| Overall Statistics |
|
Total Trades
3341
Average Win
0.04%
Average Loss
-0.04%
Compounding Annual Return
8.979%
Drawdown
30.700%
Expectancy
0.809
Net Profit
644.521%
Sharpe Ratio
0.583
Probabilistic Sharpe Ratio
0.600%
Loss Rate
14%
Win Rate
86%
Profit-Loss Ratio
1.11
Alpha
0.038
Beta
0.517
Annual Standard Deviation
0.117
Annual Variance
0.014
Information Ratio
0.091
Tracking Error
0.114
Treynor Ratio
0.133
Total Fees
$3373.99
Estimated Strategy Capacity
$0
Lowest Capacity Asset
CME_ES1.QuantpediaFutures 2S
Portfolio Turnover
0.32%
|
from AlgorithmImports import *
import numpy as np
from scipy.optimize import minimize
import statsmodels.api as sm
sp100_stocks = ['AAPL','MSFT','AMZN','FB','BRKB','GOOGL','GOOG','JPM','JNJ','V','PG','XOM','UNH','BAC','MA','T','DIS','INTC','HD','VZ','MRK','PFE','CVX','KO','CMCSA','CSCO','PEP','WFC','C','BA','ADBE','WMT','CRM','MCD','MDT','BMY','ABT','NVDA','NFLX','AMGN','PM','PYPL','TMO','COST','ABBV','ACN','HON','NKE','UNP','UTX','NEE','IBM','TXN','AVGO','LLY','ORCL','LIN','SBUX','AMT','LMT','GE','MMM','DHR','QCOM','CVS','MO','LOW','FIS','AXP','BKNG','UPS','GILD','CHTR','CAT','MDLZ','GS','USB','CI','ANTM','BDX','TJX','ADP','TFC','CME','SPGI','COP','INTU','ISRG','CB','SO','D','FISV','PNC','DUK','SYK','ZTS','MS','RTN','AGN','BLK']
def MonthDiff(d1, d2):
return (d1.year - d2.year) * 12 + d1.month - d2.month
def Return(values):
return (values[-1] - values[0]) / values[0]
def Volatility(values):
values = np.array(values)
returns = (values[1:] - values[:-1]) / values[:-1]
return np.std(returns)
def MultipleLinearRegression(x, y):
x = np.array(x).T
x = sm.add_constant(x)
result = sm.OLS(endog=y, exog=x).fit()
return result
# Custom fee model.
class CustomFeeModel(FeeModel):
def GetOrderFee(self, parameters):
fee = parameters.Security.Price * parameters.Order.AbsoluteQuantity * 0.00005
return OrderFee(CashAmount(fee, "USD"))
# Quandl free data
class QuandlFutures(PythonQuandl):
def __init__(self):
self.ValueColumnName = "settle"
# Quandl "value" data
class QuandlValue(PythonQuandl):
def __init__(self):
self.ValueColumnName = 'Value'
# Quandl short interest data.
class QuandlFINRA_ShortVolume(PythonQuandl):
def __init__(self):
self.ValueColumnName = 'SHORTVOLUME' # also 'TOTALVOLUME' is accesible
# Commitments of Traders data.
# NOTE: IMPORTANT: Data order must be ascending (datewise).
# Data source: https://commitmentsoftraders.org/cot-data/
# Data description: https://commitmentsoftraders.org/wp-content/uploads/Static/CoTData/file_key.html
class CommitmentsOfTraders(PythonData):
def GetSource(self, config, date, isLiveMode):
return SubscriptionDataSource("data.quantpedia.com/backtesting_data/futures/cot/{0}.PRN".format(config.Symbol.Value), SubscriptionTransportMedium.RemoteFile, FileFormat.Csv)
# File example.
# DATE OPEN HIGH LOW CLOSE VOLUME OI
# ---- ---- ---- --- ----- ------ --
# DATE LARGE SPECULATOR COMMERCIAL HEDGER SMALL TRADER
# LONG SHORT LONG SHORT LONG SHORT
def Reader(self, config, line, date, isLiveMode):
data = CommitmentsOfTraders()
data.Symbol = config.Symbol
if not line[0].isdigit(): return None
split = line.split(',')
# Prevent lookahead bias.
data.Time = datetime.strptime(split[0], "%Y%m%d") + timedelta(days=1)
data['LARGE_SPECULATOR_LONG'] = int(split[1])
data['LARGE_SPECULATOR_SHORT'] = int(split[2])
data['COMMERCIAL_HEDGER_LONG'] = int(split[3])
data['COMMERCIAL_HEDGER_SHORT'] = int(split[4])
data['SMALL_TRADER_LONG'] = int(split[5])
data['SMALL_TRADER_SHORT'] = int(split[6])
data['open_interest'] = int(split[1]) + int(split[2]) + int(split[3]) + int(split[4]) + int(split[5]) + int(split[6])
data.Value = int(split[1])
return data
# Quantpedia bond yield data.
# NOTE: IMPORTANT: Data order must be ascending (datewise)
class QuantpediaIndices(PythonData):
def GetSource(self, config, date, isLiveMode):
return SubscriptionDataSource("data.quantpedia.com/backtesting_data/index/{0}.csv".format(config.Symbol.Value), SubscriptionTransportMedium.RemoteFile, FileFormat.Csv)
def Reader(self, config, line, date, isLiveMode):
data = QuantpediaIndices()
data.Symbol = config.Symbol
if not line[0].isdigit(): return None
split = line.split(',')
data.Time = datetime.strptime(split[0], "%Y-%m-%d") + timedelta(days=1)
data['close'] = float(split[1])
data.Value = float(split[1])
return data
# Quantpedia bond yield data.
# NOTE: IMPORTANT: Data order must be ascending (datewise)
class QuantpediaBondYield(PythonData):
def GetSource(self, config, date, isLiveMode):
return SubscriptionDataSource("data.quantpedia.com/backtesting_data/bond_yield/{0}.csv".format(config.Symbol.Value), SubscriptionTransportMedium.RemoteFile, FileFormat.Csv)
def Reader(self, config, line, date, isLiveMode):
data = QuantpediaBondYield()
data.Symbol = config.Symbol
if not line[0].isdigit(): return None
split = line.split(',')
data.Time = datetime.strptime(split[0], "%Y-%m-%d") + timedelta(days=1)
data['yield'] = float(split[1])
data.Value = float(split[1])
return data
# Quantpedia data.
# NOTE: IMPORTANT: Data order must be ascending (datewise)
class QuantpediaFutures(PythonData):
def GetSource(self, config, date, isLiveMode):
return SubscriptionDataSource("data.quantpedia.com/backtesting_data/futures/{0}.csv".format(config.Symbol.Value), SubscriptionTransportMedium.RemoteFile, FileFormat.Csv)
def Reader(self, config, line, date, isLiveMode):
data = QuantpediaFutures()
data.Symbol = config.Symbol
if not line[0].isdigit(): return None
split = line.split(';')
data.Time = datetime.strptime(split[0], "%d.%m.%Y") + timedelta(days=1)
data['back_adjusted'] = float(split[1])
data['spliced'] = float(split[2])
data.Value = float(split[1])
return data
# Commitments of Traders data.
# NOTE: IMPORTANT: Data order must be ascending (datewise).
# Data source: https://commitmentsoftraders.org/cot-data/
# Data description: https://commitmentsoftraders.org/wp-content/uploads/Static/CoTData/file_key.html
class CommitmentsOfTraders(PythonData):
def GetSource(self, config, date, isLiveMode):
return SubscriptionDataSource("data.quantpedia.com/backtesting_data/futures/cot/{0}.PRN".format(config.Symbol.Value), SubscriptionTransportMedium.RemoteFile, FileFormat.Csv)
# File example.
# DATE OPEN HIGH LOW CLOSE VOLUME OI
# ---- ---- ---- --- ----- ------ --
# DATE LARGE SPECULATOR COMMERCIAL HEDGER SMALL TRADER
# LONG SHORT LONG SHORT LONG SHORT
def Reader(self, config, line, date, isLiveMode):
data = CommitmentsOfTraders()
data.Symbol = config.Symbol
if not line[0].isdigit(): return None
split = line.split(',')
# Prevent lookahead bias.
data.Time = datetime.strptime(split[0], "%Y%m%d") + timedelta(days=1)
data['LARGE_SPECULATOR_LONG'] = int(split[1])
data['LARGE_SPECULATOR_SHORT'] = int(split[2])
data['COMMERCIAL_HEDGER_LONG'] = int(split[3])
data['COMMERCIAL_HEDGER_SHORT'] = int(split[4])
data['SMALL_TRADER_LONG'] = int(split[5])
data['SMALL_TRADER_SHORT'] = int(split[6])
data.Value = int(split[1])
return data
# NOTE: Manager for new trades. It's represented by certain count of equally weighted brackets for long and short positions.
# If there's a place for new trade, it will be managed for time of holding period.
class TradeManager():
def __init__(self, algorithm, long_size, short_size, holding_period):
self.algorithm = algorithm # algorithm to execute orders in.
self.long_size = long_size
self.short_size = short_size
self.long_len = 0
self.short_len = 0
# Arrays of ManagedSymbols
self.symbols = []
self.holding_period = holding_period # Days of holding.
# Add stock symbol object
def Add(self, symbol, long_flag):
# Open new long trade.
managed_symbol = ManagedSymbol(symbol, self.holding_period, long_flag)
if long_flag:
# If there's a place for it.
if self.long_len < self.long_size:
self.symbols.append(managed_symbol)
self.algorithm.SetHoldings(symbol, 1 / self.long_size)
self.long_len += 1
else:
self.algorithm.Log("There's not place for additional trade.")
# Open new short trade.
else:
# If there's a place for it.
if self.short_len < self.short_size:
self.symbols.append(managed_symbol)
self.algorithm.SetHoldings(symbol, - 1 / self.short_size)
self.short_len += 1
else:
self.algorithm.Log("There's not place for additional trade.")
# Decrement holding period and liquidate symbols.
def TryLiquidate(self):
symbols_to_delete = []
for managed_symbol in self.symbols:
managed_symbol.days_to_liquidate -= 1
# Liquidate.
if managed_symbol.days_to_liquidate == 0:
symbols_to_delete.append(managed_symbol)
self.algorithm.Liquidate(managed_symbol.symbol)
if managed_symbol.long_flag: self.long_len -= 1
else: self.short_len -= 1
# Remove symbols from management.
for managed_symbol in symbols_to_delete:
self.symbols.remove(managed_symbol)
def LiquidateTicker(self, ticker):
symbol_to_delete = None
for managed_symbol in self.symbols:
if managed_symbol.symbol.Value == ticker:
self.algorithm.Liquidate(managed_symbol.symbol)
symbol_to_delete = managed_symbol
if managed_symbol.long_flag: self.long_len -= 1
else: self.short_len -= 1
break
if symbol_to_delete: self.symbols.remove(symbol_to_delete)
else: self.algorithm.Debug("Ticker is not held in portfolio!")
class ManagedSymbol():
def __init__(self, symbol, days_to_liquidate, long_flag):
self.symbol = symbol
self.days_to_liquidate = days_to_liquidate
self.long_flag = long_flag
class PortfolioOptimization(object):
def __init__(self, df_return, risk_free_rate, num_assets):
self.daily_return = df_return
self.risk_free_rate = risk_free_rate
self.n = num_assets # numbers of risk assets in portfolio
self.target_vol = 0.05
def annual_port_return(self, weights):
# calculate the annual return of portfolio
return np.sum(self.daily_return.mean() * weights) * 252
def annual_port_vol(self, weights):
# calculate the annual volatility of portfolio
return np.sqrt(np.dot(weights.T, np.dot(self.daily_return.cov() * 252, weights)))
def min_func(self, weights):
# method 1: maximize sharp ratio
return - self.annual_port_return(weights) / self.annual_port_vol(weights)
# method 2: maximize the return with target volatility
#return - self.annual_port_return(weights) / self.target_vol
def opt_portfolio(self):
# maximize the sharpe ratio to find the optimal weights
cons = ({'type': 'eq', 'fun': lambda x: np.sum(x) - 1})
bnds = tuple((0, 1) for x in range(2)) + tuple((0, 0.25) for x in range(self.n - 2))
opt = minimize(self.min_func, # object function
np.array(self.n * [1. / self.n]), # initial value
method='SLSQP', # optimization method
bounds=bnds, # bounds for variables
constraints=cons) # constraint conditions
opt_weights = opt['x']
return opt_weights
# https://quantpedia.com/strategies/crude-oil-predicts-equity-returns/
#
# Several types of oil can be used (Brent, WTI, Dubai etc.) without big differences in results. The source paper for
# this anomaly uses Arab Light crude oil. Monthly oil returns are used in the regression equation as an independent
# variable and equity returns are used as a dependent variable. The model is re-estimated every month and
# observations of the last month are added. The investor determines whether the expected stock market return in
# a specific month (based on regression results and conditional on the oil price change in the previous month) is higher
# or lower than the risk-free rate. The investor is fully invested in the market portfolio if the expected
# return is higher (bull market); he invests in cash if the expected return is lower (bear market).
from data_tools import QuantpediaFutures, QuandlValue, CustomFeeModel
from AlgorithmImports import *
import numpy as np
from collections import deque
from scipy import stats
class CrudeOilPredictsEquityReturns(QCAlgorithm):
def Initialize(self):
self.SetStartDate(2000, 1, 1)
self.SetCash(100000)
self.data = {}
self.symbols = [
"CME_ES1", # E-mini S&P 500 Futures, Continuous Contract #1
"CME_CL1" # Crude Oil Futures, Continuous Contract #1
]
self.cash = self.AddEquity('SHY', Resolution.Daily).Symbol
self.risk_free_rate = self.AddData(QuandlValue, 'FRED/DGS3MO', Resolution.Daily).Symbol
# Monhtly price data.
self.data = {}
for symbol in self.symbols:
data = self.AddData(QuantpediaFutures, symbol, Resolution.Daily)
data.SetLeverage(5)
data.SetFeeModel(CustomFeeModel())
self.data[symbol] = deque()
self.recent_month = -1
def OnData(self, data):
rebalance_flag = False
for symbol in self.symbols:
if symbol in data:
if self.recent_month != self.Time.month:
rebalance_flag = True
if data[symbol]:
price = data[symbol].Value
self.data[symbol].append(price)
if rebalance_flag:
self.recent_month = self.Time.month
rf_rate = 0
if self.Securities[self.risk_free_rate].GetLastData() and (self.Time.date() - self.Securities[self.risk_free_rate].GetLastData().Time.date()).days < 5:
rf_rate = self.Securities[self.risk_free_rate].Price
else:
return
if self.Securities[self.cash].GetLastData() and (self.Time.date() - self.Securities[self.cash].GetLastData().Time.date()).days >= 5:
return
market_prices = np.array(self.data[self.symbols[0]])
oil_prices = np.array(self.data[self.symbols[1]])
# At least one year of data is ready.
if len(market_prices) < 13 or len(oil_prices) < 13:
return
# Trim price series lenghts.
min_size = min(len(market_prices), len(oil_prices))
market_prices = market_prices[-min_size:]
oil_prices = oil_prices[-min_size:]
market_returns = (market_prices[1:] - market_prices[:-1]) / market_prices[:-1]
oil_returns = (oil_prices[1:] - oil_prices[:-1]) / oil_prices[:-1]
# Simple Linear Regression
# Y = C + (M * X)
# Y = α + (β ∗ X)
# Y = Dependent variable (output/outcome/prediction/estimation)
# C/α = Constant (Y-Intercept)
# M/β = Slope of the regression line (the effect that X has on Y)
# X = Independent variable (input variable used in the prediction of Y)
slope, intercept, r_value, p_value, std_err = stats.linregress(oil_returns[:-1], market_returns[1:])
X = oil_returns[-1]
expected_market_return = intercept + (slope * X)
if expected_market_return > rf_rate:
self.SetHoldings(self.symbols[0], 1)
else:
if self.Securities[self.cash].Price != 0:
self.SetHoldings(self.cash, 1)