Time Series Reversal of Momentum on Futures
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Time Series Reversal of Financial Assets
Jiadong Liu; Fotis Papailias
- Queen's University Belfast
- ?Queen's University Belfast - Queen's Management School
- King's College London
- University of London
- ?Quantf Research
- ?University of London, King's College London, Department of Management
Strategy in a nutshell
This strategy trades 24 commodity futures, 9 forex futures, 9 developed equity indexes, and 13 government bonds. Trend-following signals are generated using 12-month simple moving averages (SMA) from months T-23 to T-12. Futures with negative SMA signals but positive recent returns (“Fault Losers”) are selected and held for month T+1. Positions are rebalanced monthly, and returns are scaled by annualized ex-ante volatility, ensuring systematic risk-adjusted portfolio management.
Economic rationale
The strategy exploits short-term under-reaction and delayed over-reaction in markets. Time-series reversal arises from a security’s autocorrelation, while trend continuation and reversal interplay, reflecting behavioral patterns in asset returns and supporting systematic momentum and reversal strategies.
Backtest performance
Annualised return24.4%
Volatility20.9%
Beta0.231
Sharpe ratio1.17
Sortino ratio0.313
Maximum drawdown-26.2%
Win rate54%
Full Python code
import numpy as np
from AlgorithmImports import *
class TimeSeriesReversal(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
"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
"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 # Short history ~2007
"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_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
#"ASX_YT1", # 3 Year Commonwealth Treasury Bond Futures, Continuous Contract #1
"EUREX_FGBL1", # Euro-Bund (10Y) Futures, Continuous Contract #1
#"EUREX_FBTP1", # Long-Term Euro-BTP Futures, Continuous Contract #1 # Short history ~2010
"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
]
self.data = {}
self.lookup_period = 24*21
self.SetWarmUp(self.lookup_period)
for symbol in self.symbols:
data = self.AddData(QuantpediaFutures, symbol, Resolution.Daily)
data.SetFeeModel(CustomFeeModel())
data.SetLeverage(5)
self.data[symbol] = RollingWindow[float](self.lookup_period)
self.Schedule.On(self.DateRules.MonthStart(self.symbols[0]), self.TimeRules.At(0, 0), self.Rebalance)
def OnData(self, data):
for symbol in self.symbols:
if symbol in data and data[symbol]:
price = data[symbol].Value
if price != 0:
self.data[symbol].Add(price)
def Rebalance(self):
if self.IsWarmingUp: return
# Return sorting
returns = {}
volatility = {}
for symbol in self.symbols:
if self.data[symbol].IsReady:
if self.Securities[symbol].GetLastData() and self.Time.date() < QuantpediaFutures.get_last_update_date()[symbol]:
prices = [x for x in self.data[symbol]]
returns[symbol] = self.Return(prices)
# prices = prices[-60:]
prices = prices[:60]
volatility[symbol] = self.Volatility(prices)
if len(returns) == 0:
self.Liquidate()
return
# Return selection
long = []
short = []
half_period = int(self.lookup_period / 2)
for symbol, return_value in returns.items():
prices = [x for x in self.data[symbol]]
first_half_return = self.Return(prices[:half_period])
second_half_return = self.Return(prices[-half_period:])
if first_half_return < 0 and second_half_return > 0:
long.append(symbol)
elif first_half_return > 0 and second_half_return < 0:
short.append(symbol)
if len(long + short) == 0:
self.Liquidate()
return
# Volatility weighting
total_vol_long = sum([1 / volatility[x] for x in long if volatility[x] != 0])
total_vol_short = sum([1 / volatility[x] for x in short if volatility[x] != 0])
weight = {}
if total_vol_long != 0:
# Calculate long stocks weights
for symbol in long:
vol = volatility[symbol]
if vol != 0:
weight[symbol] = (1 / vol) / total_vol_long
if total_vol_short != 0:
# Calculate short stocks weights
for symbol in short:
vol = volatility[symbol]
if vol != 0:
weight[symbol] = (1 / vol) / total_vol_short
# Trade execution
invested = [x.Key for x in self.Portfolio if x.Value.Invested]
for symbol in invested:
if symbol not in weight:
self.Liquidate(symbol)
for symbol, w in weight.items():
self.SetHoldings(symbol, w)
def Return(self, history):
return (history[0] - history[-1]) / history[-1]
def Volatility(self, history):
prices = np.array(history)
returns = (prices[:-1]-prices[1:])/prices[1:]
return np.std(returns)
# Custom fee model.
class CustomFeeModel(FeeModel):
def GetOrderFee(self, parameters):
fee = parameters.Security.Price * parameters.Order.AbsoluteQuantity * 0.00005
return OrderFee(CashAmount(fee, "USD"))
# Quantpedia data
class QuantpediaFutures(PythonData):
_last_update_date:Dict[Symbol, datetime.date] = {}
@staticmethod
def get_last_update_date() -> Dict[Symbol, datetime.date]:
return QuantpediaFutures._last_update_date
def GetSource(self, config, date, isLiveMode):
return SubscriptionDataSource("http://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
try:
if not line[0].isdigit(): return None
split = line.split(';')
data.Time = datetime.strptime(split[0], "%d.%m.%Y") + timedelta(days=1)
data['settle'] = float(split[1])
data.Value = float(split[1])
except:
return None
if config.Symbol.Value not in QuantpediaFutures._last_update_date:
QuantpediaFutures._last_update_date[config.Symbol.Value] = datetime(1,1,1).date()
if data.Time.date() > QuantpediaFutures._last_update_date[config.Symbol.Value]:
QuantpediaFutures._last_update_date[config.Symbol.Value] = data.Time.date()
return data