volatility[dt_loc], |
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'algo_volatility': |
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self.algorithm_volatility[dt_loc], |
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'treasury_period_return': self.treasury_period_return, |
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# Though the two following keys say period return, |
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# they would be more accurately called the cumulative return. |
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# However, the keys need to stay the same, for now, for backwards |
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# compatibility with existing consumers. |
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'algorithm_period_return': |
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self.algorithm_cumulative_returns[dt_loc], |
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'benchmark_period_return': |
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self.benchmark_cumulative_returns[dt_loc], |
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'beta': self.beta[dt_loc], |
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'alpha': self.alpha[dt_loc], |
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'sharpe': self.sharpe[dt_loc], |
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'sortino': self.sortino[dt_loc], |
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'information': self.information[dt_loc], |
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'excess_return': self.excess_returns[dt_loc], |
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'max_drawdown': self.max_drawdown, |
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'max_leverage': self.max_leverage, |
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'period_label': period_label |
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} |
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return {k: (None if check_entry(k, v) else v) |
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for k, v in iteritems(rval)} |
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def __repr__(self): |
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statements = [] |
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for metric in self.METRIC_NAMES: |
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value = getattr(self, metric)[-1] |
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if isinstance(value, list): |
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if len(value) == 0: |
338
|
|
|
value = np.nan |
339
|
|
|
else: |
340
|
|
|
value = value[-1] |
341
|
|
|
statements.append("{m}:{v}".format(m=metric, v=value)) |
342
|
|
|
|
343
|
|
|
return '\n'.join(statements) |
344
|
|
|
|
345
|
|
|
def calculate_cumulative_returns(self, returns): |
346
|
|
|
return (1. + returns).prod() - 1 |
347
|
|
|
|
348
|
|
|
def update_current_max(self): |
349
|
|
|
if len(self.algorithm_cumulative_returns) == 0: |
350
|
|
|
return |
351
|
|
|
current_cumulative_return = \ |
352
|
|
|
self.algorithm_cumulative_returns[self.latest_dt_loc] |
353
|
|
|
if self.current_max < current_cumulative_return: |
354
|
|
|
self.current_max = current_cumulative_return |
355
|
|
|
|
356
|
|
|
def calculate_max_drawdown(self): |
357
|
|
|
if len(self.algorithm_cumulative_returns) == 0: |
358
|
|
|
return self.max_drawdown |
359
|
|
|
|
360
|
|
|
# The drawdown is defined as: (high - low) / high |
361
|
|
|
# The above factors out to: 1.0 - (low / high) |
362
|
|
|
# |
363
|
|
|
# Instead of explicitly always using the low, use the current total |
364
|
|
|
# return value, and test that against the max drawdown, which will |
365
|
|
|
# exceed the previous max_drawdown iff the current return is lower than |
366
|
|
|
# the previous low in the current drawdown window. |
367
|
|
|
cur_drawdown = 1.0 - ( |
368
|
|
|
(1.0 + self.algorithm_cumulative_returns[self.latest_dt_loc]) |
369
|
|
|
/ |
370
|
|
|
(1.0 + self.current_max)) |
371
|
|
|
|
372
|
|
|
self.drawdowns[self.latest_dt_loc] = cur_drawdown |
373
|
|
|
|
374
|
|
|
if self.max_drawdown < cur_drawdown: |
375
|
|
|
return cur_drawdown |
376
|
|
|
else: |
377
|
|
|
return self.max_drawdown |
378
|
|
|
|
379
|
|
|
def calculate_max_leverage(self): |
380
|
|
|
# The leverage is defined as: the gross_exposure/net_liquidation |
381
|
|
|
# gross_exposure = long_exposure + abs(short_exposure) |
382
|
|
|
# net_liquidation = ending_cash + long_exposure + short_exposure |
383
|
|
|
cur_leverage = self.algorithm_cumulative_leverages_cont[ |
384
|
|
|
self.latest_dt_loc] |
385
|
|
|
|
386
|
|
|
return max(cur_leverage, self.max_leverage) |
387
|
|
|
|
388
|
|
|
def calculate_sharpe(self): |
389
|
|
|
""" |
390
|
|
|
http://en.wikipedia.org/wiki/Sharpe_ratio |
391
|
|
|
""" |
392
|
|
|
return sharpe_ratio( |
393
|
|
|
self.algorithm_volatility[self.latest_dt_loc], |
394
|
|
|
self.annualized_mean_returns_cont[self.latest_dt_loc], |
395
|
|
|
self.daily_treasury[self.latest_dt.date()]) |
396
|
|
|
|
397
|
|
|
def calculate_sortino(self): |
398
|
|
|
""" |
399
|
|
|
http://en.wikipedia.org/wiki/Sortino_ratio |
400
|
|
|
""" |
401
|
|
|
return sortino_ratio( |
402
|
|
|
self.annualized_mean_returns_cont[self.latest_dt_loc], |
403
|
|
|
self.daily_treasury[self.latest_dt.date()], |
404
|
|
|
self.downside_risk[self.latest_dt_loc]) |
405
|
|
|
|
406
|
|
|
def calculate_information(self): |
407
|
|
|
""" |
408
|
|
|
http://en.wikipedia.org/wiki/Information_ratio |
409
|
|
|
""" |
410
|
|
|
return information_ratio( |
411
|
|
|
self.algorithm_volatility[self.latest_dt_loc], |
412
|
|
|
self.annualized_mean_returns_cont[self.latest_dt_loc], |
413
|
|
|
self.annualized_mean_benchmark_returns_cont[self.latest_dt_loc]) |
414
|
|
|
|
415
|
|
|
def calculate_alpha(self): |
416
|
|
|
""" |
417
|
|
|
http://en.wikipedia.org/wiki/Alpha_(investment) |
418
|
|
|
""" |
419
|
|
|
return alpha( |
420
|
|
|
self.annualized_mean_returns_cont[self.latest_dt_loc], |
421
|
|
|
self.treasury_period_return, |
422
|
|
|
self.annualized_mean_benchmark_returns_cont[self.latest_dt_loc], |
423
|
|
|
self.beta[self.latest_dt_loc]) |
424
|
|
|
|
425
|
|
|
def calculate_volatility(self, daily_returns): |
426
|
|
|
if len(daily_returns) <= 1: |
427
|
|
|
return 0.0 |
428
|
|
|
return np.std(daily_returns, ddof=1) * math.sqrt(252) |
429
|
|
|
|
430
|
|
|
def calculate_downside_risk(self): |
431
|
|
|
return downside_risk(self.algorithm_returns, |
432
|
|
|
self.mean_returns, |
433
|
|
|
252) |
434
|
|
|
|
435
|
|
|
def calculate_beta(self): |
436
|
|
|
""" |
437
|
|
|
|
438
|
|
|
.. math:: |
439
|
|
|
|
440
|
|
|
\\beta_a = \\frac{\mathrm{Cov}(r_a,r_p)}{\mathrm{Var}(r_p)} |
441
|
|
|
|
442
|
|
|
http://en.wikipedia.org/wiki/Beta_(finance) |
443
|
|
|
""" |
444
|
|
|
# it doesn't make much sense to calculate beta for less than two |
445
|
|
|
# values, so return none. |
446
|
|
|
if len(self.algorithm_returns) < 2: |
447
|
|
|
return 0.0 |
448
|
|
|
|
449
|
|
|
returns_matrix = np.vstack([self.algorithm_returns, |
450
|
|
|
self.benchmark_returns]) |
451
|
|
|
C = np.cov(returns_matrix, ddof=1) |
452
|
|
|
algorithm_covariance = C[0][1] |
453
|
|
|
benchmark_variance = C[1][1] |
454
|
|
|
beta = algorithm_covariance / benchmark_variance |
455
|
|
|
|
456
|
|
|
return beta |
457
|
|
|
|
458
|
|
|
def __getstate__(self): |
459
|
|
|
state_dict = {k: v for k, v in iteritems(self.__dict__) |
460
|
|
|
if not k.startswith('_')} |
461
|
|
|
|
462
|
|
|
STATE_VERSION = 3 |
463
|
|
|
state_dict[VERSION_LABEL] = STATE_VERSION |
464
|
|
|
|
465
|
|
|
return state_dict |
466
|
|
|
|
467
|
|
|
def __setstate__(self, state): |
468
|
|
|
|
469
|
|
|
OLDEST_SUPPORTED_STATE = 3 |
470
|
|
|
version = state.pop(VERSION_LABEL) |
471
|
|
|
|
472
|
|
|
if version < OLDEST_SUPPORTED_STATE: |
473
|
|
|
raise BaseException("RiskMetricsCumulative \ |
474
|
|
|
saved state is too old.") |
475
|
|
|
|
476
|
|
|
self.__dict__.update(state) |
477
|
|
|
|