Residual Alpha Momentum Strategy on Large-Cap US Stocks

1import numpy as np
2from AlgoLib import *
3import statsmodels.api as sm
4
5class ResidualMomentumFactor(XXX):
6
7def Initialize(self):
8self.SetStartDate(2000, 1, 1)
9self.SetCash(100000)
10
11# Monthly price data.
12self.data:Dict[Symbol, RollingWindow] = {}
13self.period:int = 37
14
15# Warmup market monthly data.
16self.symbol:Symbol = self.AddEquity('SPY', Resolution.Daily).Symbol
17self.data[self.symbol] = RollingWindow[float](self.period)
18
19history = self.History(self.symbol, self.period * 21, Resolution.Daily)
20if history.empty:
21    self.Log(f"Not enough data for {self.symbol} yet.")
22else:    
23    closes = history.loc[self.symbol].close
24    closes_len = len(closes.keys())
25    # Find monthly closes.
26    for index, time_close in enumerate(closes.items()):
27        # index out of bounds check.
28        if index + 1 < closes_len:
29            date_month = time_close[0].date().month
30            next_date_month = closes.keys()[index + 1].month
31        
32            # Found last day of month.
33            if date_month != next_date_month:
34                self.data[self.symbol].Add(time_close[1])        
35
36# Factors.
37self.size_factor_symbols:List[Symbol] = []                                   # Symbol,long_flag tuple.
38self.size_factor_vector:RollingWindow = RollingWindow[float](self.period - 1) # Monthly performance.
39
40self.value_factor_symbols:List[Symbol] = []
41self.value_factor_vector:RollingWindow = RollingWindow[float](self.period - 1)
42
43# Monthly residual returns for each stock.
44self.residual_return:Dict[Symbol, RollingWindow] = {}
45self.residual_momentum_period:int = 12
46
47self.long:List[Symbol] = []
48self.short:List[Symbol] = []
49
50self.fundamental_count:int = 500
51self.fundamental_sorting_key = lambda x: x.DollarVolume
52
53self.factor_quantile:int = 5
54self.quantile:int = 10
55self.leverage:int = 3
56
57self.last_month:int = -1
58self.selection_flag:bool = False
59self.UniverseSettings.Resolution = Resolution.Daily
60self.AddUniverse(self.FundamentalSelectionFunction)
61self.Settings.MinimumOrderMarginPortfolioPercentage = 0
62
63def OnSecuritiesChanged(self, changes: SecurityChanges) -> None:
64for security in changes.AddedSecurities:
65    security.SetLeverage(self.leverage)
66    security.SetFeeModel(CustomFeeModel())
67
68def FundamentalSelectionFunction(self, fundamental: List[Fundamental]) -> List[Symbol]:
69if not self.selection_flag:
70    return Universe.Unchanged
71
72# Update the rolling window every month.
73for stock in fundamental:
74    symbol = stock.Symbol
75    
76    # Store monthly market price.
77    if symbol == self.symbol:
78        self.data[self.symbol].Add(stock.AdjustedPrice)
79    else:
80        # Store monthly stock price.
81        if symbol in self.data:
82            self.data[symbol].Add(stock.AdjustedPrice)
83
84selected:List[Fundamental] = [x for x in fundamental if x.HasFundamentalData and x.Market == 'usa' and x.MarketCap != 0 and x.CompanyReference.IsREIT == 0 and \
85    ((x.SecurityReference.ExchangeId == "NYS") or (x.SecurityReference.ExchangeId == "NAS") or (x.SecurityReference.ExchangeId == "ASE"))
86    ]
87
88if len(selected) > self.fundamental_count:
89    selected = [x for x in sorted(selected, key=self.fundamental_sorting_key, reverse=True)[:self.fundamental_count]]
90    
91# Warmup price rolling windows.
92for stock in selected:
93    symbol:Symbol = stock.Symbol
94    
95    if symbol in self.data: continue
96
97    self.data[symbol] = RollingWindow[float](self.period)
98    history = self.History(symbol, self.period * 21, Resolution.Daily)
99    if history.empty:
100        self.Log(f"Not enough data for {symbol} yet.")
101        continue
102    closes = history.loc[symbol].close
103    
104    closes_len = len(closes.keys())
105    # Find monthly closes.
106    for index, time_close in enumerate(closes.items()):
107        # index out of bounds check.
108        if index + 1 < closes_len:
109            date_month = time_close[0].date().month
110            next_date_month = closes.keys()[index + 1].month
111        
112            # Found last day of month.
113            if date_month != next_date_month:
114                self.data[symbol].Add(time_close[1])
115    
116selected = [x for x in selected if self.data[x.Symbol].IsReady]
117
118if len(selected) == 0:
119    return Universe.Unchanged
120
121# Size factor.
122sorted_by_market_cap:List[Fundamental] = sorted(selected, key=lambda x: x.MarketCap, reverse=True)
123quantile:int = int(len(sorted_by_market_cap) / self.factor_quantile)
124size_factor_long:List[Tuple] = [ (i.Symbol, True) for i in sorted_by_market_cap[-quantile:]]
125size_factor_short:List[Tuple] = [(i.Symbol, False) for i in sorted_by_market_cap[:quantile]]
126# Calculate last month's performance.
127if len(self.size_factor_symbols) != 0:
128    monthly_return:float = self.CalculateFactorPerformance(self.data, self.size_factor_symbols)
129    if monthly_return != 0:
130        self.size_factor_vector.Add(monthly_return)
131# Store new factor symbols.
132self.size_factor_symbols = size_factor_long + size_factor_short
133        
134# Value factor.
135sorted_by_pb:List[Fundamental] = sorted(selected, key = lambda x:(x.ValuationRatios.PBRatio), reverse=False)
136quantile:int = int(len(sorted_by_pb) / self.factor_quantile)
137value_factor_long:List[Tuple] = [(i.Symbol, True) for i in sorted_by_pb[:quantile]]
138value_factor_short:List[Tuple] = [(i.Symbol, False) for i in sorted_by_pb[-quantile:]]
139# Calculate last month's performance.
140if len(self.value_factor_symbols) != 0:
141    monthly_return:float = self.CalculateFactorPerformance(self.data, self.value_factor_symbols)
142    if monthly_return != 0:
143        self.value_factor_vector.Add(monthly_return)
144# Store new factor symbols.
145self.value_factor_symbols = value_factor_long + value_factor_short
146    
147# Every factor vector is ready.
148if self.size_factor_vector.IsReady and self.value_factor_vector.IsReady:
149    
150    # Market factor.
151    if self.symbol in self.data and self.data[self.symbol].IsReady:
152        market_factor_prices:np.ndarray = np.array([x for x in self.data[self.symbol]])
153        market_factor:np.ndarray = (market_factor_prices[:-1] - market_factor_prices[1:]) / market_factor_prices[1:]
154    
155        if len(market_factor) == (self.period - 1): 
156            # Residual return calc.
157            x:List[List[float]] = [
158                list(market_factor), 
159                list(self.size_factor_vector), 
160                list(self.value_factor_vector)
161            ]
162            
163            standardized_residual_momentum:Dict[Symbol, float] = {}
164            for stock in sorted_by_market_cap:
165                symbol:Symbol = stock.Symbol
166                monthly_prices:np.ndarray = np.array([x for x in self.data[symbol]])
167                monthly_returns:np.ndarray = (monthly_prices[:-1] - monthly_prices[1:]) / monthly_prices[1:]
168                
169                regression_model = self.MultipleLinearRegression(x, monthly_returns)
170                alpha:float = regression_model.params[0]
171                
172                if symbol not in self.residual_return:
173                    self.residual_return[symbol] = RollingWindow[float](self.residual_momentum_period)
174                self.residual_return[symbol].Add(alpha)
175                
176                # Residual data for 12 months is ready.
177                if self.residual_return[symbol].IsReady:
178                    residual_returns:List[float] = [x for x in self.residual_return[symbol]]
179                    standardized_residual_momentum[symbol] = sum(residual_returns) / np.std(residual_returns)
180
181            sorted_by_resid_momentum:List[Symbol] = sorted(standardized_residual_momentum, key=standardized_residual_momentum.get , reverse=True)
182            quantile:int = int(len(sorted_by_resid_momentum) / self.quantile)
183            self.long = sorted_by_resid_momentum[:quantile]
184            self.short = sorted_by_resid_momentum[-quantile:]
185 
186return self.long + self.short
187
188def OnData(self, data: Slice) -> None:
189if self.Time.month != self.last_month:
190    self.last_month = self.Time.month
191    self.selection_flag = True
192    return
193
194if not self.selection_flag:
195    return
196self.selection_flag = False
197
198# Trade execution.
199targets:List[PortfolioTarget] = []
200for i, portfolio in enumerate([self.long, self.short]):
201    for symbol in portfolio:
202        if symbol in data and data[symbol]:
203            targets.append(PortfolioTarget(symbol, ((-1) ** i) / len(portfolio)))
204
205self.SetHoldings(targets, True)
206
207self.long.clear()
208self.short.clear()
209
210def CalculateFactorPerformance(self, data, factor_symbols) -> float:
211monthly_return = 0
212if len(factor_symbols) != 0:
213    for symbol, long_flag in factor_symbols:
214        if symbol in data and data[symbol].Count >= 2:
215            closes = [x for x in data[symbol]]
216            if long_flag:
217                monthly_return += ((closes[0] / closes[1] - 1) / len(factor_symbols))
218            else:
219                monthly_return -= ((closes[0] / closes[1] - 1) / len(factor_symbols))
220
221return monthly_return
222
223def MultipleLinearRegression(self, x, y):
224x = np.array(x).T
225x = sm.add_constant(x)
226result = sm.OLS(endog=y, exog=x).fit()
227return result
228
229# Custom fee model.
230class CustomFeeModel(FeeModel):
231def GetOrderFee(self, parameters):
232fee = parameters.Security.Price * parameters.Order.AbsoluteQuantity * 0.00005
233return OrderFee(CashAmount(fee, "USD"))