BIZNIQUE / LINEAR ALGEBRA / 20
Explore shared variation in return data
Explore shared variation in return data
Use a fictional covariance example to separate mathematical structure from an investment claim.
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THE IDEA
Read the example.
Read the example.
In the example, two standardised fictional series have positive covariance. A direction near their sum captures shared variation; the difference direction captures a different component. PCA can summarise observed co-movement.
Covariance eigenvectors define principal directions
Use it well
Use it well
Historical covariance can change. Component signs are arbitrary, economic interpretation needs evidence, and this illustration does not provide a trading or risk-management recommendation.
TRY IT YOURSELF
A quick check.
A quick check.
For covariance [[2, 1], [1, 2]], what fraction of total variance belongs to the (1, 1) direction?
Check your reasoning
Check your reasoning
Its eigenvalue is 3 out of total variance 4, so it accounts for 75% in this fictional example.
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