Describe how do you build a factor model whats the challenge

Imagine yourself as a young researcher in Yahoo Finance. You have access to a database which contains monthly observations from Jan-1991 to Dec-2015 to study the return of 200 portfolios (r_it). All variables contain full information for the whole period. The set of independent variables of the study includes 150 factors that may affect the returns of the portfolios. For example, this set of variables includes the factors of the Fama-French three and five factor models but also many others. This is the factor Zoo, and your task is to find the most important ones and eliminate the rest who do not add much to explain the return of these portfolios.

a) Using tools you have learned in Quantitative Finance, develop an estimation strategy to find what the best model would be from this Factor Zoo. Explain how you can build a model with factors that are the most important ones, as well as the main challenges to face.

b)Making use of a similar dataset, Feng, Giglio and Xiu (2020, see link to the paper at the start of the exercise) propose a method to select the most important factors. What are the main differences with the approach you have proposed in a)? Explain any similarities between the two approaches and the main advantages of Feng, Giglio and Xiu (2020)