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趋势追随与动量结合在商品期货中的应用

学术论文

Trend Following, Risk Parity and Momentum in Commodity Futures

作者托马斯

机构

?克莱尔、西顿、史密斯，伦敦城市大学商学院，伦敦城市大学贝叶斯商学院，伦敦城市大学商学院，约克大学经济与相关研究系
?澳大利亚国立大学（ANU）应用宏观经济分析中心（CAMA）

论文摘要

我们证明，将动量策略与趋势跟随策略结合应用于单个商品期货，可以构建出提供有吸引力的风险调整收益的投资组合，其表现优于单纯的动量策略。当我们将这些收益暴露于广泛的系统性风险来源时，发现稳健的阿尔法仍然存在。实验表明，采用风险平价投资组合加权对结果的影响有限，尤其有利于多空策略；相比之下，在风险调整收益和降低下行风险方面，趋势跟随方法的边际影响远远超过动量策略和风险平价调整。总体而言，该策略为商品期货投资提供了一种有吸引力的方法，并强调了趋势跟随策略在商品期货投资中的重要性。

论文链接https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2126813

策略概要

该策略使用道琼斯-UBS 大宗商品超额回报指数，涵盖 28 种大宗商品，并通过相应的期货进行交易。每月根据过去 12 个月的表现对大宗商品进行四分位排序。投资组合包括表现最好的（赢家）和表现最差的（输家）大宗商品，并采用风险平价方法进行加权，权重与其 60 天波动率成反比。此外，应用趋势跟随过滤器：大宗商品需高于其 6 个月简单移动平均线才能被视为赢家，或低于该均线才能被视为输家。投资者对符合筛选标准的赢家做多，对输家做空，从而构建一个平衡且基于表现的投资组合，同时实现系统性风险管理。

策略合理性

学术研究对趋势跟随策略的历史成功提出了多种解释，包括投资者对新闻的反应不足以及羊群行为。动量效应通常被归因于投资者的非理性行为，因为他们未能完全将新信息纳入交易价格。此外，动量投资者可能利用其他市场参与者的行为偏差（如羊群效应、过度反应、反应不足和确认偏误），以把握可预测的价格趋势并从中获利。

回测表现

波动率19.33%

夏普比率0.76

索提诺比率0.089

最大回撤-31.87%

胜率55%

完整 Python 代码

import numpy as np
from AlgorithmImports import *
class TrendfollowingwithMomentum(QCAlgorithm):
def Initialize(self):
 self.SetStartDate(1991, 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_DA1",  # Class III Milk Futures
     "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
 ]
 self.winners = []
 self.losers = []
 self.data = {}
 self.period = 12*21
 self.SetWarmUp(self.period)
 
 for symbol in self.symbols:
     data = self.AddData(QuantpediaFutures, symbol, Resolution.Daily)
     data.SetLeverage(10)
     data.SetFeeModel(CustomFeeModel())
     
     ma = self.SMA(symbol, 6*21, Resolution.Daily)
     self.data[symbol] = SymbolData(symbol, 60, self.period, ma)
 
 self.rebalance_flag: bool = False
 self.Schedule.On(self.DateRules.MonthEnd(self.symbols[0]), self.TimeRules.At(0, 0), self.Rebalance)

def OnData(self, data):
 for symbol, symbol_data in self.data.items():
     if self.securities[symbol].get_last_data() and self.time.date() > QuantpediaFutures.get_last_update_date()[symbol]:
         self.liquidate(symbol)
         symbol_data.History.reset()
         continue
     symbol_obj = self.Symbol(symbol)
     if symbol_obj in data.Keys:
         if data[symbol_obj]:
             price = data[symbol_obj].Value
             if price != 0:
                 self.data[symbol].Update(price)
 
 if not self.rebalance_flag:
     return
 self.rebalance_flag = False
 targets: List[PortfolioTarget] = []
 for i, portfolio in enumerate([self.winners, self.losers]):
     for symbol_data in portfolio:
         if symbol_data[1].Weight != 0:
             if symbol_data[0] in data and data[symbol_data[0]]:
                 targets.append(PortfolioTarget(symbol_data[0], ((-1) ** i) * symbol_data[1].Weight))
 self.SetHoldings(targets, True)
 self.winners.clear()
 self.losers.clear()
def Rebalance(self):
 # Return sorting
 return_values = []
 for data in self.data.items():
     if data[1].IsReady():
         return_values.append(data[1].Return())
 
 if len(return_values) == 0: return

 high_percentile = np.percentile(return_values, 75)
 low_percentile = np.percentile(return_values, 25)
 winners_by_ret = list(data for data in self.data.items() if data[1].IsReady() and data[1].Return() > high_percentile)
 losers_by_ret = list(data for data in self.data.items() if data[1].IsReady() and data[1].Return() < low_percentile)
 
 # Weighting
 total_vol = sum((1.0/data[1].Volatility()) for data in winners_by_ret if data[1].IsReady()) + sum((1.0/data[1].Volatility()) for data in losers_by_ret if data[1].IsReady())
 for data in winners_by_ret + losers_by_ret:
     if data[1].IsReady():
         vol = data[1].Volatility()
         data[1].Weight = (1.0 / vol) / total_vol
 # Trend sorting
 self.winners = list(data for data in winners_by_ret if data[1].Price > data[1].MA.Current.Value)
 self.losers = list(data for data in losers_by_ret if data[1].Price < data[1].MA.Current.Value)
 self.rebalance_flag = True
class SymbolData:
def __init__(self, symbol, volatility_lookback, return_lookback, ma):
 self.Symbol = symbol
 self.History = RollingWindow[float](return_lookback)
 self.Price = 0.0
 self.MA = ma
 self.Weight = 0.0
 self.Volatility_lookback = volatility_lookback
def IsReady(self) -> bool:
 return self.History.IsReady
     
def Update(self, value: float):
 self.Price = value
 self.History.Add(float(value))

def Return(self) -> float:
 prices = [x for x in self.History]
 return prices[0] / prices[-1] - 1

def Volatility(self) -> float:
 prices = np.array([x for x in self.History])[-self.Volatility_lookback:]
 returns = prices[:-1] / prices[1:] - 1
 return np.std(returns) * np.sqrt(252)

# Quantpedia data.
# NOTE: IMPORTANT: Data order must be ascending (datewise)
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("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])
 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
# Custom fee model.
class CustomFeeModel(FeeModel):
def GetOrderFee(self, parameters):
 fee = parameters.Security.Price * parameters.Order.AbsoluteQuantity * 0.00005
 return OrderFee(CashAmount(fee, "USD"))