Overview

Statistical arbitrage is a popular trading strategy in quantitative finance that seeks to capitalize on price discrepancies between related financial instruments. This approach combines statistical methods and mathematical models to identify opportunities for profit. In this blog post, we will delve into statistical arbitrage strategies and provide Python implementations to illustrate these concepts.

Understanding Statistical Arbitrage

At its core, statistical arbitrage involves the use of statistical techniques to exploit inefficiencies in the pricing of securities. It typically involves pairs trading, where investors go long on an undervalued security while simultaneously shorting an overvalued one. The goal is to make a profit when the prices converge.

1. Pairs Trading

Pairs trading is one of the most straightforward forms of statistical arbitrage. It involves identifying two correlated securities and trading based on the divergence in their price relationship.

2. Cointegration Testing

To identify suitable pairs for trading, we first need to test for cointegration. Coinintegrated pairs have a stable long-term relationship, making them suitable for pairs trading. The following Python code demonstrates the cointegration test using the statsmodels library:

import numpy as np
import pandas as pd
from statsmodels.tsa.stattools import coint
 
# Generate synthetic price data for two assets
np.random.seed(0)
asset1 = np.random.normal(0, 1, 1000).cumsum() + 100
asset2 = asset1 + np.random.normal(0, 0.5, 1000)
 
# Perform cointegration test
score, p_value, _ = coint(asset1, asset2)
print(f'Cointegration test p-value: {p_value:.5f}')

3. Trading Strategy

Once we have established which pairs are cointegrated, we can develop our trading strategy. A common approach is to create a z-score based on the spread of the two assets:

# Calculate the spread
spread = asset1 - asset2
 
# Calculate z-score
z_score = (spread - np.mean(spread)) / np.std(spread)
 
# Define entry and exit thresholds
entry_threshold = 1.0
exit_threshold = 0.0
 
# Trading signals
long_signal = z_score < -entry_threshold
short_signal = z_score > entry_threshold
 
# Create a DataFrame to store signals
signals = pd.DataFrame({'long_signal': long_signal, 'short_signal': short_signal})

4. Backtesting the Strategy

To assess the effectiveness of our strategy, we can conduct a backtest. This involves simulating trades based on historical data to evaluate performance:

# Backtesting logic (simplified)
portfolio = 100000  # Initialize portfolio value
 
for i in range(1, len(signals)):
    if signals['long_signal'][i]:
        portfolio *= (1 + (asset1[i] - asset2[i]) / asset2[i - 1])  # Long trade
    elif signals['short_signal'][i]:
        portfolio *= (1 - (asset1[i] - asset2[i]) / asset1[i - 1])  # Short trade
 
print(f'Final portfolio value: ${portfolio:.2f}')

Conclusion

Statistical arbitrage offers a systematic approach to trading that leverages statistical relationships between securities. By employing mean-reversion strategies like pairs trading and utilizing Python for implementation, traders can enhance their decision-making process and potentially improve their trading performance. However, it is essential to continuously monitor market conditions and adapt strategies accordingly.