Overall Statistics Total Trades 2225 Average Win 1.60% Average Loss -1.15% Compounding Annual Return 17.711% Drawdown 40.000% Expectancy 0.320 Net Profit 2855.372% Sharpe Ratio 0.843 Probabilistic Sharpe Ratio 13.493% Loss Rate 45% Win Rate 55% Profit-Loss Ratio 1.39 Alpha 0.166 Beta 0.008 Annual Standard Deviation 0.198 Annual Variance 0.039 Information Ratio 0.379 Tracking Error 0.265 Treynor Ratio 21.934 Total Fees \$11269.20
import numpy as np
from scipy.optimize import minimize

def Return(values):
return (values[-1] - values) / values

def Volatility(values):
values = np.array(values)
returns = (values[1:] - values[:-1]) / values[:-1]
return np.std(returns)

# Custom fee model
class CustomFeeModel(FeeModel):
def GetOrderFee(self, parameters):
fee = parameters.Security.Price * parameters.Order.AbsoluteQuantity * 0.00005
return OrderFee(CashAmount(fee, "USD"))

# Quandl free data
class QuandlFutures(PythonQuandl):
def __init__(self):
self.ValueColumnName = "settle"

# Quantpedia data
# NOTE: IMPORTANT: Data order must be ascending (datewise)
class QuantpediaFutures(PythonData):
def GetSource(self, config, date, isLiveMode):
return SubscriptionDataSource("data.quantpedia.com/backtesting_data/futures/{0}.csv".format(config.Symbol.Value), SubscriptionTransportMedium.RemoteFile, FileFormat.Csv)

def Reader(self, config, line, date, isLiveMode):
data = QuantpediaFutures()
data.Symbol = config.Symbol

if not line.isdigit(): return None
split = line.split(';')

data.Time = datetime.strptime(split, "%d.%m.%Y") + timedelta(days=1)
data['settle'] = float(split)
data.Value = float(split)

return data

# NOTE: Manager for new trades. It's represented by certain count of equally weighted brackets for long and short positions.
# If there's a place for new trade, it will be managed for time of holding period.
def __init__(self, algorithm, long_size, short_size, holding_period):
self.algorithm = algorithm  # algorithm to execute orders in.

self.long_size = long_size
self.short_size = short_size
self.weight = 1 / (self.long_size + self.short_size)

self.long_len = 0
self.short_len = 0

# Arrays of ManagedSymbols
self.symbols = []

self.holding_period = holding_period    # Days of holding.

managed_symbol = ManagedSymbol(symbol, self.holding_period, long_flag)

if long_flag:
# If there's a place for it.
if self.long_len < self.long_size:
self.symbols.append(managed_symbol)
self.algorithm.SetHoldings(symbol, self.weight)
self.long_len += 1
else:
# If there's a place for it.
if self.long_len < self.short_size:
self.symbols.append(managed_symbol)
self.algorithm.SetHoldings(symbol, - self.weight)
self.short_len += 1

# Decrement holding period and liquidate symbols.
def TryLiquidate(self):
symbols_to_delete = []
for managed_symbol in self.symbols:
managed_symbol.days_to_liquidate -= 1

# Liquidate.
if managed_symbol.days_to_liquidate == 0:
symbols_to_delete.append(managed_symbol)
self.algorithm.Liquidate(managed_symbol.symbol)
if managed_symbol.long_flag: self.long_len -= 1
else: self.short_len -= 1

# Remove symbols from management.
for managed_symbol in symbols_to_delete:
self.symbols.remove(managed_symbol)

class ManagedSymbol():
def __init__(self, symbol, days_to_liquidate, long_flag):
self.symbol = symbol
self.days_to_liquidate = days_to_liquidate
self.long_flag = long_flag

class PortfolioOptimization(object):
def __init__(self, df_return, risk_free_rate, num_assets):
self.daily_return = df_return
self.risk_free_rate = risk_free_rate
self.n = num_assets # numbers of risk assets in portfolio
self.target_vol = 0.05

def annual_port_return(self, weights):
# calculate the annual return of portfolio
return np.sum(self.daily_return.mean() * weights) * 252

def annual_port_vol(self, weights):
# calculate the annual volatility of portfolio
return np.sqrt(np.dot(weights.T, np.dot(self.daily_return.cov() * 252, weights)))

def min_func(self, weights):
# method 1: maximize sharp ratio
return - self.annual_port_return(weights) / self.annual_port_vol(weights)

# method 2: maximize the return with target volatility
#return - self.annual_port_return(weights) / self.target_vol

def opt_portfolio(self):
# maximize the sharpe ratio to find the optimal weights
cons = ({'type': 'eq', 'fun': lambda x: np.sum(x) - 1})
bnds = tuple((0, 1) for x in range(2)) + tuple((0, 0.25) for x in range(self.n - 2))
opt = minimize(self.min_func,                               # object function
np.array(self.n * [1. / self.n]),            # initial value
method='SLSQP',                              # optimization method
bounds=bnds,                                 # bounds for variables
constraints=cons)                            # constraint conditions

opt_weights = opt['x']

return opt_weights
# https://quantpedia.com/strategies/skewness-effect-in-commodities/
#
# The investment universe consists of 27 futures contracts on commodities. Each month, investor calculates skewness (3rd moment of returns)
# from daily returns from data going 12 months into the past for all futures. Commodities are then sorted into quintiles and investor goes
# long quintile containing the commodities with the 20% lowest total skewness and short quintile containing the commodities with the 20% highest
# total skewness (over a ranking period of 12 months). The resultant portfolio is equally weighted and rebalanced each month.

import numpy as np
import fk_tools
from scipy.stats import skew

class SkewnessEffect(QCAlgorithm):

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

self.symbols = [
"CME_S1",   # Soybean Futures, Continuous Contract
"CME_W1",   # Wheat Futures, Continuous Contract
"CME_SM1",  # Soybean Meal Futures, Continuous Contract
"CME_BO1",  # Soybean Oil Futures, Continuous Contract
"CME_C1",   # Corn Futures, Continuous Contract
"CME_O1",   # Oats Futures, Continuous Contract
"CME_LC1",  # Live Cattle Futures, Continuous Contract
"CME_FC1",  # Feeder Cattle Futures, Continuous Contract
"CME_LN1",  # Lean Hog Futures, Continuous Contract
"CME_GC1",  # Gold Futures, Continuous Contract
"CME_SI1",  # Silver Futures, Continuous Contract
"CME_PL1",  # Platinum Futures, Continuous Contract
"CME_CL1",  # Crude Oil Futures, Continuous Contract
"CME_HG1",  # Copper Futures, Continuous Contract
"CME_LB1",  # Random Length Lumber Futures, Continuous Contract
"CME_NG1",  # Natural Gas (Henry Hub) Physical Futures, Continuous Contract
"CME_PA1",  # Palladium Futures, Continuous Contract
"CME_RR1",  # Rough Rice Futures, Continuous Contract

"ICE_CC1",  # Cocoa Futures, Continuous Contract
"ICE_CT1",  # Cotton No. 2 Futures, Continuous Contract
"ICE_KC1",  # Coffee C Futures, Continuous Contract
"ICE_O1",   # Heating Oil Futures, Continuous Contract
"ICE_OJ1",  # Orange Juice Futures, Continuous Contract
"ICE_SB1",  # Sugar No. 11 Futures, Continuous Contract
]

self.period = 12 * 21
self.SetWarmup(self.period)
self.data = {}

# True -> Quantpedia data
# False -> Quandl free data
self.use_quantpedia_data = True

if not self.use_quantpedia_data:
self.symbols = ['CHRIS/' + x for x in self.symbols]

for symbol in self.symbols:
data = None
if self.use_quantpedia_data:
else:

data.SetFeeModel(fk_tools.CustomFeeModel(self))
data.SetLeverage(5)
self.data[symbol] = RollingWindow[float](self.period)

self.Schedule.On(self.DateRules.MonthStart(self.symbols), self.TimeRules.AfterMarketOpen(self.symbols), self.Rebalance)

def OnData(self, data):
for symbol in self.symbols:
symbol_obj = self.Symbol(symbol)
if symbol_obj in data.Keys:
price = data[symbol_obj].Value
if price != 0:

def Rebalance(self):
if self.IsWarmingUp: return

# Skewness calculation
skewness_data = {}
for symbol in self.symbols:
prices = np.array([x for x in self.data[symbol]])
returns = (prices[:-1] / prices[1:]) - 1
if len(returns) == self.period - 1:
# NOTE: Manual skewness calculation example
# avg = np.average(returns)
# std = np.std(returns)
# skewness = (sum(np.power((x - avg), 3) for x in returns)) / ((self.return_history[symbol].maxlen-1) * np.power(std, 3))
skewness_data[symbol] = skew(returns)

# Skewness sorting
sorted_by_skewness = sorted(skewness_data.items(), key = lambda x: x, reverse = True)
quintile = int(len(sorted_by_skewness) / 5)
long = [x for x in sorted_by_skewness[-quintile:]]
short = [x for x in sorted_by_skewness[:quintile]]

self.SetHoldings(symbol, -1 / len(short))