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June 4, 2022 18:49
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Time Series Momentum
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# The investment universe consists of 24 commodity futures, 12 cross-currency pairs (with 9 underlying currencies), 9 developed equity indices, and 13 | |
# 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, simple historical volatility is used in this code. | |
# for more info on trading strategies visit miltonfmr.com | |
from math import sqrt | |
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(self)) | |
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")) | |
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