I was wondering how to compute an extra-financial score of a portfolio like, for instance, the ESG score. This score can is typical bounded between 0 and 10 (or 100) (see for example IVA methodology of MSCI. How would one get the score of a portfolio from its constituents? What is the score of a shorted stock?
More generally I am interested in the construction of portfolios with a minimum score but that is trivial after the above question is solved.
A note added later
A comment and an answer below suggests taking a weighted average of the scores. Indeed this is what MSCI apparently does MSCI apparently does. However this gives some counterintuitive results. Imagine a portfolio of a good company G with weight $w_G=2$ and score $s_G=10$ and a bad company B with weight $w_B=-1$ and score $s_B=2$ (recall scores are between 0 and 10). The weights add up to one but the portfolios score according to this prescription is $s_P = 2 s_G - s_B$ and counterintuitively the affect of shorting the bad stock is reducing the score of the portfolio.