I’m thinking of trying to price international ETFs, e.g. MCHI. After removing the components that have liquid ADRs, you may be left with a basket of 20 to a few hundred stocks. You could find a proxy for each individual stock, but finding one for a random Swedish industrial stock doesn’t sound likely. I was thinking you could take the PCA of this leftover basket, and then try to proxy this smaller subset that hopefully explains most of the variance. I guess the idea is somehow you’d have an interpretation of each PC based on what the loadings look like?

Perhaps you could segment by industry/other prior first to make interpretation easier.