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TL;DR

A dimensionality reduction technique that finds orthogonal directions of maximum variance in the data. Mathematically, PCA computes the eigendecomposition of the covariance matrix and projects data onto the top eigenvectors.

By Valenke Exam Prep Team·Last updated 2026-06-03

Principal Component Analysis

A dimensionality reduction technique that finds orthogonal directions of maximum variance in the data. Mathematically, PCA computes the eigendecomposition of the covariance matrix and projects data onto the top eigenvectors.

Why it matters for interviews

PCA is the standard tool for factor decomposition in quant finance: identifying market factors, reducing dimensionality of yield curves, and constructing statistical arbitrage strategies. Tested in both math and finance interviews.

Definition and Mathematical Foundation

A dimensionality reduction technique that finds orthogonal directions of maximum variance in the data. Mathematically, PCA computes the eigendecomposition of the covariance matrix and projects data onto the top eigenvectors.

Application in Quantitative Finance

PCA is the standard tool for factor decomposition in quant finance: identifying market factors, reducing dimensionality of yield curves, and constructing statistical arbitrage strategies. Tested in both math and finance interviews.

Related Terms

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Frequently Asked Questions

How is PCA used for yield curve modeling?▼
The first 3 principal components of yield changes typically explain >95% of variance and correspond to level, slope, and curvature shifts. This reduces a high-dimensional yield curve to 3 factors.
What is the scree plot and how do you choose the number of components?▼
A scree plot shows eigenvalues in decreasing order. The 'elbow' suggests where additional components add mostly noise. Alternatively, retain components explaining a target percentage (e.g., 95%) of total variance.
What are the limitations of PCA?▼
PCA captures only linear relationships, is sensitive to outliers, assumes stationarity, and the components may not be economically interpretable. Alternatives include ICA (Independent Component Analysis) and autoencoders.