correlation-analysis

Correlation Analysis

Cross-asset correlation analysis for diversification assessment, risk management, pairs trading signal generation, and portfolio construction.

Why Correlation Matters

Correlation measures how assets move together. In crypto markets this is critical for:

• Diversification: holding correlated assets provides no diversification benefit — you are effectively holding one concentrated position
• Risk management: portfolio risk depends on the correlation structure, not just individual asset volatility
• Pairs trading: highly correlated assets that temporarily diverge create mean-reversion opportunities
• Portfolio construction: optimal allocation requires accurate correlation estimates
• Crash protection: understanding tail dependence reveals whether assets crash together

Correlation Methods

Pearson Correlation

Linear correlation assuming normality. Most common but least robust for crypto.

import pandas as pd
import numpy as np

# Always compute on returns, never on prices
returns_a = prices_a.pct_change().dropna()
returns_b = prices_b.pct_change().dropna()

pearson_corr = returns_a.corr(returns_b)  # default is Pearson

• Range: -1 (perfect inverse) to +1 (perfect co-movement)
• Assumes: linear relationship, normally distributed returns, no outliers
• Limitation: crypto returns are heavy-tailed — Pearson underestimates extreme co-movement

Spearman Rank Correlation

Converts values to ranks, then computes Pearson on ranks. Captures monotonic (not just linear) relationships.

spearman_corr = returns_a.corr(returns_b, method='spearman')

• More robust to outliers and non-linear relationships
• Better for crypto due to heavy-tailed return distributions
• Slightly lower power than Pearson when normality holds

Kendall Tau Correlation

Counts concordant vs discordant pairs. Most robust to outliers.

kendall_corr = returns_a.corr(returns_b, method='kendall')