correlation-analysis
Cross-asset correlation analysis including rolling correlation, hierarchical clustering, tail dependence, and regime-dependent correlation
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Install
Works with every agent the skills CLI supports.
npx skills add https://github.com/agiprolabs/claude-trading-skills --skill correlation-analysis- 01
Install
Run the command in your project. The CLI asks which agents to install for.
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Describe the task
Ask your agent for something this skill covers. It loads correlation-analysis automatically when relevant.
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Review the result
The agent follows the SKILL.md steps, scripts and references bundled with the skill.
SKILL.md
The instructions your agent reads when the skill is triggered.
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')
- Most robust to outliers of the three methods
- Computationally slower on large datasets
- Best for small samples or heavily skewed data
Rolling Correlation
Static correlation hides regime changes. Rolling correlation reveals how relationships evolve.
Window-Based Rolling Correlation
# Rolling Pearson correlation
rolling_corr = returns_a.rolling(window=60).corr(returns_b)
# Multiple windows for different time horizons
windows = {
'short': 20, # ~1 month of trading days
'medium': 60, # ~3 months
'long': 120, # ~6 months
}
for label, w in windows.items():
df[f'corr_{label}'] = returns_a.rolling(w).corr(returns_b)
EWMA Correlation
Exponentially weighted — more responsive to recent changes.
def ewma_correlation(x: pd.Series, y: pd.Series, span: int = 60) -> pd.Series:
"""Compute EWMA correlation between two return series."""
cov_xy = x.mul(y).ewm(span=span).mean() - x.ewm(span=span).mean() * y.ewm(span=span).mean()
std_x = x.ewm(span=span).std()
std_y = y.ewm(span=span).std()
return cov_xy / (std_x * std_y)
Typical Windows
| Window | Days | Use Case |
|---|---|---|
| Short | 20 | Tactical trading, pairs entry/exit |
| Medium | 60 | Strategy allocation, regime detection |
| Long | 120 | Portfolio construction, strategic allocation |
Correlation Matrix Analysis
Computing the Full Matrix
# Build return matrix for multiple assets
returns = pd.DataFrame({
'BTC': btc_returns,
'ETH': eth_returns,
'SOL': sol_returns,
'AVAX': avax_returns,
})
# Correlation matrix (Pearson)
corr_matrix = returns.corr()
# Spearman (better for crypto)
spearman_matrix = returns.corr(method='spearman')
Eigenvalue Decomposition
Decompose the correlation matrix to identify driving factors.
eigenvalues, eigenvectors = np.linalg.eigh(corr_matrix.values)
# Sort descending
idx = eigenvalues.argsort()[::-1]
eigenvalues = eigenvalues[idx]
eigenvectors = eigenvectors[:, idx]
# First eigenvalue = market factor (explains most variance)
# Subsequent eigenvalues = sector/style factors
market_factor_pct = eigenvalues[0] / eigenvalues.sum() * 100
- First eigenvector: the market factor — when this dominates (>60% variance), everything moves together
- Subsequent eigenvectors: sector or style factors
- Small eigenvalues: noise / idiosyncratic risk
Minimum Variance Portfolio
from numpy.linalg import inv
cov_matrix = returns.cov()
ones = np.ones(len(cov_matrix))
inv_cov = inv(cov_matrix.values)
# Minimum variance weights
weights = inv_cov @ ones / (ones @ inv_cov @ ones)
Hierarchical Clustering
Group assets by correlation similarity to identify natural clusters.
from scipy.cluster.hierarchy import linkage, fcluster
from scipy.spatial.distance import squareform
# Convert correlation to distance
dist_matrix = np.sqrt(2 * (1 - corr_matrix.values))
np.fill_diagonal(dist_matrix, 0)
# Hierarchical clustering
condensed = squareform(dist_matrix)
linkage_matrix = linkage(condensed, method='ward')
# Cut at threshold to get clusters
clusters = fcluster(linkage_matrix, t=1.0, criterion='distance')
Applications:
- Sector detection: assets in the same cluster behave similarly
- Diversification: select one asset per cluster for maximum diversification
- Risk allocation: allocate risk budget across clusters, not individual assets
Tail Dependence
Normal correlation understates co-movement during crashes. Tail dependence measures how often assets experience extreme returns simultaneously.
Lower Tail Dependence
def tail_dependence(x: pd.Series, y: pd.Series, quantile: float = 0.05) -> float:
"""Estimate lower tail dependence coefficient.
Measures P(Y < q | X < q) for quantile q.
Higher values mean assets crash together more often.
"""
threshold_x = x.quantile(quantile)
threshold_y = y.quantile(quantile)
joint_extreme = ((x < threshold_x) & (y < threshold_y)).sum()
marginal_extreme = (x < threshold_x).sum()
return joint_extreme / marginal_extreme if marginal_extreme > 0 else 0.0
Crypto-Specific Tail Behavior
In crypto markets, tail dependence typically exceeds normal correlation:
- Normal correlation of 0.6 between two altcoins might have tail dependence of 0.8
- During market panics, correlations spike toward 1.0 across all risk assets
- This means diversification benefits disappear exactly when needed most
Regime-Dependent Correlation
Correlation is not constant — it changes with market regime.
| Regime | Typical Correlation | Implication |
|---|---|---|
| Bull (trending up) | 0.4–0.7 | Moderate — some diversification works |
| Range-bound | 0.2–0.5 | Lower — best diversification environment |
| Bear (crash) | 0.8–0.95 | Very high — diversification fails |
| Recovery | 0.5–0.7 | Declining from crash highs |
Detecting Correlation Regime Shifts
def correlation_zscore(rolling_corr: pd.Series, lookback: int = 252) -> pd.Series:
"""Z-score of rolling correlation vs its own history."""
mean = rolling_corr.rolling(lookback).mean()
std = rolling_corr.rolling(lookback).std()
return (rolling_corr - mean) / std
# Flag regime shift when z-score exceeds threshold
zscore = correlation_zscore(rolling_corr_60d)
regime_shift = zscore.abs() > 2.0
Crypto-Specific Correlation Patterns
Typical Correlation Ranges
| Pair | Normal Range | Notes |
|---|---|---|
| BTC / ETH | 0.7–0.9 | Highest among majors |
| BTC / SOL | 0.6–0.85 | SOL more volatile, slightly less correlated |
| BTC / Altcoin | 0.5–0.8 | Varies by market cap and sector |
| Meme / BTC | 0.2–0.5 | Lower normal correlation |
| Meme / Meme | 0.1–0.4 | Low normal but high tail dependence |
| Stablecoin / BTC | -0.1–0.1 | Should be near zero |
Key Observations
- Most altcoins are highly correlated with BTC (0.6–0.9) — the market factor dominates
- Meme and PumpFun tokens show lower normal correlation but higher tail dependence
- SOL ecosystem tokens correlate strongly with SOL price
- Stablecoins should be uncorrelated with risk assets — if correlation appears, investigate (depeg risk)
- Correlation tends to increase during high-volatility regimes
- New token launches may show temporarily low correlation until price discovery stabilizes
Integration with Other Skills
- risk-management: use correlation to compute portfolio-level VaR and stress scenarios
- portfolio-analytics: correlation matrix feeds optimal allocation algorithms
- regime-detection: correlation regime shifts are an input to regime classification
- cointegration-analysis: pairs with high correlation are candidates for cointegration testing
- position-sizing: correlation-adjusted sizing prevents correlated concentration
Files
References
references/methodology.md— Correlation formulas, statistical tests, estimation methodsreferences/portfolio_applications.md— Diversification metrics, pairs trading, risk decomposition
Scripts
scripts/correlation_matrix.py— Multi-asset correlation matrix, clustering, diversification metricsscripts/rolling_correlation.py— Rolling correlation, regime detection, tail dependence analysis
FAQ
What does the correlation-analysis skill do?
Cross-asset correlation analysis including rolling correlation, hierarchical clustering, tail dependence, and regime-dependent correlation
How do I install correlation-analysis?
Run npx skills add https://github.com/agiprolabs/claude-trading-skills --skill correlation-analysis in your project. The skills CLI detects the agents you use and copies the skill into the right folder. For Claude Code you can also place the skill folder at ~/.claude/skills/correlation-analysis/ (personal) or .claude/skills/correlation-analysis/ (project).
Which AI agents can use correlation-analysis?
Any agent that supports the open Agent Skills format (a folder with a SKILL.md file), including Claude Code, Codex, Cursor, GitHub Copilot, Gemini CLI, Windsurf, Cline, OpenCode and more.
Is correlation-analysis safe to install?
No partner security audit is available yet. Skills can run commands and scripts, so read the SKILL.md and any bundled files before installing.
Who maintains correlation-analysis?
It is published by agiprolabs in agiprolabs/claude-trading-skills. It has 468 recorded installs.
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