Original paper
Abstract
In this paper, we analyze the process of constructing cointegrated portfolios of cryptocurrencies. Our procedure involves a series of statistical tests, including the Johansen cointegration test and Engle-Granger two-step approach. Among our results, we construct cointegrated portfolios involving four cryptocurrencies: Bitcoin (BTC), Ethereum (ETH), Bitcoin Cash (BCH), and Litecoin (LTC). We develop a number of trading strategies under different entry/exit thresholds and risk constraints, and examine their performance in details through backtesting and comparison analysis. Our methodology can be applied more generally to create new cointegrated portfolio using other cryptocurrencies.
Keywords: Cryptocurrencies, Cointegration, Mean Reversion, Stationarity, Trading Strategies
Trading rules
- Start with a linear model: (at time t)
- Determine beta coefficients using Ordinary Least Squares (OLS)
- Define spread S at time t:
- To purchase 1 unit of spread S:
- Buy 1 unit of BTC, unit of ETH, unit of LTC, and unit of BCH
- If beta coefficients are negative, short sell the respective currency using CFDs
- Long the spread or exit short position if:
- Spread S < mean value of spread - c * standard deviation of spread (c = 0.5, but other values possible)
- Short the spread or exit long position if:
- Spread S > mean value of spread + c * standard deviation of spread
- Maintain exposure to only 1 unit of the spread at a time
Python code
Backtrader
import numpy as np
import pandas as pd
import statsmodels.api as sm
import backtrader as bt
class CointegratedCrypto(bt.Strategy):
params = ( ('c', 0.5), )
def __init__(self):
self.btc = self.datas[0]
self.eth = self.datas[1]
self.ltc = self.datas[2]
self.bch = self.datas[3]
def next(self):
# Prepare data
data = pd.DataFrame({'BTC': self.btc.get(size=100), 'ETH': self.eth.get(size=100), 'LTC': self.ltc.get(size=100), 'BCH': self.bch.get(size=100)})
# OLS Regression
X = data[['ETH', 'LTC', 'BCH']]
X = sm.add_constant(X)
y = data['BTC']
model = sm.OLS(y, X).fit()
beta1, beta2, beta3 = model.params[1], model.params[2], model.params[3]
# Calculate spread S
spread = self.btc[0] + beta1 * self.eth[0] + beta2 * self.ltc[0] + beta3 * self.bch[0]
# Calculate mean and standard deviation of spread
mean_spread = np.mean(data['BTC'])
std_spread = np.std(data['BTC'])
# Trading logic
long_condition = spread < mean_spread - self.params.c * std_spread
short_condition = spread > mean_spread + self.params.c * std_spread
if long_condition:
self.buy(data=self.btc)
self.buy(data=self.eth, size=beta1)
self.buy(data=self.ltc, size=beta2)
self.buy(data=self.bch, size=beta3)
elif short_condition:
self.sell(data=self.btc)
self.sell(data=self.eth, size=beta1)
self.sell(data=self.ltc, size=beta2)
self.sell(data=self.bch, size=beta3)