A covariance matrix is the input to almost every risk model, and it is also the easiest input to get wrong. This skill gives you the decompositions that explain it, with short checks (numbers you compute, steps you order, concepts you match) and finance examples: why the first principal component of stock returns is the market, why the three components of a yield curve are level, slope and curvature, why a sample covariance of many assets has eigenvalues that are too spread out, and how a noisy matrix produces a minimum-variance portfolio that disappoints out of sample. The capstone is a code lab in which you build the repairs yourself and test them on real returns.
