Using LDA to Classify Tail-Risk Events in a Statistical Arbitrage Portfolio

Summary

The article explains Linear Discriminant Analysis (LDA) as a supervised method for classifying observations and estimating the probability of belonging to a class. It contrasts LDA with logistic regression and describes LDA’s use of Bayes’ theorem, class priors, and class-specific feature distributions. The method assumes Gaussian distributions with a shared variance across classes, an assumption that shapes its predictions and suitability for a dataset.

The practical example applies LDA to risk management for a portfolio of cointegrated stock pairs. It outlines building the statistical arbitrage portfolio, estimating Value at Risk with Monte Carlo simulation, and defining a class label for returns that breach a chosen loss threshold. Predictor variables are then used to classify potential tail-risk events. The article reports that changing model parameters raised precision from 38% to 52%. This is an example-specific result, not evidence of general performance; the approach depends on the portfolio construction, feature choices, and LDA assumptions, and the article does not establish out-of-sample reliability.

Key ideas

• LDA estimates class probabilities using Bayes’ theorem and class-specific feature distributions.
• The method assumes Gaussian feature distributions with a shared variance across classes.
• The example uses cointegrated stock pairs to construct a statistical arbitrage portfolio.
• Monte Carlo simulation is used to estimate Value at Risk before classifying losses beyond a selected threshold.
• The article reports that changing model parameters improved precision in its example, but does not establish broader predictive reliability.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.