Multi-Asset Momentum Strategy with Volatility-Adjusted Positioning
Log in to collectStrategy in a nutshell
The investment universe consists of 24 commodity futures, 12 cross-currency pairs (with nine underlying currencies), nine 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
Economic rationale
Academic research states that the time-series momentum effect is consistent with behavioral theories of investors’ initial under-reaction and delayed over-reaction applied to information dissemination.
III. SOURCE PAPER
Time Series Momentum [Click to Open PDF]
Tobias J. Moskowitz, University of Chicago Booth School of Business and NBER
Yao Hua Ooi, AQR Capital Management
Lasse Heje Pedersen, New York University, Copenhagen Business School
We document significant ‘‘time series momentum’’ in equity index, currency, commodity, and bond futures for each of the 58 liquid instruments we consider. We find
persistence in returns for one to 12 months that partially reverses over longer horizons,
consistent with sentiment theories of initial under-reaction and delayed over-reaction.
A diversified portfolio of time series momentum strategies across all asset classes
delivers substantial abnormal returns with little exposure to standard asset pricing
factors and performs best during extreme markets. Examining the trading activities of
speculators and hedgers, we find that speculators profit from time series momentum at
the expense of hedgers
Backtest performance
Annualised return20.7%
Volatility15.74%
Beta-0.1
Sharpe ratio0.427
Sortino ratio0.511
Maximum drawdown28.4%
Win rate55%
Full Python code
from math import sqrt
from AlgoLib import *
import numpy as np
import pandas as pd
class TimeSeriesMomentum(XXX):
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"))