Interview Question: Decomposing for Profit

Sample Question #171 (applied statistics)

Explain the concept of principal component analysis (PCA). What’s its goal? How do you carry out PCA?

(Comment: PCA is a popular quantitative technique used on Wall Street; for example, it’s often part of the toolbox among statistical arbitrage and index arbitrage traders)

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One Response to Interview Question: Decomposing for Profit

  1. Brett says:

    ANSWER
     
    PCA is an example of a statistical factor model, where the factors in the linear model are statistically derived. PCA is used to extract factors that explain the covariance structure in the original dataset consisting of several time series; in mathematical terms, it finds the directions of maximum variance. Each such factor is known as a component. The components are orthogonal to one another.
     
    Performing PCA involves finding the eigenvalues and eigenvectors of the sample covariance matrix first and then transforming (decomposing) the original dataset. In essence, the components are weighted averages of the original data.
     
    More details on PCA can be found by searching on the Internet (click the link to see results). But remember, just memorizing what PCA is does not help you in getting a job. If you’re interested in PCA, you should get a good understanding of matrix operations, factor analsis, and variance-covariance analysis, too.
     

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