Overall Statistics Total Trades 10182 Average Win 0.12% Average Loss -0.16% Compounding Annual Return 7.644% Drawdown 20.000% Expectancy 0.169 Net Profit 352.086% Sharpe Ratio 0.793 Probabilistic Sharpe Ratio 12.428% Loss Rate 34% Win Rate 66% Profit-Loss Ratio 0.78 Alpha 0.066 Beta 0 Annual Standard Deviation 0.083 Annual Variance 0.007 Information Ratio 0.016 Tracking Error 0.197 Treynor Ratio -139.807 Total Fees \$7891.40
import numpy as np
from scipy.optimize import minimize

def MonthDiff(d1, d2):
return (d1.year - d2.year) * 12 + d1.month - d2.month

def Return(values):
return (values[-1] - values) / values

def Volatility(values):
values = np.array(values)
returns = (values[1:] - values[:-1]) / values[:-1]
return np.std(returns)

def GetFutureMulitpliers(algorithm):
symbol_multiplier = {}

mulitpliers_lines = csv_string_file.split('\r\n')
for line in mulitpliers_lines:
symbol, multiplier = line.split(';')
symbol_multiplier[symbol] = float(multiplier)

return symbol_multiplier

# 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 short interest data.
class QuandlFINRA_ShortVolume(PythonQuandl):
def __init__(self):
self.ValueColumnName = 'SHORTVOLUME'    # also 'TOTALVOLUME' is accesible

# 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.isdigit(): return None
split = line.split(';')

data.Time = datetime.strptime(split, "%d.%m.%Y") + timedelta(days=1)
data['spliced'] = float(split)
data.Value = float(split)

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.
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.weight = 1 / (self.long_size + self.short_size)

self.long_len = 0
self.short_len = 0

# Arrays of ManagedSymbols
self.symbols = []

self.holding_period = holding_period    # Days of holding.

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, self.weight)
self.long_len += 1
else:

else:
# If there's a place for it.
if self.short_len < self.short_size:
self.symbols.append(managed_symbol)
self.algorithm.SetHoldings(symbol, - self.weight)
self.short_len += 1
else:

# 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/time-series-momentum-effect/
#
# The investment universe consists of 24 commodity futures, 12 cross-currency pairs (with 9 underlying currencies), 9 developed equity indices, and 13 developed
# government bond futures.
# Every month, the investor considers whether the excess return of each asset over the past 12 months is positive or negative and goes long on the contract if it is
# positive and short if negative. The position size is set to be inversely proportional to the instrument’s volatility. A univariate GARCH model is used to estimated
# ex-ante volatility in the source paper. However, other simple models could probably be easily used with good results (for example, the easiest one would be using
# historical volatility instead of estimated volatility). The portfolio is rebalanced monthly.

from collections import deque
import fk_tools
from math import sqrt

class TimeSeriesMomentum(QCAlgorithm):

def Initialize(self):
self.SetStartDate(2000, 1, 1)
self.SetCash(100000)

self.symbols = [
"CME_S1",   # Soybean Futures, Continuous Contract
"CME_W1",   # Wheat Futures, Continuous Contract
"CME_SM1",  # Soybean Meal Futures, Continuous Contract
"CME_BO1",  # Soybean Oil Futures, Continuous Contract
"CME_C1",   # Corn Futures, Continuous Contract
"CME_O1",   # Oats Futures, Continuous Contract
"CME_LC1",  # Live Cattle Futures, Continuous Contract
"CME_FC1",  # Feeder Cattle Futures, Continuous Contract
"CME_LN1",  # Lean Hog Futures, Continuous Contract
"CME_GC1",  # Gold Futures, Continuous Contract
"CME_SI1",  # Silver Futures, Continuous Contract
"CME_PL1",  # Platinum Futures, Continuous Contract
"CME_CL1",  # Crude Oil Futures, Continuous Contract
"CME_HG1",  # Copper Futures, Continuous Contract
"CME_LB1",  # Random Length Lumber Futures, Continuous Contract
"CME_NG1",  # Natural Gas (Henry Hub) Physical Futures, Continuous Contract
"CME_PA1",  # Palladium Futures, Continuous Contract
"CME_RR1",  # Rough Rice Futures, Continuous Contract
"CME_CU1",  # Chicago Ethanol (Platts) Futures
"CME_DA1",  # Class III Milk Futures

"ICE_CC1",  # Cocoa Futures, Continuous Contract
"ICE_CT1",  # Cotton No. 2 Futures, Continuous Contract
"ICE_KC1",  # Coffee C Futures, Continuous Contract
"ICE_O1",   # Heating Oil Futures, Continuous Contract
"ICE_OJ1",  # Orange Juice Futures, Continuous Contract
"ICE_SB1",  # Sugar No. 11 Futures, Continuous Contract

"CME_AD1", # Australian Dollar Futures, Continuous Contract #1
"CME_BP1", # British Pound Futures, Continuous Contract #1
"CME_CD1", # Canadian Dollar Futures, Continuous Contract #1
"CME_EC1", # Euro FX Futures, Continuous Contract #1
"CME_JY1", # Japanese Yen Futures, Continuous Contract #1
"CME_MP1", # Mexican Peso Futures, Continuous Contract #1
"CME_NE1", # New Zealand Dollar Futures, Continuous Contract #1
"CME_SF1", # Swiss Franc Futures, Continuous Contract #1

"ICE_DX1",      # US Dollar Index Futures, Continuous Contract #1
"CME_NQ1",      # E-mini NASDAQ 100 Futures, Continuous Contract #1
"EUREX_FDAX1",  # DAX Futures, Continuous Contract #1
"CME_ES1",      # E-mini S&P 500 Futures, Continuous Contract #1
"EUREX_FSMI1",  # SMI Futures, Continuous Contract #1
"EUREX_FSTX1",  # STOXX Europe 50 Index Futures, Continuous Contract #1
"LIFFE_FCE1",   # CAC40 Index Futures, Continuous Contract #1
"LIFFE_Z1",     # FTSE 100 Index Futures, Continuous Contract #1
"SGX_NK1",      # SGX Nikkei 225 Index Futures, Continuous Contract #1
"CME_MD1",      # E-mini S&P MidCap 400 Futures

"CME_TY1",      # 10 Yr Note Futures, Continuous Contract #1
"CME_FV1",      # 5 Yr Note Futures, Continuous Contract #1
"CME_TU1",      # 2 Yr Note Futures, Continuous Contract #1
"ASX_XT1",     # 10 Year Commonwealth Treasury Bond Futures, Continuous Contract #1   # 'Settlement price' instead of 'settle' on quandl.
"ASX_YT1",     # 3 Year Commonwealth Treasury Bond Futures, Continuous Contract #1    # 'Settlement price' instead of 'settle' on quandl.
"EUREX_FGBL1",  # Euro-Bund (10Y) Futures, Continuous Contract #1
"EUREX_FBTP1", # Long-Term Euro-BTP Futures, Continuous Contract #1
"EUREX_FGBM1",  # Euro-Bobl Futures, Continuous Contract #1
"EUREX_FGBS1",  # Euro-Schatz Futures, Continuous Contract #1
"SGX_JB1",      # SGX 10-Year Mini Japanese Government Bond Futures
"LIFFE_R1"      # Long Gilt Futures, Continuous Contract #1
"MX_CGB1",     # Ten-Year Government of Canada Bond Futures, Continuous Contract #1    # 'Settlement price' instead of 'settle' on quandl.
]

self.period = 12 * 21
self.SetWarmUp(self.period)

self.targeted_volatility = 0.10

# Daily rolled data.
self.data = {}

for symbol in self.symbols:
data = None

# Back adjusted and spliced data import.

data.SetFeeModel(fk_tools.CustomFeeModel(self))
data.SetLeverage(20)

self.data[symbol] = deque(maxlen=self.period)

self.Schedule.On(self.DateRules.MonthStart(self.symbols), self.TimeRules.AfterMarketOpen(self.symbols), self.Rebalance)

def OnData(self, data):
# Store daily data.
for symbol in self.symbols:
if self.Securities.ContainsKey(symbol):
price = self.Securities[symbol].Price
if price != 0:
self.data[symbol].append(price)
else:
# Append latest price as a next one in case there's 0 as price.
if len(self.data[symbol]) > 0:
last_price = self.data[symbol][-1]
self.data[symbol].append(last_price)

def Rebalance(self):
# Performance / volatility data.
performance_volatility = {}
for symbol in self.symbols:
if len(self.data[symbol]) == self.data[symbol].maxlen:
back_adjusted_prices = [x for x in self.data[symbol]]

performance_volatility[symbol] = [performance, volatility_1M]

if len(performance_volatility) == 0: return

# Performance sorting.
long = [x for x in performance_volatility.items() if x > 0]
short = [x for x in performance_volatility.items() if x < 0]

# Volatility weighting.
total_volatility_inversed = sum([(1 / x) for x in long + short])
if total_volatility_inversed == 0: return

# count = len(long + short)
count = len(long + short) * 2

# Volatility targeting.
portfolio_volatility = sum([((x) / count) for x in long + short]) * sqrt(252)
volatility_target_leverage = 2 * self.targeted_volatility / portfolio_volatility

long_symbols = [x for x in long]
short_symbols = [x for x in short]

weight = {}
for symbol_data in long + short:
symbol = symbol_data
volatility = symbol_data
if volatility != 0:
# 2x leverage - 100% long / 100% short.
final_leverage = 2.0 * volatility_target_leverage
# self.Log(f"Leverage: {final_leverage}")

if symbol in long_symbols:
weight[symbol] = (final_leverage / volatility) / total_volatility_inversed
else:
weight[symbol] = - (final_leverage / volatility) / total_volatility_inversed
else:
weight[symbol] = 0

self.SetHoldings(symbol, w)