# 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
from pandas.core.frame import DataFrame
from typing import List, Dict

class BettingAgainstBetaFactorinStocks(QCAlgorithm):

    def Initialize(self):
        self.SetStartDate(2000, 1, 1)
        self.SetCash(100000)

        # daily price data
        self.data:Dict[Symbol, RollingWindow] = {}
        self.period:int = 12 * 21

        self.symbol:Symbol = self.AddEquity('SPY', Resolution.Daily).Symbol
        self.data[self.symbol] = RollingWindow[float](self.period)
        
        self.long:List[Symbol] = []
        self.short:List[Symbol] = []
        self.long_lvg:float = 1.   # leverage for long portfolio calculated from average beta
        self.short_lvg:float = 1.  # leverage for short portfolio calculated from average beta
        self.leverage_cap:float = 2.
        
        self.coarse_count:int = 1000
        self.quantile:int = 10
        self.min_share_price:float = 5.
        
        self.selection_flag:bool = False
        self.UniverseSettings.Resolution = Resolution.Daily
        self.AddUniverse(self.FundamentalSelectionFunction)
        self.Schedule.On(self.DateRules.MonthStart(self.symbol), self.TimeRules.AfterMarketOpen(self.symbol), self.Selection)

        self.settings.daily_precise_end_time = False

    def OnSecuritiesChanged(self, changes: SecurityChanges) -> None:
        for security in changes.AddedSecurities:
            security.SetFeeModel(CustomFeeModel())
            security.SetLeverage(self.leverage_cap*3)
            
    def FundamentalSelectionFunction(self, fundamental: List[Fundamental]) -> List[Symbol]:
        # update the rolling window every day
        for stock in fundamental:
            symbol: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:List[Symbol] = [x.Symbol
            for x in sorted([x for x in fundamental if x.HasFundamentalData and x.Market == 'usa' and x.Price >= self.min_share_price and x.MarketCap != 0],
                key = lambda x: x.DollarVolume, reverse = True)[:self.coarse_count]]
        
        rebalance:bool = False
        if self.data[self.symbol].IsReady:
            rebalance = True

        beta:Dict[Symbol, float] = {}

        for symbol in selected:
            # warmup price rolling windows
            if symbol not in self.data:
                self.data[symbol] = RollingWindow[float](self.period)
                history:DataFrame = self.History(symbol, self.period, Resolution.Daily)
                if history.empty:
                    self.Log(f"Not enough data for {symbol} yet")
                    continue
                closes:pd.Series = history.loc[symbol].close
                for time, close in closes.items():
                    self.data[symbol].Add(close)
            
            if rebalance:
                if self.data[symbol].IsReady:
                    market_closes:np.ndarray = np.array([x for x in self.data[self.symbol]])
                    stock_closes:np.ndarray = np.array([x for x in self.data[symbol]])
                    
                    market_returns:np.ndarray = (market_closes[:-1] - market_closes[1:]) / market_closes[1:]
                    stock_returns:np.ndarray = (stock_closes[:-1] - stock_closes[1:]) / stock_closes[1:]
                    
                    cov:float = np.cov(stock_returns[::-1], market_returns[::-1])[0][1]
                    market_variance:float = np.var(market_returns)
                    beta[symbol] = cov / market_variance

        if len(beta) >= self.quantile:
            # sort by beta
            sorted_by_beta:List = sorted(beta.items(), key = lambda x: x[1], reverse=True)
            quantile:int = int(len(sorted_by_beta) / self.quantile)
            self.long = [x for x in sorted_by_beta[-quantile:]]
            self.short = [x for x in sorted_by_beta[:quantile]]
            
            # create zero-beta portfolio
            long_mean_beta:float = np.mean([x[1] for x in self.long])
            short_mean_beta:float = 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]
            
            # cap leverage
            self.long_lvg = min(self.leverage_cap, abs(1. / long_mean_beta))
            self.short_lvg = min(self.leverage_cap, abs(1. / short_mean_beta))

        return self.long + self.short
    
    def OnData(self, data: Slice) -> None:
        if not self.selection_flag:
            return
        self.selection_flag = False
        
        # trade execution
        stocks_invested:List[Symbol] = [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:int = len(self.long)
        short_len:int = len(self.short)
        
        for symbol in self.long:
            if symbol in data and data[symbol]:
                self.SetHoldings(symbol, (1 / long_len) * self.long_lvg)

        for symbol in self.short:
            if symbol in data and data[symbol]:
                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) -> None:
        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"))