Need help with mean-variance portfolio optimization implementation

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from sklearn.ensemble import RandomForestRegressor
from sklearn.model_selection import train_test_split
import pandas as pd
import numpy as np
from pypfopt.efficient_frontier import EfficientFrontier
from pypfopt import risk_models
from pypfopt import expected_returns

class AlphaFiveUSTreasuries(QCAlgorithm):

def Initialize(self):

#1. Required: Five years of backtest history
self.SetStartDate(2001, 1, 1)

#2. Required: Alpha Streams Models:
self.SetBrokerageModel(BrokerageName.AlphaStreams)

#3. Required: Significant AUM Capacity
self.SetCash(100000)

self.UniverseSettings.Resolution = Resolution.Daily
self.AddUniverse(self.CoarseUniverseSelection)

self.AddEquity("SPY",Resolution.Daily)

#4. Required: Benchmark to SPY
self.SetBenchmark("SPY")

self.SetPortfolioConstruction(InsightWeightingPortfolioConstructionModel())
self.SetExecution(ImmediateExecutionModel())

self.assets = []

self.symbols = {}

self.portfolioValue = RollingWindow[Decimal](500)

self.SetWarmup(500)

# initializing security with last known price
# self.SetSecurityInitializer(lambda x: x.SetMarketPrice(self.GetLastKnownPrice(x)))

# fine tune how frequent training is to obtain best results
# self.Schedule.On(self.DateRules.Every(DayOfWeek.Monday), self.TimeRules.AfterMarketOpen("SPY", 30), self.EveryDayAfterMarketOpen)
# self.Schedule.On(self.DateRules.MonthEnd(), self.TimeRules.AfterMarketOpen("SPY",0), self.EveryMonthAfterMarketClose)

# Portfolio Optimization using Mean-Variance
# def OptimalPortfolio(self, coarse):
# pass


def CoarseUniverseSelection(self, coarse):
# if self.lastMonth == algorithm.Time.month:
# return Universe.Unchanged
# self.lastMonth = algorithm.Time.month

# if self.IsWarmingUp:
# return

sortedByDollarVolume = sorted([x for x in coarse if x.HasFundamentalData], key=lambda x: x.DollarVolume, reverse=True)

self.Debug(f"test going in sort dollar volume")

for i in range(10):
if len(self.assets) <10 and sortedByDollarVolume[i] not in self.assets:
self.assets.append(sortedByDollarVolume[i].Symbol)

self.df = pd.DataFrame()

# if self.df.iloc[0:,1].count() == 252:
# self.assets.append()

# for i in range(len(self.assets)):
# self.symbols[self.assets[i]] = self.AddEquity( self.assets[i] ,Resolution.Hour)

for x in range(len(self.assets)):
self.AddEquity( self.assets[x] ,Resolution.Daily)

# for asset in self.assets, count column less than 252 then drop
self.df = self.History(self.assets, 252)

# check if historical data 252 days available in asset
self.df = self.df["close"].unstack(level=0)

weights = np.array([0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1])

self.returns = self.df.pct_change()

# show annualized covariance matrix
self.cov_matrix_annual = self.returns.cov() * 252

# self.Debug(self.cov_matrix_annual.iloc[:,1])

# calculate portfolio variance
self.port_variance = np.dot(weights.T, np.dot(self.cov_matrix_annual, weights))

# calculate portfolio volatility
self.port_volatility = np.sqrt(self.port_variance)

# self.Debug(f"returns mean")
# self.Debug(self.returns.mean())

# Calculate annual portfolio return
self.portfolioSimpleAnnualReturn = np.sum(self.returns.mean() * weights) * 252

# show expected annual return, volatility (risk), variance
self.percent_var = str(round(self.port_variance, 2) * 100) + '%'
self.percent_vols = str(round(self.port_volatility, 2) * 100) + '%'
self.percent_ret = str(round(self.portfolioSimpleAnnualReturn, 2) * 100) + '%'

self.Debug(f'Expected annual return: ')
self.Debug(self.percent_ret)

self.Debug('Annual volatility / risk: ')
self.Debug(self.percent_vols)

self.Debug('Annual variance: ')
self.Debug(self.percent_var)

# Portfolio Optimization

# Calulate the expected returns and annualized sample covariance matrix of asset returns
self.mu = expected_returns.mean_historical_return(self.df)

self.S = risk_models.sample_cov(self.df)

self.ef = EfficientFrontier(self.mu, self.S)

self.weights = (self.ef).max_sharpe()

self.cleaned_weights = self.ef.clean_weights()

self.cleaned_weights = [round(float(x), 2) for x in self.cleaned_weights.values()]

# fix cleaned weights
# self.Debug(f"show updated weights")
self.Debug(self.cleaned_weights)

# self.Debug(self.ef.portfolio_performance(verbose = True))

return [Symbol.Create(x, SecurityType.Equity, Market.USA) for x in self.symbols.values()]

Hi guys, I'm currently trying to implement mean-variance portfolio optimization in QuantConnect. However, I realised that there is a problem with my annual returns. It starts off positive and ends up being negative. 

The algorithm also crashes after running for a while and the following runtime error will be displayed "Runtime Error: OptimizationError : Please check your objectives/constraints or use a different solver.at CoarseUniverseSelection in main.py:line 130 :: self.weights = (self.ef).max_sharpe()".

Any help is appreciated, thank you!

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The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by QuantConnect. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. QuantConnect makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances. All investments involve risk, including loss of principal. You should consult with an investment professional before making any investment decisions.


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The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by QuantConnect. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. QuantConnect makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances. All investments involve risk, including loss of principal. You should consult with an investment professional before making any investment decisions.


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