zipline.finance.risk.RiskMetricsCumulative.calculate_alpha() - Code Metrics - quantopian/zipline - Measure and Improve Code Quality continuously with Scrutinizer

calculate_alpha() A
last analyzed 2016-01-08 22:03 UTC

↳ Parent: zipline.finance.risk.RiskMetricsCumulative

Complexity

Conditions

Size

Total Lines

Duplication

Lines	0
Ratio	0 %

Metric	Value
cc	1
dl	0
loc	9
rs	9.6667

#
# Copyright 2014 Quantopian, Inc.
#
# 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.

import functools
import logbook
import math
import numpy as np

import zipline.utils.math_utils as zp_math

import pandas as pd
from pandas.tseries.tools import normalize_date

from six import iteritems

from . risk import (
    alpha,
    check_entry,
    choose_treasury,
    downside_risk,
    sharpe_ratio,
    sortino_ratio,
)

from zipline.utils.serialization_utils import (
    VERSION_LABEL
)

log = logbook.Logger('Risk Cumulative')


choose_treasury = functools.partial(choose_treasury, lambda *args: '10year',
                                    compound=False)


def information_ratio(algo_volatility, algorithm_return, benchmark_return):
    """
    http://en.wikipedia.org/wiki/Information_ratio

    Args:
        algorithm_returns (np.array-like):
            All returns during algorithm lifetime.
        benchmark_returns (np.array-like):
            All benchmark returns during algo lifetime.

    Returns:
        float. Information ratio.
    """
    if zp_math.tolerant_equals(algo_volatility, 0):
        return np.nan

    # The square of the annualization factor is in the volatility,
    # because the volatility is also annualized,
    # i.e. the sqrt(annual factor) is in the volatility's numerator.
    # So to have the the correct annualization factor for the
    # Sharpe value's numerator, which should be the sqrt(annual factor).
    # The square of the sqrt of the annual factor, i.e. the annual factor
    # itself, is needed in the numerator to factor out the division by
    # its square root.
    return (algorithm_return - benchmark_return) / algo_volatility


class RiskMetricsCumulative(object):
    """
    :Usage:
        Instantiate RiskMetricsCumulative once.
        Call update() method on each dt to update the metrics.
    """

    METRIC_NAMES = (
        'alpha',
        'beta',
        'sharpe',
        'algorithm_volatility',
        'benchmark_volatility',
        'downside_risk',
        'sortino',
        'information',
    )

    def __init__(self, sim_params, env,
                 create_first_day_stats=False):
        self.treasury_curves = env.treasury_curves
        self.start_date = sim_params.period_start.replace(
            hour=0, minute=0, second=0, microsecond=0
        )
        self.end_date = sim_params.period_end.replace(
            hour=0, minute=0, second=0, microsecond=0
        )

        self.trading_days = env.days_in_range(self.start_date, self.end_date)

        # Hold on to the trading day before the start,
        # used for index of the zero return value when forcing returns
        # on the first day.
        self.day_before_start = self.start_date - env.trading_days.freq

        last_day = normalize_date(sim_params.period_end)
        if last_day not in self.trading_days:
            last_day = pd.tseries.index.DatetimeIndex(
                [last_day]
            )
            self.trading_days = self.trading_days.append(last_day)

        self.sim_params = sim_params
        self.env = env

        self.create_first_day_stats = create_first_day_stats

        cont_index = self.trading_days

        self.cont_index = cont_index
        self.cont_len = len(self.cont_index)

        empty_cont = np.full(self.cont_len, np.nan)

        self.algorithm_returns_cont = empty_cont.copy()
        self.benchmark_returns_cont = empty_cont.copy()
        self.algorithm_cumulative_leverages_cont = empty_cont.copy()
        self.mean_returns_cont = empty_cont.copy()
        self.annualized_mean_returns_cont = empty_cont.copy()
        self.mean_benchmark_returns_cont = empty_cont.copy()
        self.annualized_mean_benchmark_returns_cont = empty_cont.copy()

        # The returns at a given time are read and reset from the respective
        # returns container.
        self.algorithm_returns = None
        self.benchmark_returns = None
        self.mean_returns = None
        self.annualized_mean_returns = None
        self.mean_benchmark_returns = None
        self.annualized_mean_benchmark_returns = None

        self.algorithm_cumulative_returns = empty_cont.copy()
        self.benchmark_cumulative_returns = empty_cont.copy()
        self.algorithm_cumulative_leverages = empty_cont.copy()
        self.excess_returns = empty_cont.copy()

        self.latest_dt_loc = 0
        self.latest_dt = cont_index[0]

        self.benchmark_volatility = empty_cont.copy()
        self.algorithm_volatility = empty_cont.copy()
        self.beta = empty_cont.copy()
        self.alpha = empty_cont.copy()
        self.sharpe = empty_cont.copy()
        self.downside_risk = empty_cont.copy()
        self.sortino = empty_cont.copy()
        self.information = empty_cont.copy()

        self.drawdowns = empty_cont.copy()
        self.max_drawdowns = empty_cont.copy()
        self.max_drawdown = 0
        self.max_leverages = empty_cont.copy()
        self.max_leverage = 0
        self.current_max = -np.inf
        self.daily_treasury = pd.Series(index=self.trading_days)
        self.treasury_period_return = np.nan

        self.num_trading_days = 0

    def update(self, dt, algorithm_returns, benchmark_returns, leverage):
        # Keep track of latest dt for use in to_dict and other methods
        # that report current state.
        self.latest_dt = dt
        dt_loc = self.cont_index.get_loc(dt)
        self.latest_dt_loc = dt_loc

        self.algorithm_returns_cont[dt_loc] = algorithm_returns
        self.algorithm_returns = self.algorithm_returns_cont[:dt_loc + 1]

        self.num_trading_days = len(self.algorithm_returns)

        if self.create_first_day_stats:
            if len(self.algorithm_returns) == 1:
                self.algorithm_returns = np.append(0.0, self.algorithm_returns)

        self.algorithm_cumulative_returns[dt_loc] = \
            self.calculate_cumulative_returns(self.algorithm_returns)

        algo_cumulative_returns_to_date = \
            self.algorithm_cumulative_returns[:dt_loc + 1]

        self.mean_returns_cont[dt_loc] = \
            algo_cumulative_returns_to_date[dt_loc] / self.num_trading_days

        self.mean_returns = self.mean_returns_cont[:dt_loc + 1]

        self.annualized_mean_returns_cont[dt_loc] = \
            self.mean_returns_cont[dt_loc] * 252

        self.annualized_mean_returns = \
            self.annualized_mean_returns_cont[:dt_loc + 1]

        if self.create_first_day_stats:
            if len(self.mean_returns) == 1:
                self.mean_returns = np.append(0.0, self.mean_returns)
                self.annualized_mean_returns = np.append(
                    0.0, self.annualized_mean_returns)

        self.benchmark_returns_cont[dt_loc] = benchmark_returns
        self.benchmark_returns = self.benchmark_returns_cont[:dt_loc + 1]

        if self.create_first_day_stats:
            if len(self.benchmark_returns) == 1:
                self.benchmark_returns = np.append(0.0, self.benchmark_returns)

        self.benchmark_cumulative_returns[dt_loc] = \
            self.calculate_cumulative_returns(self.benchmark_returns)

        benchmark_cumulative_returns_to_date = \
            self.benchmark_cumulative_returns[:dt_loc + 1]

        self.mean_benchmark_returns_cont[dt_loc] = \
            benchmark_cumulative_returns_to_date[dt_loc] / \
            self.num_trading_days

        self.mean_benchmark_returns = self.mean_benchmark_returns_cont[:dt_loc]

        self.annualized_mean_benchmark_returns_cont[dt_loc] = \
            self.mean_benchmark_returns_cont[dt_loc] * 252

        self.annualized_mean_benchmark_returns = \
            self.annualized_mean_benchmark_returns_cont[:dt_loc + 1]

        self.algorithm_cumulative_leverages_cont[dt_loc] = leverage
        self.algorithm_cumulative_leverages = \
            self.algorithm_cumulative_leverages_cont[:dt_loc + 1]

        if self.create_first_day_stats:
            if len(self.algorithm_cumulative_leverages) == 1:
                self.algorithm_cumulative_leverages = np.append(
                    0.0,
                    self.algorithm_cumulative_leverages)

        if not len(self.algorithm_returns) and len(self.benchmark_returns):
            message = "Mismatch between benchmark_returns ({bm_count}) and \
algorithm_returns ({algo_count}) in range {start} : {end} on {dt}"
            message = message.format(
                bm_count=len(self.benchmark_returns),
                algo_count=len(self.algorithm_returns),
                start=self.start_date,
                end=self.end_date,
                dt=dt
            )
            raise Exception(message)

        self.update_current_max()
        self.benchmark_volatility[dt_loc] = \
            self.calculate_volatility(self.benchmark_returns)
        self.algorithm_volatility[dt_loc] = \
            self.calculate_volatility(self.algorithm_returns)

        # caching the treasury rates for the minutely case is a
        # big speedup, because it avoids searching the treasury
        # curves on every minute.
        # In both minutely and daily, the daily curve is always used.
        treasury_end = dt.replace(hour=0, minute=0)
        if np.isnan(self.daily_treasury[treasury_end]):
            treasury_period_return = choose_treasury(
                self.treasury_curves,
                self.start_date,
                treasury_end,
                self.env,
            )
            self.daily_treasury[treasury_end] = treasury_period_return
        self.treasury_period_return = self.daily_treasury[treasury_end]
        self.excess_returns[dt_loc] = (
            self.algorithm_cumulative_returns[dt_loc] -
            self.treasury_period_return)
        self.beta[dt_loc] = self.calculate_beta()
        self.alpha[dt_loc] = self.calculate_alpha()
        self.sharpe[dt_loc] = self.calculate_sharpe()
        self.downside_risk[dt_loc] = \
            self.calculate_downside_risk()
        self.sortino[dt_loc] = self.calculate_sortino()
        self.information[dt_loc] = self.calculate_information()
        self.max_drawdown = self.calculate_max_drawdown()
        self.max_drawdowns[dt_loc] = self.max_drawdown
        self.max_leverage = self.calculate_max_leverage()
        self.max_leverages[dt_loc] = self.max_leverage

    def to_dict(self):
        """
        Creates a dictionary representing the state of the risk report.
        Returns a dict object of the form:
        """
        dt = self.latest_dt
        dt_loc = self.latest_dt_loc
        period_label = dt.strftime("%Y-%m")
        rval = {
            'trading_days': self.num_trading_days,
            'benchmark_volatility':
            self.benchmark_volatility[dt_loc],
            'algo_volatility':
            self.algorithm_volatility[dt_loc],
            'treasury_period_return': self.treasury_period_return,
            # Though the two following keys say period return,
            # they would be more accurately called the cumulative return.
            # However, the keys need to stay the same, for now, for backwards
            # compatibility with existing consumers.
            'algorithm_period_return':
            self.algorithm_cumulative_returns[dt_loc],
            'benchmark_period_return':
            self.benchmark_cumulative_returns[dt_loc],
            'beta': self.beta[dt_loc],
            'alpha': self.alpha[dt_loc],
            'sharpe': self.sharpe[dt_loc],
            'sortino': self.sortino[dt_loc],
            'information': self.information[dt_loc],
            'excess_return': self.excess_returns[dt_loc],
            'max_drawdown': self.max_drawdown,
            'max_leverage': self.max_leverage,
            'period_label': period_label
        }

        return {k: (None if check_entry(k, v) else v)
                for k, v in iteritems(rval)}

    def __repr__(self):
        statements = []
        for metric in self.METRIC_NAMES:
            value = getattr(self, metric)[-1]
            if isinstance(value, list):
                if len(value) == 0:
                    value = np.nan
                else:
                    value = value[-1]
            statements.append("{m}:{v}".format(m=metric, v=value))

        return '\n'.join(statements)

    def calculate_cumulative_returns(self, returns):
        return (1. + returns).prod() - 1

    def update_current_max(self):
        if len(self.algorithm_cumulative_returns) == 0:
            return
        current_cumulative_return = \
            self.algorithm_cumulative_returns[self.latest_dt_loc]
        if self.current_max < current_cumulative_return:
            self.current_max = current_cumulative_return

    def calculate_max_drawdown(self):
        if len(self.algorithm_cumulative_returns) == 0:
            return self.max_drawdown

        # The drawdown is defined as: (high - low) / high
        # The above factors out to: 1.0 - (low / high)
        #
        # Instead of explicitly always using the low, use the current total
        # return value, and test that against the max drawdown, which will
        # exceed the previous max_drawdown iff the current return is lower than
        # the previous low in the current drawdown window.
        cur_drawdown = 1.0 - (
            (1.0 + self.algorithm_cumulative_returns[self.latest_dt_loc])
            /
            (1.0 + self.current_max))

        self.drawdowns[self.latest_dt_loc] = cur_drawdown

        if self.max_drawdown < cur_drawdown:
            return cur_drawdown
        else:
            return self.max_drawdown

    def calculate_max_leverage(self):
        # The leverage is defined as: the gross_exposure/net_liquidation
        # gross_exposure = long_exposure + abs(short_exposure)
        # net_liquidation = ending_cash + long_exposure + short_exposure
        cur_leverage = self.algorithm_cumulative_leverages_cont[
            self.latest_dt_loc]

        return max(cur_leverage, self.max_leverage)

    def calculate_sharpe(self):
        """
        http://en.wikipedia.org/wiki/Sharpe_ratio
        """
        return sharpe_ratio(
            self.algorithm_volatility[self.latest_dt_loc],
            self.annualized_mean_returns_cont[self.latest_dt_loc],
            self.daily_treasury[self.latest_dt.date()])

    def calculate_sortino(self):
        """
        http://en.wikipedia.org/wiki/Sortino_ratio
        """
        return sortino_ratio(
            self.annualized_mean_returns_cont[self.latest_dt_loc],
            self.daily_treasury[self.latest_dt.date()],
            self.downside_risk[self.latest_dt_loc])

    def calculate_information(self):
        """
        http://en.wikipedia.org/wiki/Information_ratio
        """
        return information_ratio(
            self.algorithm_volatility[self.latest_dt_loc],
            self.annualized_mean_returns_cont[self.latest_dt_loc],
            self.annualized_mean_benchmark_returns_cont[self.latest_dt_loc])

    def calculate_alpha(self):
        """
        http://en.wikipedia.org/wiki/Alpha_(investment)
        """
        return alpha(
            self.annualized_mean_returns_cont[self.latest_dt_loc],
            self.treasury_period_return,
            self.annualized_mean_benchmark_returns_cont[self.latest_dt_loc],
            self.beta[self.latest_dt_loc])

    def calculate_volatility(self, daily_returns):
        if len(daily_returns) <= 1:
            return 0.0
        return np.std(daily_returns, ddof=1) * math.sqrt(252)

    def calculate_downside_risk(self):
        return downside_risk(self.algorithm_returns,
                             self.mean_returns,
                             252)

    def calculate_beta(self):
        """

        .. math::

            \\beta_a = \\frac{\mathrm{Cov}(r_a,r_p)}{\mathrm{Var}(r_p)}

        http://en.wikipedia.org/wiki/Beta_(finance)
        """
        # it doesn't make much sense to calculate beta for less than two
        # values, so return none.
        if len(self.algorithm_returns) < 2:
            return 0.0

        returns_matrix = np.vstack([self.algorithm_returns,
                                    self.benchmark_returns])
        C = np.cov(returns_matrix, ddof=1)
        algorithm_covariance = C[0][1]
        benchmark_variance = C[1][1]
        beta = algorithm_covariance / benchmark_variance

        return beta

    def __getstate__(self):
        state_dict = {k: v for k, v in iteritems(self.__dict__)
                      if not k.startswith('_')}

        STATE_VERSION = 3
        state_dict[VERSION_LABEL] = STATE_VERSION

        return state_dict

    def __setstate__(self, state):

        OLDEST_SUPPORTED_STATE = 3
        version = state.pop(VERSION_LABEL)

        if version < OLDEST_SUPPORTED_STATE:
            raise BaseException("RiskMetricsCumulative \
                    saved state is too old.")

        self.__dict__.update(state)


1			#
2			# Copyright 2014 Quantopian, Inc.
3			#
4			# Licensed under the Apache License, Version 2.0 (the "License");
5			# you may not use this file except in compliance with the License.
6			# You may obtain a copy of the License at
7			#
8			# http://www.apache.org/licenses/LICENSE-2.0
9			#
10			# Unless required by applicable law or agreed to in writing, software
11			# distributed under the License is distributed on an "AS IS" BASIS,
12			# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13			# See the License for the specific language governing permissions and
14			# limitations under the License.
15
16			import functools
17			import logbook
18			import math
19			import numpy as np
20
21			import zipline.utils.math_utils as zp_math
22
23			import pandas as pd
24			from pandas.tseries.tools import normalize_date
25
26			from six import iteritems
27
28			from . risk import (
29			alpha,
30			check_entry,
31			choose_treasury,
32			downside_risk,
33			sharpe_ratio,
34			sortino_ratio,
35			)
36
37			from zipline.utils.serialization_utils import (
38			VERSION_LABEL
39			)
40
41			log = logbook.Logger('Risk Cumulative')
42
43
44			choose_treasury = functools.partial(choose_treasury, lambda *args: '10year',
45			compound=False)
46
47
48			def information_ratio(algo_volatility, algorithm_return, benchmark_return):
49			"""
50			http://en.wikipedia.org/wiki/Information_ratio
51
52			Args:
53			algorithm_returns (np.array-like):
54			All returns during algorithm lifetime.
55			benchmark_returns (np.array-like):
56			All benchmark returns during algo lifetime.
57
58			Returns:
59			float. Information ratio.
60			"""
61			if zp_math.tolerant_equals(algo_volatility, 0):
62			return np.nan
63
64			# The square of the annualization factor is in the volatility,
65			# because the volatility is also annualized,
66			# i.e. the sqrt(annual factor) is in the volatility's numerator.
67			# So to have the the correct annualization factor for the
68			# Sharpe value's numerator, which should be the sqrt(annual factor).
69			# The square of the sqrt of the annual factor, i.e. the annual factor
70			# itself, is needed in the numerator to factor out the division by
71			# its square root.
72			return (algorithm_return - benchmark_return) / algo_volatility
73
74
75			class RiskMetricsCumulative(object):
76			"""
77			:Usage:
78			Instantiate RiskMetricsCumulative once.
79			Call update() method on each dt to update the metrics.
80			"""
81
82			METRIC_NAMES = (
83			'alpha',
84			'beta',
85			'sharpe',
86			'algorithm_volatility',
87			'benchmark_volatility',
88			'downside_risk',
89			'sortino',
90			'information',
91			)
92
93			def __init__(self, sim_params, env,
94			create_first_day_stats=False):
95			self.treasury_curves = env.treasury_curves
96			self.start_date = sim_params.period_start.replace(
97			hour=0, minute=0, second=0, microsecond=0
98			)
99			self.end_date = sim_params.period_end.replace(
100			hour=0, minute=0, second=0, microsecond=0
101			)
102
103			self.trading_days = env.days_in_range(self.start_date, self.end_date)
104
105			# Hold on to the trading day before the start,
106			# used for index of the zero return value when forcing returns
107			# on the first day.
108			self.day_before_start = self.start_date - env.trading_days.freq
109
110			last_day = normalize_date(sim_params.period_end)
111			if last_day not in self.trading_days:
112			last_day = pd.tseries.index.DatetimeIndex(
113			[last_day]
114			)
115			self.trading_days = self.trading_days.append(last_day)
116
117			self.sim_params = sim_params
118			self.env = env
119
120			self.create_first_day_stats = create_first_day_stats
121
122			cont_index = self.trading_days
123
124			self.cont_index = cont_index
125			self.cont_len = len(self.cont_index)
126
127			empty_cont = np.full(self.cont_len, np.nan)
128
129			self.algorithm_returns_cont = empty_cont.copy()
130			self.benchmark_returns_cont = empty_cont.copy()
131			self.algorithm_cumulative_leverages_cont = empty_cont.copy()
132			self.mean_returns_cont = empty_cont.copy()
133			self.annualized_mean_returns_cont = empty_cont.copy()
134			self.mean_benchmark_returns_cont = empty_cont.copy()
135			self.annualized_mean_benchmark_returns_cont = empty_cont.copy()
136
137			# The returns at a given time are read and reset from the respective
138			# returns container.
139			self.algorithm_returns = None
140			self.benchmark_returns = None
141			self.mean_returns = None
142			self.annualized_mean_returns = None
143			self.mean_benchmark_returns = None
144			self.annualized_mean_benchmark_returns = None
145
146			self.algorithm_cumulative_returns = empty_cont.copy()
147			self.benchmark_cumulative_returns = empty_cont.copy()
148			self.algorithm_cumulative_leverages = empty_cont.copy()
149			self.excess_returns = empty_cont.copy()
150
151			self.latest_dt_loc = 0
152			self.latest_dt = cont_index[0]
153
154			self.benchmark_volatility = empty_cont.copy()
155			self.algorithm_volatility = empty_cont.copy()
156			self.beta = empty_cont.copy()
157			self.alpha = empty_cont.copy()
158			self.sharpe = empty_cont.copy()
159			self.downside_risk = empty_cont.copy()
160			self.sortino = empty_cont.copy()
161			self.information = empty_cont.copy()
162
163			self.drawdowns = empty_cont.copy()
164			self.max_drawdowns = empty_cont.copy()
165			self.max_drawdown = 0
166			self.max_leverages = empty_cont.copy()
167			self.max_leverage = 0
168			self.current_max = -np.inf
169			self.daily_treasury = pd.Series(index=self.trading_days)
170			self.treasury_period_return = np.nan
171
172			self.num_trading_days = 0
173
174			def update(self, dt, algorithm_returns, benchmark_returns, leverage):
175			# Keep track of latest dt for use in to_dict and other methods
176			# that report current state.
177			self.latest_dt = dt
178			dt_loc = self.cont_index.get_loc(dt)
179			self.latest_dt_loc = dt_loc
180
181			self.algorithm_returns_cont[dt_loc] = algorithm_returns
182			self.algorithm_returns = self.algorithm_returns_cont[:dt_loc + 1]
183
184			self.num_trading_days = len(self.algorithm_returns)
185
186			if self.create_first_day_stats:
187			if len(self.algorithm_returns) == 1:
188			self.algorithm_returns = np.append(0.0, self.algorithm_returns)
189
190			self.algorithm_cumulative_returns[dt_loc] = \
191			self.calculate_cumulative_returns(self.algorithm_returns)
192
193			algo_cumulative_returns_to_date = \
194			self.algorithm_cumulative_returns[:dt_loc + 1]
195
196			self.mean_returns_cont[dt_loc] = \
197			algo_cumulative_returns_to_date[dt_loc] / self.num_trading_days
198
199			self.mean_returns = self.mean_returns_cont[:dt_loc + 1]
200
201			self.annualized_mean_returns_cont[dt_loc] = \
202			self.mean_returns_cont[dt_loc] * 252
203
204			self.annualized_mean_returns = \
205			self.annualized_mean_returns_cont[:dt_loc + 1]
206
207			if self.create_first_day_stats:
208			if len(self.mean_returns) == 1:
209			self.mean_returns = np.append(0.0, self.mean_returns)
210			self.annualized_mean_returns = np.append(
211			0.0, self.annualized_mean_returns)
212
213			self.benchmark_returns_cont[dt_loc] = benchmark_returns
214			self.benchmark_returns = self.benchmark_returns_cont[:dt_loc + 1]
215
216			if self.create_first_day_stats:
217			if len(self.benchmark_returns) == 1:
218			self.benchmark_returns = np.append(0.0, self.benchmark_returns)
219
220			self.benchmark_cumulative_returns[dt_loc] = \
221			self.calculate_cumulative_returns(self.benchmark_returns)
222
223			benchmark_cumulative_returns_to_date = \
224			self.benchmark_cumulative_returns[:dt_loc + 1]
225
226			self.mean_benchmark_returns_cont[dt_loc] = \
227			benchmark_cumulative_returns_to_date[dt_loc] / \
228			self.num_trading_days
229
230			self.mean_benchmark_returns = self.mean_benchmark_returns_cont[:dt_loc]
231
232			self.annualized_mean_benchmark_returns_cont[dt_loc] = \
233			self.mean_benchmark_returns_cont[dt_loc] * 252
234
235			self.annualized_mean_benchmark_returns = \
236			self.annualized_mean_benchmark_returns_cont[:dt_loc + 1]
237
238			self.algorithm_cumulative_leverages_cont[dt_loc] = leverage
239			self.algorithm_cumulative_leverages = \
240			self.algorithm_cumulative_leverages_cont[:dt_loc + 1]
241
242			if self.create_first_day_stats:
243			if len(self.algorithm_cumulative_leverages) == 1:
244			self.algorithm_cumulative_leverages = np.append(
245			0.0,
246			self.algorithm_cumulative_leverages)
247
248			if not len(self.algorithm_returns) and len(self.benchmark_returns):
249			message = "Mismatch between benchmark_returns ({bm_count}) and \
250			algorithm_returns ({algo_count}) in range {start} : {end} on {dt}"
251			message = message.format(
252			bm_count=len(self.benchmark_returns),
253			algo_count=len(self.algorithm_returns),
254			start=self.start_date,
255			end=self.end_date,
256			dt=dt
257			)
258			raise Exception(message)
259
260			self.update_current_max()
261			self.benchmark_volatility[dt_loc] = \
262			self.calculate_volatility(self.benchmark_returns)
263			self.algorithm_volatility[dt_loc] = \
264			self.calculate_volatility(self.algorithm_returns)
265
266			# caching the treasury rates for the minutely case is a
267			# big speedup, because it avoids searching the treasury
268			# curves on every minute.
269			# In both minutely and daily, the daily curve is always used.
270			treasury_end = dt.replace(hour=0, minute=0)
271			if np.isnan(self.daily_treasury[treasury_end]):
272			treasury_period_return = choose_treasury(
273			self.treasury_curves,
274			self.start_date,
275			treasury_end,
276			self.env,
277			)
278			self.daily_treasury[treasury_end] = treasury_period_return
279			self.treasury_period_return = self.daily_treasury[treasury_end]
280			self.excess_returns[dt_loc] = (
281			self.algorithm_cumulative_returns[dt_loc] -
282			self.treasury_period_return)
283			self.beta[dt_loc] = self.calculate_beta()
284			self.alpha[dt_loc] = self.calculate_alpha()
285			self.sharpe[dt_loc] = self.calculate_sharpe()
286			self.downside_risk[dt_loc] = \
287			self.calculate_downside_risk()
288			self.sortino[dt_loc] = self.calculate_sortino()
289			self.information[dt_loc] = self.calculate_information()
290			self.max_drawdown = self.calculate_max_drawdown()
291			self.max_drawdowns[dt_loc] = self.max_drawdown
292			self.max_leverage = self.calculate_max_leverage()
293			self.max_leverages[dt_loc] = self.max_leverage
294
295			def to_dict(self):
296			"""
297			Creates a dictionary representing the state of the risk report.
298			Returns a dict object of the form:
299			"""
300			dt = self.latest_dt
301			dt_loc = self.latest_dt_loc
302			period_label = dt.strftime("%Y-%m")
303			rval = {
304			'trading_days': self.num_trading_days,
305			'benchmark_volatility':
306			self.benchmark_volatility[dt_loc],
307			'algo_volatility':
308			self.algorithm_volatility[dt_loc],
309			'treasury_period_return': self.treasury_period_return,
310			# Though the two following keys say period return,
311			# they would be more accurately called the cumulative return.
312			# However, the keys need to stay the same, for now, for backwards
313			# compatibility with existing consumers.
314			'algorithm_period_return':
315			self.algorithm_cumulative_returns[dt_loc],
316			'benchmark_period_return':
317			self.benchmark_cumulative_returns[dt_loc],
318			'beta': self.beta[dt_loc],
319			'alpha': self.alpha[dt_loc],
320			'sharpe': self.sharpe[dt_loc],
321			'sortino': self.sortino[dt_loc],
322			'information': self.information[dt_loc],
323			'excess_return': self.excess_returns[dt_loc],
324			'max_drawdown': self.max_drawdown,
325			'max_leverage': self.max_leverage,
326			'period_label': period_label
327			}
328
329			return {k: (None if check_entry(k, v) else v)
330			for k, v in iteritems(rval)}
331
332			def __repr__(self):
333			statements = []
334			for metric in self.METRIC_NAMES:
335			value = getattr(self, metric)[-1]
336			if isinstance(value, list):
337			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

quantopian / zipline

calculate_alpha() A last analyzed 2016-01-08 22:03 UTC

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calculate_alpha() A
last analyzed 2016-01-08 22:03 UTC