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Bug in popular quantopian future pairs trading algo

Hi guys,

I recently posted some thoughts here about a popular futures pair trading algorithm. I took a popular pairs trading algorithm from quantopian and backtested it with different parameters. I remarked that it was suspicious that the algorithm results depended so strongly on small changes in the algorithm parameters.

I found the reason for it. That algorithm has a bug on it. In the calculation of zscore,

zscore = (np.mean(spreads[-context.short_ma]) - np.mean(spreads)) / np.std(spreads, ddof=1)

it should be np.mean(spreads[-context.short_ma:]). Instead of computing the zscore of short_ma return to long_ma returns, that algorithm is computing the zscore of a single day return, a day "short_ma days ago". Predicting anything with this is luck, that is why the algorithm is so sensitive to parameters. You can see the bug here and here.

The algorithm's behavior is a lot less attractive now because there aren't many entry points.

Note, there might also be a np.sqrt(short_ma) missing, but that's less important as people are going to be playing around with the entry threshold anyway.

Clone Algorithm
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Total Returns
--
Alpha
--
Beta
--
Sharpe
--
Sortino
--
Max Drawdown
--
Benchmark Returns
--
Volatility
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Returns 1 Month 3 Month 6 Month 12 Month
Alpha 1 Month 3 Month 6 Month 12 Month
Beta 1 Month 3 Month 6 Month 12 Month
Sharpe 1 Month 3 Month 6 Month 12 Month
Sortino 1 Month 3 Month 6 Month 12 Month
Volatility 1 Month 3 Month 6 Month 12 Month
Max Drawdown 1 Month 3 Month 6 Month 12 Month
from zipline.api import continuous_future, schedule_function
from zipline.api import time_rules, date_rules, record
#from zipline.algorithm import log
#from zipline.assets.continuous_futures import ContinuousFuture
from zipline.api import order_target_value, order_target_percent
import numpy as np
import scipy as sp
#from quantopian.algorithm import order_optimal_portfolio
#import quantopian.optimize as opt

ZSCORE_THRESHOLD_ENTER = 1.0
ZSCORE_THRESHOLD_EXIT = 0.0

SHORT_MA = 5
LONG_MA = 65

TWO_SYMBOLS = ['CL','XB']

LOGGER = False

def initialize(context):
    two_symbols = TWO_SYMBOLS # crude oil and gasoline

    context.f1 = continuous_future(two_symbols[0], roll='calendar')
    context.f2 = continuous_future(two_symbols[1], roll='calendar')

    context.long_ma = LONG_MA
    context.short_ma = SHORT_MA

    context.currently_long_the_spread = False
    context.currently_short_the_spread = False

    # Rebalance pairs every day, 30 minutes after market open
    schedule_function(func=rebalance_pairs,
                      date_rule=date_rules.every_day(),
                      time_rule=time_rules.market_open(minutes=30))
    schedule_function(record_price, 
                      date_rules.every_day(), 
                      time_rules.market_open())


def rebalance_pairs(context, data):
    zscore = calc_spread_zscore(context, data)
    target_weights = get_target_weights(context, data, zscore)

    for k,v in target_weights.items():
        if LOGGER:
            log.info("order_target_percent: ", k, v)
        order_target_percent(k, v)

def calc_spread_zscore(context, data):
    prices = data.history([context.f1,
                           context.f2],
                          'price',
                          context.long_ma,
                          '1d')

    f1_price = prices[context.f1]
    f2_price = prices[context.f2]

    f1_returns = f1_price.pct_change()[1:]
    f2_returns = f2_price.pct_change()[1:]

    regression = sp.stats.linregress(
        f2_returns[-context.long_ma:],
        f1_returns[-context.long_ma:],
    )
    spreads = f1_returns - (regression.slope * f2_returns)

    #log.info("spreads size is {}".format(len(spreads)))
    #log.info(spreads[-context.short_ma])
    log.info(len(spreads))
    log.info(context.short_ma)
    zscore = (np.mean(spreads[-context.short_ma:]) - np.mean(spreads)) / np.std(spreads, ddof=1)
#    log.info("calc spread zscore6")
    return zscore

def get_target_weights(context, data, zscore):
    # Get current contracts for both continuous futures
    f1_contract, f2_contract = data.current(
        [context.f1, context.f2],
        'contract'
    )

    target_weights = {}
    ## exit position if clause, only if we have a position
    if (context.currently_short_the_spread and zscore < ZSCORE_THRESHOLD_EXIT) or \
      (context.currently_long_the_spread and zscore > -ZSCORE_THRESHOLD_EXIT):
        target_weights[f1_contract] = 0
        target_weights[f2_contract] = 0
        if LOGGER:
            log.info('exiting position')
            log.info(target_weights)
        context.currently_long_the_spread = False
        context.currently_short_the_spread = False
    ## long position if clause, only if we aren't already long
    elif zscore < -ZSCORE_THRESHOLD_ENTER and (not context.currently_long_the_spread):
        target_weights[f1_contract] = 0.5
        target_weights[f2_contract] = -0.5
        if LOGGER:
            log.info('going long')
            log.info(target_weights)
        context.currently_long_the_spread = True
        context.currently_short_the_spread = False
    ## short position if clause, only if we aren't already short
    elif zscore > ZSCORE_THRESHOLD_ENTER and (not context.currently_short_the_spread):
        target_weights[f1_contract] = -0.5
        target_weights[f2_contract] = 0.5
        if LOGGER:
            log.info('going short')
            log.info(target_weights)
        context.currently_long_the_spread = False
        context.currently_short_the_spread = True
    return target_weights

def record_price(context, data):

    # Get current price of primary crude oil and gasoline contracts.
    crude_oil_price = data.current(context.f1, 'price')
    gasoline_price = data.current(context.f2, 'price')
      
    # Adjust price of gasoline (42x) so that both futures have same scale.
    record(Crude_Oil=crude_oil_price, Gasoline=gasoline_price*42)
There was a runtime error.
2 responses

tumbleweed

I guess this result makes the tutorial more realistic though.

Oh! Good catch. I'll be sure to update the algo.

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