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Merge branch 'main' of https://github.com/you-n-g/qlib into main

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Jactus
2020-11-02 11:06:02 +08:00
parent 5f9c8be33d 91019edcb8
commit b077d848f4
7 changed files with 831 additions and 54 deletions
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12
qlib/data/_libs/expanding.pyx
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@@ -14,7 +14,7 @@ cdef class Expanding(object):
cdef int na_count
def __init__(self):
self.na_count = 0
cdef double update(self, double val):
pass
@@ -25,7 +25,7 @@ cdef class Mean(Expanding):
def __init__(self):
super(Mean, self).__init__()
self.vsum = 0
cdef double update(self, double val):
self.barv.push_back(val)
if isnan(val):
@@ -62,7 +62,7 @@ cdef class Slope(Expanding):
return (N*self.xy_sum - self.x_sum*self.y_sum) / \
(N*self.x2_sum - self.x_sum*self.x_sum)
cdef class Resi(Expanding):
"""1-D array expanding residuals"""
cdef double x_sum
@@ -94,7 +94,7 @@ cdef class Resi(Expanding):
interp = y_mean - slope*x_mean
return val - (slope*size + interp)
cdef class Rsquare(Expanding):
"""1-D array expanding rsquare"""
cdef double x_sum
@@ -117,7 +117,7 @@ cdef class Rsquare(Expanding):
self.na_count += 1
else:
self.x_sum += size
self.x2_sum += size
self.x2_sum += size * size
self.y_sum += val
self.y2_sum += val * val
self.xy_sum += size * val
@@ -126,7 +126,7 @@ cdef class Rsquare(Expanding):
sqrt((N*self.x2_sum - self.x_sum*self.x_sum) * (N*self.y2_sum - self.y_sum*self.y_sum))
return rvalue * rvalue
cdef np.ndarray[double, ndim=1] expanding(Expanding r, np.ndarray a):
cdef int i
cdef int N = len(a)

51
qlib/data/dataset/handler.py
View File

@@ -5,7 +5,7 @@
import abc
import bisect
import logging
from typing import Union, Tuple, List
from typing import Union, Tuple, List, Iterator, Optional
import pandas as pd
import numpy as np
@@ -113,8 +113,7 @@ class DataHandler(Serializable):
CS_ALL = "__all"
def _fetch_df_by_col(self, df: pd.DataFrame, col_set: str) -> pd.DataFrame:
cln = len(df.columns.levels)
if cln == 1:
if not isinstance(df.columns, pd.MultiIndex):
return df
elif col_set == self.CS_ALL:
return df.droplevel(axis=1, level=0)
@@ -126,6 +125,7 @@ class DataHandler(Serializable):
selector: Union[pd.Timestamp, slice, str],
level: Union[str, int] = "datetime",
col_set: Union[str, List[str]] = CS_ALL,
squeeze: bool = False
) -> pd.DataFrame:
"""
fetch data from underlying data source
@@ -141,13 +141,22 @@ class DataHandler(Serializable):
select a set of meaningful columns.(e.g. features, columns)
if isinstance(col_set, List[str]):
select several sets of meaningful columns, the returned data has multiple levels
squeeze : bool
whether squeeze columns and index
Returns
-------
pd.DataFrame:
"""
df = self._fetch_df_by_index(self._data, selector, level)
return self._fetch_df_by_col(df, col_set)
df = self._fetch_df_by_col(df, col_set)
if squeeze:
# squeeze columns
df = df.squeeze()
# squeeze index
if isinstance(selector, (str, pd.Timestamp)):
df = df.reset_index(level=level, drop=True)
return df
def get_cols(self, col_set=CS_ALL) -> list:
"""
@@ -167,6 +176,40 @@ class DataHandler(Serializable):
df = self._fetch_df_by_col(df, col_set)
return df.columns.to_list()
def get_range_selector(self, cur_date: Union[pd.Timestamp, str], periods: int) -> slice:
"""
get range selector by number of periods
Args:
cur_date (pd.Timestamp or str): current date
periods (int): number of periods
"""
trading_dates = self._data.index.unique(level='datetime')
cur_loc = trading_dates.get_loc(cur_date)
pre_loc = cur_loc - periods + 1
if pre_loc < 0:
warnings.warn('`periods` is too large. the first date will be returned.')
pre_loc = 0
ref_date = trading_dates[pre_loc]
return slice(ref_date, cur_date)
def get_range_iterator(self, periods: int, min_periods: Optional[int] = None,
**kwargs) -> Iterator[Tuple[pd.Timestamp, pd.DataFrame]]:
"""
get a iterator of sliced data with given periods
Args:
periods (int): number of periods
min_periods (int): minimum periods for sliced dataframe
kwargs (dict): will be passed to `self.fetch`
"""
trading_dates = self._data.index.unique(level='datetime')
if min_periods is None:
min_periods = periods
for cur_date in trading_dates[min_periods:]:
selector = self.get_range_selector(cur_date, periods)
yield cur_date, self.fetch(selector, **kwargs)
class DataHandlerLP(DataHandler):
"""

85
qlib/data/dataset/loader.py
View File

@@ -1,78 +1,75 @@
# Copyright (c) Microsoft Corporation.
# Licensed under the MIT License.
from abc import ABC, abstractmethod
import abc
import warnings
import pandas as pd
from qlib.data import D
from typing import Tuple
from qlib.data import D
class DataLoader(ABC):
"""
class DataLoader(abc.ABC):
'''
DataLoader is designed for loading raw data from original data source.
"""
@abstractmethod
'''
@abc.abstractmethod
def load(self, instruments, start_time=None, end_time=None) -> pd.DataFrame:
"""
load the data as pd.DataFrame
load the data as pd.DataFrame
Parameters
----------
self : [TODO:type]
[TODO:description]
instruments : [TODO:type]
[TODO:description]
start_time : [TODO:type]
[TODO:description]
end_time : [TODO:type]
[TODO:description]
Parameters
----------
self : [TODO:type]
[TODO:description]
instruments : [TODO:type]
[TODO:description]
start_time : [TODO:type]
[TODO:description]
end_time : [TODO:type]
[TODO:description]
Returns
-------
pd.DataFrame:
data load from the under layer source
Returns
-------
pd.DataFrame:
data load from the under layer source
Example of the data:
The multi-index of the columns is optional.
feature label
$close $volume Ref($close, 1) Mean($close, 3) $high-$low LABEL0
datetime instrument
2010-01-04 SH600000 81.807068 17145150.0 83.737389 83.016739 2.741058 0.0032
SH600004 13.313329 11800983.0 13.313329 13.317701 0.183632 0.0042
SH600005 37.796539 12231662.0 38.258602 37.919757 0.970325 0.0289
Example of the data:
(The multi-index of the columns is optional.)
feature label
$close $volume Ref($close, 1) Mean($close, 3) $high-$low LABEL0
datetime instrument
2010-01-04 SH600000 81.807068 17145150.0 83.737389 83.016739 2.741058 0.0032
SH600004 13.313329 11800983.0 13.313329 13.317701 0.183632 0.0042
SH600005 37.796539 12231662.0 38.258602 37.919757 0.970325 0.0289
"""
pass
class QlibDataLoader(DataLoader):
"""Same as QlibDataLoader. The fields can be define by config"""
'''Same as QlibDataLoader. The fields can be define by config'''
def __init__(self, config: Tuple[list, tuple, dict], filter_pipe=None):
"""
Parameters
----------
config : Tuple[list ,tuple, dict]
config : Tuple[list, tuple, dict]
Config will be used to describe the fields and column names
<config> := {
"group_name1": <fields_info1>
"group_name2": <fields_info2>
}
or
<config> := <fields_info>
<fields_info> := ["expr", ...] | (["expr", ...], ["col_name", ...])
Here is a few examples to describe the fields
TODO:
"""
self.is_group = isinstance(config, dict)
self.is_group = isinstance(config, dict)
if self.is_group:
self.fields = {grp: self._parse_fields_info(fields_info) for grp, fields_info in config.items()}
else:
self.fields = self._parse_fields_info(fields_info)
self.fields = self._parse_fields_info(config)
self.filter_pipe = filter_pipe
@@ -86,14 +83,18 @@ class QlibDataLoader(DataLoader):
return exprs, names
def load(self, instruments, start_time=None, end_time=None) -> pd.DataFrame:
if isinstance(instruments, str):
instruments = D.instruments(instruments, filter_pipe=self.filter_pipe)
elif self.filter_pipe is not None:
warnings.warn('`filter_pipe` is not None, but it will not be used with `instruments` as list')
def _get_df(exprs, names):
df = D.features(D.instruments(instruments, filter_pipe=self.filter_pipe), exprs, start_time, end_time)
df = D.features(instruments, exprs, start_time, end_time)
df.columns = names
return df
if self.is_group:
df = pd.concat({grp: _get_df(exprs, names) for grp, (exprs, names) in self.fields.items()}, axis=1)
else:
exprs, names = self.fields
df = _get_df(exprs, names)
df = df.swaplevel().sort_index()
df = df.swaplevel().sort_index() # NOTE: always return <datetime, instrument>
return df

17
qlib/data/ops.py
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@@ -8,6 +8,8 @@ from __future__ import print_function
import numpy as np
import pandas as pd
from scipy.stats import percentileofscore
from .base import Expression, ExpressionOps
from ..log import get_module_logger
@@ -687,6 +689,8 @@ class Rolling(ExpressionOps):
# isnull = series.isnull() # NOTE: isnull = NaN, inf is not null
if self.N == 0:
series = getattr(series.expanding(min_periods=1), self.func)()
elif 0 < self.N < 1:
series = series.ewm(alpha=self.N, min_periods=1).mean()
else:
series = getattr(series.rolling(self.N, min_periods=1), self.func)()
# series.iloc[:self.N-1] = np.nan
@@ -696,6 +700,8 @@ class Rolling(ExpressionOps):
def get_longest_back_rolling(self):
if self.N == 0:
return np.inf
if 0 < self.N < 1:
return int(np.log(1e-6) / np.log(1 - self.N)) # (1 - N)**window == 1e-6
return self.feature.get_longest_back_rolling() + self.N - 1
def get_extended_window_size(self):
@@ -704,6 +710,11 @@ class Rolling(ExpressionOps):
# remove such support for N == 0?
get_module_logger(self.__class__.__name__).warning("The Rolling(ATTR, 0) will not be accurately calculated")
return self.feature.get_extended_window_size()
elif 0 < self.N < 1:
lft_etd, rght_etd = self.feature.get_extended_window_size()
size = int(np.log(1e-6) / np.log(1 - self.N))
lft_etd = max(lft_etd + size - 1, lft_etd)
return lft_etd, rght_etd
else:
lft_etd, rght_etd = self.feature.get_extended_window_size()
lft_etd = max(lft_etd + self.N - 1, lft_etd)
@@ -1087,7 +1098,7 @@ class Rank(Rolling):
x1 = x[~np.isnan(x)]
if x1.shape[0] == 0:
return np.nan
return (x1.argsort()[-1] + 1) / len(x1)
return percentileofscore(x1, x1[-1]) / len(x1)
if self.N == 0:
series = series.expanding(min_periods=1).apply(rank, raw=True)
@@ -1273,7 +1284,7 @@ class EMA(Rolling):
----------
feature : Expression
feature instance
N : int
N : int, float
rolling window size
Returns
@@ -1296,6 +1307,8 @@ class EMA(Rolling):
if self.N == 0:
series = series.expanding(min_periods=1).apply(exp_weighted_mean, raw=True)
elif 0 < self.N < 1:
series = series.ewm(alpha=self.N, min_periods=1).mean()
else:
series = series.ewm(span=self.N, min_periods=1).mean()
return series

455
qlib/model/riskmodel.py Normal file
View File

@@ -0,0 +1,455 @@
# Copyright (c) Microsoft Corporation.
# Licensed under the MIT License.
import warnings
import numpy as np
import pandas as pd
from typing import Union
from qlib.model.base import BaseModel
class RiskModel(BaseModel):
"""Risk Model
A risk model is used to estimate the covariance matrix of stock returns.
"""
MASK_NAN = 'mask'
FILL_NAN = 'fill'
IGNORE_NAN = 'ignore'
def __init__(self, nan_option: str = 'ignore', assume_centered: bool = False, scale_return: bool = True):
"""
Args:
nan_option (str): nan handling option (`ignore`/`mask`/`fill`)
assume_centered (bool): whether the data is assumed to be centered
scale_return (bool): whether scale returns as percentage
"""
# nan
assert nan_option in [self.MASK_NAN, self.FILL_NAN, self.IGNORE_NAN], \
f'`nan_option={nan_option}` is not supported'
self.nan_option = nan_option
self.assume_centered = assume_centered
self.scale_return = scale_return
def predict(self, X: Union[pd.Series, pd.DataFrame, np.ndarray],
return_corr: bool = False, is_price: bool = True) -> Union[pd.DataFrame, np.ndarray]:
"""
Args:
X (pd.Series, pd.DataFrame or np.ndarray): data from which to estimate the covariance,
with variables as columns and observations as rows.
return_corr (bool): whether return the correlation matrix
is_price (bool): whether `X` contains price (if not assume stock returns)
Returns:
pd.DataFrame or np.ndarray: estimated covariance (or correlation)
"""
# transform input into 2D array
if not isinstance(X, (pd.Series, pd.DataFrame)):
columns = None
else:
if isinstance(X.index, pd.MultiIndex):
if isinstance(X, pd.DataFrame):
X = X.iloc[:, 0].unstack(level='instrument') # always use the first column
else:
X = X.unstack(level='instrument')
else:
# X is 2D DataFrame
pass
columns = X.columns # will be used to restore dataframe
X = X.values
# calculate pct_change
if is_price:
X = X[1:] / X[:-1] - 1 # NOTE: resulting `n - 1` rows
# scale return
if self.scale_return:
X *= 100
# handle nan and centered
X = self._preprocess(X)
# estimate covariance
S = self._predict(X)
# return correlation if needed
if return_corr:
vola = np.sqrt(np.diag(S))
corr = S / np.outer(vola, vola)
if columns is None:
return corr
return pd.DataFrame(corr, index=columns, columns=columns)
# return covariance
if columns is None:
return S
return pd.DataFrame(S, index=columns, columns=columns)
def _predict(self, X: np.ndarray) -> np.ndarray:
"""covariance estimation implementation
This method should be overridden by child classes.
By default, this method implements the empirical covariance estimation.
Args:
X (np.ndarray): data matrix containing multiple variables (columns) and observations (rows)
Returns:
np.ndarray: covariance matrix
"""
xTx = np.asarray(X.T.dot(X))
N = len(X)
if isinstance(X, np.ma.MaskedArray):
M = 1 - X.mask
N = M.T.dot(M) # each pair has distinct number of samples
return xTx / N
def _preprocess(self, X: np.ndarray) -> Union[np.ndarray, np.ma.MaskedArray]:
"""handle nan and centerize data
Note:
if `nan_option='mask'` then the returned array will be `np.ma.MaskedArray`
"""
# handle nan
if self.nan_option == self.FILL_NAN:
X = np.nan_to_num(X)
elif self.nan_option == self.MASK_NAN:
X = np.ma.masked_invalid(X)
# centerize
if not self.assume_centered:
X = X - np.nanmean(X, axis=0)
return X
class ShrinkCovEstimator(RiskModel):
"""Shrinkage Covariance Estimator
This estimator will shrink the sample covariance matrix towards
an identify matrix:
S_hat = (1 - alpha) * S + alpha * F
where `alpha` is the shrink parameter and `F` is the shrinking target.
The following shrinking parameters (`alpha`) are supported:
- `lw` [1][2][3]: use Ledoit-Wolf shrinking parameter
- `oas` [4]: use Oracle Approximating Shrinkage shrinking parameter
- float: directly specify the shrink parameter, should be between [0, 1]
The following shrinking targets (`F`) are supported:
- `const_var` [1][4][5]: assume stocks have the same constant variance and zero correlation
- `const_corr` [2][6]: assume stocks have different variance but equal correlation
- `single_factor` [3][7]: assume single factor model as the shrinking target
- np.ndarray: provide the shrinking targets directly
Note:
- The optimal shrinking parameter depends on the selection of the shrinking target.
Currently, `oas` is not supported for `const_corr` and `single_factor`.
- Remember to set `nan_option` to `fill` or `mask` if your data has missing values.
References:
[1] Ledoit, O., & Wolf, M. (2004). A well-conditioned estimator for large-dimensional covariance matrices.
Journal of Multivariate Analysis, 88(2), 365–411. https://doi.org/10.1016/S0047-259X(03)00096-4
[2] Ledoit, O., & Wolf, M. (2004). Honey, I shrunk the sample covariance matrix.
Journal of Portfolio Management, 30(4), 1–22. https://doi.org/10.3905/jpm.2004.110
[3] Ledoit, O., & Wolf, M. (2003). Improved estimation of the covariance matrix of stock returns
with an application to portfolio selection.
Journal of Empirical Finance, 10(5), 603–621. https://doi.org/10.1016/S0927-5398(03)00007-0
[4] Chen, Y., Wiesel, A., Eldar, Y. C., & Hero, A. O. (2010). Shrinkage algorithms for MMSE covariance estimation.
IEEE Transactions on Signal Processing, 58(10), 5016–5029. https://doi.org/10.1109/TSP.2010.2053029
[5] https://www.econ.uzh.ch/dam/jcr:ffffffff-935a-b0d6-0000-00007f64e5b9/cov1para.m.zip
[6] https://www.econ.uzh.ch/dam/jcr:ffffffff-935a-b0d6-ffff-ffffde5e2d4e/covCor.m.zip
[7] https://www.econ.uzh.ch/dam/jcr:ffffffff-935a-b0d6-0000-0000648dfc98/covMarket.m.zip
"""
SHR_LW = 'lw'
SHR_OAS = 'oas'
TGT_CONST_VAR = 'const_var'
TGT_CONST_CORR = 'const_corr'
TGT_SINGLE_FACTOR = 'single_factor'
def __init__(self, alpha: Union[str, float] = 0.0, target: Union[str, np.ndarray] = 'const_var', **kwargs):
"""
Args:
alpha (str or float): shrinking parameter or estimator (`lw`/`oas`)
target (str or np.ndarray): shrinking target (`const_var`/`const_corr`/`single_factor`)
kwargs: see `RiskModel` for more information
"""
super().__init__(**kwargs)
# alpha
if isinstance(alpha, str):
assert alpha in [self.SHR_LW, self.SHR_OAS], \
f'shrinking method `{alpha}` is not supported'
elif isinstance(alpha, (float, np.floating)):
assert 0 <= alpha <= 1, 'alpha should be between [0, 1]'
else:
raise TypeError('invalid argument type for `alpha`')
self.alpha = alpha
# target
if isinstance(target, str):
assert target in [self.TGT_CONST_VAR, self.TGT_CONST_CORR, self.TGT_SINGLE_FACTOR], \
f'shrinking target `{target} is not supported'
elif isinstance(target, np.ndarray):
pass
else:
raise TypeError('invalid argument type for `target`')
if alpha == self.SHR_OAS and target != self.TGT_CONST_VAR:
raise NotImplementedError('currently `oas` can only support `const_var` as target')
self.target = target
def _predict(self, X: np.ndarray) -> np.ndarray:
# sample covariance
S = super()._predict(X)
# shrinking target
F = self._get_shrink_target(X, S)
# get shrinking parameter
alpha = self._get_shrink_param(X, S, F)
# shrink covariance
if alpha > 0:
S *= (1 - alpha)
F *= alpha
S += F
return S
def _get_shrink_target(self, X: np.ndarray, S: np.ndarray) -> np.ndarray:
"""get shrinking target `F`"""
if self.target == self.TGT_CONST_VAR:
return self._get_shrink_target_const_var(X, S)
if self.target == self.TGT_CONST_CORR:
return self._get_shrink_target_const_corr(X, S)
if self.target == self.TGT_SINGLE_FACTOR:
return self._get_shrink_target_single_factor(X, S)
def _get_shrink_target_const_var(self, X: np.ndarray, S: np.ndarray) -> np.ndarray:
"""get shrinking target with constant variance
This target assumes zero pair-wise correlation and constant variance.
The constant variance is estimated by averaging all sample's variances.
"""
n = len(S)
F = np.eye(n)
np.fill_diagonal(F, np.mean(np.diag(S)))
return F
def _get_shrink_target_const_corr(self, X: np.ndarray, S: np.ndarray) -> np.ndarray:
"""get shrinking target with constant correlation
This target assumes constant pair-wise correlation but keep the sample variance.
The constant correlation is estimated by averaging all pairwise correlations.
"""
n = len(S)
var = np.diag(S)
sqrt_var = np.sqrt(var)
covar = np.outer(sqrt_var, sqrt_var)
r_bar = (np.sum(S / covar) - n) / (n * (n - 1))
F = r_bar * covar
np.fill_diagonal(F, var)
return F
def _get_shrink_target_single_factor(self, X: np.ndarray, S: np.ndarray) -> np.ndarray:
"""get shrinking target with single factor model"""
X_mkt = np.nanmean(X, axis=1)
cov_mkt = np.asarray(X.T.dot(X_mkt) / len(X))
var_mkt = np.asarray(X_mkt.dot(X_mkt) / len(X))
F = np.outer(cov_mkt, cov_mkt) / var_mkt
np.fill_diagonal(F, np.diag(S))
return F
def _get_shrink_param(self, X: np.ndarray, S: np.ndarray, F: np.ndarray) -> float:
"""get shrinking parameter `alpha`
Note:
The Ledoit-Wolf shrinking parameter estimator consists of three different
"""
if self.alpha == self.SHR_OAS:
return self._get_shrink_param_oas(X, S, F)
elif self.alpha == self.SHR_LW:
if self.target == self.TGT_CONST_VAR:
return self._get_shrink_param_lw_const_var(X, S, F)
if self.target == self.TGT_CONST_CORR:
return self._get_shrink_param_lw_const_corr(X, S, F)
if self.target == self.TGT_SINGLE_FACTOR:
return self._get_shrink_param_lw_single_factor(X, S, F)
return self.alpha
def _get_shrink_param_oas(self, X: np.ndarray, S: np.ndarray, F: np.ndarray) -> float:
"""Oracle Approximating Shrinkage Estimator
This method uses the following formula to estimate the `alpha`
parameter for the shrink covariance estimator:
A = (1 - 2 / p) * trace(S^2) + trace^2(S)
B = (n + 1 - 2 / p) * (trace(S^2) - trace^2(S) / p)
alpha = A / B
where `n`, `p` are the dim of observations and variables respectively.
"""
trS2 = np.sum(S**2)
tr2S = np.trace(S)**2
n, p = X.shape
A = (1 - 2 / p) * (trS2 + tr2S)
B = (n + 1 - 2 / p) * (trS2 + tr2S / p)
alpha = A / B
return alpha
def _get_shrink_param_lw_const_var(self, X: np.ndarray, S: np.ndarray, F: np.ndarray) -> float:
"""Ledoit-Wolf Shrinkage Estimator (Constant Variance)
This method shrinks the covariance matrix towards the constand variance target.
"""
t, n = X.shape
y = X**2
phi = np.sum(y.T.dot(y) / t - S**2)
gamma = np.linalg.norm(S - F, 'fro')**2
kappa = phi / gamma
alpha = max(0, min(1, kappa / t))
return alpha
def _get_shrink_param_lw_const_corr(self, X: np.ndarray, S: np.ndarray, F: np.ndarray) -> float:
"""Ledoit-Wolf Shrinkage Estimator (Constant Correlation)
This method shrinks the covariance matrix towards the constand correlation target.
"""
t, n = X.shape
var = np.diag(S)
sqrt_var = np.sqrt(var)
r_bar = (np.sum(S / np.outer(sqrt_var, sqrt_var)) - n) / (n * (n - 1))
y = X**2
phi_mat = y.T.dot(y) / t - S**2
phi = np.sum(phi_mat)
theta_mat = (X**3).T.dot(X) / t - var[:, None] * S
np.fill_diagonal(theta_mat, 0)
rho = np.sum(np.diag(phi_mat)) + r_bar * np.sum(np.outer(1 / sqrt_var, sqrt_var) * theta_mat)
gamma = np.linalg.norm(S - F, 'fro')**2
kappa = (phi - rho) / gamma
alpha = max(0, min(1, kappa / t))
return alpha
def _get_shrink_param_lw_single_factor(self, X: np.ndarray, S: np.ndarray, F: np.ndarray) -> float:
"""Ledoit-Wolf Shrinkage Estimator (Single Factor Model)
This method shrinks the covariance matrix towards the single factor model target.
"""
t, n = X.shape
X_mkt = np.nanmean(X, axis=1)
cov_mkt = np.asarray(X.T.dot(X_mkt) / len(X))
var_mkt = np.asarray(X_mkt.dot(X_mkt) / len(X))
y = X**2
phi = np.sum(y.T.dot(y)) / t - np.sum(S**2)
rdiag = np.sum(y**2) / t - np.sum(np.diag(S)**2)
z = X * X_mkt[:, None]
v1 = y.T.dot(z) / t - cov_mkt[:, None] * S
roff1 = np.sum(v1 * cov_mkt[:, None].T) / var_mkt - np.sum(np.diag(v1) * cov_mkt) / var_mkt
v3 = z.T.dot(z) / t - var_mkt * S
roff3 = np.sum(v3 * np.outer(cov_mkt, cov_mkt)) / var_mkt**2 - np.sum(np.diag(v3) * cov_mkt**2) / var_mkt**2
roff = 2 * roff1 - roff3
rho = rdiag + roff
gamma = np.linalg.norm(S - F, 'fro')**2
kappa = (phi - rho) / gamma
alpha = max(0, min(1, kappa / t))
return alpha
class POETCovEstimator(RiskModel):
"""Principal Orthogonal Complement Thresholding Estimator (POET)
Reference:
[1] Fan, J., Liao, Y., & Mincheva, M. (2013). Large covariance estimation by thresholding principal orthogonal complements.
Journal of the Royal Statistical Society. Series B: Statistical Methodology, 75(4), 603–680. https://doi.org/10.1111/rssb.12016
[2] http://econweb.rutgers.edu/yl1114/papers/poet/POET.m
"""
THRESH_SOFT = 'soft'
THRESH_HARD = 'hard'
THRESH_SCAD = 'scad'
def __init__(self, num_factors: int = 0, thresh: float = 1.0, thresh_method: str = 'soft', **kwargs):
"""
Args:
num_factors (int): number of factors (if set to zero, no factor model will be used)
thresh (float): the positive constant for thresholding
thresh_method (str): thresholding method, which can be
- 'soft': soft thresholding
- 'hard': hard thresholding
- 'scad': scad thresholding
kwargs: see `RiskModel` for more information
"""
super().__init__(**kwargs)
assert num_factors >= 0, '`num_factors` requires a positive integer'
self.num_factors = num_factors
assert thresh >= 0, '`thresh` requires a positive float number'
self.thresh = thresh
assert thresh_method in [self.THRESH_HARD, self.THRESH_SOFT, self.THRESH_SCAD], \
'`thresh_method` should be `soft`/`hard`/`scad`'
self.thresh_method = thresh_method
def _predict(self, X: np.ndarray) -> np.ndarray:
Y = X.T # NOTE: to match POET's implementation
p, n = Y.shape
if self.num_factors > 0:
Dd, V = np.linalg.eig(Y.T.dot(Y))
V = V[:, np.argsort(Dd)]
F = V[:, -self.num_factors:][:, ::-1] * np.sqrt(n)
LamPCA = Y.dot(F) / n
uhat = np.asarray(Y - LamPCA.dot(F.T))
Lowrank = np.asarray(LamPCA.dot(LamPCA.T))
rate = 1 / np.sqrt(p) + np.sqrt(np.log(p) / n)
else:
uhat = np.asarray(Y)
rate = np.sqrt(np.log(p) / n)
Lowrank = 0
lamb = rate * self.thresh
SuPCA = uhat.dot(uhat.T) / n
SuDiag = np.diag(np.diag(SuPCA))
R = np.linalg.inv(SuDiag**0.5).dot(SuPCA).dot(np.linalg.inv(SuDiag**0.5))
if self.thresh_method == self.THRESH_HARD:
M = R * (np.abs(R) > lamb)
elif self.thresh_method == self.THRESH_SOFT:
res = (np.abs(R) - lamb)
res = (res + np.abs(res)) / 2
M = np.sign(R) * res
else:
M1 = (np.abs(R) < 2 * lamb) * np.sign(R) * (np.abs(R) - lamb) * (np.abs(R) > lamb)
M2 = (np.abs(R) < 3.7 * lamb) * (np.abs(R) >= 2 * lamb) * (2.7 * R - 3.7 * np.sign(R) * lamb) / 1.7
M3 = (np.abs(R) >= 3.7 * lamb) * R
M = M1 + M2 + M3
Rthresh = M - np.diag(np.diag(M)) + np.eye(p)
SigmaU = (SuDiag**0.5).dot(Rthresh).dot(SuDiag**0.5)
SigmaY = SigmaU + Lowrank
return SigmaY

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# Copyright (c) Microsoft Corporation.
# Licensed under the MIT License.
import warnings
import numpy as np
import pandas as pd
import scipy.optimize as so
from typing import Optional, Union, Callable, List
class PortfolioOptimizer(object):
"""Portfolio Optimizer
The following optimization algorithms are supported:
- `gmv`: Global Minimum Variance Portfolio
- `mvo`: Mean Variance Optimized Portfolio
- `rp`: Risk Parity
- `inv`: Inverse Volatility
Note:
This optimizer always assumes full investment and no-shorting.
"""
OPT_GMV = 'gmv'
OPT_MVO = 'mvo'
OPT_RP = 'rp'
OPT_INV = 'inv'
def __init__(self, method: str = 'inv', lamb: float = 0, delta: float = 0,
alpha: float = 0.0, scale_alpha: bool = True, tol: float = 1e-8):
"""
Args:
method (str): portfolio optimization method
lamb (float): risk aversion parameter (larger `lamb` means more focus on return)
delta (float): turnover rate limit
alpha (float): l2 norm regularizer
tol (float): tolerance for optimization termination
"""
assert method in [self.OPT_GMV, self.OPT_MVO, self.OPT_RP, self.OPT_INV], \
f'method `{method}` is not supported'
self.method = method
assert lamb >= 0, f'risk aversion parameter `lamb` should be positive'
self.lamb = lamb
assert delta >= 0, f'turnover limit `delta` should be positive'
self.delta = delta
assert alpha >= 0, f'l2 norm regularizer `alpha` should be positive'
self.alpha = alpha
self.tol = tol
def __call__(self, S: Union[np.ndarray, pd.DataFrame],
u: Optional[Union[np.ndarray, pd.Series]] = None,
w0: Optional[Union[np.ndarray, pd.Series]] = None) -> Union[np.ndarray, pd.Series]:
"""
Args:
S (np.ndarray or pd.DataFrame): covariance matrix
u (np.ndarray or pd.Series): expected returns (a.k.a., alpha)
w0 (np.ndarray or pd.Series): initial weights (for turnover control)
Returns:
np.ndarray or pd.Series: optimized portfolio allocation
"""
# transform dataframe into array
index = None
if isinstance(S, pd.DataFrame):
index = S.index
S = S.values
# transform alpha
if u is not None:
assert len(u) == len(S), '`u` has mismatched shape'
if isinstance(u, pd.Series):
assert all(u.index == index), '`u` has mismatched index'
u = u.values
# transform initial weights
if w0 is not None:
assert len(w0) == len(S), '`w0` has mismatched shape'
if isinstance(w0, pd.Series):
assert all(w0.index == index), '`w0` has mismatched index'
w0 = w0.values
# scale alpha to match volatility
if u is not None:
u = u / u.std()
u *= np.mean(np.diag(S))**0.5
# optimize
w = self._optimize(S, u, w0)
# restore index if needed
if index is not None:
w = pd.Series(w, index=index)
return w
def _optimize(self, S: np.ndarray, u: Optional[np.ndarray] = None,
w0: Optional[np.ndarray] = None) -> np.ndarray:
# inverse volatility
if self.method == self.OPT_INV:
if u is not None:
warnings.warn('`u` is set but will not be used for `inv` portfolio')
if w0 is not None:
warnings.warn('`w0` is set but will not be used for `inv` portfolio')
return self._optimize_inv(S)
# global minimum variance
if self.method == self.OPT_GMV:
if u is not None:
warnings.warn('`u` is set but will not be used for `gmv` portfolio')
return self._optimize_gmv(S, w0)
# mean-variance
if self.method == self.OPT_MVO:
return self._optimize_mvo(S, u, w0)
# risk parity
if self.method == self.OPT_RP:
if u is not None:
warnings.warn('`u` is set but will not be used for `rp` portfolio')
return self._optimize_rp(S, w0)
def _optimize_inv(self, S: np.ndarray) -> np.ndarray:
"""Inverse volatility"""
vola = np.diag(S)**0.5
w = 1 / vola
w /= w.sum()
return w
def _optimize_gmv(self, S: np.ndarray, w0: Optional[np.ndarray] = None) -> np.ndarray:
"""optimize global minimum variance portfolio
This method solves the following optimization problem
min_w w' S w
s.t. w >= 0, sum(w) == 1
where `S` is the covariance matrix.
"""
return self._solve(
len(S),
self._get_objective_gmv(S),
*self._get_constrains(w0)
)
def _optimize_mvo(self, S: np.ndarray, u: Optional[np.ndarray] = None,
w0: Optional[np.ndarray] = None) -> np.ndarray:
"""optimize mean-variance portfolio
This method solves the following optimization problem
min_w - w' u + lamb * w' S w
s.t. w >= 0, sum(w) == 1
where `S` is the covariance matrix, `u` is the expected returns,
and `lamb` is the risk aversion parameter.
"""
return self._solve(
len(S),
self._get_objective_mvo(S, u),
*self._get_constrains(w0)
)
def _optimize_rp(self, S: np.ndarray, w0: Optional[np.ndarray] = None) -> np.ndarray:
"""optimize risk parity portfolio
This method solves the following optimization problem
min_w sum_i [w_i - (w' S w) / ((S w)_i * N)]**2
s.t. w >= 0, sum(w) == 1
where `S` is the covariance matrix and `N` is the number of stocks.
"""
return self._solve(
len(S),
self._get_objective_rp(S),
*self._get_constrains(w0)
)
def _get_objective_gmv(self, S: np.ndarray) -> np.ndarray:
"""global minimum variance optimization objective
Optimization objective
min_w w' S w
"""
def func(x):
return x @ S @ x
return func
def _get_objective_mvo(self, S: np.ndarray, u: np.ndarray = None) -> np.ndarray:
"""mean-variance optimization objective
Optimization objective
min_w - w' u + lamb * w' S w
"""
def func(x):
risk = x @ S @ x
ret = x @ u
return -ret + self.lamb * risk
return func
def _get_objective_rp(self, S: np.ndarray) -> np.ndarray:
"""risk-parity optimization objective
Optimization objective
min_w sum_i [w_i - (w' S w) / ((S w)_i * N)]**2
"""
def func(x):
N = len(x)
Sx = S @ x
xSx = x @ Sx
return np.sum((x - xSx / Sx / N)**2)
return func
def _get_constrains(self, w0: Optional[np.ndarray] = None):
"""optimization constraints
Defines the following constraints:
- no shorting and leverage: 0 <= w <= 1
- full investment: sum(w) == 1
- turnover constraint: |w - w0| <= delta
"""
# no shorting and leverage
bounds = so.Bounds(0.0, 1.0)
# full investment constraint
cons = [
{'type': 'eq', 'fun': lambda x: np.sum(x) - 1} # == 0
]
# turnover constraint
if w0 is not None:
cons.append(
{'type': 'ineq', 'fun': lambda x: self.delta - np.sum(np.abs(x - w0))} # >= 0
)
return bounds, cons
def _solve(self, n: int, obj: Callable, bounds: so.Bounds, cons: List) -> np.ndarray:
"""solve optimization
Args:
n (int): number of parameters
obj (callable): optimization objective
bounds (Bounds): bounds of parameters
cons (list): optimization constraints
"""
# add l2 regularization
wrapped_obj = obj
if self.alpha > 0:
wrapped_obj = lambda x: obj(x) + self.alpha * np.sum(np.square(x))
# solve
x0 = np.ones(n) / n # init results
sol = so.minimize(wrapped_obj, x0, bounds=bounds, constraints=cons, tol=self.tol)
if not sol.success:
warnings.warn(f'optimization not success ({sol.status})')
return sol.x