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S&P500
MOMENTS
Return Statistics
Factor Model
ready
Overview
Moments
Rolling
Cross-Section
Relationships
Vs Index
Sectors
Stability
From
To
Full sample
Pre-2020
2021-present
Last 1Y
Last 3Y
Apply window
Sector performance map
Box size = market cap · color = mean daily return in window
Top / bottom performers in window (mean daily return)
Summary of cross-sectional statistics (describe)
Per-stock statistics
S&P 500 index — 30-day rolling mean / variance / skewness / kurtosis
Cross-sectional density of stock returns over time (3-D)
Sampled every N-th trading day for performance — adjust with the control below.
Sampling stride:
every 5 days
every 10 days
every 20 days
every 40 days
Daily cross-sectional variance / skewness / kurtosis
Pairwise relationships between the six statistics
Distribution of each stock's correlation with the S&P 500 index
Correlation with index — full table
Within-sector vs. between-sector pairwise correlations
Mean pairwise correlation by sector
Compare two sub-periods and test stability (Kolmogorov-Smirnov)
Period A
to
Period B
to
Compare
Period A — 30-day rolling index moments
Period B — 30-day rolling index moments
Kolmogorov-Smirnov stability tests (Period A vs Period B)
Factor loadings by sector (Fama-French 5-factor betas)
Alpha ranking (Benjamini-Hochberg FDR corrected)
Unsupervised style clustering
k
Auto (silhouette-selected)
2
3
4
5
6
7
8
9
10
Recompute
Cluster vs. GICS sector crosstab
Rolling factor loadings
Full sample, trailing ~2-year windows -- not affected by the date picker above.
Ticker:
Contemporaneous vs. predictive (t+1)
Daily vs. monthly frequency
Linear (OLS) vs. random forest — out-of-sample
Out-of-sample R² — OLS vs. random forest, per stock