I have to deal with a factor investing strategy, with the particularity that I can't get a value for the factor for each date for each stock. Practically speaking, this is due to the fact that this factor comes from option data, and I can't get enough of them for all of the stocks in my universe. How would you deal with this kind of issues ?
Let's take an example of an universe of 20 stocks, with a factor value for 15 of them. My first intuition was to conduct a PCA analysis on the returns of the 5 other stocks and simply calculate the factor for them as a linear combinaison of the 15 others. Would it be ok ? What if I have only 2 stocks with a factor, and 18 others without ?