core practice · implementation task
Compute covariance and correlation matrix
Given 3 aligned series (n=20 each), compute the 3×3 sample covariance matrix and correlation matrix by hand or in code (loops only). Verify diagonal covariances equal variances and corr diagonal = 1.
The mechanism
Covariance is signed co-fluctuation with units. Correlation divides by both standard deviations so scale cancels. Zero correlation means no linear relationship, not independence.
Expected evidence
Symmetric matrices; corr[i,j] = cov[i,j]/(σ_i σ_j).
Try this drill in the practice workspace →
Hints when you need them
- Center each series first for covariance.
- Correlation is scale-free.
Watch for these mistakes
- Treating correlation 0 as unrelated when nonlinear dependence exists
- Computing correlation on price levels instead of returns
- Mixing sample n vs n−1 denominators