Overall Statistics
Total Orders
568
Average Win
0.11%
Average Loss
-0.02%
Compounding Annual Return
13.249%
Drawdown
19.200%
Expectancy
5.513
Start Equity
10000000
End Equity
21137647.05
Net Profit
111.376%
Sharpe Ratio
0.587
Sortino Ratio
0.686
Probabilistic Sharpe Ratio
34.858%
Loss Rate
5%
Win Rate
95%
Profit-Loss Ratio
5.85
Alpha
-0.007
Beta
0.677
Annual Standard Deviation
0.106
Annual Variance
0.011
Information Ratio
-0.642
Tracking Error
0.063
Treynor Ratio
0.091
Total Fees
$2920.25
Estimated Strategy Capacity
$1200000.00
Lowest Capacity Asset
WOOD U3RDKMG7QNHH
Portfolio Turnover
0.10%
Drawdown Recovery
712
#region imports
from AlgorithmImports import *
#endregion
from clr import AddReference
AddReference("QuantConnect.Common")
AddReference("QuantConnect.Algorithm.Framework")

from QuantConnect import Resolution, Extensions
from QuantConnect.Algorithm.Framework.Alphas import *
from QuantConnect.Algorithm.Framework.Portfolio import *
from itertools import groupby
from datetime import datetime, timedelta

class EqualWeightingPortfolioConstructionModel(PortfolioConstructionModel):
    '''Provides an implementation of IPortfolioConstructionModel that gives equal weighting to all securities.
    The target percent holdings of each security is 1/N where N is the number of securities.
    For insights of direction InsightDirection.Up, long targets are returned and
    for insights of direction InsightDirection.Down, short targets are returned.'''

    def __init__(self, rebalance = Resolution.Daily, portfolioBias = PortfolioBias.LongShort):
        '''Initialize a new instance of EqualWeightingPortfolioConstructionModel
        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)'''
        self.portfolioBias = portfolioBias

        # 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 DetermineTargetPercent(self, activeInsights):
        '''Will determine the target percent for each insight
        Args:
            activeInsights: The active insights to generate a target for'''
        result = {}

        # give equal weighting to each security
        count = sum(x.Direction != InsightDirection.Flat and self.RespectPortfolioBias(x) for x in activeInsights)
        percent = 0 if count == 0 else 1.0 / count
        for insight in activeInsights:
            result[insight] = (insight.Direction if self.RespectPortfolioBias(insight) else InsightDirection.Flat) * percent
        return result

    def RespectPortfolioBias(self, insight):
        '''Method that will determine if a given insight respects the portfolio bias
        Args:
            insight: The insight to create a target for
        '''
        return self.portfolioBias == PortfolioBias.LongShort or insight.Direction == self.portfolioBias

# Your New Python File
#region imports
from AlgorithmImports import *
#endregion
from clr import AddReference
AddReference("QuantConnect.Algorithm.Framework")
AddReference("QuantConnect.Indicators")
AddReference("QuantConnect.Common")

from QuantConnect import *
from QuantConnect.Indicators import *
from QuantConnect.Algorithm.Framework.Alphas import *
from datetime import timedelta

class HistoricalReturnsAlphaModel(AlphaModel):
    '''Uses Historical returns to create insights.'''

    def __init__(self, *args, **kwargs):
        '''Initializes a new default instance of the HistoricalReturnsAlphaModel class.
        Args:
            lookback(int): Historical return lookback period
            resolution: The resolution of historical data'''
        self.lookback = kwargs['lookback'] if 'lookback' in kwargs else 1
        self.resolution = kwargs['resolution'] if 'resolution' in kwargs else Resolution.Daily
        self.predictionInterval = Time.Multiply(Extensions.ToTimeSpan(self.resolution), self.lookback)
        self.symbolDataBySymbol = {}

    def Update(self, algorithm, data):
        '''Updates this alpha model with the latest data from the algorithm.
        This is called each time the algorithm receives data for subscribed securities
        Args:
            algorithm: The algorithm instance
            data: The new data available
        Returns:
            The new insights generated'''
        insights = []

        for symbol, symbolData in self.symbolDataBySymbol.items():
            if symbolData.CanEmit:

                direction = InsightDirection.Flat
                magnitude = symbolData.Return
                if magnitude > 0: direction = InsightDirection.Up
                if magnitude < 0: direction = InsightDirection.Down

                insights.append(Insight.Price(symbol, self.predictionInterval, direction, magnitude, None))

        return insights

    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'''

        # clean up data for removed securities
        for removed in changes.RemovedSecurities:
            symbolData = self.symbolDataBySymbol.pop(removed.Symbol, None)
            if symbolData is not None:
                symbolData.RemoveConsolidators(algorithm)

        # initialize data for added securities
        symbols = [ x.Symbol for x in changes.AddedSecurities ]
        history = algorithm.History(symbols, self.lookback, self.resolution)
        if history.empty: return

        tickers = history.index.levels[0]
        for ticker in tickers:
            symbol = SymbolCache.GetSymbol(ticker)

            if symbol not in self.symbolDataBySymbol:
                symbolData = SymbolData(symbol, self.lookback)
                self.symbolDataBySymbol[symbol] = symbolData
                symbolData.RegisterIndicators(algorithm, self.resolution)
                symbolData.WarmUpIndicators(history.loc[ticker])


class SymbolData:
    '''Contains data specific to a symbol required by this model'''
    def __init__(self, symbol, lookback):
        self.Symbol = symbol
        self.ROC = RateOfChange('{}.ROC({})'.format(symbol, lookback), lookback)
        self.Consolidator = None
        self.previous = 0

    def RegisterIndicators(self, algorithm, resolution):
        self.Consolidator = algorithm.ResolveConsolidator(self.Symbol, resolution)
        algorithm.RegisterIndicator(self.Symbol, self.ROC, self.Consolidator)

    def RemoveConsolidators(self, algorithm):
        if self.Consolidator is not None:
            algorithm.SubscriptionManager.RemoveConsolidator(self.Symbol, self.Consolidator)

    def WarmUpIndicators(self, history):
        for tuple in history.itertuples():
            self.ROC.Update(tuple.Index, tuple.close)

    @property
    def Return(self):
        return float(self.ROC.Current.Value)

    @property
    def CanEmit(self):
        if self.previous == self.ROC.Samples:
            return False

        self.previous = self.ROC.Samples
        return self.ROC.IsReady

    def __str__(self, **kwargs):
        return '{}: {:.2%}'.format(self.ROC.Name, (1 + self.Return)**252 - 1)
#region imports
from AlgorithmImports import *
#endregion
from clr import AddReference
AddReference("System")
AddReference("QuantConnect.Algorithm")
AddReference("QuantConnect.Algorithm.Framework")
AddReference("QuantConnect.Common")
AddReference("QuantConnect.Indicators")

from System import *
from QuantConnect import *
from QuantConnect.Indicators import *
from QuantConnect.Algorithm import *
from QuantConnect.Algorithm.Framework import *
from QuantConnect.Algorithm.Framework.Portfolio import *
from Portfolio.MinimumVariancePortfolioOptimizer import MinimumVariancePortfolioOptimizer
from datetime import timedelta
import numpy as np
import pandas as pd

### <summary>
### Provides an implementation of Mean-Variance portfolio optimization based on modern portfolio theory.
### The default model uses the MinimumVariancePortfolioOptimizer that accepts a 63-row matrix of 1-day returns.
### </summary>
class MeanVarianceOptimizationPortfolioConstructionModel(PortfolioConstructionModel):
    def __init__(self,
                 rebalance = Resolution.Daily,
                 portfolioBias = PortfolioBias.LongShort,
                 lookback = 1,
                 period = 63,
                 resolution = Resolution.Daily,
                 targetReturn = 0.02,
                 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
            optimizer(class): Method used to compute the portfolio weights"""
        self.lookback = lookback
        self.period = period
        self.resolution = resolution
        self.portfolioBias = portfolioBias
        self.sign = lambda x: -1 if x < 0 else (1 if x > 0 else 0)

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

        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):
        if len(PortfolioConstructionModel.FilterInvalidInsightMagnitude(self.Algorithm, [insight])) == 0:
            return False

        symbolData = self.symbolDataBySymbol.get(insight.Symbol)
        if insight.Magnitude is None:
            self.algorithm.SetRunTimeError(ArgumentNullException('MeanVarianceOptimizationPortfolioConstructionModel does not accept \'None\' as Insight.Magnitude. Please checkout the selected Alpha Model specifications.'))
            return False
        symbolData.Add(self.Algorithm.Time, insight.Magnitude)

        return True

    def DetermineTargetPercent(self, activeInsights):
        """
         Will determine the target percent for each insight
        Args:
        Returns:
        """
        targets = {}
        symbols = [insight.Symbol for insight in activeInsights]

        # Create a dictionary keyed by the symbols in the insights with an pandas.Series as value to create a data frame
        returns = { str(symbol) : data.Return for symbol, data in self.symbolDataBySymbol.items() if symbol in symbols }
        returns = pd.DataFrame(returns)

        # The portfolio optimizer finds the optional weights for the given data
        weights = self.optimizer.Optimize(returns)
        weights = pd.Series(weights, index = returns.columns)

        # Create portfolio targets from the specified insights
        for insight in activeInsights:
            weight = weights[str(insight.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 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'''

        # clean up data for removed securities
        super().OnSecuritiesChanged(algorithm, changes)
        for removed in changes.RemovedSecurities:
            symbolData = self.symbolDataBySymbol.pop(removed.Symbol, None)
            symbolData.Reset()

        # initialize data for added securities
        symbols = [ x.Symbol for x in changes.AddedSecurities ]
        history = algorithm.History(symbols, self.lookback * self.period, self.resolution)
        if history.empty: return

        tickers = history.index.levels[0]
        for ticker in tickers:
            symbol = SymbolCache.GetSymbol(ticker)

            if symbol not in self.symbolDataBySymbol:
                symbolData = self.MeanVarianceSymbolData(symbol, self.lookback, self.period)
                symbolData.WarmUpIndicators(history.loc[ticker])
                self.symbolDataBySymbol[symbol] = symbolData

    class MeanVarianceSymbolData:
        '''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 WarmUpIndicators(self, history):
            for tuple in history.itertuples():
                self.roc.Update(tuple.Index, tuple.close)

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

        def Add(self, time, value):
            item = IndicatorDataPoint(self.symbol, time, value)
            self.window.Add(item)

        @property
        def Return(self):
            return pd.Series(
                data = [(1 + float(x.Value))**252 - 1 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 '{}: {:.2%}'.format(self.roc.Name, (1 + self.window[0])**252 - 1)
from AlgorithmImports import *

class ConstantAlphaModel(AlphaModel):
    ''' Provides an implementation of IAlphaModel that always returns the same insight for each security'''

    def __init__(self, type, direction, period, magnitude=None, confidence=None, weight=None):
        '''Initializes a new instance of the ConstantAlphaModel class
        Args:
            type: The type of insight
            direction: The direction of the insight
            period: The period over which the insight will come to fruition
            magnitude: The predicted change in magnitude as a +- percentage
            confidence: The confidence in the insight
            weight: The portfolio weight of the insights
        '''
        self.type = type
        self.direction = direction
        self.period = period
        self.magnitude = magnitude
        self.confidence = confidence
        self.weight = weight
        self.securities = []
        self.insightsTimeBySymbol = {}

        typeString = Extensions.GetEnumString(type, InsightType)
        directionString = Extensions.GetEnumString(direction, InsightDirection)

        self.Name = '{}({},{},{}'.format(self.__class__.__name__, typeString, directionString, strfdelta(period))
        if magnitude is not None:
            self.Name += ',{}'.format(magnitude)
        if confidence is not None:
            self.Name += ',{}'.format(confidence)
        self.Name += ')'

    def Update(self, algorithm, data):
        '''Creates a constant insight for each security as specified via the constructor
        Args:
            algorithm: The algorithm instance
            data: The new data available
        Returns:
            The new insights generated
        '''
        insights = []
        for security in self.securities:
            if security.Price != 0 and self.ShouldEmitInsight(algorithm.UtcTime, security.Symbol):
                insights.append(Insight(security.Symbol, self.period, self.type, self.direction,
                                        self.magnitude, self.confidence, weight=self.weight))
        return insights

    def OnSecuritiesChanged(self, algorithm, changes):
        '''Event fired each time 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
        '''
        for added in changes.AddedSecurities:
            self.securities.append(added)

        for removed in changes.RemovedSecurities:
            if removed in self.securities:
                self.securities.remove(removed)
            if removed.Symbol in self.insightsTimeBySymbol:
                self.insightsTimeBySymbol.pop(removed.Symbol)

    def ShouldEmitInsight(self, utcTime, symbol):
        '''Determines whether a new insight should be emitted'''
        generatedTimeUtc = self.insightsTimeBySymbol.get(symbol)

        if generatedTimeUtc is not None:
            if utcTime - generatedTimeUtc < self.period:
                return False

        self.insightsTimeBySymbol[symbol] = utcTime
        return True

def strfdelta(tdelta):
    d = tdelta.days
    h, rem = divmod(tdelta.seconds, 3600)
    m, s = divmod(rem, 60)
    return "{}.{:02d}:{:02d}:{:02d}".format(d, h, m, s)
#region imports
from AlgorithmImports import *
#endregion
from clr import AddReference
AddReference("QuantConnect.Common")
AddReference("QuantConnect.Algorithm")
AddReference("QuantConnect.Algorithm.Framework")
AddReference("QuantConnect.Indicators")

from QuantConnect import *
from QuantConnect.Indicators import *
from QuantConnect.Algorithm import *
from QuantConnect.Algorithm.Framework import *
from QuantConnect.Algorithm.Framework.Alphas import *


class EmaCrossAlphaModel(AlphaModel):
    '''Alpha model that uses an EMA cross to create insights'''

    def __init__(self,
                 fastPeriod = 12,
                 slowPeriod = 26,
                 resolution = Resolution.Daily):
        '''Initializes a new instance of the EmaCrossAlphaModel class
        Args:
            fastPeriod: The fast EMA period
            slowPeriod: The slow EMA period'''
        self.fastPeriod = fastPeriod
        self.slowPeriod = slowPeriod
        self.resolution = resolution
        self.predictionInterval = Time.Multiply(Extensions.ToTimeSpan(resolution), fastPeriod)
        self.symbolDataBySymbol = {}

        resolutionString = Extensions.GetEnumString(resolution, Resolution)
        self.Name = '{}({},{},{})'.format(self.__class__.__name__, fastPeriod, slowPeriod, resolutionString)


    def Update(self, algorithm, data):
        '''Updates this alpha model with the latest data from the algorithm.
        This is called each time the algorithm receives data for subscribed securities
        Args:
            algorithm: The algorithm instance
            data: The new data available
        Returns:
            The new insights generated'''
        insights = []
        for symbol, symbolData in self.symbolDataBySymbol.items():
            if symbolData.Fast.IsReady and symbolData.Slow.IsReady:

                if symbolData.FastIsOverSlow:
                    if symbolData.Slow > symbolData.Fast:
                        insights.append(Insight.Price(symbolData.Symbol, self.predictionInterval, InsightDirection.Down))

                elif symbolData.SlowIsOverFast:
                    if symbolData.Fast > symbolData.Slow:
                        insights.append(Insight.Price(symbolData.Symbol, self.predictionInterval, InsightDirection.Up))

            symbolData.FastIsOverSlow = symbolData.Fast > symbolData.Slow

        return insights

    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'''
        for added in changes.AddedSecurities:
            symbolData = self.symbolDataBySymbol.get(added.Symbol)
            if symbolData is None:
                # create fast/slow EMAs
                symbolData = SymbolData(added)
                symbolData.Fast = algorithm.EMA(added.Symbol, self.fastPeriod, self.resolution)
                symbolData.Slow = algorithm.EMA(added.Symbol, self.slowPeriod, self.resolution)
                self.symbolDataBySymbol[added.Symbol] = symbolData
            else:
                # a security that was already initialized was re-added, reset the indicators
                symbolData.Fast.Reset()
                symbolData.Slow.Reset()


class SymbolData:
    '''Contains data specific to a symbol required by this model'''
    def __init__(self, security):
        self.Security = security
        self.Symbol = security.Symbol
        self.Fast = None
        self.Slow = None

        # True if the fast is above the slow, otherwise false.
        # This is used to prevent emitting the same signal repeatedly
        self.FastIsOverSlow = False

    @property
    def SlowIsOverFast(self):
        return not self.FastIsOverSlow

# Your New Python File
#region imports
from AlgorithmImports import *
#endregion


"""
COMPREHENSIVE STRATEGY EXPLANATION

This strategy uses the QuantConnect Algorithm Framework. It is a multi-asset ETF
allocation model that combines manual universe selection, a constant alpha model,
mean-variance portfolio construction, immediate execution, and benchmark plotting.

The universe is a diversified ETF basket. It includes U.S. equities, international
equities, emerging markets, bonds, real estate, gold, equity factor ETFs, sector
ETFs, and industry ETFs. The objective is to create a broad allocation universe
rather than a single-asset or single-factor strategy.

The alpha model is intentionally simple. It emits constant long-only Up insights
for the selected ETF universe. This keeps the example pedagogical: the expected
return assumption is not coming from a complex forecasting model. Instead, the
portfolio construction model is responsible for determining the allocation based
on historical return and risk relationships.

The portfolio construction model is QuantConnect's
MeanVarianceOptimizationPortfolioConstructionModel. It estimates portfolio weights
using recent historical returns and a mean-variance optimizer. This framework
approach lets the algorithm separate the investment process into clear layers:
the universe defines what can be owned, the alpha model defines directional
views, the portfolio construction model determines weights, and the execution
model places trades.

Because mean-variance optimization can sometimes produce unstable allocations,
the model is kept pedagogical and conservative. The universe is diversified,
duplicate tickers are removed, the end date is standardized to May 5, 2026, and
the benchmark is a balanced 60% SPY and 40% AGG portfolio. This benchmark is more
appropriate than 100% SPY because the strategy invests across equities, fixed
income, real estate, commodities, and factors.

The code also includes enhanced diagnostics. It plots the strategy equity curve,
the custom benchmark, invested weight, cash weight, active holdings, and both
strategy and benchmark drawdowns.
"""


class MeanVarianceOptimizationAlgorithm(QCAlgorithm):

    def Initialize(self):

        # ------------------------------------------------------------
        # 1. BACKTEST SETTINGS
        # ------------------------------------------------------------
        self.SetStartDate(2020, 5, 1)
        self.SetEndDate(2026, 5, 5)

        self.initial_cash = 10000000
        self.SetCash(self.initial_cash)

        # ------------------------------------------------------------
        # 2. UNIVERSE SELECTION
        # ------------------------------------------------------------
        self.UniverseSettings.Resolution = Resolution.Daily

        tickers = [
            # Aggregate indices
            "IEFA", "AGG", "IWM", "EEM", "EWJ", "EPP",

            # Fixed income and real estate
            "IYR", "LQD", "EMB", "IEF", "IEI",

            # Commodities
            "IAU",

            # Factors
            "USMV", "DGRO", "QUAL", "DVY", "MTUM", "VLUE",
            "EFAV", "EEMV", "IDV", "IQLT",

            # Sectors and industries
            "IBB", "IHI", "IYW", "IGF", "IYH", "IYF",
            "IXC", "PICK", "IYE", "KXI", "WOOD",

            # Broad U.S. equity anchor
            "SPY"
        ]

        symbols = [
            Symbol.Create(ticker, SecurityType.Equity, Market.USA)
            for ticker in tickers
        ]

        self.SetUniverseSelection(
            ManualUniverseSelectionModel(symbols)
        )

        # ------------------------------------------------------------
        # 3. ALPHA MODEL
        # ------------------------------------------------------------
        # Constant long-only alpha.
        # This keeps the alpha layer simple and lets portfolio construction
        # determine the allocation.
        self.AddAlpha(
            ConstantAlphaModel(
                InsightType.Price,
                InsightDirection.Up,
                timedelta(days=35),
                0.025,
                None
            )
        )

        # ------------------------------------------------------------
        # 4. PORTFOLIO CONSTRUCTION MODEL
        # ------------------------------------------------------------
        # Mean-variance optimization using daily data and a 30-day period.
        # This respects the QC Algorithm Framework approach.
        self.SetPortfolioConstruction(
            MeanVarianceOptimizationPortfolioConstructionModel(
                resolution=Resolution.Daily,
                period=30
            )
        )

        # ------------------------------------------------------------
        # 5. EXECUTION MODEL
        # ------------------------------------------------------------
        self.SetExecution(
            ImmediateExecutionModel()
        )

        # ------------------------------------------------------------
        # 6. BENCHMARK
        # ------------------------------------------------------------
        self._benchmark_spy = self.AddEquity(
            "SPY",
            Resolution.Daily,
            Market.USA
        ).Symbol

        self._benchmark_agg = self.AddEquity(
            "AGG",
            Resolution.Daily,
            Market.USA
        ).Symbol

        self.SetBenchmark(self._benchmark_spy)

        self.initial_spy_price = None
        self.initial_agg_price = None

        # Custom benchmark:
        # 60% SPY and 40% AGG.
        self.benchmark_spy_weight = 0.60
        self.benchmark_agg_weight = 0.40

        # ------------------------------------------------------------
        # 7. DIAGNOSTIC STATE VARIABLES
        # ------------------------------------------------------------
        self.strategy_peak = self.initial_cash
        self.benchmark_peak = self.initial_cash

    def OnData(self, data):

        # ------------------------------------------------------------
        # 1. CHECK BENCHMARK DATA
        # ------------------------------------------------------------
        if self._benchmark_spy not in data or data[self._benchmark_spy] is None:
            return

        if self._benchmark_agg not in data or data[self._benchmark_agg] is None:
            return

        spy_price = self.Securities[self._benchmark_spy].Price
        agg_price = self.Securities[self._benchmark_agg].Price

        if spy_price <= 0 or agg_price <= 0:
            return

        if self.initial_spy_price is None:
            self.initial_spy_price = spy_price

        if self.initial_agg_price is None:
            self.initial_agg_price = agg_price

        # ------------------------------------------------------------
        # 2. CUSTOM BENCHMARK VALUE
        # ------------------------------------------------------------
        benchmark_value = (
            self.initial_cash
            * (
                self.benchmark_spy_weight
                * spy_price
                / self.initial_spy_price
                +
                self.benchmark_agg_weight
                * agg_price
                / self.initial_agg_price
            )
        )

        # ------------------------------------------------------------
        # 3. PLOT STRATEGY EQUITY AND BENCHMARK
        # ------------------------------------------------------------
        self.Plot(
            "Strategy Equity",
            "Portfolio Value",
            self.Portfolio.TotalPortfolioValue
        )

        self.Plot(
            "Strategy Equity",
            "Benchmark 60 pct SPY 40 pct AGG",
            benchmark_value
        )

        # ------------------------------------------------------------
        # 4. PORTFOLIO STATE DIAGNOSTICS
        # ------------------------------------------------------------
        invested_value = 0
        active_holdings = 0

        for holding in self.Portfolio.Values:

            if holding.Invested:
                invested_value += abs(holding.HoldingsValue)
                active_holdings += 1

        if self.Portfolio.TotalPortfolioValue > 0:

            invested_weight = (
                invested_value
                / self.Portfolio.TotalPortfolioValue
            )

            cash_weight = 1 - invested_weight

            self.Plot(
                "Portfolio State",
                "Invested Weight",
                invested_weight
            )

            self.Plot(
                "Portfolio State",
                "Cash Weight",
                cash_weight
            )

            self.Plot(
                "Portfolio Diagnostics",
                "Active Holdings",
                active_holdings
            )

        # ------------------------------------------------------------
        # 5. DRAWDOWN DIAGNOSTICS
        # ------------------------------------------------------------
        self.strategy_peak = max(
            self.strategy_peak,
            self.Portfolio.TotalPortfolioValue
        )

        self.benchmark_peak = max(
            self.benchmark_peak,
            benchmark_value
        )

        strategy_drawdown = (
            self.Portfolio.TotalPortfolioValue
            / self.strategy_peak
            - 1
        )

        benchmark_drawdown = (
            benchmark_value
            / self.benchmark_peak
            - 1
        )

        self.Plot(
            "Drawdown",
            "Strategy Drawdown",
            strategy_drawdown
        )

        self.Plot(
            "Drawdown",
            "Benchmark Drawdown",
            benchmark_drawdown
        )