Lecture 54

# Example: Pairs Trading on Futures

## Introduction

Example algorithm to demonstrate a pair trade on futures contracts.

## Prerequisites

```import itertools

import numpy as np
import pandas as pd
import scipy as sp
from statsmodels.tsa.stattools import coint

from quantopian.algorithm import order_optimal_portfolio
import quantopian.optimize as opt

month_idx = 0

def initialize(context):
# Quantopian backtester specific variables

context.futures_pairs = [
(
continuous_future(
'LC',
offset=month_idx,
roll='calendar',
),
continuous_future(
'FC',
offset=month_idx,
roll='calendar',
),
),
(
continuous_future(
'CL',
offset=month_idx,
roll='calendar',
),
continuous_future(
'XB',
offset=month_idx,
roll='calendar',
),
),
(
continuous_future(
'SM',
offset=month_idx,
roll='calendar',
),
continuous_future(
'BO',
offset=month_idx,
roll='calendar',
),
),
]

context.futures_list = list(itertools.chain.from_iterable(context.futures_pairs))

context.num_pairs = len(context.futures_pairs)
# strategy specific variables
context.long_ma = 63
context.short_ma = 5

context.inLong = {
(pair.root_symbol, pair.root_symbol): False for pair in context.futures_pairs
}
context.inShort = {
(pair.root_symbol, pair.root_symbol): False for pair in context.futures_pairs
}

context.long_term_weights = {cont_future.root_symbol: 0 for cont_future in context.futures_list}
context.current_weights = {}

schedule_function(func=rebalance_pairs, date_rule=date_rules.every_day(), time_rule=time_rules.market_open(minutes=30))

# Will be called on every trade event for the securities you specify.
def handle_data(context, data):
# Our work is now scheduled in check_pair_status
pass

def rebalance_pairs(context, data):
if get_open_orders():
return

prices = data.history(context.futures_list, 'price', context.long_ma, '1d')

for future_y, future_x in context.futures_pairs:
Y = prices[future_y]
X = prices[future_x]

y_log = np.log(Y)
x_log = np.log(X)

pvalue = coint(y_log, x_log)
if pvalue > 0.10:
log.info(
'({} {}) no longer cointegrated, no new positions.'.format(
future_y.root_symbol,
future_x.root_symbol,
),
)
continue

regression = sp.stats.linregress(
x_log[-context.long_ma:],
y_log[-context.long_ma:],
)

spreads = Y - (regression.slope * X)

zscore = (

future_y_contract, future_x_contract = data.current(
[future_y, future_x],
'contract',
)

context.current_weights[future_y_contract] = context.long_term_weights[future_y_contract.root_symbol]
context.current_weights[future_x_contract] = context.long_term_weights[future_x_contract.root_symbol]

hedge_ratio = regression.slope

if context.inShort[(future_y.root_symbol, future_x.root_symbol)] and zscore < 0.0:
context.long_term_weights[future_y_contract.root_symbol] = 0
context.long_term_weights[future_x_contract.root_symbol] = 0
context.current_weights[future_y_contract] = context.long_term_weights[future_y_contract.root_symbol]
context.current_weights[future_x_contract] = context.long_term_weights[future_x_contract.root_symbol]

context.inLong[(future_y.root_symbol, future_x.root_symbol)] = False
context.inShort[(future_y.root_symbol, future_x.root_symbol)] = False
continue

if context.inLong[(future_y.root_symbol, future_x.root_symbol)] and zscore > 0.0:
context.long_term_weights[future_y_contract.root_symbol] = 0
context.long_term_weights[future_x_contract.root_symbol] = 0
context.current_weights[future_y_contract] = context.long_term_weights[future_y_contract.root_symbol]
context.current_weights[future_x_contract] = context.long_term_weights[future_x_contract.root_symbol]

context.inLong[(future_y.root_symbol, future_x.root_symbol)] = False
context.inShort[(future_y.root_symbol, future_x.root_symbol)] = False
continue

if zscore < -1.0 and (not context.inLong[(future_y.root_symbol, future_x.root_symbol)]):
y_target_contracts = 1
x_target_contracts = hedge_ratio
context.inLong[(future_y.root_symbol, future_x.root_symbol)] = True
context.inShort[(future_y.root_symbol, future_x.root_symbol)] = False

(y_target_pct, x_target_pct) = computeHoldingsPct(
y_target_contracts,
x_target_contracts,
future_y_contract.multiplier * Y[-1],
future_x_contract.multiplier * X[-1]
)

context.long_term_weights[future_y_contract.root_symbol] = y_target_pct
context.long_term_weights[future_x_contract.root_symbol] = -x_target_pct
context.current_weights[future_y_contract] = context.long_term_weights[future_y_contract.root_symbol]
context.current_weights[future_x_contract] = context.long_term_weights[future_x_contract.root_symbol]
continue

if zscore > 1.0 and (not context.inShort[(future_y.root_symbol, future_x.root_symbol)]):
y_target_contracts = 1
x_target_contracts = hedge_ratio

context.inLong[(future_y.root_symbol, future_x.root_symbol)] = False
context.inShort[(future_y.root_symbol, future_x.root_symbol)] = True

(y_target_pct, x_target_pct) = computeHoldingsPct(
y_target_contracts,
x_target_contracts,
future_y_contract.multiplier * Y[-1],
future_x_contract.multiplier * X[-1]
)

context.long_term_weights[future_y_contract.root_symbol] = -y_target_pct
context.long_term_weights[future_x_contract.root_symbol] = x_target_pct
context.current_weights[future_y_contract] = context.long_term_weights[future_y_contract.root_symbol]
context.current_weights[future_x_contract] = context.long_term_weights[future_x_contract.root_symbol]
continue

k: v / (len(context.futures_pairs)) for k, v in context.current_weights.items()
})

order_optimal_portfolio(
constraints=[
opt.MaxGrossExposure(1.0),
],
)

def computeHoldingsPct(yShares, xShares, yPrice, xPrice):
yDol = yShares * yPrice
xDol = xShares * xPrice
notionalDol =  abs(yDol) + abs(xDol)
y_target_pct = yDol / notionalDol
x_target_pct = xDol / notionalDol
return (y_target_pct, x_target_pct)

```

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