bonds, commodities, currencies, equities · Global · CFDs, futures · Monthly · Global Free

Cross-Asset Skewness Effect

Academic paper

AuthorsNick Baltas; Gabriel Salinas

Institute

Goldman Sachs (United States)
?Goldman Sachs International
?Imperial College Business School
Texas Board of Nursing
?Teacher Retirement System of Texas

Paper linkhttps://papers.ssrn.com/sol3/papers.cfm?abstract_id=3505422

Strategy in a nutshell

The strategy trades 19 equity index futures, 9 government bond futures, 9 currency forwards, and 24 commodity futures. Monthly, daily returns are used to compute 12-month rolling skewness via Pearson’s coefficient. A zero-cost skewness portfolio is built per asset class, going $1 long the most negatively skewed and $1 short the most positively skewed. A global skewness factor combines all asset-class portfolios, scaled to 10% volatility and equally weighted, aiming to profit from asymmetries in returns across markets.

Economic rationale

Investors prefer positively skewed assets, overweighing low-probability gains and avoiding shorting them, creating a skewness risk premium. This dynamic persists even without short-selling constraints, as investors selectively hedge to minimize risk while maximizing skewness. The preference for skewness drives underperformance of positively skewed assets, generating exploitable opportunities across markets.

Backtest performance

Annualised return3.5%

Volatility4.86%

Beta0.142

Sharpe ratio0.72

Sortino ratio0.157

Win rate55%

Full Python code

1import numpy as np
2from scipy.stats import skew
3from AlgorithmImports import *
4class CrossAssetSkewnessEffect(QCAlgorithm):
5def Initialize(self):
6 self.SetStartDate(2010, 1, 1)
7 self.SetCash(100000)
8 
9 self.leverage = 2
10 
11 commodities = ["CME_S1",   # Soybean Futures, Continuous Contract
12                 "CME_W1",   # Wheat Futures, Continuous Contract
13                 "CME_SM1",  # Soybean Meal Futures, Continuous Contract
14                 "CME_BO1",  # Soybean Oil Futures, Continuous Contract
15                 "CME_C1",   # Corn Futures, Continuous Contract
16                 "CME_O1",   # Oats Futures, Continuous Contract
17                 "CME_LC1",  # Live Cattle Futures, Continuous Contract
18                 "CME_FC1",  # Feeder Cattle Futures, Continuous Contract
19                 "CME_LN1",  # Lean Hog Futures, Continuous Contract
20                 "CME_GC1",  # Gold Futures, Continuous Contract
21                 "CME_SI1",  # Silver Futures, Continuous Contract
22                 "CME_PL1",  # Platinum Futures, Continuous Contract
23                 "CME_CL1",  # Crude Oil Futures, Continuous Contract
24                 "CME_HG1",  # Copper Futures, Continuous Contract
25                 "CME_LB1",  # Random Length Lumber Futures, Continuous Contract
26                 # "CME_NG1",  # Natural Gas (Henry Hub) Physical Futures, Continuous Contract
27                 "CME_PA1",  # Palladium Futures, Continuous Contract 
28                 "CME_RR1",  # Rough Rice Futures, Continuous Contract
29                 
30                 "ICE_CC1",  # Cocoa Futures, Continuous Contract 
31                 "ICE_CT1",  # Cotton No. 2 Futures, Continuous Contract
32                 "ICE_KC1",  # Coffee C Futures, Continuous Contract
33                 "ICE_O1",   # Heating Oil Futures, Continuous Contract
34                 "ICE_OJ1",  # Orange Juice Futures, Continuous Contract
35                 "ICE_SB1",  # Sugar No. 11 Futures, Continuous Contract
36                 ]
37                 
38 currencies = ["CME_AD1", # Australian Dollar Futures, Continuous Contract #1
39             "CME_BP1", # British Pound Futures, Continuous Contract #1
40             "CME_CD1", # Canadian Dollar Futures, Continuous Contract #1
41             "CME_EC1", # Euro FX Futures, Continuous Contract #1
42             "CME_JY1", # Japanese Yen Futures, Continuous Contract #1
43             "CME_MP1", # Mexican Peso Futures, Continuous Contract #1
44             "CME_NE1",# New Zealand Dollar Futures, Continuous Contract #1
45             "CME_SF1", # Swiss Franc Futures, Continuous Contract #1
46             ]
47                 
48 equities = ["ICE_DX1",      # US Dollar Index Futures, Continuous Contract #1
49             "CME_NQ1",      # E-mini NASDAQ 100 Futures, Continuous Contract #1
50             "EUREX_FDAX1",  # DAX Futures, Continuous Contract #1
51             "CME_ES1",      # E-mini S&P 500 Futures, Continuous Contract #1
52             "EUREX_FSMI1",  # SMI Futures, Continuous Contract #1
53             "EUREX_FSTX1",  # STOXX Europe 50 Index Futures, Continuous Contract #1
54             "LIFFE_FCE1",   # CAC40 Index Futures, Continuous Contract #1
55             "LIFFE_Z1",     # FTSE 100 Index Futures, Continuous Contract #1
56             "SGX_NK1",      # SGX Nikkei 225 Index Futures, Continuous Contract #1
57             ]
58             
59 bonds = ["CME_TY1",      # 10 Yr Note Futures, Continuous Contract #1
60         "CME_FV1",      # 5 Yr Note Futures, Continuous Contract #1
61         "CME_TU1",      # 2 Yr Note Futures, Continuous Contract #1
62         "ASX_XT1",     # 10 Year Commonwealth Treasury Bond Futures, Continuous Contract #1
63         "ASX_YT1",     # 3 Year Commonwealth Treasury Bond Futures, Continuous Contract #1
64         "EUREX_FGBL1",  # Euro-Bund (10Y) Futures, Continuous Contract #1
65         "EUREX_FBTP1", # Long-Term Euro-BTP Futures, Continuous Contract #1
66         "EUREX_FGBM1",  # Euro-Bobl Futures, Continuous Contract #1
67         "EUREX_FGBS1",  # Euro-Schatz Futures, Continuous Contract #1 
68         "SGX_JB1",      # SGX 10-Year Mini Japanese Government Bond Futures
69         "LIFFE_R1"      # Long Gilt Futures, Continuous Contract #1
70         "MX_CGB1",     # Ten-Year Government of Canada Bond Futures, Continuous Contract #1
71         ]
72 self.asset_classes = {}
73 self.asset_classes['commodities'] = commodities
74 self.asset_classes['currencies'] = currencies
75 self.asset_classes['equities'] = equities
76 self.asset_classes['bonds'] = bonds
77 
78 self.data = {}
79 self.period = 12 * 21
80 
81 for symbol in commodities + currencies + equities + bonds:
82     # Quantpedia #1 Contract.
83     data = self.AddData(QuantpediaFutures, symbol, Resolution.Daily)
84     data.SetFeeModel(CustomFeeModel())
85     data.SetLeverage(self.leverage)
86     
87     self.data[symbol] = RollingWindow[float](self.period)
88     
89 self.rebalance_flag: bool = False
90 self.Schedule.On(self.DateRules.MonthStart(commodities[0]), self.TimeRules.At(0, 0), self.Rebalance)
91 self.settings.minimum_order_margin_portfolio_percentage = 0.
92
93def OnData(self, data):
94 # store daily prices
95 for asset_class in self.asset_classes:
96     for symbol in self.asset_classes[asset_class]:
97         if symbol in data and data[symbol]:
98             price = data[symbol].Value
99             self.data[symbol].Add(price)
100 if not self.rebalance_flag:
101     return
102 self.rebalance_flag = False
103 class_count = len(self.asset_classes)
104 weight = {}
105 
106 for asset_class in self.asset_classes:
107     
108     class_symbols = self.asset_classes[asset_class]
109     class_symbols_count = len(class_symbols)
110     
111     skewness_data = {}
112     for symbol in class_symbols:
113         if self.data[symbol].IsReady:
114             if self.Securities[symbol].GetLastData() and self.Time.date() < QuantpediaFutures.get_last_update_date()[symbol]:
115                 prices = np.array([x for x in self.data[symbol]])
116                 returns = (prices[:-1]-prices[1:])/prices[1:]
117                 if len(returns) == self.period-1:
118                     skewness_data[symbol] = skew(returns)
119             
120     if len(skewness_data) == 0: continue
121     
122     # Sort by skewness return.
123     sorted_by_skewness = sorted(skewness_data.items(), key = lambda x: x[1], reverse = True)
124     positive_skewness = [x for x in sorted_by_skewness if x[1] > 0]
125     negative_skewness = [x for x in sorted_by_skewness if x[1] < 0]
126     
127     # Ranking.
128     rank = {}
129     score = len(negative_skewness)
130     for symbol_data in negative_skewness:
131         rank[symbol_data[0]] = score
132         score -= 1
133         
134     score = -1
135     for symbol_data in positive_skewness:
136         rank[symbol_data[0]] = score
137         score -= 1
138     
139     # Weighting within class. - Skewness based.
140     total_items = len(positive_skewness + negative_skewness)
141     if total_items == 0: continue
142     partial_weight = 1 / sum([abs(score) for symbol, score in rank.items()])
143     
144     # Weighting within portfolio. - Equally weighted.
145     for symbol, r in rank.items():
146         weight[symbol] = (1 / class_count) * (r * partial_weight)
147 
148 if len(weight) == 0: return
149 # Trade execution
150 portfolio: List[PortfolioTarget] = [PortfolioTarget(symbol, self.leverage * w) for symbol, w in weight.items() if data.contains_key(symbol) and data[symbol]]
151 self.SetHoldings(portfolio, True)
152def Rebalance(self):
153 self.rebalance_flag = True
154# Custom fee model
155class CustomFeeModel(FeeModel):
156def GetOrderFee(self, parameters):
157 fee = parameters.Security.Price * parameters.Order.AbsoluteQuantity * 0.00005
158 return OrderFee(CashAmount(fee, "USD"))
159# Quantpedia data.
160# NOTE: IMPORTANT: Data order must be ascending (datewise)
161class QuantpediaFutures(PythonData):
162_last_update_date:Dict[Symbol, datetime.date] = {}
163@staticmethod
164def get_last_update_date() -> Dict[Symbol, datetime.date]:
165return QuantpediaFutures._last_update_date
166def GetSource(self, config, date, isLiveMode):
167 return SubscriptionDataSource("data.quantpedia.com/backtesting_data/futures/{0}.csv".format(config.Symbol.Value), SubscriptionTransportMedium.RemoteFile, FileFormat.Csv)
168def Reader(self, config, line, date, isLiveMode):
169 data = QuantpediaFutures()
170 data.Symbol = config.Symbol
171 
172 if not line[0].isdigit(): return None
173 split = line.split(';')
174 
175 data.Time = datetime.strptime(split[0], "%d.%m.%Y") + timedelta(days=1)
176 data['back_adjusted'] = float(split[1])
177 data['spliced'] = float(split[2])
178 data.Value = float(split[1])
179 if config.Symbol.Value not in QuantpediaFutures._last_update_date:
180     QuantpediaFutures._last_update_date[config.Symbol.Value] = datetime(1,1,1).date()
181 if data.Time.date() > QuantpediaFutures._last_update_date[config.Symbol.Value]:
182     QuantpediaFutures._last_update_date[config.Symbol.Value] = data.Time.date()
183 return data