We give complete algorithms and source code for constructing statistical risk models, including methods for fixing the number of risk factors. One such method is based on eRank (effective rank) and yields results similar to (and further validates) the method set forth in an earlier paper by one of us. We also give a complete algorithm and source code for computing eigenvectors and eigenvalues of a sample covariance matrix which requires i) no costly iterations and ii) the number of operations linear in the number of returns. The presentation is intended to be pedagogical and oriented toward practical applications.

44 pages; a trivial typo corrected, references updated; to appear in The Journal of Investment Strategies. arXiv admin note: text overlap with arXiv:1602.04902, arXiv:1508.04883, arXiv:1604.08743