Skewness Effect in Country Equity Indexes

1import numpy as np
2from AlgorithmImports import *
3from scipy.stats import skew
4class SkewnessEffectEquities(QCAlgorithm):
5def Initialize(self):
6self.SetStartDate(2000, 1, 1)
7self.SetCash(100000)
8
9self.symbols = ["EWJ",  # iShares MSCI Japan Index ETF
10                "EZU",  # iShares MSCI Eurozone ETF
11                "EFNL", # iShares MSCI Finland Capped Investable Market Index ETF
12                "EWW",  # iShares MSCI Mexico Inv. Mt. Idx
13                "ERUS", # iShares MSCI Russia ETF
14                "IVV",  # iShares S&P 500 Index
15                "ICOL", # Consumer Discretionary Select Sector SPDR Fund
16                "AAXJ", # iShares MSCI All Country Asia ex Japan Index ETF
17                "AUD",  # Australia Bond Index Fund
18                "EWQ",  # iShares MSCI France Index ETF
19                "BUND", # Pimco Germany Bond Index Fund
20                "EWH",  # iShares MSCI Hong Kong Index ETF
21                "EPI",  # WisdomTree India Earnings ETF
22                "EIDO"  # iShares MSCI Indonesia Investable Market Index ETF
23                "EWI",  # iShares MSCI Italy Index ETF
24                "GAF",  # SPDR S&P Emerging Middle East & Africa ETF
25                "ENZL", # iShares MSCI New Zealand Investable Market Index Fund
26                "NORW"  # Global X FTSE Norway 30 ETF
27                "EWY",  # iShares MSCI South Korea Index ETF
28                "EWP",  # iShares MSCI Spain Index ETF
29                "EWD",  # iShares MSCI Sweden Index ETF
30                "EWL",  # iShares MSCI Switzerland Index ETF
31                "GXC",  # SPDR S&P China ETF
32                "EWC",  # iShares MSCI Canada Index ETF
33                "EWZ",  # iShares MSCI Brazil Index ETF
34                "ARGT", # Global X FTSE Argentina 20 ETF
35                "AND",  # Global X FTSE Andean 40 ETF
36                "AIA",  # iShares S&P Asia 50 Index ETF
37                "EWO",  # iShares MSCI Austria Investable Mkt Index ETF
38                "EWK",  # iShares MSCI Belgium Investable Market Index ETF
39                "BRAQ", # Global X Brazil Consumer ETF
40                "ECH",  # iShares MSCI Chile Investable Market Index ETF
41                "CHIB", # Global X China Technology ETF
42                "EGPT", # Market Vectors Egypt Index ETF
43                "ADRU"  # BLDRS Europe 100 ADR Index ETF
44                ]
45
46self.lookup_period = 24 * 21
47self.SetWarmup(self.lookup_period)
48self.data = {}
49
50for symbol in self.symbols:
51    data = self.AddEquity(symbol, Resolution.Daily)
52    data.SetLeverage(10)
53    self.data[symbol] = RollingWindow[float](self.lookup_period)
54    
55self.Schedule.On(self.DateRules.MonthStart(self.symbols[0]), self.TimeRules.AfterMarketOpen(self.symbols[0]), self.Rebalance)
56
57def OnData(self, data):
58for symbol in self.data:
59    if symbol in data and data[symbol]:
60        price = data[symbol].Value
61        if price != 0:
62            self.data[symbol].Add(price)
63        
64def Rebalance(self):
65if self.IsWarmingUp: return
66
67# Skewness calculation
68skewness_data = {}
69for symbol in self.symbols:
70    if self.data[symbol].IsReady and self.Securities[symbol].IsTradable and (self.Time.date() - self.Securities[symbol].GetLastData().Time.date()).days < 5:
71        prices = np.array([x for x in self.data[symbol]])
72        returns = (prices[:-1]-prices[1:])/prices[1:]
73        if len(returns) == self.lookup_period-1:
74            # NOTE: Manual skewness calculation example
75            # avg = np.average(returns)
76            # std = np.std(returns)
77            # skewness = (sum(np.power((x - avg), 3) for x in returns)) / ((self.return_history[symbol].maxlen-1) * np.power(std, 3))
78            skewness_data[symbol] = skew(returns)
79        
80# Skewness sorting
81sorted_by_skewness = sorted(skewness_data.items(), key = lambda x: x[1], reverse = True)
82quintile = int(len(sorted_by_skewness)/5)
83long = [x[0] for x in sorted_by_skewness[-quintile:]]
84short = [x[0] for x in sorted_by_skewness[:quintile]]
85
86# Trade execution
87invested = [x.Key.Value for x in self.Portfolio if x.Value.Invested]
88for symbol in invested:
89    if symbol not in long + short:
90        self.Liquidate(symbol)
91long_count = len(long)
92short_count = len(short)
93
94for symbol in long:
95    self.SetHoldings(symbol, 1 / long_count)
96for symbol in short:
97    self.SetHoldings(symbol, -1 / short_count)