It’s important to be familiar with the cross-sectional approach as it’s the one that most commercial risk models are based, and commercial risk models are widely used by institutional investors. In academic research, it’s common to see the time series approach, whereas in industry, practitioners usually either purchase a commercial risk model such as the ones built and maintained by MSCI Barra, Axioma, or Northfield, or they may use a third approach, principal component analysis, which we’ll learn about in the next lesson. One challenge of constructing a risk model on your own is that you need to decide for yourself which risk factors to use in the model, and don’t have an easy way to enforce the assumption that the factors are independent of each other, or that the specific returns of the stocks are independent of each other as well. Commercial risk models can be purchased off the shelf so that institutional investors can focus their attention on researching Alpha factors. The machine-learning approach with PCA, which we’ll learn in the next lesson, is nice because it derives latent factors which are by definition explaining the most variance in the distribution of returns while also enforcing that each latent factor is independent of all the others.