Contango-Backwardation VIX Futures Hedge Strategy

1import numpy as np
2import pandas as pd
3import statsmodels.api as sm
4from collections import deque
5
6class ExploitingTermStructureVIXFutures(XXX):
7
8def Initialize(self):
9self.SetStartDate(2011, 1, 1)
10self.SetCash(100000)
11
12self.vix = self.AddData(QuandlVix, "CBOE/VIX", Resolution.Daily).Symbol              # Add Quandl VIX price (daily)
13self.vx1 = self.AddData(QuandlFutures, "CHRIS/CBOE_VX1", Resolution.Daily).Symbol    # Add Quandl VIX front month futures data (daily)
14self.es1 = self.AddData(QuandlFutures, "CHRIS/CME_ES1", Resolution.Daily).Symbol     # Add Quandl E-mini S&P500 front month futures data (daily)
15
16vx_data = self.AddFuture(Futures.Indices.VIX)
17vx_data.SetFilter(timedelta(0), timedelta(days=180))
18vx_data.MarginModel = BuyingPowerModel(5) # leverage
19
20es_data = self.AddFuture(Futures.Indices.SP500EMini)
21es_data.SetFilter(timedelta(0), timedelta(days=180))
22es_data.MarginModel = BuyingPowerModel(5) # leverage
23
24self.front_VX = None
25self.front_ES = None
26
27# request the history to warm-up the price and time-to-maturity 
28hist = self.History([self.vx1, self.es1], timedelta(days=450), Resolution.Daily)
29settle = hist['settle'].unstack(level=0)
30
31# the rolling window to save the front month VX future price
32self.price_VX = deque(maxlen=252)   
33# the rolling window to save the front month ES future price
34self.price_ES = deque(maxlen=252)   
35# the rolling window to save the time-to-maturity of the contract
36self.days_to_maturity = deque(maxlen=252) 
37
38expiry_date = self.get_expiry_calendar()
39df = pd.concat([settle, expiry_date], axis=1, join='inner')
40
41for index, row in df.iterrows():
42    self.price_VX.append(row[str(self.vx1) + ' 2S'])
43    self.price_ES.append(row[str(self.es1) + ' 2S'])
44    self.days_to_maturity.append((row['expiry']-index).days)
45    
46self.Schedule.On(self.DateRules.EveryDay(self.vix), self.TimeRules.AfterMarketOpen(self.vix), self.Rebalance)
47
48def OnData(self, data):
49# select the nearest VIX and E-mini S&P500 futures with at least 10 trading days to maturity 
50# if the front contract expires, roll forward to the next nearest contract
51for chain in data.FutureChains:
52    future_indices = chain.Key.Value[1:] # First letter in this variable is '/'
53    
54    if future_indices == Futures.Indices.VIX:
55        if self.front_VX is None or ((self.front_VX.Expiry-self.Time).days <= 1):
56            contracts = list(filter(lambda x: x.Expiry >= self.Time + timedelta(days = 10), chain.Value))
57            self.front_VX = sorted(contracts, key = lambda x: x.Expiry)[0]
58    if future_indices == Futures.Indices.SP500EMini:
59        if self.front_ES is None or ((self.front_ES.Expiry-self.Time).days <= 1):
60            contracts = list(filter(lambda x: x.Expiry >= self.Time + timedelta(days = 10), chain.Value))
61            self.front_ES = sorted(contracts, key = lambda x: x.Expiry)[0]
62
63def Rebalance(self):
64if self.Securities.ContainsKey(self.vx1) and self.Securities.ContainsKey(self.es1):
65    # update the rolling window price and time-to-maturity series every day
66    if self.front_VX and self.front_ES:
67        self.price_VX.append(float(self.Securities[self.vx1].Price))
68        self.price_ES.append(float(self.Securities[self.es1].Price))
69        self.days_to_maturity.append((self.front_VX.Expiry-self.Time).days)
70    
71        # calculate the daily roll
72        daily_roll = (self.Securities[self.vx1].Price - self.Securities[self.vix].Price)/(self.front_VX.Expiry-self.Time).days
73
74        if not self.Portfolio[self.front_VX.Symbol].Invested:
75            # Short if the contract is in contango with adaily roll greater than 0.10 
76            if daily_roll > 0.1:
77                hedge_ratio = self.CalculateHedgeRatio()
78                self.SetHoldings(self.front_VX.Symbol, -0.4)
79                self.SetHoldings(self.front_ES.Symbol, -0.4*hedge_ratio)
80            # Long if the contract is in backwardation with adaily roll less than -0.10
81            elif daily_roll < -0.1:
82                hedge_ratio = self.CalculateHedgeRatio()
83                self.SetHoldings(self.front_VX.Symbol, 0.4)
84                self.SetHoldings(self.front_ES.Symbol, 0.4*hedge_ratio)
85        
86        # exit if the daily roll being less than 0.05 if holding short positions                 
87        if self.Portfolio[self.front_VX.Symbol].IsShort and daily_roll < 0.05:
88            self.Liquidate()
89            self.front_VX = None
90            self.front_ES = None
91            return
92        
93        # exit if the daily roll being greater than -0.05 if holding long positions                    
94        if self.Portfolio[self.front_VX.Symbol].IsLong and daily_roll > -0.05:
95            self.Liquidate()
96            self.front_VX = None
97            self.front_ES = None
98            return
99        
100if self.front_VX and self.front_ES:
101    # if these exit conditions are not triggered, trades are exited two days before it expires
102    if self.Portfolio[self.front_VX.Symbol].Invested and self.Portfolio[self.front_ES.Symbol].Invested: 
103        if (self.front_VX.Expiry-self.Time).days <=2 or (self.front_ES.Expiry-self.Time).days <=2:
104            self.Liquidate()
105            self.front_VX = None
106            self.front_ES = None
107            return
108        
109def CalculateHedgeRatio(self):
110price_VX = np.array(self.price_VX)
111price_ES = np.array(self.price_ES)
112delta_VX = np.diff(price_VX)
113
114res_ES = np.diff(price_ES) / price_ES[:-1]*100
115tts = np.array(self.days_to_maturity)[1:]
116df = pd.DataFrame({"delta_VX":delta_VX, "SPRET":res_ES, "product":res_ES*tts}).dropna()
117
118# remove rows with zero value
119df = df[(df != 0).all(1)]
120y = df['delta_VX'].astype(float)
121X = df[['SPRET', "product"]].astype(float)
122X = sm.add_constant(X)
123
124model = sm.OLS(y, X).fit()
125beta_1 = model.params[1]
126beta_2 = model.params[2]
127
128hedge_ratio = abs((1000*beta_1 + beta_2*((self.front_VX.Expiry-self.Time).days)*1000)/(0.01*50*float(self.Securities[self.es1].Price)))
129
130return hedge_ratio
131
132def get_expiry_calendar(self):
133# import the futures expiry calendar
134url = "data.quantpedia.com/backtesting_data/economic/vix_futures_expiration.csv"
135csv_string_file = self.Download(url)
136dates = csv_string_file.split('\r\n')
137dates = [datetime.strptime(x, "%Y-%m-%d") for x in dates]
138df_date = pd.DataFrame(dates, index = dates, columns = [ 'expiry'])
139
140# convert the index and expiry column to datetime format
141# df_date.index = pd.to_datetime(df_date.index)
142df_date['expiry'] = pd.to_datetime(df_date['expiry'])
143# idx = pd.date_range('19-01-2005', '16-12-2020')
144
145# populate the date index and backward fill the dataframe    
146# return df_date.reindex(idx, method='bfill')
147return df_date
148
149class QuandlVix(PythonQuandl):
150def __init__(self):
151self.ValueColumnName = "close"
152
153class QuandlFutures(PythonQuandl):
154def __init__(self):
155self.ValueColumnName = "settle"