Correlation Structure Analysis AI Prompt

Analyze the correlation structure of this multi-asset portfolio and identify instabilities.

Assets: {{asset_list}}
Return frequency: {{frequency}}
Period: {{period}}

1. Static correlation matrix:
   - Compute Pearson correlation matrix
   - Visualize as heatmap with hierarchical clustering (assets with similar correlations grouped together)
   - Report the range: minimum and maximum pairwise correlations
   - Flag pairs with correlation > 0.9 (potential redundancy) and < -0.5 (potential hedge)

2. Robust correlation estimation:
   Pearson correlation is sensitive to outliers. Apply:
   - Spearman rank correlation: robust to outliers, captures monotonic relationships
   - Ledoit-Wolf shrinkage: regularized covariance matrix — critical for portfolio optimization with many assets
   - Minimum covariance determinant (MCD): downweights outliers automatically
   Compare: how much do robust estimates differ from Pearson for each pair?

3. Rolling correlation analysis:
   - 63-day rolling pairwise correlations for all pairs
   - Plot selected pairs over time
   - Identify correlation regime changes: periods when correlations were notably higher or lower
   - Crisis correlation: do correlations spike during market stress? (Diversification typically fails when needed most)

4. Principal Component Analysis (PCA):
   - Apply PCA to the correlation matrix
   - Report: variance explained by each PC (scree plot)
   - How many PCs explain 80% of variance? (Indicates effective dimensionality of the portfolio)
   - PC1 loadings: usually the 'market factor' — uniform positive loadings on all assets
   - PC2 onward: often sector or style tilts
   - Track PC1 explained variance over time: rising explained variance indicates increasing co-movement (correlation risk)

5. Instability metrics:
   - Correlation instability index: average change in pairwise correlations across rolling windows
   - Lowest-correlation period vs highest-correlation period: what drove the change?
   - Correlation between asset pairs during down markets vs up markets (asymmetric correlation)

6. Implications for portfolio construction:
   - Which correlations are most unstable? (Least reliable for diversification)
   - What is the maximum theoretical diversification benefit given current correlations?

Return: correlation matrix heatmap, Ledoit-Wolf estimate, rolling correlation plots, PCA results, instability metrics, and portfolio construction implications.