Overall Statistics Total Trades 5506 Average Win 0.13% Average Loss -0.18% Compounding Annual Return 2.589% Drawdown 37.500% Expectancy 0.037 Net Profit 33.317% Sharpe Ratio 0.234 Probabilistic Sharpe Ratio 0.216% Loss Rate 39% Win Rate 61% Profit-Loss Ratio 0.70 Alpha 0.026 Beta 0.024 Annual Standard Deviation 0.124 Annual Variance 0.015 Information Ratio -0.503 Tracking Error 0.197 Treynor Ratio 1.234 Total Fees $1859.64 Estimated Strategy Capacity$0
# 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.
#
# QC implementation changes:
#   - instead of GARCH model volatility, we have used simple historical volatility.

from math import sqrt
import numpy as np

class TimeSeriesMomentum(QCAlgorithm):

def Initialize(self):
self.SetStartDate(2010, 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
"CME_RB2",  # Gasoline Futures, Continuous Contract
"CME_KW2",  # Wheat Kansas, Continuous Contract

"ICE_RS1",  # Canola Futures, Continuous Contract
"ICE_GO1",  # Gas Oil Futures, Continuous Contract
"CME_RB2",  # Gasoline Futures, Continuous Contract
"CME_KW2",  # Wheat Kansas, Continuous Contract
"ICE_WT1",  # WTI Crude Futures, Continuous Contract

"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
"ICE_RS1",  # Canola Futures, Continuous Contract
"ICE_GO1",  # Gas Oil Futures, Continuous Contract
"ICE_WT1",  # WTI Crude 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(CustomFeeModel(self))
data.SetLeverage(20)

self.data[symbol] = RollingWindow[float](self.period)

self.Schedule.On(self.DateRules.MonthStart(self.symbols[0]), self.TimeRules.BeforeMarketClose(self.symbols[0]), self.Rebalance)

def OnData(self, data):
# Store daily data.
for symbol in self.symbols:
if symbol in data and data[symbol]:
price = data[symbol].Value
if price != 0:

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

volatility_1M = np.std(daily_returns) * sqrt(252)

performance_volatility[symbol] = (performance, volatility_1M)

if len(performance_volatility) == 0: return

# Performance sorting.
long = [x for x in performance_volatility.items() if x[1][0] > 0]
short = [x for x in performance_volatility.items() if x[1][0] < 0]

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

count = len(long + short) * 2

# Volatility targeting.
portfolio_volatility = sum([((x[1][1]) / count) for x in long + short])
volatility_target_leverage = 2 * self.targeted_volatility / portfolio_volatility

long_symbols = [x[0] for x in long]
short_symbols = [x[0] for x in short]

weight = {}
for symbol_data in long + short:
symbol = symbol_data[0]
volatility = symbol_data[1][1]
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

invested = [x.Key.Value for x in self.Portfolio if x.Value.Invested]
for symbol in invested:
if symbol not in long_symbols + short_symbols:
self.Liquidate(symbol)

for symbol, w in weight.items():
self.SetHoldings(symbol, w)

# 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)
return OrderFee(CashAmount(fee, "USD"))