Principal Component Analysis
Principal Component Analysis decomposes asset return variation into orthogonal components. Inspect variance concentration and loadings to see which return patterns assets share.
On this page
What it answers
- A dominant first component means many assets are moving together.
- Effective component count summarizes how evenly variance is spread. The cumulative curve shows how many components reach a chosen share.
- The loading table shows which assets define each principal component.
Covariance vs correlation
- Covariance PCA preserves absolute volatility, so high-volatility assets can dominate.
- Correlation PCA standardizes each asset first to measure co-movement independently of volatility scale.
Use correlation PCA to compare co-movement across assets with different volatility. Use covariance PCA when absolute risk concentration matters.
Inputs and workflow
- Each portfolio row of the analysis is one decomposition of its holdings. Every tool of the tool bar reads the same rows and dates, so a portfolio from Portfolio Backtest needs no new entry here.
- A row with one fixed set of weights also gets Portfolio variance by component. The tool analyzes a row that switches holdings on a signal or changes weights over time without weights, and the row says why. A row with one holding stays in the table with the reason.
- Use daily mode for short-term return patterns. Monthly mode reduces day-to-day noise when comparing longer-term relationships.
- One Run sends every row in one request. Save keeps every row. Share sends the selected row.
- Reopening a saved or shared analysis replays each row as it ran, in the mode it recorded. An edit to the row then analyzes the row as edited.
Interpretation
PCA components describe statistical relationships. If the first component is broad and positive across equities, it suggests a common market driver. The components alone do not establish a cause.
How to read the output
- Start with the table. Top component is the share of variance on the first component. If one component explains almost half the variance, the holdings are less diversified than their count suggests.
- Then compare Effective components and Components for 80% across the rows. These summarize how many dimensions carry each portfolio's behavior.
- Select a row to read its detail. In the loading table, similar signs and magnitudes indicate common movement. Opposite signs indicate an offset to that theme.
- Portfolio variance by component projects the weights of the row onto covariance components and gives each component's share of portfolio variance. It always uses covariance decomposition. Thus, correlation mode can show different components in the loading table.