# 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 from AlgorithmImports import * import numpy as np import pandas as pd class TimeSeriesMomentum(QCAlgorithm): def Initialize(self): self.SetStartDate(2000, 1, 1) self.SetCash(10000000) 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_DA1", # Class III Milk Futures "CME_RB1", # Gasoline Futures, Continuous Contract "CME_KW1", # Wheat Kansas, 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, Resolution.Daily) self.targeted_volatility = 0.10 self.vol_target_period = 60 self.leverage_cap = 4 # Daily rolled data. self.data = {} for symbol in self.symbols: data = None # Back adjusted and spliced data import. data = self.AddData(QuantpediaFutures, symbol, Resolution.Daily) data.SetFeeModel(CustomFeeModel()) data.SetLeverage(20) self.data[symbol] = RollingWindow[float](self.period) self.recent_month = -1 def OnData(self, data): # Store daily data. for symbol in self.symbols: if symbol in data and data[symbol]: price = data[symbol].Value self.data[symbol].Add(price) if self.recent_month == self.Time.month: return self.recent_month = self.Time.month # Performance and volatility data. performance_volatility = {} daily_returns = {} for symbol in self.symbols: if self.data[symbol].IsReady: if ( self.Securities[symbol].GetLastData() and ( self.Time.date() - self.Securities[symbol].GetLastData().Time.date() ).days < 5 ): back_adjusted_prices = np.array([x for x in self.data[symbol]]) performance = back_adjusted_prices[0] / back_adjusted_prices[-1] - 1 daily_rets = ( back_adjusted_prices[:-1] / back_adjusted_prices[1:] - 1 ) back_adjusted_prices = back_adjusted_prices[ : self.vol_target_period ] daily_rets = ( back_adjusted_prices[:-1] / back_adjusted_prices[1:] - 1 ) volatility_3M = np.std(daily_rets) * sqrt(252) daily_returns[symbol] = daily_rets[::-1][: self.vol_target_period] performance_volatility[symbol] = (performance, volatility_3M) if len(performance_volatility) == 0: return # Performance sorting. long = [x[0] for x in performance_volatility.items() if x[1][0] > 0] short = [x[0] for x in performance_volatility.items() if x[1][0] < 0] weight_by_symbol = {} # Volatility weighting long and short leg separately. ls_leverage = [] # long and short leverage for sym_i, symbols in enumerate([long, short]): total_volatility = sum([1 / performance_volatility[x][1] for x in symbols]) # Inverse volatility weighting. weights = np.array( [(1 / performance_volatility[x][1]) / total_volatility for x in symbols] ) weights_sum = sum(weights) weights = weights / weights_sum df = pd.DataFrame() i = 0 for symbol in symbols: df[str(symbol)] = [x for x in daily_returns[symbol]] weight_by_symbol[symbol] = weights[i] if sym_i == 0 else -weights[i] i += 1 # volatility targeting portfolio_vol = np.sqrt( np.dot(weights.T, np.dot(df.cov() * 252, weights.T)) ) leverage = self.targeted_volatility / portfolio_vol leverage = min(self.leverage_cap, leverage) # cap max leverage ls_leverage.append(leverage) # Trade execution. invested = [x.Key.Value for x in self.Portfolio if x.Value.Invested] for symbol in invested: if symbol not in long + short: self.Liquidate(symbol) for symbol, w in weight_by_symbol.items(): if w >= 0: self.SetHoldings(symbol, w * ls_leverage[0]) # self.SetHoldings(symbol, w) else: self.SetHoldings(symbol, w * ls_leverage[1]) # 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) data["back_adjusted"] = float(split[1]) data["spliced"] = float(split[2]) data.Value = float(split[1]) return data # Custom fee model. class CustomFeeModel(FeeModel): def GetOrderFee(self, parameters): fee = parameters.Security.Price * parameters.Order.AbsoluteQuantity * 0.00005 return OrderFee(CashAmount(fee, "USD"))