Overall Statistics
Total Trades
Average Win
Average Loss
Compounding Annual Return
Net Profit
Sharpe Ratio
Probabilistic Sharpe Ratio
Loss Rate
Win Rate
Profit-Loss Ratio
Annual Standard Deviation
Annual Variance
Information Ratio
Tracking Error
Treynor Ratio
Total Fees
Estimated Strategy Capacity
Lowest Capacity Asset
from Alphas.EmaCrossAlphaModel import EmaCrossAlphaModel
from Alphas.MacdAlphaModel import MacdAlphaModel
from Alphas.RsiAlphaModel import RsiAlphaModel
from Execution.VolumeWeightedAveragePriceExecutionModel import VolumeWeightedAveragePriceExecutionModel
from Portfolio.BlackLittermanOptimizationPortfolioConstructionModel import BlackLittermanOptimizationPortfolioConstructionModel
from Risk.MaximumDrawdownPercentPerSecurity import MaximumDrawdownPercentPerSecurity

#For BT 1 ONLY
from BuyAndHoldAlphaCreation import BuyAndHoldAlphaCreationModel

from LiquidGrowthUniverse import SMIDGrowth

from ManualInputs import ManualInputs

Purpose of this algo is to learn how to consolidate alphas
Thesis: using a combination of EMACross, MACD and RSI to generate alpha
Optimized using the black - litterman optimization model
First BT is using a buy and hold model to test the isolated optimizer.

5.18.21: Look into why the algo is not trading, theres no trading logic.
This logic should be located in the optimizer. 
There is a disconnect between insights from alpha and the port constructor.

class MeasuredRedAnt(QCAlgorithm):

    def Initialize(self):
        self.SetStartDate(2020, 11, 17)  # Set Start Date
        self.SetEndDate(2020, 11, 23)  # Set Start Date
        self.SetCash(100000)  # Set Strategy Cash
        # self.AddEquity("SPY", Resolution.Minute)
        #Create an instance of our LiquidValueUniverseSelectionModel and set to hourly resolution
        self.UniverseSettings.Resolution = Resolution.Minute
        self.UniverseSettings.FillForward = False
        self.UniverseSettings.DataNormalizationMode = DataNormalizationMode.Raw
        # self.AddAlpha(EmaCrossAlphaModel(50, 200, Resolution.Minute))

        # self.AddAlpha(MacdAlphaModel(12, 26, 9, MovingAverageType.Simple, Resolution.Daily))

        # self.AddAlpha(RsiAlphaModel(60, Resolution.Minute))




        ### Charts --------------------------------------------------------------------------------------------------
        # let's plot the series of daily total portfolio exposure %
        portfolioExposurePlot = Chart('Chart Total Portfolio Exposure %')
        portfolioExposurePlot.AddSeries(Series('Daily Portfolio Exposure %', SeriesType.Line, ''))
        # let's plot the series of daily number of open longs and shorts
        nLongShortPlot = Chart('Chart Number Of Longs/Shorts')
        nLongShortPlot.AddSeries(Series('Daily N Longs', SeriesType.Line, ''))
        nLongShortPlot.AddSeries(Series('Daily N Shorts', SeriesType.Line, ''))
        # let's plot the series of drawdown % from the most recent high
        drawdownPlot = Chart('Chart Drawdown %')
        drawdownPlot.AddSeries(Series('Drawdown %', SeriesType.Line, '%'))

    def OnData(self, data):
        '''OnData event is the primary entry point for your algorithm. Each new data point will be pumped in here.
                data: Slice object keyed by symbol containing the stock data

        # if not self.Portfolio.Invested:
        #    self.SetHoldings("SPY", 1)

    def security_initializer(self, security):
            Initialize the security with adjusted prices
            security: Security which characteristics we want to change
        #security.SetMarketPrice = self.GetLastKnownPrice(security)
        if security.Type == SecurityType.Option:

    def OnOrderEvent(self, OrderEvent):
        #Event when the order is filled. Debug log the order fill. :OrderEvent:```

        if OrderEvent.FillQuantity == 0:

        fetched = self.Transactions.GetOrderById(OrderEvent.OrderId)

        self.Debug("{} was filled. Symbol: {}. Quantity: {}. Direction: {}"
from clr import AddReference

from System import *
from QuantConnect import *
from QuantConnect.Algorithm import *
from QuantConnect.Algorithm.Framework import *
from QuantConnect.Algorithm.Framework.Alphas import AlphaModel, Insight, InsightType, InsightDirection

class BuyAndHoldAlphaCreationModel(AlphaModel):
        This Alpha model creates InsightDirection.Up (to go Long) for a duration of 1 day, every day for all active securities in our Universe
        The important thing to understand here is the concept of Insight:
            - A prediction about the future of the security, indicating an expected Up, Down or Flat move
            - This prediction has an expiration time/date, meaning we think the insight holds for some amount of time
            - In the case of a Buy and Hold strategy, we are just updating every day the Up prediction for another extra day
            - In other words, every day we are making the conscious decision of staying invested in the security one more day

    def __init__(self, resolution = Resolution.Daily):
        self.insightExpiry = Time.Multiply(Extensions.ToTimeSpan(resolution), 0.25) # insight duration
        self.insightDirection = InsightDirection.Up # insight direction
        self.securities = [] # list to store securities to consider
    def Update(self, algorithm, data):

        insights = [] # list to store the new insights to be created
        # loop through securities and generate insights
        for security in self.securities:
            # check if there's new data for the security or we're already invested
            # if there's no new data but we're invested, we keep updating the insight since we don't really need to place orders
            if data.ContainsKey(security.Symbol) or algorithm.Portfolio[security.Symbol].Invested:
                # append the insights list with the prediction for each symbol
                insights.append(Insight.Price(security.Symbol, self.insightExpiry, self.insightDirection, .1, None, 'BuyAndHoldAlphaCreationModel', None))
                algorithm.Log('(Alpha) excluding this security due to missing data: ' + str(security.Symbol.Value))
        return insights
    def OnSecuritiesChanged(self, algorithm, changes):
            Event fired each time the we add/remove securities from the data feed
            algorithm: The algorithm instance that experienced the change in securities
            changes: The security additions and removals from the algorithm
        # add new securities
        for added in changes.AddedSecurities:

        # remove securities
        for removed in changes.RemovedSecurities:
            if removed in self.securities:
from clr import AddReference

from datetime import timedelta
from QuantConnect.Data.UniverseSelection import *
from Selection.FundamentalUniverseSelectionModel import FundamentalUniverseSelectionModel

from HelperFunctions import GetFundamentalDataDict, MakeCalculations, GetLongShortLists, UpdatePlots
#from RiskManagement import *
from ManualInputs import ManualInputs

import pandas as pd
import numpy as np

# Define the Universe Model Class
class SMIDGrowth(FundamentalUniverseSelectionModel):
    def __init__(self,
                benchmark = 'SPY',
                nStocks = 500,
                lookback = 252,
                maxNumberOfPositions = 20,
                rebalancingFunc = Expiry.EndOfMonth,
                filterFineData = True,
                universeSettings = None,
                securityInitializer = None):
        self.benchmark = benchmark
        self.nStocks = nStocks
        self.lookback = lookback
        self.maxNumberOfPositions = maxNumberOfPositions

        self.rebalancingFunc = rebalancingFunc
        self.nextRebalance = None
        self.initBenchmarkPrice = 0
        self.portfolioValueHigh = 0 # initialize portfolioValueHigh for drawdown calculation
        self.portfolioValueHighInitialized = False # initialize portfolioValueHighInitialized for drawdown calculation
        super().__init__(filterFineData, universeSettings, securityInitializer)

        #Declare Variables
        tickers = ManualInputs.m_tickers
        self.averages = { }
        self.hist = RollingWindow[float](390*22)
        self.contract = None
        self.buys = []
        self.sells = []
        self.contract_by_equity = {}
        for x in ManualInputs.m_tickers:
            self.AddEquity(x, Resolution.Daily)  
    #SelectCoarse() method with its parameters    
    def SelectCoarse(self, algorithm, coarse):
        # update plots -----------------------------------------------------------------------------------------------
        UpdatePlots(self, algorithm)

        #If it isn't time to update data, return the previous symbols
        if self.lastMonth == algorithm.Time.month:
            return Universe.Unchanged
        # Update self.lastMonth with current month to make sure only process once per month
        self.lastMonth = algorithm.Time.month
        sortedByDollarVolume = sorted([x for x in coarse if x.HasFundamentalData and x.Price > 10],
            key=lambda x: x.DollarVolume, reverse=True)
        coarseSymbols = [x.Symbol for x in sortedByDollarVolume][:(self.nStocks * 2)]
        #Return the top 100 Symbols by Dollar Volume
        return coarseSymbols
    #Add an empty SelectFine() method with is parameters
    def SelectFine(self, algorithm, fine):
        #Sort by SMID Cap Growth Criteria
        sortedByRatios = sorted([f for f in fine if 5e6 < f.MarketCap < 1e10 
                                                and f.ValuationRatios.PERatio > 5 
                                                and f.ValuationRatios.PBRatio > 5
                                                and f.Symbol not in ManualInputs.restrictedList
                                                or f.Symbol in ManualInputs.m_tickers],
            key=lambda f: f.ValuationRatios.PBRatio, reverse=True)[:self.nStocks]

        #Take top 10 most profitable stocks -- and bottom 10 least profitable stocks | Save to the variable universe
        #universe = sortedByRatios[:self.nStocks]
        #Return the symbol objects by iterating through self.universe with list comprehension
        # generate dictionary with factors -----------------------------------------------------------------------------
        fundamentalDataBySymbolDict = GetFundamentalDataDict(algorithm, sortedByRatios, 'universe')
        # make calculations to create long/short lists -----------------------------------------------------------------
        fineSymbols = list(fundamentalDataBySymbolDict.keys())
        calculations = MakeCalculations(algorithm, fineSymbols, self.lookback, Resolution.Daily, fundamentalDataBySymbolDict)
        # get long/short lists of symbols
        longs, shorts = GetLongShortLists(self, algorithm, calculations, 'universe')
        finalSymbols = longs + shorts

        return finalSymbols

    #Method for monitoring if universe has changed
    def OnSecuritiesChanged(self, changes):
        self.Log(f'New Securities Added: {[security.Symbol.Value for security in changes.AddedSecurities]}')
        self.Log(f'Securities Removed{[security.Symbol.Value for security in changes.RemovedSecurities]}')
        for security in changes.AddedSecurities:
            self.contract_by_equity[security.Symbol] = self.BuyPut(security.Symbol)
        for security in changes.RemovedSecurities:

    #Sell Put on equity assets
    def BuyPut(self, symbol):    
        contracts = self.OptionChainProvider.GetOptionContractList(symbol, self.Time)
        self.Debug(f"BuyPut: {symbol} {len(contracts)}")
        #contracts = self.OptionChainProvider.GetOptionChains(self.Symbol, self.Time.date())
        if len(contracts) == 0: return
        min_expiry = 0
        max_expiry = 40
        filtered_contracts = [i for i in contracts if min_expiry <= (i.ID.Date.date() - self.Time.date()).days <= max_expiry]
        put = [x for x in filtered_contracts if x.ID.OptionRight == 1] 
        if len(put) == 0: return
        price = self.Securities[symbol].Price
        # sorted the contracts according to their expiration dates and choose the ATM options
        self.contract = sorted(sorted(put, key = lambda x: abs(price - x.ID.StrikePrice)), 
                                        key = lambda x: x.ID.Date, reverse=True)[0]
        self.AddOptionContract(self.contract, Resolution.Minute)
        self.MarketOrder(self.contract, 1)
        return self.contract
import pandas as pd
from scipy.stats import zscore
from classSymbolData import SymbolData

def MakeCalculations(algorithm, symbols, lookback, resolution, fundamentalDataBySymbolDict):
        Make required calculations using historical data for each symbol
        symbols: The symbols to make calculations for
        lookback: Lookback period for historical data
        resolution: Resolution for historical data
        fundamentalDataBySymbolDict: Dictionary of symbols containing factors and the direction of the factor (for sorting)
        calculations: Dictionary containing the calculations per symbol
    # store calculations
    calculations = {}

    if len(symbols) > 0:
        # get historical prices for new symbols
        history = GetHistory(algorithm, symbols,
                            lookbackPeriod = lookback,
                            resolution = resolution)
        for symbol in symbols:
            # if symbol has no historical data continue the loop
            if (symbol not in history.index
            or len(history.loc[symbol]['close']) < lookback
            or history.loc[symbol].get('close') is None
            or history.loc[symbol].get('close').isna().any()):
                algorithm.Log('no history found for: ' + str(symbol.Value))

                # add symbol to calculations
                calculations[symbol] = SymbolData(symbol)
                    calculations[symbol].CalculateFactors(history, fundamentalDataBySymbolDict)
                except Exception as e:
                    algorithm.Log('removing from calculations due to ' + str(e))
    return calculations
def GetFundamentalDataDict(algorithm, securitiesData, module = 'universe'):
    ''' Create a dictionary of symbols and fundamental factors ready for sorting '''

    fundamentalDataBySymbolDict = {}
    # loop through data and get fundamental data
    for x in securitiesData:
        if module == 'alpha':
            if not x.Symbol in algorithm.ActiveSecurities.Keys:
            fundamental = algorithm.ActiveSecurities[x.Symbol].Fundamentals
        elif module == 'universe':
            fundamental = x
            raise ValueError('module argument must be either universe or alpha')
        # dictionary of symbols containing factors and the direction of the factor (1 for sorting descending and -1 for sorting ascending)
        fundamentalDataBySymbolDict[x.Symbol] = {
                                                    #fundamental.ValuationRatios.BookValuePerShare: 1,
                                                    #fundamental.FinancialStatements.BalanceSheet.TotalEquity.Value: -1,
                                                    #fundamental.OperationRatios.OperationMargin.Value: 1,
                                                    #fundamental.OperationRatios.ROE.Value: 1,
                                                    #fundamental.OperationRatios.TotalAssetsGrowth.Value: 1,
                                                    #fundamental.ValuationRatios.NormalizedPERatio: 1,
                                                    fundamental.ValuationRatios.PBRatio: -1,
                                                    #fundamental.OperationRatios.TotalDebtEquityRatio.Value: -1,
                                                    fundamental.ValuationRatios.FCFRatio: -1,
                                                    fundamental.ValuationRatios.PEGRatio: -1,
                                                    #fundamental.MarketCap: 1,
        # check validity of data
        if None in list(fundamentalDataBySymbolDict[x.Symbol].keys()):
    return fundamentalDataBySymbolDict
def GetLongShortLists(self, algorithm, calculations, module = 'universe'):
    ''' Create lists of long/short stocks '''
    # get factors
    factorsDict = { symbol: symbolData.factorsList for symbol, symbolData in calculations.items() if symbolData.factorsList is not None }
    factorsDf = pd.DataFrame.from_dict(factorsDict, orient = 'index')
    # normalize factor
    normFactorsDf = factorsDf.apply(zscore)
    normFactorsDf.columns = ['Factor_' + str(x + 1) for x in normFactorsDf.columns]
    # combine factors using equal weighting
    #normFactorsDf['combinedFactor'] = normFactorsDf.sum(axis = 1)
    normFactorsDf['combinedFactor'] = normFactorsDf['Factor_1'] * 1 + normFactorsDf['Factor_2'] * 1
    # sort descending
    sortedNormFactorsDf = normFactorsDf.sort_values(by = 'combinedFactor', ascending = False) # descending
    # create long/short lists
    positionsEachSide = int(self.maxNumberOfPositions / 2)
    longs = list(sortedNormFactorsDf[:positionsEachSide].index)
    shorts = list(sortedNormFactorsDf[-positionsEachSide:].index)
    shorts = [x for x in shorts if x not in longs]
    if module == 'alpha' and algorithm.LiveMode:
        algorithm.Log({'longs': {x.Value: factorsDict[x] for x in longs}, 'shorts': {x.Value: factorsDict[x] for x in shorts}})
    return longs, shorts

def GetHistory(algorithm, symbols, lookbackPeriod, resolution):
    ''' Pull historical data in batches '''
    total = len(symbols)
    batchsize = 50
    if total <= batchsize:
        history = algorithm.History(symbols, lookbackPeriod, resolution)
        history = algorithm.History(symbols[0:batchsize], lookbackPeriod, resolution)
        for i in range(batchsize, total + 1, batchsize):
            batch = symbols[i:(i + batchsize)]
            historyTemp = algorithm.History(batch, lookbackPeriod, resolution)
            history = pd.concat([history, historyTemp])
    return history
def UpdateBenchmarkValue(self, algorithm):
    ''' Simulate buy and hold the Benchmark '''
    if self.initBenchmarkPrice == 0:
        self.initBenchmarkCash = algorithm.Portfolio.Cash
        self.initBenchmarkPrice = algorithm.Benchmark.Evaluate(algorithm.Time)
        self.benchmarkValue = self.initBenchmarkCash
        currentBenchmarkPrice = algorithm.Benchmark.Evaluate(algorithm.Time)
        self.benchmarkValue = (currentBenchmarkPrice / self.initBenchmarkPrice) * self.initBenchmarkCash
def UpdatePlots(self, algorithm):
    ''' Update Portfolio Exposure and Drawdown plots '''
    # simulate buy and hold the benchmark and plot its daily value --------------
    UpdateBenchmarkValue(self, algorithm)
    algorithm.Plot('Strategy Equity', self.benchmark, self.benchmarkValue)

    # get current portfolio value
    currentTotalPortfolioValue = algorithm.Portfolio.TotalPortfolioValue
    # plot the daily total portfolio exposure % --------------------------------
    longHoldings = sum([x.HoldingsValue for x in algorithm.Portfolio.Values if x.IsLong])
    shortHoldings = sum([x.HoldingsValue for x in algorithm.Portfolio.Values if x.IsShort])
    totalHoldings = longHoldings + shortHoldings
    totalPortfolioExposure = (totalHoldings / currentTotalPortfolioValue) * 100
    algorithm.Plot('Chart Total Portfolio Exposure %', 'Daily Portfolio Exposure %', totalPortfolioExposure)
    # plot the daily number of longs and shorts --------------------------------
    nLongs = sum(x.IsLong for x in algorithm.Portfolio.Values)
    nShorts = sum(x.IsShort for x in algorithm.Portfolio.Values)
    algorithm.Plot('Chart Number Of Longs/Shorts', 'Daily N Longs', nLongs)
    algorithm.Plot('Chart Number Of Longs/Shorts', 'Daily N Shorts', nShorts)
    # plot the drawdown % from the most recent high ---------------------------
    if not self.portfolioValueHighInitialized:
        self.portfolioHigh = currentTotalPortfolioValue # set initial portfolio value
        self.portfolioValueHighInitialized = True
    # update trailing high value of the portfolio
    if self.portfolioValueHigh < currentTotalPortfolioValue:
        self.portfolioValueHigh = currentTotalPortfolioValue

    currentDrawdownPercent = ((float(currentTotalPortfolioValue) / float(self.portfolioValueHigh)) - 1.0) * 100
    algorithm.Plot('Chart Drawdown %', 'Drawdown %', currentDrawdownPercent)
    symbols = []
    # loop through the tickers list and create symbols for the universe
    for i in range(len(algorithm.Portfolio.Values)):
        symbols.append(Symbol.Create(tickers[i], SecurityType.Equity, Market.USA))
        allocationPlot.AddSeries(Series(tickers[i], SeriesType.Line, ''))
    #algorithm.Plot('Optimal Allocation', )
import pandas as pd
import numpy as np
from scipy.stats import skew, kurtosis

class SymbolData:
    ''' Perform calculations '''
    def __init__(self, symbol):
        self.Symbol = symbol
        self.fundamentalDataDict = {}
        self.momentum = None
        self.volatility = None
        self.skewness = None
        self.kurt = None
        self.positionVsHL = None
        self.meanOvernightReturns = None
    def CalculateFactors(self, history, fundamentalDataBySymbolDict):
        self.fundamentalDataDict = fundamentalDataBySymbolDict[self.Symbol]
        self.momentum = self.CalculateMomentum(history)
        self.volatility = self.CalculateVolatility(history)
        #self.skewness = self.CalculateSkewness(history)
        #self.kurt = self.CalculateKurtosis(history)
        #self.distanceVsHL = self.CalculateDistanceVsHL(history)
        #self.meanOvernightReturns = self.CalculateMeanOvernightReturns(history)
    def CalculateMomentum(self, history):
        closePrices = history.loc[self.Symbol]['close']
        momentum = (closePrices[-1] / closePrices[-252]) - 1
        return momentum
    def CalculateVolatility(self, history):
        closePrices = history.loc[self.Symbol]['close']
        returns = closePrices.pct_change().dropna()
        volatility = np.nanstd(returns, axis = 0)
        return volatility
    def CalculateSkewness(self, history):
        closePrices = history.loc[self.Symbol]['close']
        returns = closePrices.pct_change().dropna()
        skewness = skew(returns)
        return skewness
    def CalculateKurtosis(self, history):
        closePrices = history.loc[self.Symbol]['close']
        returns = closePrices.pct_change().dropna()
        kurt = kurtosis(returns)
        return kurt
    def CalculateDistanceVsHL(self, history):
        closePrices = history.loc[self.Symbol]['close']
        annualHigh = max(closePrices)
        annualLow = min(closePrices)
        distanceVsHL = (closePrices[-1] - annualLow) / (annualHigh - annualLow)
        return distanceVsHL
    def CalculateMeanOvernightReturns(self, history):
        overnnightReturns = (history.loc[self.Symbol]['open'] / history.loc[self.Symbol]['close'].shift(1)) - 1
        meanOvernightReturns = np.nanmean(overnnightReturns, axis = 0)
        return meanOvernightReturns
    def factorsList(self):
        technicalFactors = [self.momentum, self.volatility]
        fundamentalFactors = [float(key) * value for key, value in self.fundamentalDataDict.items()]
        if all(v is not None for v in technicalFactors):
            return technicalFactors + fundamentalFactors
            return None
class ManualInputs:

    #m_tickers = ['AAPL', 'AMZN', 'NFLX', 'GOOG','FB']
    m_tickers = ['AMZN', 'ARKK']
    #m_tickers = []
    restrictedList = ["GME"]
# QUANTCONNECT.COM - Democratizing Finance, Empowering Individuals.
# Lean Algorithmic Trading Engine v2.0. Copyright 2014 QuantConnect Corporation.
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# See the License for the specific language governing permissions and
# limitations under the License.

from clr import AddReference

from System import *
from QuantConnect import *
from QuantConnect.Indicators import *
from QuantConnect.Algorithm import *
from QuantConnect.Logging import Log
from QuantConnect.Algorithm.Framework import *
from QuantConnect.Algorithm.Framework.Alphas import InsightCollection, InsightDirection
from QuantConnect.Algorithm.Framework.Portfolio import PortfolioConstructionModel, PortfolioTarget, PortfolioBias
from Portfolio.MaximumSharpeRatioPortfolioOptimizer import MaximumSharpeRatioPortfolioOptimizer
from datetime import datetime, timedelta
from itertools import groupby
import pandas as pd
import numpy as np
from numpy import dot, transpose
from numpy.linalg import inv

### <summary>
### Provides an implementation of Black-Litterman portfolio optimization. The model adjusts equilibrium market
### returns by incorporating views from multiple alpha models and therefore to get the optimal risky portfolio
### reflecting those views. If insights of all alpha models have None magnitude or there are linearly dependent
### vectors in link matrix of views, the expected return would be the implied excess equilibrium return.
### The interval of weights in optimization method can be changed based on the long-short algorithm.
### The default model uses the 0.0025 as weight-on-views scalar parameter tau and
### MaximumSharpeRatioPortfolioOptimizer that accepts a 63-row matrix of 1-day returns.
### </summary>
class BlackLittermanOptimizationPortfolioConstructionModel(PortfolioConstructionModel):
    def __init__(self,
                 rebalance = Resolution.Daily,
                 portfolioBias = PortfolioBias.LongShort,
                 lookback = 1,
                 period = 63,
                 resolution = Resolution.Daily,
                 risk_free_rate = 0,
                 delta = 2.5,
                 tau = 0.05,
                 optimizer = None):
        """Initialize the model
            rebalance: Rebalancing parameter. If it is a timedelta, date rules or Resolution, it will be converted into a function.
                              If None will be ignored.
                              The function returns the next expected rebalance time for a given algorithm UTC DateTime.
                              The function returns null if unknown, in which case the function will be called again in the
                              next loop. Returning current time will trigger rebalance.
            portfolioBias: Specifies the bias of the portfolio (Short, Long/Short, Long)
            lookback(int): Historical return lookback period
            period(int): The time interval of history price to calculate the weight
            resolution: The resolution of the history price
            risk_free_rate(float): The risk free rate
            delta(float): The risk aversion coeffficient of the market portfolio
            tau(float): The model parameter indicating the uncertainty of the CAPM prior"""
        self.lookback = lookback
        self.period = period
        self.resolution = resolution
        self.risk_free_rate = risk_free_rate
        self.delta = delta
        self.tau = tau
        self.portfolioBias = portfolioBias

        lower = 0 if portfolioBias == PortfolioBias.Long else -1
        upper = 0 if portfolioBias == PortfolioBias.Short else 1
        self.optimizer = MaximumSharpeRatioPortfolioOptimizer(lower, upper, risk_free_rate) if optimizer is None else optimizer

        self.sign = lambda x: -1 if x < 0 else (1 if x > 0 else 0)
        self.symbolDataBySymbol = {}

        # If the argument is an instance of Resolution or Timedelta
        # Redefine rebalancingFunc
        rebalancingFunc = rebalance
        if isinstance(rebalance, int):
            rebalance = Extensions.ToTimeSpan(rebalance)
        if isinstance(rebalance, timedelta):
            rebalancingFunc = lambda dt: dt + rebalance
        if rebalancingFunc:

    def ShouldCreateTargetForInsight(self, insight):
        return len(PortfolioConstructionModel.FilterInvalidInsightMagnitude(self.Algorithm, [ insight ])) != 0

    def DetermineTargetPercent(self, lastActiveInsights):
        targets = {}

        # Get view vectors
        P, Q = self.get_views(lastActiveInsights)
        if P is not None:
            returns = dict()
            # Updates the BlackLittermanSymbolData with insights
            # Create a dictionary keyed by the symbols in the insights with an pandas.Series as value to create a data frame
            for insight in lastActiveInsights:
                symbol = insight.Symbol
                symbolData = self.symbolDataBySymbol.get(symbol, self.BlackLittermanSymbolData(symbol, self.lookback, self.period))
                if insight.Magnitude is None:
                    self.Algorithm.SetRunTimeError(ArgumentNullException('BlackLittermanOptimizationPortfolioConstructionModel does not accept \'None\' as Insight.Magnitude. Please make sure your Alpha Model is generating Insights with the Magnitude property set.'))
                    return targets
                symbolData.Add(insight.GeneratedTimeUtc, insight.Magnitude)
                returns[symbol] = symbolData.Return

            returns = pd.DataFrame(returns)

            # Calculate prior estimate of the mean and covariance
            Pi, Sigma = self.get_equilibrium_return(returns)

            # Calculate posterior estimate of the mean and covariance
            Pi, Sigma = self.apply_blacklitterman_master_formula(Pi, Sigma, P, Q)

            # Create portfolio targets from the specified insights
            weights = self.optimizer.Optimize(returns, Pi, Sigma)
            weights = pd.Series(weights, index = Sigma.columns)

            for symbol, weight in weights.items():
                for insight in lastActiveInsights:
                    if str(insight.Symbol) == str(symbol):
                        # don't trust the optimizer
                        if self.portfolioBias != PortfolioBias.LongShort and self.sign(weight) != self.portfolioBias:
                            weight = 0
                        targets[insight] = weight

        return targets

    def GetTargetInsights(self):
        # Get insight that haven't expired of each symbol that is still in the universe
        activeInsights = self.InsightCollection.GetActiveInsights(self.Algorithm.UtcTime)

        # Get the last generated active insight for each symbol
        lastActiveInsights = []
        for sourceModel, f in groupby(sorted(activeInsights, key = lambda ff: ff.SourceModel), lambda fff: fff.SourceModel):
            for symbol, g in groupby(sorted(list(f), key = lambda gg: gg.Symbol), lambda ggg: ggg.Symbol):
                lastActiveInsights.append(sorted(g, key = lambda x: x.GeneratedTimeUtc)[-1])
        return lastActiveInsights

    def OnSecuritiesChanged(self, algorithm, changes):
        '''Event fired each time the we add/remove securities from the data feed
            algorithm: The algorithm instance that experienced the change in securities
            changes: The security additions and removals from the algorithm'''

        # Get removed symbol and invalidate them in the insight collection
        super().OnSecuritiesChanged(algorithm, changes)

        for security in changes.RemovedSecurities:
            symbol = security.Symbol
            symbolData = self.symbolDataBySymbol.pop(symbol, None)
            if symbolData is not None:

        # initialize data for added securities
        addedSymbols = { x.Symbol: x.Exchange.TimeZone for x in changes.AddedSecurities }
        history = algorithm.History(list(addedSymbols.keys()), self.lookback * self.period, self.resolution)

        if history.empty:

        history = history.close.unstack(0)
        symbols = history.columns

        for symbol, timezone in addedSymbols.items():
            if str(symbol) not in symbols:

            symbolData = self.symbolDataBySymbol.get(symbol, self.BlackLittermanSymbolData(symbol, self.lookback, self.period))
            for time, close in history[symbol].items():
                utcTime = Extensions.ConvertToUtc(time, timezone)
                symbolData.Update(utcTime, close)

            self.symbolDataBySymbol[symbol] = symbolData

    def apply_blacklitterman_master_formula(self, Pi, Sigma, P, Q):
        '''Apply Black-Litterman master formula
            Pi: Prior/Posterior mean array
            Sigma: Prior/Posterior covariance matrix
            P: A matrix that identifies the assets involved in the views (size: K x N)
            Q: A view vector (size: K x 1)'''
        ts = self.tau * Sigma

        # Create the diagonal Sigma matrix of error terms from the expressed views
        omega = np.dot(np.dot(P, ts), P.T) * np.eye(Q.shape[0])
        if np.linalg.det(omega) == 0:
            return Pi, Sigma

        A = np.dot(np.dot(ts, P.T), inv(np.dot(np.dot(P, ts), P.T) + omega))

        Pi = np.squeeze(np.asarray((
            np.expand_dims(Pi, axis=0).T +
            np.dot(A, (Q - np.expand_dims(np.dot(P, Pi.T), axis=1))))

        M = ts - np.dot(np.dot(A, P), ts)
        Sigma = (Sigma + M) * self.delta

        return Pi, Sigma

    def get_equilibrium_return(self, returns):
        '''Calculate equilibrium returns and covariance
            returns: Matrix of returns where each column represents a security and each row returns for the given date/time (size: K x N)
            equilibrium_return: Array of double of equilibrium returns
            cov: Multi-dimensional array of double with the portfolio covariance of returns (size: K x K)'''

        size = len(returns.columns)
        # equal weighting scheme
        W = np.array([1/size]*size)
        # the covariance matrix of excess returns (N x N matrix)
        cov = returns.cov()*252
        # annualized return
        annual_return = np.sum(((1 + returns.mean())**252 -1) * W)
        # annualized variance of return
        annual_variance = dot(W.T, dot(cov, W))
        # the risk aversion coefficient
        risk_aversion = (annual_return - self.risk_free_rate ) / annual_variance
        # the implied excess equilibrium return Vector (N x 1 column vector)
        equilibrium_return = dot(dot(risk_aversion, cov), W)

        return equilibrium_return, cov

    def get_views(self, insights):
        '''Generate views from multiple alpha models
            insights: Array of insight that represent the investors' views
            P: A matrix that identifies the assets involved in the views (size: K x N)
            Q: A view vector (size: K x 1)'''
            P = {}
            Q = {}
            for model, group in groupby(insights, lambda x: x.SourceModel):
                group = list(group)

                up_insights_sum = 0.0
                dn_insights_sum = 0.0
                for insight in group:
                    if insight.Direction == InsightDirection.Up:
                        up_insights_sum = up_insights_sum + np.abs(insight.Magnitude)
                    if insight.Direction == InsightDirection.Down:
                        dn_insights_sum = dn_insights_sum + np.abs(insight.Magnitude)

                q = up_insights_sum if up_insights_sum > dn_insights_sum else dn_insights_sum
                if q == 0:

                Q[model] = q

                # generate the link matrix of views: P
                P[model] = dict()
                for insight in group:
                    value = insight.Direction * np.abs(insight.Magnitude)
                    P[model][insight.Symbol] = value / q
                # Add zero for other symbols that are listed but active insight
                for symbol in self.symbolDataBySymbol.keys():
                    if symbol not in P[model]:
                        P[model][symbol] = 0

            Q = np.array([[x] for x in Q.values()])
            if len(Q) > 0:
                P = np.array([list(x.values()) for x in P.values()])
                return P, Q

        return None, None

    class BlackLittermanSymbolData:
        '''Contains data specific to a symbol required by this model'''
        def __init__(self, symbol, lookback, period):
            self.symbol = symbol
            self.roc = RateOfChange(f'{symbol}.ROC({lookback})', lookback)
            self.roc.Updated += self.OnRateOfChangeUpdated
            self.window = RollingWindow[IndicatorDataPoint](period)

        def Reset(self):
            self.roc.Updated -= self.OnRateOfChangeUpdated

        def Update(self, utcTime, close):
            self.roc.Update(utcTime, close)

        def OnRateOfChangeUpdated(self, roc, value):
            if roc.IsReady:

        def Add(self, time, value):
            if self.window.Samples > 0 and self.window[0].EndTime == time:

            item = IndicatorDataPoint(self.symbol, time, value)

        def Return(self):
            return pd.Series(
                data = [x.Value for x in self.window],
                index = [x.EndTime for x in self.window])

        def IsReady(self):
            return self.window.IsReady

        def __str__(self, **kwargs):
            return f'{self.roc.Name}: {(1 + self.window[0])**252 - 1:.2%}'