correlation-analysis

Files (5)

• SKILL.md
• methodology.md · references/
• portfolio_applications.md · references/
• correlation_matrix.py · scripts/
• rolling_correlation.py · scripts/

SKILL.md (first lines)

# 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.

```python
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.

```python
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.

```python
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

```python
# 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.

```python
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

```python
# 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')
```

From Serennity007/awesome-stock-quant-skills, MIT.

More from Serennity007/awesome-stock-quant-skills