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betting-against-beta-factor-in-stocks.py
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betting-against-beta-factor-in-stocks.py
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# https://quantpedia.com/strategies/betting-against-beta-factor-in-stocks/
#
# The investment universe consists of all stocks from the CRSP database. The beta for each stock is calculated with respect to the MSCI US Equity Index using a 1-year
# rolling window. Stocks are then ranked in ascending order on the basis of their estimated beta. The ranked stocks are assigned to one of two portfolios: low beta and
# high beta. Securities are weighted by the ranked betas, and portfolios are rebalanced every calendar month. Both portfolios are rescaled to have a beta of one at portfolio
# formation. The “Betting-Against-Beta” is the zero-cost zero-beta portfolio that is long on the low-beta portfolio and short on the high-beta portfolio. There are a lot of
# simple modifications (like going long on the bottom beta decile and short on the top beta decile), which could probably improve the strategy’s performance.
#
# QC implementation changes:
# - The investment universe consists of 1000 most liquid US stocks with price > 5$.
from scipy import stats
from AlgorithmImports import *
import numpy as np
class BettingAgainstBetaFactorinStocks(QCAlgorithm):
def Initialize(self):
self.SetStartDate(2000, 1, 1)
self.SetCash(100000)
# Daily price data.
self.data = {}
self.period = 12 * 21
self.symbol = self.AddEquity('SPY', Resolution.Daily).Symbol
self.data[self.symbol] = RollingWindow[float](self.period)
self.weight = {}
self.long = []
self.short = []
self.long_lvg = 1 # leverage for long portfolio calculated from average beta
self.short_lvg = 1 # leverage for short portfolio calculated from average beta
self.leverage_cap = 2
self.coarse_count = 1000
self.selection_flag = False
self.UniverseSettings.Resolution = Resolution.Daily
self.AddUniverse(self.CoarseSelectionFunction, self.FineSelectionFunction)
self.Schedule.On(self.DateRules.MonthStart(self.symbol), self.TimeRules.AfterMarketOpen(self.symbol), self.Selection)
def OnSecuritiesChanged(self, changes):
for security in changes.AddedSecurities:
security.SetFeeModel(CustomFeeModel())
security.SetLeverage(self.leverage_cap*3)
def CoarseSelectionFunction(self, coarse):
# Update the rolling window every day.
for stock in coarse:
symbol = stock.Symbol
if symbol in self.data:
# Store daily price.
self.data[symbol].Add(stock.AdjustedPrice)
# Selection once a month.
if not self.selection_flag:
return Universe.Unchanged
# selected = [x.Symbol for x in coarse if x.HasFundamentalData and x.Market == 'usa' and x.Price > 5]
selected = [x.Symbol
for x in sorted([x for x in coarse if x.HasFundamentalData and x.Market == 'usa' and x.Price > 5],
key = lambda x: x.DollarVolume, reverse = True)[:self.coarse_count]]
# Warmup price rolling windows.
for symbol in selected:
if symbol in self.data:
continue
self.data[symbol] = RollingWindow[float](self.period)
history = self.History(symbol, self.period, Resolution.Daily)
if history.empty:
self.Log(f"Not enough data for {symbol} yet")
continue
closes = history.loc[symbol].close
for time, close in closes.iteritems():
self.data[symbol].Add(close)
return [x for x in selected if self.data[x].IsReady]
def FineSelectionFunction(self, fine):
fine = [x for x in fine if x.MarketCap != 0]
# if len(fine) > self.coarse_count:
# sorted_by_market_cap = sorted(fine, key = lambda x: x.MarketCap, reverse=True)
# top_by_market_cap = sorted_by_market_cap[:self.coarse_count]
# else:
# top_by_market_cap = fine
beta = {}
if not self.data[self.symbol].IsReady: return []
for stock in fine:
symbol = stock.Symbol
market_closes = np.array([x for x in self.data[self.symbol]])
stock_closes = np.array([x for x in self.data[symbol]])
market_returns = (market_closes[:-1] - market_closes[1:]) / market_closes[1:]
stock_returns = (stock_closes[:-1] - stock_closes[1:]) / stock_closes[1:]
cov = np.cov(stock_returns[::-1], market_returns[::-1])[0][1]
market_variance = np.var(market_returns)
beta[symbol] = cov / market_variance
# beta_, intercept, r_value, p_value, std_err = stats.linregress(market_returns[::-1], stock_returns[::-1])
# beta[symbol] = beta_
if len(beta) >= 10:
# sort by beta
sorted_by_beta = sorted(beta.items(), key = lambda x:x[1], reverse=True)
decile = int(len(sorted_by_beta) / 10)
self.long = [x for x in sorted_by_beta[-decile:]]
self.short = [x for x in sorted_by_beta[:decile]]
# create zero-beta portfolio
long_mean_beta = np.mean([x[1] for x in self.long])
short_mean_beta = np.mean([x[1] for x in self.short])
self.long = [x[0] for x in self.long]
self.short = [x[0] for x in self.short]
self.long_lvg = 1/long_mean_beta
self.short_lvg = 1/short_mean_beta
# cap leverage
if self.long_lvg <= 0:
self.long_lvg = self.leverage_cap
else:
self.long_lvg = min(self.leverage_cap, self.long_lvg)
if self.short_lvg <= 0:
self.short_lvg = self.leverage_cap
else:
self.short_lvg = min(self.leverage_cap, self.short_lvg)
return self.long + self.short
def OnData(self, data):
if not self.selection_flag:
return
self.selection_flag = False
# Trade execution.
stocks_invested = [x.Key for x in self.Portfolio if x.Value.Invested]
for symbol in stocks_invested:
if symbol not in self.long + self.short:
self.Liquidate(symbol)
long_len = len(self.long)
short_len = len(self.short)
for symbol in self.long:
self.SetHoldings(symbol, (1/long_len)*self.long_lvg)
for symbol in self.short:
self.SetHoldings(symbol, -(1/short_len)*self.short_lvg)
self.long.clear()
self.short.clear()
self.long_lvg = 1
self.short_lvg = 1
def Selection(self):
self.selection_flag = True
# Custom fee model.
class CustomFeeModel(FeeModel):
def GetOrderFee(self, parameters):
fee = parameters.Security.Price * parameters.Order.AbsoluteQuantity * 0.00005
return OrderFee(CashAmount(fee, "USD"))