期货动量的时间序列反转

“该策略基于简单移动平均线（SMA）和回报趋势选择“故障输家”，每月重新平衡，并使用年化波动率缩放回报，系统投资组合管理的临界值为40%。”

资产类别: 差价合约、期货 | 地区: 全球 | 周期:
每月 | 市场: 债券、大宗商品、外汇、股票 | 关键词: 时间序列、反转动量

I. 策略概要

投资策略包括24种商品期货、9种外汇期货、9种发达股票指数和13种政府债券。计算月度回报，并使用T-23至T-12个月的简单移动平均线（SMA）确定趋势跟踪信号。选择SMA信号为负但T-11至T个月回报为正的期货（“故障输家”），并在T+1个月持有。生成月度交易信号，并重新平衡头寸规模。使用年化事前波动率缩放回报，年波动率的临界值为40%，以确保系统投资组合管理。

II. 策略合理性

动量和反转的合理性与许多著名的行为理论相关。其背后的原理与短期反应不足和延迟过度反应有关。时间序列反转是由证券自身的时间序列自相关而不是横截面相关引起的。人们还认为，时间序列延续和时间序列反转之间存在某种联系。

III. 来源论文

Time Series Reversal of Financial Assets [点击查看论文]

• 刘佳东 和 福提斯·帕派利亚斯，贝尔法斯特女王大学 – 女王管理学院，伦敦国王学院 – 国王商学院；Knot Analytics 有限公司

<摘要>

本文实证研究了时间序列背景下趋势跟踪信号形成后的反转模式。这种反转模式在统计学上是显著的，通常发生在趋势跟踪信号形成后的12至24个月之间。使用55种流动性期货的投资范围，我们发现趋势跟踪投资组合中具有卖出信号的工具（“输家”）促成了这种类型的反转，即使它们的利润没有实现。趋势跟踪投资组合中具有买入信号的工具（“赢家”）的贡献要小得多。基于回报延续和反转的双重排序投资策略产生的投资组合收益明显高于相应的趋势跟踪策略。

IV. 回测表现

年化回报	24.4%
波动率	20.9%
β值	0.231
夏普比率	1.17
索提诺比率	0.313
最大回撤	-26.2%
胜率	54%

V. 完整的 Python 代码

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