Oil Beta Uncertainty and Global Stock Returns

1from AlgorithmImports import *
2import statsmodels.api as sm
3import data_tools
4# endregion
5
6class CasualApricotSalamander(QCAlgorithm):
7
8def Initialize(self):
9self.SetStartDate(2010, 1, 1)
10self.SetCash(100000)
11
12tickers:list[str] = [
13    'EWA',  # iShares MSCI Australia Index ETF
14    'EWO',  # iShares MSCI Austria Investable Mkt Index ETF
15    'EWK',  # iShares MSCI Belgium Investable Market Index ETF
16    'EWZ',  # iShares MSCI Brazil Index ETF
17    'EWC',  # iShares MSCI Canada Index ETF
18    'FXI',  # iShares China Large-Cap ETF
19    'EWQ',  # iShares MSCI France Index ETF
20    'EWG',  # iShares MSCI Germany ETF 
21    'EWH',  # iShares MSCI Hong Kong Index ETF
22    'EWI',  # iShares MSCI Italy Index ETF
23    'EWJ',  # iShares MSCI Japan Index ETF
24    'EWM',  # iShares MSCI Malaysia Index ETF
25    'EWW',  # iShares MSCI Mexico Inv. Mt. Idx
26    'EWN',  # iShares MSCI Netherlands Index ETF
27    'EWS',  # iShares MSCI Singapore Index ETF
28    'EZA',  # iShares MSCI South Africe Index ETF
29    'EWY',  # iShares MSCI South Korea ETF
30    'EWP',  # iShares MSCI Spain Index ETF
31    'EWD',  # iShares MSCI Sweden Index ETF
32    'EWL',  # iShares MSCI Switzerland Index ETF
33    'EWT',  # iShares MSCI Taiwan Index ETF
34    'THD',  # iShares MSCI Thailand Index ETF
35    'EWU',  # iShares MSCI United Kingdom Index ETF
36    'SPY',  # SPDR S&P 500 ETF
37]
38
39self.min_prices:int = 15
40self.regression_period:int = 24
41
42self.beta_index:int = 2 # relevant regression beta position
43self.t:float = 2.074    # https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf
44
45self.quantile:int = 5
46self.data:dict[Symbol, data_tools.SymbolData] = {}
47
48for ticker in tickers:
49    security = self.AddEquity(ticker, Resolution.Daily)
50    security.SetLeverage(5)
51
52    self.data[security.Symbol] = data_tools.SymbolData(self.regression_period)
53
54self.msci_world:Symbol = self.AddEquity('URTH', Resolution.Daily).Symbol
55self.data[self.msci_world] = data_tools.SymbolData(self.regression_period)
56
57self.oil:Symbol = self.AddData(data_tools.QuantpediaFutures, 'CME_CL1', Resolution.Daily).Symbol
58self.data[self.oil] = data_tools.SymbolData(self.regression_period)
59
60self.recent_month:int = -1
61
62def OnData(self, data: Slice):
63# update prices
64for symbol, symbol_obj in self.data.items():
65    if symbol in data and data[symbol] and data[symbol].Value != 0:
66        symbol_obj.update_prices(data[symbol].Value)
67
68# monthly rebalance
69if self.recent_month != self.Time.month:
70    self.recent_month = self.Time.month
71    curr_date:datetime.date = self.Time.date()
72
73    # update all regression data
74    for symbol, symbol_obj in self.data.items():
75        if symbol_obj.prices_ready(self.min_prices):
76            symbol_obj.update_regression_data(curr_date)
77        else:
78            # reset regression data in case of missing month -> makes sure data are consecutive
79            symbol_obj.reset_regression_data()
80
81        # clear space for next month prices
82        symbol_obj.reset_prices()
83
84    # get regression_x if possible
85    regression_x:list[list[float]] = [
86        self.data[self.msci_world].get_regression_data(),
87        self.data[self.oil].get_regression_data()
88    ] if self.data[self.msci_world].regression_data_ready() and \
89         self.data[self.oil].regression_data_ready() else None
90
91    if regression_x == None:
92        # liquidate when regression x isn't ready
93        self.Liquidate()
94        return 
95
96    oil_beta_uncertainty:dict[Symbol, float] = {}
97
98    for symbol, symbol_obj in self.data.items():
99        if symbol_obj.regression_data_ready() and symbol not in [self.msci_world, self.oil]:
100            # calculate the measure of the oil beta uncertainty for stock market i in month t as a difference between the highest and lowest 95% confidence interval
101            regression_y:list[float] = symbol_obj.get_regression_data()
102
103            regression_model = self.MultipleLinearRegression(regression_x, regression_y)
104
105            oil_beta:float = regression_model.params[self.beta_index]
106            SE:float = regression_model.bse[self.beta_index]
107            
108            top_conf_interval:float = oil_beta + (self.t * SE)
109            bottom_conf_interval:float = oil_beta - (self.t * SE)
110
111            intervals_diff:float = top_conf_interval - bottom_conf_interval
112
113            oil_beta_uncertainty[symbol] = intervals_diff
114
115    # perform selection and trade
116    if len(oil_beta_uncertainty) >= self.quantile:
117        quantile:int = int(len(oil_beta_uncertainty) / self.quantile)
118        sorted_by_uncertainty:list[Symbol] = [x[0] for x in sorted(oil_beta_uncertainty.items(), key=lambda item: item[1])]
119
120        # buy quantile with highest values
121        long_leg:list[Symbol] = sorted_by_uncertainty[-quantile:]
122        # short quantile with lowest values
123        short_leg:list[Symbol] = sorted_by_uncertainty[:quantile]
124
125        # trade execution
126        invested = [x.Key for x in self.Portfolio if x.Value.Invested]
127        for symbol in invested:
128            if symbol not in long_leg + short_leg:
129                self.Liquidate(symbol)
130
131        long_length:int = len(long_leg)
132        for symbol in long_leg:
133            if symbol in data and data[symbol]:
134                self.SetHoldings(symbol, 1 / long_length)
135
136        short_length:int = len(short_leg)
137        for symbol in short_leg:
138            if symbol in data and data[symbol]:
139                self.SetHoldings(symbol, -1 / short_length)
140    else:
141        self.Liquidate()
142
143def MultipleLinearRegression(self, x:list, y:list):
144x:np.ndarray = np.array(x).T
145x = sm.add_constant(x)
146result = sm.OLS(endog=y, exog=x).fit()
147return result