Using PCA Eigenvectors to Set Weights in a Multi-Leg Spread

Summary

The document offers a concise way to extend a principal component analysis hedge-ratio method from two instruments to a basket with multiple legs. It proposes building the covariance matrix for the instruments, finding its eigenvectors, and selecting an eigenvector whose signs match the desired long and short directions. The vector’s components then serve as the basket weights or spread ratios.

This is a high-level suggestion rather than a worked procedure. It does not specify whether to use prices or returns, how to standardize instruments, which eigenvector to select beyond the sign condition, or how to validate the resulting spread. Those choices matter: covariance scale and the choice of component can materially affect the weights, and the note provides no performance evidence or risk controls.

Key ideas

• Build the covariance matrix across all legs before applying PCA.
• Use an eigenvector with signs aligned to the intended long and short positions.
• Treat the selected eigenvector’s components as the multi-leg basket weights.
• The note leaves data preparation and eigenvector selection criteria unspecified.

Tags

# How can I use PCA to determine spread ratios for multiple legs?


# How can I use PCA to determine spread ratios for multiple legs?












I would like to generalize Paul Teetor's A Better Hedge Ratio, which uses prcomp() to determine a ratio between two legs. I am hoping to extend this to multiple legs, but am having trouble finding accurate results. Any suggestions?

## Answer by RockScience (score 1)

https://quant.stackexchange.com/a/10797

In the case of N components:

- compute the NxN covariance matrix

- compute the N eiggenvectors and take the one that has the signs that you want

- the weights of this eiggen vector corresponds to the basket of N components that you wish to create

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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