Overall Statistics |
Total Trades 1270 Average Win 0.01% Average Loss -0.01% Compounding Annual Return 14.112% Drawdown 2.800% Expectancy -0.577 Net Profit 0.253% Sharpe Ratio 0.986 Probabilistic Sharpe Ratio 49.444% Loss Rate 78% Win Rate 22% Profit-Loss Ratio 0.89 Alpha 0.714 Beta 1.678 Annual Standard Deviation 0.204 Annual Variance 0.041 Information Ratio 4.304 Tracking Error 0.118 Treynor Ratio 0.12 Total Fees $1278.46 Estimated Strategy Capacity $1400000.00 Lowest Capacity Asset WWFE RP03K24T1IED |
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.AddUniverseSelection(SMIDGrowth()) 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)) self.AddAlpha(BuyAndHoldAlphaCreationModel()) self.SetExecution(VolumeWeightedAveragePriceExecutionModel()) self.SetPortfolioConstruction(BlackLittermanOptimizationPortfolioConstructionModel()) self.SetRiskManagement(MaximumDrawdownPercentPerSecurity(0.01)) self.SetWarmup(50) ### 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, '')) self.AddChart(portfolioExposurePlot) # 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, '')) self.AddChart(nLongShortPlot) # let's plot the series of drawdown % from the most recent high drawdownPlot = Chart('Chart Drawdown %') drawdownPlot.AddSeries(Series('Drawdown %', SeriesType.Line, '%')) self.AddChart(drawdownPlot) def OnData(self, data): '''OnData event is the primary entry point for your algorithm. Each new data point will be pumped in here. Arguments: data: Slice object keyed by symbol containing the stock data ''' # if not self.Portfolio.Invested: # self.SetHoldings("SPY", 1) def security_initializer(self, security): ''' Description: Initialize the security with adjusted prices Args: security: Security which characteristics we want to change ''' security.SetDataNormalizationMode(DataNormalizationMode.Adjusted) #security.SetMarketPrice = self.GetLastKnownPrice(security) if security.Type == SecurityType.Option: security.SetMarketPrice(self.GetLastKnownPrice(security)) def OnOrderEvent(self, OrderEvent): #Event when the order is filled. Debug log the order fill. :OrderEvent:``` if OrderEvent.FillQuantity == 0: return fetched = self.Transactions.GetOrderById(OrderEvent.OrderId) self.Debug("{} was filled. Symbol: {}. Quantity: {}. Direction: {}" .format(str(fetched.Type), str(OrderEvent.Symbol), str(OrderEvent.FillQuantity), str(OrderEvent.Direction)))
from clr import AddReference AddReference("System") AddReference("QuantConnect.Common") AddReference("QuantConnect.Algorithm") AddReference("QuantConnect.Algorithm.Framework") 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): ''' Description: This Alpha model creates InsightDirection.Up (to go Long) for a duration of 1 day, every day for all active securities in our Universe Details: 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)) else: algorithm.Log('(Alpha) excluding this security due to missing data: ' + str(security.Symbol.Value)) return insights def OnSecuritiesChanged(self, algorithm, changes): ''' Description: Event fired each time the we add/remove securities from the data feed Args: 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: self.securities.append(added) # remove securities for removed in changes.RemovedSecurities: if removed in self.securities: self.securities.remove(removed)
from clr import AddReference AddReference("System") AddReference("QuantConnect.Common") AddReference("QuantConnect.Indicators") AddReference("QuantConnect.Algorithm.Framework") 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.SetSecurityInitializer(self.security_initializer) 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.buys.append(security) self.contract_by_equity[security.Symbol] = self.BuyPut(security.Symbol) for security in changes.RemovedSecurities: self.sells.append(security) #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): ''' Description: Make required calculations using historical data for each symbol Args: 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) Return: 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)) continue else: # add symbol to calculations calculations[symbol] = SymbolData(symbol) try: calculations[symbol].CalculateFactors(history, fundamentalDataBySymbolDict) except Exception as e: algorithm.Log('removing from calculations due to ' + str(e)) calculations.pop(symbol) continue 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: continue fundamental = algorithm.ActiveSecurities[x.Symbol].Fundamentals elif module == 'universe': fundamental = x else: 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()): fundamentalDataBySymbolDict.pop(x.Symbol) 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) else: 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 else: 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 @property 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 else: 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, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. from clr import AddReference AddReference("System") AddReference("QuantConnect.Algorithm") AddReference("QuantConnect.Common") AddReference("QuantConnect.Logging") AddReference("QuantConnect.Indicators") 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 Args: 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: self.SetRebalancingFunc(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 break; 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 Args: 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: symbolData.Reset() # 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: return history = history.close.unstack(0) symbols = history.columns for symbol, timezone in addedSymbols.items(): if str(symbol) not in symbols: continue 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 http://www.blacklitterman.org/cookbook.html Args: 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 Args: returns: Matrix of returns where each column represents a security and each row returns for the given date/time (size: K x N) Returns: 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 Args insights: Array of insight that represent the investors' views Returns P: A matrix that identifies the assets involved in the views (size: K x N) Q: A view vector (size: K x 1)''' try: 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: continue 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 except: pass 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 self.roc.Reset() self.window.Reset() def Update(self, utcTime, close): self.roc.Update(utcTime, close) def OnRateOfChangeUpdated(self, roc, value): if roc.IsReady: self.window.Add(value) def Add(self, time, value): if self.window.Samples > 0 and self.window[0].EndTime == time: return; item = IndicatorDataPoint(self.symbol, time, value) self.window.Add(item) @property def Return(self): return pd.Series( data = [x.Value for x in self.window], index = [x.EndTime for x in self.window]) @property def IsReady(self): return self.window.IsReady def __str__(self, **kwargs): return f'{self.roc.Name}: {(1 + self.window[0])**252 - 1:.2%}'