Commodity Futures Skewness-Based Long-Short Monthly Strategy
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Commodities as Lotteries: Skewness and the Returns of Commodity Futures
Adrián Fernández-Pérez; Bart Frijns; Ana-Marı́a Fuertes; Joëlle Miffre
- NZAuckland University of Technology
- NLOpen University of the Netherlands
- ?Open University of the Netherlands - School of Management
- City, University of London
- ?Bayes Business School, City, University of London
- Audencia Business School
Strategy in a nutshell
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.
Economic rationale
Academic studies explain skewness effect in all assets by investors are willing to pay a higher price, and to earn a lower expected return, on assets with lottery-like payoffs. A recent study shows that skewness affects commodity futures returns and documents that skewness is priced in different markets than the ones where retail investors typically trade. Hence, its findings suggest that the effect of skewness on asset returns is not merely a consequence of retail investor preferences. Rather this indicates that other groups of traders have these heterogeneous preferences.
Backtest performance
Full Python code
import numpy as np
from AlgoLib import *
from scipy.stats import skew
class SkewnessEffect(XXX):
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
"CME_DA1", # Class III Milk Futures
"ICE_RS1", # Canola Futures, Continuous Contract
"ICE_GO1", # Gas Oil Futures, Continuous Contract
"CME_RB2", # Gasoline Futures, Continuous Contract
"CME_KW2", # Wheat Kansas, Continuous Contract
"ICE_WT1", # WTI Crude 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.quantile = 5
self.SetWarmup(self.period)
self.data = {}
for symbol in self.symbols:
data = self.AddData(QuantpediaFutures, symbol, Resolution.Daily)
data.SetFeeModel(CustomFeeModel())
data.SetLeverage(5)
self.data[symbol] = RollingWindow[float](self.period)
self.Schedule.On(self.DateRules.MonthStart(self.symbols[0]), self.TimeRules.At(0, 0), 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:
self.data[symbol].Add(price)
def Rebalance(self):
if self.IsWarmingUp: return
# Skewness calculation
skewness_data = {}
for symbol in self.symbols:
if self.data[symbol].IsReady:
if self.Securities[symbol].GetLastData() and (self.Time.date() - self.Securities[symbol].GetLastData().Time.date()).days < 5:
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)
long = []
short = []
if len(skewness_data) >= self.quantile:
# Skewness sorting
sorted_by_skewness = sorted(skewness_data.items(), key = lambda x: x[1], reverse = True)
quintile = int(len(sorted_by_skewness) / self.quantile)
long = [x[0] for x in sorted_by_skewness[-quintile:]]
short = [x[0] for x in sorted_by_skewness[:quintile]]
# Trade execution
invested = [x.Key.Value for x in self.Portfolio if x.Value.Invested]
for symbol in invested:
if symbol not in long + short:
self.Liquidate(symbol)
for symbol in long:
self.SetHoldings(symbol, 1 / len(long))
for symbol in short:
self.SetHoldings(symbol, -1 / len(short))
# 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[0].isdigit(): return None
split = line.split(';')
data.Time = datetime.strptime(split[0], "%d.%m.%Y") + timedelta(days=1)
data['back_adjusted'] = float(split[1])
data['spliced'] = float(split[2])
data.Value = float(split[1])
return data
# Custom fee model.
class CustomFeeModel(FeeModel):
def GetOrderFee(self, parameters):
fee = parameters.Security.Price * parameters.Order.AbsoluteQuantity * 0.00005
return OrderFee(CashAmount(fee, "USD"))