Sector Rotation Strategy Based on Multivariate Regression Analysis

1from collections import deque
2from AlgorithmImports import *
3from scipy import stats
4import numpy as np
5import statsmodels.api as sm
6class SectorRotationStrategyBasedonMultivariateRegressionAnalysis(QCAlgorithm):
7def Initialize(self):
8self.SetStartDate(2000, 1, 1)
9self.SetCash(100000)
10
11self.symbols = [
12    'XLV',
13    'XLI',
14    'XLY',
15    'XLP',
16    'XLB',
17    'XLK',
18    'XLU',
19    'XLE',
20    'XLF'
21    ]
22
23# Daily close data.
24self.data = {}
25self.period = 21
26# Regression data.
27self.regression_period = 13
28self.regression_data = {}
29self.market = self.AddEquity('SPY', Resolution.Daily).Symbol
30self.data[self.market] = deque(maxlen = self.period)
31
32self.cash = self.AddEquity('SHY', Resolution.Daily).Symbol
33
34for symbol in self.symbols:
35    self.AddEquity(symbol, Resolution.Daily)
36    self.regression_data[symbol] = deque(maxlen = self.regression_period)
37    self.data[symbol] = deque(maxlen = self.period)
38
39self.Schedule.On(self.DateRules.MonthStart(self.symbols[0]), self.TimeRules.BeforeMarketClose(self.symbols[0]), self.Rebalance)
40
41def OnData(self, data):
42for symbol in self.symbols + [self.market]:
43    if symbol in data and data[symbol]:
44        price = data[symbol].Value
45        self.data[symbol].append(price)
46def Rebalance(self):
47long = []
48
49for symbol in self.symbols:
50    # Data is ready.
51    if len(self.data[symbol]) == self.data[symbol].maxlen and len(self.data[self.market]) == self.data[self.market].maxlen:
52        # Calculate regression independent variables.
53        
54        # Sector return.
55        sector_return = np.log( self.data[symbol][-1] / self.data[symbol][0] )
56        
57        # Volatility.
58        volatility = Volatility(self.data[symbol])
59        
60        # Drawdown.
61        drawdown = min(0, sector_return)
62        
63        # The regression slope.
64        x = range(1, len(self.data[symbol]) + 1)
65        y = [x for x in self.data[symbol]]
66        slope, intercept, r_value, p_value, std_err = stats.linregress(x, y)
67        
68        # Excess return.
69        market_return = np.log( self.data[self.market][-1] / self.data[self.market][0] )
70        ex_return = sector_return - market_return
71        
72        self.regression_data[symbol].append( (sector_return, volatility, drawdown, slope, ex_return) )
73        
74        # Regression data is ready.
75        if len(self.regression_data[symbol]) == self.regression_data[symbol].maxlen:
76            regression_data = [x for x in self.regression_data[symbol]]
77            
78            returns = [x[0] for x in self.regression_data[symbol]]
79            volatilities = [x[1] for x in self.regression_data[symbol]]
80            drawdowns = [x[2] for x in self.regression_data[symbol]]
81            slopes = [x[3] for x in self.regression_data[symbol]]
82            ex_returns = [x[4] for x in self.regression_data[symbol]]
83            
84            # Predict return for sector.
85            x = [ returns[:-1], volatilities[:-1], drawdowns[:-1], slopes[:-1], ex_returns[:-1] ]
86            y = returns[1:]
87            regression_model = MultipleLinearRegression(x, y)
88            
89            alpha = regression_model.params[0]
90            return_predict = np.array([returns[-1], volatilities[-1], drawdowns[-1], slopes[-1], ex_returns[-1]])
91            betas = np.array(regression_model.params[1:])
92            Y = alpha + sum(np.multiply(betas, return_predict))
93            if Y > 0:
94                long.append(symbol)
95    
96# Trade execution.
97self.Liquidate()
98
99weight = 1 / len(self.symbols)
100for symbol in long:
101    if self.Securities[symbol].Price != 0:
102        self.SetHoldings(symbol, weight)
103
104cash_weight = (len(self.symbols) - len(long)) / len(self.symbols)
105if self.Securities[self.cash].Price != 0:
106    self.SetHoldings(self.cash, cash_weight)
107def Volatility(values):
108values = np.array(values)
109returns = (values[1:] - values[:-1]) / values[:-1]
110return np.std(returns)
111
112def MultipleLinearRegression(x, y):
113x = np.array(x).T
114x = sm.add_constant(x)
115result = sm.OLS(endog=y, exog=x).fit()
116return result