Enhanced Betting Against Beta Strategy in Equities

1import numpy as np
2from AlgorithmImports import *
3import pandas as pd
4from typing import List, Dict
5class EnhancedBettingAgainstBetaStrategyEquities(QCAlgorithm):
6
7def Initialize(self):
8self.SetStartDate(2000, 1, 1)
9self.SetCash(100000)
10self.SetSecurityInitializer(lambda x: x.SetMarketPrice(self.GetLastKnownPrice(x)))
11
12# Daily price data.
13self.data:Dict[Symbol, SymbolData] = {}
14
15self.period:int = 4*12*21
16self.beta_period:int = 12*21
17self.leverage:int = 10
18self.quantile:int = 5
19self.beta_thresholds:List[float] = [0.3, 2.]
20self.exchange_codes:List[str] = ['NYS', 'NAS']	
21self.market:Symbol = self.AddEquity('SPY', Resolution.Daily).Symbol
22# Warmup market data.
23self.data[self.market] = SymbolData(self.period)
24history:DataFrame = self.History(self.market, self.period, Resolution.Daily)
25if not history.empty:
26    closes:Series = history.loc[self.market].close
27    for time, close in closes.items():
28        self.data[self.market].update(close)        
29    
30self.weight:Dict[Symbol, float] = {}
31
32self.fundamental_count:int = 1000
33self.fundamental_sorting_key = lambda x: x.DollarVolume
34self.selection_flag:bool = True
35self.Settings.MinimumOrderMarginPortfolioPercentage = 0.
36self.UniverseSettings.Resolution = Resolution.Daily
37self.AddUniverse(self.FundamentalSelectionFunction)
38self.Schedule.On(self.DateRules.MonthEnd(self.market), self.TimeRules.AfterMarketOpen(self.market), self.Selection)
39self.settings.daily_precise_end_time = False
40def OnSecuritiesChanged(self, changes: SecurityChanges) -> None:
41for security in changes.AddedSecurities:
42    security.SetFeeModel(CustomFeeModel())
43    security.SetLeverage(self.leverage)
44def FundamentalSelectionFunction(self, fundamental: List[Fundamental]) -> List[Symbol]:
45# Update the rolling window every day.
46for stock in fundamental:
47    symbol:Symbol = stock.Symbol
48    
49    # Store monthly price.
50    if symbol in self.data:
51        self.data[symbol].update(stock.AdjustedPrice)
52if not self.selection_flag:
53    return Universe.Unchanged
54selected:List[Fundamental] = [x for x in fundamental if x.HasFundamentalData and x.Market == 'usa' and x.MarketCap != 0 and 
55                              x.SecurityReference.ExchangeId in self.exchange_codes]
56if len(selected) > self.fundamental_count:
57    selected = [x for x in sorted(selected, key=self.fundamental_sorting_key, reverse=True)[:self.fundamental_count]]
58# Warmup price rolling windows.
59for stock in selected:
60    symbol:Symbol = stock.Symbol
61    if symbol in self.data:
62        continue
63    
64    self.data[symbol] = SymbolData(self.period)
65    history:DataFrame = self.History(symbol, self.period, Resolution.Daily)
66    if history.empty:
67        self.Log(f"Not enough data for {symbol} yet.")
68        continue
69    closes:Series = history.loc[symbol].close
70    for time, close in closes.items():
71        self.data[symbol].update(close)
72    
73stock_data:Dict[Symbol, StockData] = {}
74
75market_closes:np.ndarray = np.array([x for x in self.data[self.market]._price][:self.beta_period])
76market_returns:np.ndarray = (market_closes[1:] - market_closes[:-1]) / market_closes[:-1]
77
78if len(market_returns) != 0:
79    for stock in selected:
80        symbol:Symbol = stock.Symbol
81        
82        if not self.data[symbol].is_ready():
83            continue
84        # Data is ready.
85        stock_closes:np.ndarray = np.array([x for x in self.data[symbol]._price][:self.beta_period])
86        stock_returns:np.ndarray = (stock_closes[1:] - stock_closes[:-1]) / stock_closes[:-1]
87            
88        # Manual beta calc.
89        cov:np.ndarray = np.cov(market_returns, stock_returns)[0][1]
90        market_variance:float = np.std(market_returns) ** 2
91        beta:float = cov / market_variance            
92            
93        if beta >= self.beta_thresholds[0] and beta <= self.beta_thresholds[1]:
94            # Return calc.
95            ret = self.data[symbol].performance()
96            stock_data[symbol] = StockData(beta, ret, stock.MarketCap)
97
98if len(stock_data) >= self.quantile: 
99    # Value weighted return sorting.
100    total_market_cap:float = sum([x[1]._market_cap for x in stock_data.items()])
101    sorted_by_return:[List[Tuple[Symbol, StockData]]] = sorted(stock_data.items(), key = lambda x: x[1]._performance * (x[1]._market_cap / total_market_cap), reverse = True)
102    quintile:int = int(len(sorted_by_return) / self.quantile)
103    top_by_ret:List[StockData] = [x for x in sorted_by_return[:quintile]]
104    
105    sorted_by_beta:[List[Tuple[Symbol, StockData]]] = sorted(top_by_ret, key = lambda x: x[1]._beta, reverse = True)
106    
107    beta_median:float = np.median([x[1]._beta for x in sorted_by_beta])
108    
109    low_beta_stocks:List[Tuple[StockData, float]] = [(x, abs(beta_median - x[1]._beta)) for x in sorted_by_beta if x[1]._beta < beta_median]
110    high_beta_stocks:List[Tuple[StockData, float]] = [(x, abs(beta_median - x[1]._beta)) for x in sorted_by_beta if x[1]._beta > beta_median]
111    
112    # Beta diff weighting.
113    for i, portfolio in enumerate([low_beta_stocks, high_beta_stocks]):
114        total_diff:float = sum(list(map(lambda x: x[1], portfolio)))
115        for symbol_data, diff in portfolio:
116            self.weight[symbol_data[0]] = ((-1)**i) * (diff / total_diff)
117
118return [x[0] for x in self.weight.items()]
119
120def OnData(self, data: Slice) -> None:
121if not self.selection_flag:
122    return
123self.selection_flag = False
124
125portfolio:List[PortfolioTarget] = [PortfolioTarget(symbol, w) for symbol, w in self.weight.items() if symbol in data and data[symbol]]
126self.SetHoldings(portfolio, True)
127
128self.weight.clear()
129
130def Selection(self) -> None:
131self.selection_flag = True
132class StockData():
133def __init__(self, beta:float, performance:float, market_cap:float):
134self._beta:float = beta
135self._performance:float = performance
136self._market_cap:float = market_cap
137class SymbolData():
138def __init__(self, period:int):
139self._price:RollingWindow = RollingWindow[float](period)
140
141def update(self, value:float) -> None:
142self._price.Add(value)
143
144def is_ready(self) -> bool:
145return self._price.IsReady
146
147def performance(self) -> float:
148return (self._price[0] / self._price[self._price.Count - 1] - 1)
149# Custom fee model.
150class CustomFeeModel(FeeModel):
151def GetOrderFee(self, parameters):
152fee = parameters.Security.Price * parameters.Order.AbsoluteQuantity * 0.00005
153return OrderFee(CashAmount(fee, "USD"))