correlation-analysis

Name: correlation-analysis
Author: agiprolabs

235stars53forks

How to install correlation-analysis?

agiprolabs/claude-trading-skills/correlation-analysis

$npx -y skills add agiprolabs/claude-trading-skills --skill correlation-analysis

Installs into the current project.

Summary

Cross-asset correlation analysis including rolling correlation, hierarchical clustering, tail dependence, and regime-dependent correlation

Files · 1

View on GitHub

SKILL.md

1	# Correlation Analysis
2
3	Cross-asset correlation analysis for diversification assessment, risk management, pairs trading signal generation, and portfolio construction.
4
5	## Why Correlation Matters
6
7	Correlation measures how assets move together. In crypto markets this is critical for:
8
9	- Diversification: holding correlated assets provides no diversification benefit — you are effectively holding one concentrated position
10	- Risk management: portfolio risk depends on the correlation structure, not just individual asset volatility
11	- Pairs trading: highly correlated assets that temporarily diverge create mean-reversion opportunities
12	- Portfolio construction: optimal allocation requires accurate correlation estimates
13	- Crash protection: understanding tail dependence reveals whether assets crash together
14
15	## Correlation Methods
16
17	### Pearson Correlation
18
19	Linear correlation assuming normality. Most common but least robust for crypto.
20
21	```python
22	import pandas as pd
23	import numpy as np
24
25	# Always compute on returns, never on prices
26	returns_a = prices_a.pct_change().dropna()
27	returns_b = prices_b.pct_change().dropna()
28
29	pearson_corr = returns_a.corr(returns_b) # default is Pearson
30	```
31
32	- Range: -1 (perfect inverse) to +1 (perfect co-movement)
33	- Assumes: linear relationship, normally distributed returns, no outliers
34	- Limitation: crypto returns are heavy-tailed — Pearson underestimates extreme co-movement
35
36	### Spearman Rank Correlation
37
38	Converts values to ranks, then computes Pearson on ranks. Captures monotonic (not just linear) relationships.
39
40	```python
41	spearman_corr = returns_a.corr(returns_b, method='spearman')
42	```
43
44	- More robust to outliers and non-linear relationships
45	- Better for crypto due to heavy-tailed return distributions
46	- Slightly lower power than Pearson when normality holds
47
48	### Kendall Tau Correlation
49
50	Counts concordant vs discordant pairs. Most robust to outliers.
51
52	```python
53	kendall_corr = returns_a.corr(returns_b, method='kendall')
54	```
55
56	- Most robust to outliers of the three methods
57	- Computationally slower on large datasets
58	- Best for small samples or heavily skewed data
59
60	## Rolling Correlation
61
62	Static correlation hides regime changes. Rolling correlation reveals how relationships evolve.
63
64	### Window-Based Rolling Correlation
65
66	```python
67	# Rolling Pearson correlation
68	rolling_corr = returns_a.rolling(window=60).corr(returns_b)
69
70	# Multiple windows for different time horizons
71	windows = {
72	'short': 20, # ~1 month of trading days
73	'medium': 60, # ~3 months
74	'long': 120, # ~6 months
75	}
76	for label, w in windows.items():
77	df[f'corr_{label}'] = returns_a.rolling(w).corr(returns_b)
78	```
79
80	### EWMA Correlation
81
82	Exponentially weighted — more responsive to recent changes.
83
84	```python
85	def ewma_correlation(x: pd.Series, y: pd.Series, span: int = 60) -> pd.Series:
86	"""Compute EWMA correlation between two return series."""
87	cov_xy = x.mul(y).ewm(span=span).mean() - x.ewm(span=span).mean() * y.ewm(span=span).mean()
88	std_x = x.ewm(span=span).std()
89	std_y = y.ewm(span=span).std()
90	return cov_xy / (std_x * std_y)
91	```
92
93	### Typical Windows
94
95	\| Window \| Days \| Use Case \|
96	\|--------\|------\|----------\|
97	\| Short \| 20 \| Tactical trading, pairs entry/exit \|
98	\| Medium \| 60 \| Strategy allocation, regime detection \|
99	\| Long \| 120 \| Portfolio construction, strategic allocation \|
100
101	## Correlation Matrix Analysis
102
103	### Computing the Full Matrix
104
105	```python
106	# Build return matrix for multiple assets
107	returns = pd.DataFrame({
108	'BTC': btc_returns,
109	'ETH': eth_returns,
110	'SOL': sol_returns,
111	'AVAX': avax_returns,
112	})
113
114	# Correlation matrix (Pearson)
115	corr_matrix = returns.corr()
116
117	# Spearman (better for crypto)
118	spearman_matrix = returns.corr(method='spearman')
119	```
120
121	### Eigenvalue Decomposition
122
123	Decompose the correlation matrix to identify driving factors.
124
125	```python
126	eigenvalues, eigenvectors = np.linalg.eigh(corr_matrix.values)
127
128	# Sort descending
129	idx = eigenvalues.argsort()[::-1]
130	eigenvalues = eigenvalues[idx]
131	eigenvectors = eigenvectors[:, idx]
132
133	# First eigenvalue = market factor (explains most variance)
134	# Subsequent eigenvalues = sector/style factors
135	market_factor_pct = eigenvalues[0] / eigenvalues.sum() * 100
136	```
137
138	- First eigenvector: the market factor — when this dominates (>60% variance), everything moves together
139	- Subsequent eigenvectors: sector or style factors
140	- Small eigenvalues: noise / idiosyncratic risk
141
142	### Minimum Variance Portfolio
143
144	```python
145	from numpy.linalg import inv
146
147	cov_matrix = returns.cov()
148	ones = np.ones(len(cov_matrix))
149	inv_cov = inv(cov_matrix.values)
150
151	# Minimum variance weights
152	weights = inv_cov @ ones / (ones @ inv_cov @ ones)
153	```
154
155	## Hierarchical Clustering
156
157	Group assets by correlation similarity to identify natural clusters.
158
159	```python
160	from scipy.cluste

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correlation-analysis

235stars53forks

View on GitHub

How to install correlation-analysis?

agiprolabs/claude-trading-skills/correlation-analysis

$npx -y skills add agiprolabs/claude-trading-skills --skill correlation-analysis

Installs into the current project.

Summary

Cross-asset correlation analysis including rolling correlation, hierarchical clustering, tail dependence, and regime-dependent correlation

Files · 1

View on GitHub

SKILL.md

1	# Correlation Analysis
2
3	Cross-asset correlation analysis for diversification assessment, risk management, pairs trading signal generation, and portfolio construction.
4
5	## Why Correlation Matters
6
7	Correlation measures how assets move together. In crypto markets this is critical for:
8
9	- Diversification: holding correlated assets provides no diversification benefit — you are effectively holding one concentrated position
10	- Risk management: portfolio risk depends on the correlation structure, not just individual asset volatility
11	- Pairs trading: highly correlated assets that temporarily diverge create mean-reversion opportunities
12	- Portfolio construction: optimal allocation requires accurate correlation estimates
13	- Crash protection: understanding tail dependence reveals whether assets crash together
14
15	## Correlation Methods
16
17	### Pearson Correlation
18
19	Linear correlation assuming normality. Most common but least robust for crypto.
20
21	```python
22	import pandas as pd
23	import numpy as np
24
25	# Always compute on returns, never on prices
26	returns_a = prices_a.pct_change().dropna()
27	returns_b = prices_b.pct_change().dropna()
28
29	pearson_corr = returns_a.corr(returns_b) # default is Pearson
30	```
31
32	- Range: -1 (perfect inverse) to +1 (perfect co-movement)
33	- Assumes: linear relationship, normally distributed returns, no outliers
34	- Limitation: crypto returns are heavy-tailed — Pearson underestimates extreme co-movement
35
36	### Spearman Rank Correlation
37
38	Converts values to ranks, then computes Pearson on ranks. Captures monotonic (not just linear) relationships.
39
40	```python
41	spearman_corr = returns_a.corr(returns_b, method='spearman')
42	```
43
44	- More robust to outliers and non-linear relationships
45	- Better for crypto due to heavy-tailed return distributions
46	- Slightly lower power than Pearson when normality holds
47
48	### Kendall Tau Correlation
49
50	Counts concordant vs discordant pairs. Most robust to outliers.
51
52	```python
53	kendall_corr = returns_a.corr(returns_b, method='kendall')
54	```
55
56	- Most robust to outliers of the three methods
57	- Computationally slower on large datasets
58	- Best for small samples or heavily skewed data
59
60	## Rolling Correlation
61
62	Static correlation hides regime changes. Rolling correlation reveals how relationships evolve.
63
64	### Window-Based Rolling Correlation
65
66	```python
67	# Rolling Pearson correlation
68	rolling_corr = returns_a.rolling(window=60).corr(returns_b)
69
70	# Multiple windows for different time horizons
71	windows = {
72	'short': 20, # ~1 month of trading days
73	'medium': 60, # ~3 months
74	'long': 120, # ~6 months
75	}
76	for label, w in windows.items():
77	df[f'corr_{label}'] = returns_a.rolling(w).corr(returns_b)
78	```
79
80	### EWMA Correlation
81
82	Exponentially weighted — more responsive to recent changes.
83
84	```python
85	def ewma_correlation(x: pd.Series, y: pd.Series, span: int = 60) -> pd.Series:
86	"""Compute EWMA correlation between two return series."""
87	cov_xy = x.mul(y).ewm(span=span).mean() - x.ewm(span=span).mean() * y.ewm(span=span).mean()
88	std_x = x.ewm(span=span).std()
89	std_y = y.ewm(span=span).std()
90	return cov_xy / (std_x * std_y)
91	```
92
93	### Typical Windows
94
95	\| Window \| Days \| Use Case \|
96	\|--------\|------\|----------\|
97	\| Short \| 20 \| Tactical trading, pairs entry/exit \|
98	\| Medium \| 60 \| Strategy allocation, regime detection \|
99	\| Long \| 120 \| Portfolio construction, strategic allocation \|
100
101	## Correlation Matrix Analysis
102
103	### Computing the Full Matrix
104
105	```python
106	# Build return matrix for multiple assets
107	returns = pd.DataFrame({
108	'BTC': btc_returns,
109	'ETH': eth_returns,
110	'SOL': sol_returns,
111	'AVAX': avax_returns,
112	})
113
114	# Correlation matrix (Pearson)
115	corr_matrix = returns.corr()
116
117	# Spearman (better for crypto)
118	spearman_matrix = returns.corr(method='spearman')
119	```
120
121	### Eigenvalue Decomposition
122
123	Decompose the correlation matrix to identify driving factors.
124
125	```python
126	eigenvalues, eigenvectors = np.linalg.eigh(corr_matrix.values)
127
128	# Sort descending
129	idx = eigenvalues.argsort()[::-1]
130	eigenvalues = eigenvalues[idx]
131	eigenvectors = eigenvectors[:, idx]
132
133	# First eigenvalue = market factor (explains most variance)
134	# Subsequent eigenvalues = sector/style factors
135	market_factor_pct = eigenvalues[0] / eigenvalues.sum() * 100
136	```
137
138	- First eigenvector: the market factor — when this dominates (>60% variance), everything moves together
139	- Subsequent eigenvectors: sector or style factors
140	- Small eigenvalues: noise / idiosyncratic risk
141
142	### Minimum Variance Portfolio
143
144	```python
145	from numpy.linalg import inv
146
147	cov_matrix = returns.cov()
148	ones = np.ones(len(cov_matrix))
149	inv_cov = inv(cov_matrix.values)
150
151	# Minimum variance weights
152	weights = inv_cov @ ones / (ones @ inv_cov @ ones)
153	```
154
155	## Hierarchical Clustering
156
157	Group assets by correlation similarity to identify natural clusters.
158
159	```python
160	from scipy.cluste

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