Return Asymmetry Effect in Commodity Futures
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Return Asymmetry in Commodity Futures
Ladislav Ďurian; Matus Padysak
- ?Quantpedia.com
- SKComenius University Bratislava
- ?Comenius University - Faculty of Mathematics, Physics and Informatics
Strategy in a nutshell
The investment universe consists of 22 commodity futures, namely: soybean oil, corn, cocoa, cotton, feeder cattle, gold, copper, heating oil, coffee, live cattle, lean hogs, natural gas, oats, orange juice, palladium, platinum, soybean, sugar, silver, soybean meal, wheat, and crude oil. Firstly, at the beginning of each month, construct the asymmetry measure (IE) for each commodity based on the latest 260 daily returns using the following formula (the formula originally consists of theoretical density and integrals, however the solution is simple when empirical distribution is utilized): IE = (number of trading days when the daily return is greater than the average plus two standard deviations) – (number of trading days when the daily return is smaller than the average minus two standard deviations). Then rank the commodities according to their IE. Buy the bottom seven commodities with the lowest IE in the previous month and sell the top seven commodities with the highest IE in the previous month. Weigh the portfolio equally and rebalance monthly.
Economic rationale
A new measure IE that asymmetric strategy relies on uses the difference between upside and downside return probabilities to capture the degree of asymmetry. The greater the measure, the greater the upside potential of the asset return. Typical risk-averse investors prefer extreme gains and avoid extreme losses. Consequently, they bid up the prices of assets with a high chance of extreme gains and pay a lower price for assets with a high likelihood of extreme losses. As a result, the high (low) IE assets become overvalued (undervalued), and their subsequent returns are lower (higher). Therefore, the asymmetric strategy goes short on the most overvalued commodities with the highest IE and long on the most undervalued commodities with the lowest IE. Besides, the correlation analysis between the proposed strategy and the corresponding skewness portfolio indicates a low positive correlation with a correlation coefficient of 0.46. Even though the skewness and asymmetry effects are related, the correlation is not that high, and both effects form distinct trading strategies.
Backtest performance
Full Python code
from AlgoLib import *
class ReturnAsymmetryEffectInCommodityFutures(XXX):
def Initialize(self):
self.SetStartDate(2000, 1, 1)
self.SetCash(100000)
self.tickers = [
"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_RB2", # Gasoline Futures, Continuous Contract
"CME_KW2", # Wheat Kansas, 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
"ICE_RS1", # Canola Futures, Continuous Contract
"ICE_GO1", # Gas Oil Futures, Continuous Contract
"ICE_WT1", # WTI Crude Futures, Continuous Contract
]
self.data = {} # storing objects of SymbolData class keyed by comodity symbols
self.period = 261 # need 261 daily prices, to calculate 260 daily returns
self.buy_count = 7 # buy n comodities on each rebalance
self.sell_count = 7 # sell n comodities on each rebalance
self.symbol = self.AddEquity("SPY", Resolution.Daily).Symbol
# subscribe to futures contracts
for ticker in self.tickers:
security = self.AddData(QuantpediaFutures, ticker, Resolution.Daily)
security.SetFeeModel(CustomFeeModel())
security.SetLeverage(5)
self.data[security.Symbol] = SymbolData(self.period)
self.rebalance_flag = False
self.Schedule.On(self.DateRules.MonthStart(self.symbol), self.TimeRules.BeforeMarketClose(self.symbol, 0), self.Rebalance)
def OnData(self, data):
# update daily closes
for symbol in self.data:
if symbol in data and data[symbol]:
close = data[symbol].Value
self.data[symbol].update_closes(close)
# rebalance monthly
if not self.rebalance_flag:
return
self.rebalance_flag = False
IE = {}
for symbol, symbol_obj in self.data.items():
# check if comodity has ready prices
if not symbol_obj.is_ready():
continue
# calculate IE
IE_value = symbol_obj.calculate_IE()
# store IE value under comodity symbol
IE[symbol] = IE_value
# make sure, there are enough comodities for rebalance
if len(IE) < (self.buy_count + self.sell_count):
return
# sort commodities based on IE values
sorted_by_IE = [x[0] for x in sorted(IE.items(), key=lambda item: item[1])]
# select long and short parts
long = sorted_by_IE[:self.buy_count]
short = sorted_by_IE[-self.sell_count:]
# trade execution
invested = [x.Key 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 / self.buy_count)
for symbol in short:
self.SetHoldings(symbol, -1 / self.sell_count)
def Rebalance(self):
self.rebalance_flag = True
class SymbolData():
def __init__(self, period):
self.closes = RollingWindow[float](period)
def update_closes(self, close):
self.closes.Add(close)
def is_ready(self):
return self.closes.IsReady
def calculate_IE(self):
closes = np.array([x for x in self.closes])
daily_returns = (closes[:-1] - closes[1:]) / closes[1:]
average_daily_returns = np.average(daily_returns)
two_daily_returns_std = 2 * np.std(daily_returns)
avg_plus_two_std = average_daily_returns + two_daily_returns_std
avg_minus_two_std = average_daily_returns - two_daily_returns_std
over_avg_plus_two_std = 0 # counting number of daily returns, which were over avg_plus_two_std
under_avg_minus_two_std = 0 # counting number of daily returns, which were under avg_minus_two_std
for daily_return in daily_returns:
if daily_return > avg_plus_two_std:
over_avg_plus_two_std += 1
elif daily_return < avg_minus_two_std:
under_avg_minus_two_std += 1
IE_value = over_avg_plus_two_std - under_avg_minus_two_std
return IE_value
# 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"))